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Download Report on the 1995 key stage 3 tests and tasks in mathematics.
The first test is to see whether pupils' achievement in other subjects, such as Mathematics and English, is also affected. In Figure 2 the Key Stage 3 Maths results are shown from the same pupils whose Science levels were shown in Figure 1.
Figure 2: Key Stage 3 Mathematics C) w. Sir John Cass. Parkside. Key Stage 3 Archive Mathematics (9) (9) KS3 Mathematics SAT Past Papers. Year. Level Level Click here to view the grade boundaries for the years Reading Task Answer Book. Writing Task Answer Book. Mark Scheme. Test. The highly acclaimed Key Stage 3 book-based course SMP Interact: Framework Edition supports a teacher-led, discussion-based approach as recommended by the Key Stage 3 Framework for Teaching Mathematics.
‘I’m sure using SMP Interact contributed to our superb Ofsted report’ Ian James, Head of Mathematics, Garibaldi School, Mansfield.
Mathematics is an interconnected subject in which pupils need to be able to move fluently between representations of mathematical ideas. The programme of study for key stage 3 is organised into apparently distinct domains, but pupils should build on key stage 2 and connections across mathematical ideas to develop fluency, mathematical reasoning andFile Size: KB.
The muddled tale of Standard Assessment Tasks at Key Stage 3’, in C. Gipps (ed), Developing Assessment for the National Curriculum, Kogan Page and London University Institute of Education, Brown, M.:Clashing Epistemologies: the Battle for Control of the National Curriculum and its Assessment, Professorial Inaugural Lecture, King Cited by: Maths Homework Booklet targeted for KS3 Maths Students.
Split into 3 stages which can be given out for each term. I recommend giving the students topics a week, in which case it would last an academic year. Please see screenshots for more info.
School Examinations and Assessment Council (SEAC):Teacher Assessment at Key Stage 3: Mathematics, SEAC, London. Google Scholar School Mathematics Project (SMP):Open Ended Tasks, School Mathematics Project, Southampton. The Task and Finish Group as part of its deliberations looked at a wide range of literature and research findings on mathematics and mathematics teaching, including the selection of quotations and documents referred to below.
The full list of sources considered can be found in Appendix 4 of the report. GCSE results at Key Stage 4. To assist teachers in arriving at an assessed level, tests and tasks can be completed in reading, writing and mathematics.
These are normally taken during May.  Key Stage 2. During May in the final year of Key Stage 2, children undertake National Curriculum Tests in the three core subjects of English, Mathematics and Science (up until Mathematics Education Section - Curriculum Guide.
(The Curriculum Development Council recommends schools to implement the revised senior secondary Mathematics curriculum for Compulsory Part progressively from S4 with effect from the school year /24 and to implement the revised curriculum for Extended Part progressively from S4 with effect from the school year /).
Optional Tests and Tasks for Key Stage 3: Geography Unit 3 (Paperback) Standards at Key Stage 3 Mathematics: Report on the National Curriculum Assessments for 14 Year Olds (Paperback) Please provide me with your latest book news, views and details of Waterstones’ special offers.
to design the test you want by cutting and pasting from across the tests. Our Key Stage 3 tests are designed to help you see how your students are engaging with mathematics and performing relative to each other; they should not be used to predict future GCSE grades and we won't offer indicative grade boundaries, as these could not currently be.
Appealing in design and meeting the key aims of the new Maths National Curriculum, these questions will test pupils on many aspects of upper KS2 and early KS3 learning stages, encouraging them to utilise a variety of problem solving skills and confirming their understanding of the key.
Mathematics Stage 2 diagnostic tasks Name: Class: Date: Stage 2 – Name: Class: Date: Stage 2 – Whole numbers Question 2 – relationship between numbers Use the greater than > or less than. Key Stages 1&2. Task demo - Using Mathematics (video) Task demo transcript - Using Mathematics; Levelling Pupil Work in Using Mathematics; Non Statutory Guidance for Assessing Using Mathematics; Levels of Progression (Levels ) Expansion of the Levels; Shape and Space 1: A teaching and learning resource for Using Mathematics.
End-of-the-Year Test - Grade 3 This test is quite long, so I do not recommend having your child/student do it in one sitting. Break it into parts and administer them either on consecutive days, or perhaps on morning/evening/morning.
This is to be used as a diagnostic test. Writing Test (Shorter Task & Answer Booklet) Spelling Test (Teacher's Version) Teacher's/ Administrator's Guide Marking Scheme. Optional Year 7 Maths Progress SATs Papers (Level can be used in years 4 or 5 for able children).
Year Mental Maths Audio Transcript Mental Maths Answer Sheet Test A Level Test B Level Few language barriers - an additional benefit becomes evident when children from non-english-speaking backgrounds are involved. The basic structures of some games are common to many cultures, and the procedures of simple games can be quickly learned through observation.
This guidance report focuses on the teaching of mathematics to pupils in Key Stages 2 and 3. It is not intended to provide a comprehensive guide to mathematics teaching. We have made recommendations where there are research findings that schools can use to make a significant difference to pupils’ learning, and have focused on the questions.
To help you review the quality typical of NFER materials, these sample materials are representative of content layout and question type you can expect to find from our NFER Tests and retain the integrity of the published standardised papers but are not the actual materials themselves.
key stage 2 mathematics – administering paper 3: reasoning Ref: ISBNSTA/19//e PDF, KB, 4 pages key stage 2 mathematics mark schemes. AQA Key Stage 3 Year 7 Baseline Test. The Year 6/7 baseline test is now available. This paper is designed to be used early in Year 7.
The nationally reported results for the end of key stages 1, 2, and 3 currently focus on English, mathematics, and science.
At the end of key stage 1, they are based on moderated teacher assessments taking account of the results of nationally designed SATs and tests. At the end of key stage 2 there are moderated teacher assessment results, but. *Clear and concise overviews, examples and 'Key Words' boxes help underpin understanding of the key topics * Tasks and exercises challenge and stimulate pupils at all levels and help develop skills * Pages of practice questions for every topic reinforce learning and test understanding.
* BBC Children in Need Free Taster Packs * Diving into Mastery * Winter * Christmas * Diwali Assessment Tests SPaG Reading Maths Planning and Assessment Adult Led Focus Plans English Revision Lesson Planning Starter and Plenary Resources Assessment and Targets Key Stage 3 English Reading Writing Comic Book Templates.
Prefix, Suffix, and. Find a sample accreditation report for supervisors who are supporting teachers working towards accreditation at Proficient Teacher.
Stage 3 (Years 5–6) Stage 4 (Years 7–8) Stage 5 (Years 9–10) Mathematics key Rationale. A Key Stage 2 Science sampling test was not created in as it was decided a new biennial pupil-level sampling system would be introduced in Approximately children will be randomly selected (based on 5 children from schools).
Key Stage 3 is the first three years of secondary school education in England, Wales and Northern Ireland, for pupils aged 11 to History. The assessments were introduced following the introduction of a National Curriculum to schools in England and Wales under the Education Reform Act As the curriculum was gradually rolled out fromstatutory assessments were introduced between andwith those in Key Stage 1 first, following by Key Stages 2 and 3 respectively as each cohort completed a full key stage.
Key Stage 3 Maths – Development of Skills. Throughout Key Stage 3 students must try to: Become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.
In Years 3 to 7, teachers assess pupil progress in the statutory curriculum (the Cross-Curricular Skills, the Areas of Learning and the Thinking Skills and Personal Capabilities) and report this progress to parents.
In Years 4 and 7, there are additional end of key stage requirements for assessment and reporting. Our Key Stage 3 year 7 science revision resources are perfect for your child as they’re starting to prepare for their first set of exams in Secondary School.
Our expert team of teachers make sure our worksheets are kept up to date with the year 7 science curriculum so your child doesn’t miss out on anything they need to know. If your child has a mobile phone, set them the task of finding the best tariff Encourage your child to look out for percentages: in a newspaper, in shops, or on adverts for credit cards Practise maths when you’re out shopping or in a restaurant – get your child to add up prices, work out how much you can save on special offers, and estimate.
Author of SMP Pupils' Pack (School Mathematics Project Primary Course), Smp Some Exprmntal Ideas for Teach (School Mathematics Project Computing in Mathematics), The School Mathematics Project Assessment Tests Section 1 (School Mathematics Project Primary Course), Further Mathematics Revision, Mechanics Student's book (Mathematics for A and AS Level), Book D Teacher's Guide, Smp Book.
attempts to minimise bias within national curriculum assessments at key stage 2 (KS2) and key stage 3 (KS3). In English schools, English, mathematics and science attainment is assessed by test for most pupils at the end of KS2 and KS3.
The issues covered The review covers these issues. Developing Independent Learning in Key Stage 3&4 Mathematics Creating a culture of independent learning in your classroom Course Trainer: Martin Jones Book on-line at @ an Ofsted report stated that "too much teaching concentrates on the acquisition of disparate skills that enable pupils to pass tests and.
Ach. At ages 9 teachers rated children’s Ach based on key stage 2 and key stage 3 National Curriculum criteria, respectively (The National Curriculum, ; also see Kovas, Haworth, Dale, & Plomin, ).The National Curriculum stipulates learning goals for children from ages 5 to 16 years at state-funded schools in England and Wales.
One of 7 assessments written for the Curriculum programmes of study for year 3. The aims assessed by each question are clearly stated and a marking scheme provided.
Why not use it with our Assessment Spreadsheets to track progress. It can be used at any point in the year as a tool to gauge prior learning or progress within the domain of Measurement.
Written test and Dirt task at the end of each half-term. These are cumulative tests which over everything a student has learned from the beginning of Year Spring. Spring 1 st half.
Unit Key Stage 3 Fractions, decimals and percentages review. Unit Percentages. Unit Probability, sets, venn and sample space diagrams. Spring 2 nd half. The muddled tale of Standard Assessment Tasks at Key Stage 3 Schools Curriculum and Assessment Authority, (), Mathematics Tests Key Stage 2London, Department for Education.
Google Scholar. SCAA – Schools Curriculum and Assessment Authority, Book Reviews: Social Class, Language and Communication. Primary socialization. specifically at aspects of Key Stage 3 National Curriculum Test papers (by 2 to years) in mathematics achievement tests (although the difference is less pronounced for maths than memory tasks.
Mathematics and Deaf Children: An exploration of barriers to success 3 DEI CRC 2/10/05 AM Page 3.In this paper we present some preliminary data from the ESRC funded ICCAMS project about current student attitudes to mathematics at Key Stage 3 in England.
Key Stage 3 students' performance.At Key Stage 3 (post-primary Years 8, 9 and 10), the curriculum builds on the learning experiences that pupils bring from primary school.
Pupils now attend classes in different subjects, and teachers typically teach specific subjects to pupils across the different Years.


There is a variety of problems where one searches for a vector such that the squared sum of the lengths of projections of points onto that vector is maximized or minimized:
This can be written as a Lagrange function by introducing a Lagrangian multiplier for the constraint:
Optimization of the original problem is equivalent to finding a solution to the following equation system:
The first line of this equation tells us that must be an eigenvector of with eigenvalue . Let’s call those and . Plugging this solution back into our original problem (and remembering that the eigenvector is not necessarily unit length) we obtain:
Depending on whether we want to obtain a minimum or a maximum we can choose the eigenvector with the smallest or largest eigenvalue respectively.


Githuku Mungai has an agreement for the sale of a plot of land. The agreed price was Sh30 million. The deal was to be completed by 31st December 2017.
If the buyer exceeded that date before completing payments, he was to be charged 15% interest on the outstanding balance.
As things turned out, only Sh8.3 million had been paid by the 31st December deadline. Still, on 31st May 2018, the buyer paid Sh700,000 and this was accepted by the seller.
But in “December 2018, the buyer conceded that he is unable to continue and so will get a portion of the land based on the Sh9 m paid.” Githuku would like to know how much interest should be charged for exceeding the deadline.
I will assume that the 15% interest is applied annually. The calculation would have been easier if the buyer had not paid the Sh700,000 in May 2018. In such a case, the seller would have simply worked out 15% of the unpaid balance; that is, (Sh30M – Sh8.3M) x 15% = Sh3,255,000.
If the buyer was still interested in the entire plot of land, he would be required to pay the interest plus the outstanding balance; that it Sh21.7M + Sh3,255,000 = Sh24,955,000. Perhaps this is the reason why he has decided to change his mind.
INTEREST STILL APPLICABLE
Now that he has changed, the interest is still applicable. So, the Sh3,255,000 should be subtracted from the amount he has paid before deciding what size of land has been paid for. That is the net payment for land is Sh8.3M - Sh3,255,000 = Sh5,045,000. Thus, he gets 16.8% of the land.
So far, so good; now let’s factor in the Sh700,000 paid in May 2018. Assuming that the interest is not compounded on a monthly basis, then the amount accumulated by the end of May is Sh3,255,000 x 5/12 = Sh1,356,250.
The buyer then paid Sh700,000 thereby reducing the balance to Sh21M. This remained unpaid for the remaining seven months of the year.
Thus, it accumulated Sh21M x 15% x 7/12 = Sh1,837,500 in interest.
Therefore, the total interest is Sh1,356,250 (for January to May) plus Sh1,837,500 (for June to December); that is Sh3,193,750.
Again; this money should be deducted from the total payment before deciding what proportion of land the buyer will get.
This is done as follows: net amount paid for land = Sh9M – Sh3,193,750 = Sh5,806,250. So, the proportion of land to be given to the buyer is 19.35%.
This transaction illustrates one important point: whether you are the buyer or the seller, be careful when you enter a sale agreement that has interest and penalties.
You might find that the amounts are much bigger than you imagined. Worse still; it might even be impossible to do the calculations!


Computation of the readout signal of an optical disk involves Fourier transforms from the objective lens pupil to the disk and, after interaction with the disk, from the disk to the objective pupil. Traditionally, the complex two-dimensional Fourier transform is numerically evaluated as a two-dimensional fast Fourier transform. To obtain sufficient resolution in the involved planes, one must choose sampling grid sizes of typically 1024 × 1024 or higher, resulting in a substantial computation time if the calculation is to be repeated many times. Discussed is an alternative method for evaluating the Fourier transform, based on the chirp z transform, by which a considerable improvement in efficiency can be obtained without loss of accuracy.
© 2002 Optical Society of AmericaFull Article | PDF Article
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We use Group Theory to solve for the dipole interaction part of the Hamiltonian of various types of one (chain), two (ring) and three (cylinder) dimensional shells of dipoles. The fabrication of such structures has been recently achieved for various plasmonic devices, such as gold nanoparticles surrounding carbon nanotubes (1). These systems present various levels of rotational and translational symmetry that can be put in correspondence with symmetry groups and their matrix representations. This mapping of our physical system onto mathematical groups enables us to use several powerful results and theorems from linear algebra to diagonalize the interaction potential tensor that appears in the Hamiltonian. The resulting eigenmodes of oscillation can thus be obtained analytically with their corresponding energies.
Christopher Devulder is a graduating senior majoring in Physics who will be returning to Lehigh for a 5th year in order to complete a second degree in Mathematics. He has been working with Prof. Roktin for almost 2 years on a plasmonic project that they hope to complete by the end of the year. Devulder wishes to pursue further graduate studies in theoretical physics to study various unifying theories and their correlation to abstract mathematics.


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For young learners, there are a plethora of apps out there to help learn how to count, and for older learners, often times a graphing calculator or scientific calculator app will do the trick. But what about all of those students in between?
You know, the ones who already know how to count, but have to learn a multitude of math concepts that most of their parents have long forgotten? We’re taking a look at 6 apps that are easy to use and teach more than just counting.
This app allows you to create virtual geometrical shapes using a grid. Different colors represent different shapes, and the tool reinforces the concept of fractions along with geometrical shapes.
This app uses everyday items (like a pizza or an apple) to demonstrate and quiz users on fractions. We think it’s great because it is simple to use, practical (because we don’t think you’re going to eat that whole pizza yourself!) and adaptive, so it continues to challenge you as you learn.
Order of Operations
Name That Number is a game based learning tool where players use five number tiles to build number sentences that equal a target number. Players can name the target number by adding, subtracting, multiplying, and/or dividing the numbers using as many tiles as possible. It offers visual and audio guidance as you go.
For students who are learning estimation, this app is basically a calculator that you plug your problem into, but it doesn’t give you an answer until you’ve made your estimate. A bar shows you if your estimate is within a reasonable range. This app is really basic, and easy to use.
A free guide for students new to line graphs, bar graphs, and pie charts. The app gives an easy to understand explanation of each type of chart along with several examples and tutorials for each kind. Also introduces the concepts of mean, median, mode, and trend lines. A good guide for students brand new to these concepts, and a good reference or review for those who have forgotten!
Ghostblasters is a game that enables users to learn (and use) multiplication tables by calculating numbers to zap ghosts! You can choose your factor (ex.5) and will have to select the right ghosts that are multiples of that factor. An easy and fun way to get kids to learn their times tables.
Source : http://edudemic.com/2012/11/7-apps-that-teach-math-concepts/


Inequality Graphing App Graphing inequalities is made simple for the beginning or intermediate calculator user with the Inequality Graphing App. Read the License before continuing. By downloading the application you indicate your agreement with the terms and conditions of the License. Subject to your payment of any applicable license fee, Texas Instruments Incorporated "TI" grants you a license to copy and use the software program s on a TI calculator and copy and use the documentation from the linked web page or CD ROM both software programs and documentation being "Licensed Materials".
Systems of Equations and Inequalities In previous chapters we solved equations with one unknown or variable. We will now study methods of solving systems of equations consisting of two equations and two variables. Represent the Cartesian coordinate system and identify the origin and axes. Given an ordered pair, locate that point on the Cartesian coordinate system.
Given a point on the Cartesian coordinate system, state the ordered pair associated with it. We have already used the number line on which we have represented numbers as points on a line.
Note that this concept contains elements from two fields of mathematics, the line from geometry and the numbers from algebra. Rene Descartes devised a method of relating points on a plane to algebraic numbers. This scheme is called the Cartesian coordinate system for Descartes and is sometimes referred to as the rectangular coordinate system.
This system is composed of two number lines that are perpendicular at their zero points. Perpendicular means that two lines are at right angles to each other. Study the diagram carefully as you note each of the following facts.
The number lines are called axes.
Example 3 Graph the solution for the linear inequality 2x - y ≥ 4. Solution Step 1: First graph 2x - y = 4. Since the line graph for 2x - y = 4 does not go through the origin (0,0), check that point in . Fit an algebraic two-variable inequality to its appropriate graph. If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains *pfmlures.com and *pfmlures.com are unblocked. Solve, Graph and Write Inequalities Make sure that you can draw a graph from an inequality and write an inequality when given a graph. Pay attention to open and closed circles.
The horizontal line is the x-axis and the vertical is the y-axis. The zero point at which they are perpendicular is called the origin. Positive is to the right and up; negative is to the left and down. The arrows indicate the number lines extend indefinitely.
Thus the plane extends indefinitely in all directions. The plane is divided into four parts called quadrants. These are numbered in a counterclockwise direction starting at the upper right. Points on the plane are designated by ordered pairs of numbers written in parentheses with a comma between them, such as 5,7.
This is called an ordered pair because the order in which the numbers are written is important. The ordered pair 5,7 is not the same as the ordered pair 7,5. Points are located on the plane in the following manner. First, start at the origin and count left or right the number of spaces designated by the first number of the ordered pair.
Second, from the point on the x-axis given by the first number count up or down the number of spaces designated by the second number of the ordered pair.
Ordered pairs are always written with x first and then y, x,y. The numbers represented by x and y are called the coordinates of the point x,y. The first number of the ordered pair always refers to the horizontal direction and the second number always refers to the vertical direction.
Check each one to determine how they are located.
What are the coordinates of the origin? Find several ordered pairs that make a given linear equation true. Locate these points on the Cartesian coordinate system.
Draw a straight line through those points that represent the graph of this equation. A graph is a pictorial representation of numbered facts.We can also graph inequalities on the number line. The following graph represents the inequality x≤2.
The dark line represents all the numbers that satisfy x≤2. If we pick any number on the dark line and plug it in for x, the inequality will be true. Write an inequality for the graph Download jpg.
Ask for details ; Follow Report by Richy1 03/09/ It is d you are right because open circle mean and it was pointing to the right so that means it was x>3. 0 votes Get the Brainly App5/5(1). Solving and Graphing Absolute Value Inequalities: Practice Problems; Studying with Flashcards.
If you are studying for a test on inequalities, these flashcards can provide a review of the main concepts.
This Write and Graph Inequalities: Temperature Video is suitable for 6th - 8th Grade. What temperature does water freeze?
Have your learners show in an inequality all the possible temperatures. The video demonstrates how to set up an inequality based on the situation given and how to graph it. This quiz and worksheet will help you assess your knowledge of writing equations with inequalities.
To pass the quiz you must be familiar with signs related to writing these equations and other. Write and graph a linear inequality that represents th situation. To start out, you have to write the inequality they are asking for. I'm assuming we can't spend any more than $48, but we don't have to spend all of $ If it costs $5 for every album (x) and $8 for every movie (y), than we'd write an inequality: App for Students.


If the Earth were flat, we could find the distance between any two points using the Pythagorean theorem. It would just be the square root of (latitude1 - latitude2)^2 + (longitude1 - longitude2)^2. However, since the Earth is not flat, a more complex formula is needed. If the two points are close to each other, the above formula will be very close to correct, but if they are distant, it will not.
Open Excel and enter the latitude of the first location in cell A1 and B1; enter degrees in A1 and minutes in B1. For example, New York City is at 40 degrees 47 minutes north, so enter 40 in A1 and 47 in B1.
Enter the longitude of the first location in cells A2 and B2, as above. New York City is at 73 degrees 58 minutes west, so enter 73 in A2 and 58 in B2.
Do similarly for the second location. For example, Honolulu is at 21 degrees 18 minutes north, 157 degrees 50 minutes west, so enter 21, 18, 157 and 50 in cells A3, B3, A4 and B4, respectively.
Convert all locations to decimal degrees. In cell C1 enter = a1 + a2/360, then copy this to cells C2, C3 and C4.
Convert all locations to radians. In cell D1 enter = c1/180*3.1415 and copy that to D3, D4 and D5.
Calculate the distance. In cell C6 enter =ACOS(SIN(D1)*SIN(D2)+COS(D1)*COS(D2)*COS(D4-D3))*6371.
Latitude 40 Degrees 47 Minutes N / Longitude 73 Degrees 58 Minutes West


K-Stem releases results to survey involving celebrities and math
K-Stem has revealed the results of a recent survey from a scholastic mathematics ability test, regarding celebrities who appear to be good and bad at math.
When asked about which celebrities appear to be good at math, approximately 152 surveyors voted for Kim Tae Hee and 108 voted for Lee Seung Gi. Participants shared their thoughts on Kim Tae Hee and said, “Because she went to Seoul National University, she is smart for real.” In terms of Lee Seung Gi, they revealed, “Lee Seung Gi seems to be good at math because he looks smart and intelligent.
The question regarding celebrities who look like they are bad at math included Boom, Suzy, and IU. Boom ranked first with 142 votes; Suzy received 102 votes; and IU followed with 80 votes.
Surveyors also voted for celebrities who seem like a math teacher. Yoo Jun Sung collected 24.3% of the votes and Kim Ha Neul came in second with 23.2% of the votes.


Between 2012 and 2018 the power of the infrastructure available for applications in artificial intelligence increased over three hundred thousand times. If it followed Moore’s law, it would have been much less, around 7 times or so.
We can apply a simple linear interpolation and view two segments, one where computing power doubles every two years, and one where it doubles every three-four months.
But it is much more useful to think in terms of increasing acceleration of computing power.
This better prepares us to face the future changes, additional increases in acceleration, when quantum computers are going to be used by AI systems to design more powerful versions of themselves.
Will the doubling rate become a few weeks, a few hours?


Quantitative Section comprises topics on mathematics, algebra, geometry, and other advanced mathematics topics. It is considered as one of the trickiest sections of almost all the government job exams such as SSC CGL, SSC CHSL, SBI PO, IBPS CLERK, etc. SSC CGL 2021 exam is round the corner and most of the candidates must have started studying for it. The quantitative section is one of the sections of the SSC CGL exam, let us discuss the time management skills required to score high in this section.
There are some topics in the Quantitative Aptitude section which need speed to solve. Let us discuss some tips to enhance the speed to solve questions of the Quantitative Aptitude section.
1. Learn the basics
There are diverse topics in the SSC CGL syllabus for the QA section. Segregate them and start from the easy topics first. Learn the basic applications of mathematics; these are addition, subtraction, multiplication, and division. Acquire accuracy in the calculations and then look for the patterns of calculations giving similar results. Do not jump to the shortcuts rather learn from the experience and practice. Work hard on basics and understand them well before applying them to any of the questions. It will help you save time once you will acquire speed in calculating.
2. Visualize the calculations
While reading the question try to solve the numbers in mind. It will enhance your speed to calculate. Instead of scribbling on the rough sheet, visualize the answer. It will save you time.
3. Read and analyze the question thoroughly
Read the question thoroughly and understand the instructions given to solve the problem. Analyze and then solve. Develop the habit of solving the practice sets in this manner to enhance speed. If you will practice more in this pattern you will be able to solve the questions quickly and accurately.
4. Learn the tables
Learn the multiplication tables from 1 to 30 and revise them daily. Besides that, learn the square root and cube root tables from 2 to 20. It will enhance your speed if you will learn them by heart. Practice dodging tables to acquire speed. Retain the tables in mind by keeping a regular practice of speed tests from online test series for the SSC CGL exam.
5. Learn Vedic mathematics
Vedic maths tricks are very helpful. Practice them a lot so that you solve big and intricate calculations in seconds. Read the question carefully and choose the adequate technique for the problem. Master the tricks by taking a lot of practice tests on Vedic maths.
6. Focus more on weak topics
Practice and focus more on weak topics by solving more questions on them. Revise them quite often and take doubt sessions if necessary from the subject expert to help you acquire accuracy and speed in solving the questions based on your weak topics. Practice as much as you can to master them rather than just learning them.
7. Learn important formulas and theorems
There is a number of formulas in mathematics. Make a list of them and revise them daily. Similarly, there are theorems in geometry, make a list of them and learn the basic application and revise them daily. Take special practice on theorems as geometry-based questions are lengthy and need speed to save time in the exam.
8. Read the question with concentration
Avoid any distractions while reading the questions to avoid wrong answers. Concentrate on the problem asked and the application required to solve it. You will be able to solve with speed and accuracy. Speed and accuracy are the ultimate tools to score high. Concentration will help you solve them quickly hence avoid looking around and read the question carefully to reach the best answer.
These are some of the significant tips to acquire speed and accuracy to solve the QA section of SSC CGL and other government job exams. Before you reach the exam date Tier 1 of the SSC CGL 2021 exam, it is advisable to master the tricks to enhance speed to solve the QA section. You may join online coaching for the SSC CGL exam or reputed SSC Exam Coaching Chandigarh or elsewhere to get the best training and coaching for the upcoming SSC CGL EXAM and other government job exams.
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function [J grad] = nnCostFunction(nn_params, ...
X, y, lambda)
%NNCOSTFUNCTION Implements the neural network cost function for a two layer
%neural network which performs classification
% [J grad] = NNCOSTFUNCTON(nn_params, hidden_layer_size, num_labels, ...
% X, y, lambda) computes the cost and gradient of the neural network. The
% parameters for the neural network are "unrolled" into the vector
% nn_params and need to be converted back into the weight matrices.
% The returned parameter grad should be a "unrolled" vector of the
% partial derivatives of the neural network.
% Reshape nn_params back into the parameters Theta1 and Theta2, the weight matrices
% for our 2 layer neural network
Theta1 = reshape(nn_params(1:hidden_layer_size * (input_layer_size + 1)), ...
hidden_layer_size, (input_layer_size + 1));
Theta2 = reshape(nn_params((1 + (hidden_layer_size * (input_layer_size + 1))):end), ...
num_labels, (hidden_layer_size + 1));
% Setup some useful variables
m = size(X, 1);
% You need to return the following variables correctly
J = 0;
Theta1_grad = zeros(size(Theta1));
Theta2_grad = zeros(size(Theta2));
% ====================== YOUR CODE HERE ======================
% Instructions: You should complete the code by working through the
% following parts.
% Part 1: Feedforward the neural network and return the cost in the
% variable J. After implementing Part 1, you can verify that your
% cost function computation is correct by verifying the cost
% computed in ex4.m
% Part 2: Implement the backpropagation algorithm to compute the gradients
% Theta1_grad and Theta2_grad. You should return the partial derivatives of
% the cost function with respect to Theta1 and Theta2 in Theta1_grad and
% Theta2_grad, respectively. After implementing Part 2, you can check
% that your implementation is correct by running checkNNGradients
% Note: The vector y passed into the function is a vector of labels
% containing values from 1..K. You need to map this vector into a
% binary vector of 1's and 0's to be used with the neural network
% cost function.
% Hint: We recommend implementing backpropagation using a for-loop
% over the training examples if you are implementing it for the
% first time.
% Part 3: Implement regularization with the cost function and gradients.
% Hint: You can implement this around the code for
% backpropagation. That is, you can compute the gradients for
% the regularization separately and then add them to Theta1_grad
% and Theta2_grad from Part 2.
a1 = [ones(m, 1) X];
% a1 has size m*401;Theta1 has size 25*401 ; z2 has size m*25
z2 = a1 * Theta1' ;
a2 = sigmoid(z2);
% a2 has size m*26 ; Theta2 has size 10*26 ; a3 has size m*num_labels
a2 = [ones(m,1) a2];
z3 = a2 * Theta2';
a3 = sigmoid(z3);
Y = zeros(m,num_labels);
Y(i,y(i)) = 1;
theta1 = Theta1;
theta2 = Theta2;
theta1(:,1) = 0;
theta2(:,1) = 0;
firstReg = sum(sum(theta1.*theta1,2));
secondReg = sum(sum(theta2.*theta2,2));
J = 1/m * sum(sum(-Y.*log(a3)-(1 - Y).*log(1-a3),2)) + lambda/(2*m)*(firstReg+secondReg);
Delta1 = zeros(size(Theta1));
Delta2 = zeros(size(Theta2));
for i = 1:m
delta3 = a3(i,:)- Y(i,:);
delta2 = (delta3*Theta2)(:,2:end).*sigmoidGradient(z2(i,:));
Delta2 = Delta2 + delta3'*a2(i,:);
Delta1 = Delta1 + delta2'*a1(i,:);
Theta1_grad = Delta1/m ;
Theta2_grad = Delta2/m ;
Theta2_grad(:,2:end) = Theta2_grad(:,2:end) .+ lambda * Theta2(:,2:end) / m;
Theta1_grad(:,2:end) = Theta1_grad(:,2:end) .+ lambda * Theta1(:,2:end) / m;
% Unroll gradients
grad = [Theta1_grad(:) ; Theta2_grad(:)];


Wednesday, April 11, 2012
School Gardens Teach More Than Just Agriculture
Teachers at a school in North Charleston are finding ways to incorporate Math and Science into their garden curriculum. WCSC in Charleston posted a great clip to show how these students are enhancing their Math and Science skills through activities in their school garden. Teachers are pleased with the outcome and say the students have enjoyed learning through hands on activities outside. Math and Science were both critical areas at this school and this is a unique way to help increase these subjects. So far, it has been very successful!


Calculus was developed by Gottfried Leibniz and Isaac Newton and is one of the most important achievements known to science and mathematics. Newton is without doubt one of the most influential mathematicians of all time. Newton’s and his efforts to find a method in mathematics that could explain universal gravitation, devised the method of fluxions.
Today it is known as Differential and integral calculus. Newton was a private and secretive man, and kept his discoveries to himself. He did not publish much, and the majority of his works.
It is now well established that Newton and Leibniz brought about the form of calculus. Newton was first by about ten years but did not publish, and that Leibniz's papers of 1600’s were the earliest publications on the subject.
Calculus is the branch of mathematics that studies the rate of change in quantities and length, area, and volume of objects.
Calculus has two main branches
It is a function that relates the values of the function to the values of its derivatives. It deals with the concept of taking a derivative, also known as differentiation.
It associated with the branch of maths and the determination of application and properties of integrals, also called integrating. Which means splitting a curve into a really small part so that you can find the total area of the space under the whole curve.
Calculus I covers very basic differential equations, limits, derivatives and some theorems like Mean Value Theorem and applications of such things e.g. rate of change problems & L'Hôpital's Rule.
Calculus II usually covers integration, series like applications of integration and Taylor series, like certain area problems.
Uses of Calculus in Daily Life
Calculus is widely used in almost every technical or scientific field.
Example: When you see a bike on the road, how do you decide if it is going fast or slow ? you inherently calculate the distance the bike has travelled by differencing its coordinates, divide it by the instance of time and decide that it’s going fast or slow. Well, you inherently calculated a derivative. Simply put, Calculus is just a method to solve simple problems like position, time, velocity and acceleration etc
Calculus covers various other topics like Limits, Numerical Integration and Numbers, Special functions Lists and Tables, Multivariable and Series.
To learn more about Maths concepts Calculus Limits, Special functions and Numbers, Numerical Integration, Lists and Tables, Multivariable, Series and Math download BYJU’s The Learning App and to know more visit @Byjus.com.


The most surprising number I’ve seen in mathematics is deeply connected with the notions of randomness and dimensionality. The first two numbers in the series that lead to this number are: 1, 1. So far so easy, one is a pretty straightforward number. To begin, I’ll reveal where these two ones come from.
Imagine a line. Imagine that line divided into equal segments. I now place a pin in the middle segment. Now I’m going to start moving this pin. Where I move it to depends on the flip of a fair coin; heads I move it left, tails I move it right. That’s the setup. Now the question: what is the probability that the pin will visit a particular segment? The answer is that, given enough coin tosses, whichever segment is selected the pin will visit it with certainty, that is the probability equals one. This probability is the first number in this series of interest. The the next number in the series, also a one.
This second number is derived from the same problem as the first with the difference that we are no longer dealing with a line, but a plane divided into equal sized square segments. Instead of a coin we randomly pick a direction to move in. Pick a starting point on a flat surface. Pick an end point. The probability that a pin, moving randomly, will eventually reach the chosen end-segment is one. No matter which end-segment you pick. Another way of putting this is that a pin moving randomly will eventually visit every single segment possible. This result is the same as for the line.
The trend in the series is becoming apparent, the number in the series at position N is the answer to the question:
What is the probability that a random walk on a lattice in N dimensions will visit an arbitrary point x?
So for one dimension, this probability was one. The same for two dimensions. Any guesses for three?
The answer for three dimensions is: 0.3405373296 . . .
This is the most surprising number I’ve ever seen. It may mostly be surprising to me as I knew and appreciated why for one and two dimensions the value is unity. On thinking about what the number could be for higher dimensions I imagined it would either remain one or decay with some series that involved a relatively simple relationship with π. The expression for this number in three dimensions is not straighforward:
In truth I find it difficult to explain just why this seems so odd to me. The most striking feature to me is that it happens in the transition from two to three dimensions, the space in which we naturally find ourselves. Could it be that random collisions in two dimensions does not allow for much fluidity, and collisions in four or more are far too infrequent to allow for many interesting reactions? Just a thought…
For those that are interested the value for four dimensions is: 0.193206 . . .
and this series of numbers is known as Pólya’s Random Walk Constants.


HOW TO CALCULATE PEDAL RATIO FOR YOUR HYDRAULIC LINKAGE.
So you want to change your clutch linkage over from mechanical or cable linkage to hydraulic linkage, why? Because you want a softer clutch pedal! Well, it doesn’t quite work that way. Your pedal pressure is a mathematical equation based on your clutch pressure at the tip of the lever, divided by your clutch linkage ratio. It doesn’t matter what type of linkage you have. So if the pressure to depress the levers of your clutch is 500 pounds and your overall linkage is 12:1, then your pedal pressure will be 41.66 lbs at the pedal pad. It can’t be any less than 41.66lbs, but it can be more, if there is added external resistance from something such as cable rubbing through it’s casing or worn out mechanical linkage.
The biggest mistake we see, when designing the hydraulic linkage, is to try and reuse the original clutch mechanical linkage attachment point. That doesn’t work and we’ll explain why. With mechanical linkage, your pedal ratio is usually 3:1, and your bell crank or Z bar ratio is usually about 2:1 and your clutch fork ratio is normally about 2:1, then you would have (3:1 pedal X 2:1 Z bar X 2:1 Fork) = 12:1. Now when you connect your master cylinder to the same 3:1 stock hole in your pedal, and you then eliminate the bell crank and the Fork, and if your master cylinder to Slave cylinder ratio is 2:1, then your overall linkage ratio would be 3:1X2:1 = 6:1. You can now see that your hydraulic linkage would be ½ of your original linkage of 12:1 .So using that same 500 lbs clutch, the original pedal pressure was 500lbs / 12:1 = 41.66 lbs, then your new hydraulic pedal pressure would be 500lbs / 6:1 = 83.33 lbs or 6:1 VS 12:1. What you’ll need to do now is, make your pedal ratio be 6:1, so that your overall hydraulic linkage ratio would be 12:1 (6:1pedal X 2:1 slave).
To calculate your pedal ratio you must start by measuring the length of your pedal from the center of the (fulcrum/pivot), to the center of the pedal pad at the bottom of the pedal, as shown in the picture to the left. If it measure 12” from center to center, and you want a 6:1 pedal ratio, you divide 12” by 6 and you’ll get 2”. Go back up to the (fulcrum/pivot) and come down 2” and you will have your 6:1 pedal ratio.
So you think you’re done, not yet. Now you need to figure out the geometry. As you can see from the picture below, I drew a 2” red circle to represent the radius around the Pivot point.
Anywhere on that red circle, is a 6:1 ratio, as compared to the length of the pedal, but we needed to push in the direction of the master cylinder with the least amount of rise or fall of the push rod as possible.
The ideal angle is a 90 degree right angle when the pedal is ½ way through its travel from the top to the bottom of the throw as measured from the fulcrum to point where the master cylinder push rod is attached to the pedal, on down to master cylinder. Now when the pedal is all the way up, it’s the same amount of degrees above right angle as it is below right angle when the pedal is down to the floor. As you can see from the picture, where the green line and white line form a right angle on the red circle, it is nowhere on the pedal. So if you notice an ear had to be added to the pedal to attach the master cylinder push rod to the correct position to give the 6:1 ratio AND keep the right angle at ½ travel. The ear was needed because the master cylinder was mounted low on the firewall to clear the brake booster and the push rod was at a steep angle. So there you have it for calculating the correct ratio and geometry. How you should have a nice soft and smooth clutch pedal with good release.
Photo: Courtesy of the Clutch & Flywheel handbook by Tom Monroe.


Stupid Word Problems
Many of the hokey word problems published in the vast majority of mathematics textbooks are really sorry excuses for real practical applications. I apologize to any readers who might be contributors to the word problem sections on which I am commenting - but come on! How many of us are going to be tracking elephant migrations for a living, or calculating when airplanes traveling at different speeds from different cities are going to cross paths? Interesting questions, but such textbook word problems are just obscure oddities. They just do not reflect what real people do every day with math, and they do not encourage the student to want to learn more math. Instead, they think of math as some stupid obscure subject.
Real Mathematical Applications
I am here to talk about coordinate geometry. Students ask “What would anyone ever use this for?” It is unfortunate that the average educator cannot expound on the simple applications presented in this article. Have you ever driven past an interstate highway interchange construction site? Just how does such a complex set of interconnecting curves and lines and bridges all come together into one smooth and continuous system on which automobiles can safely travel at 70 mph? I suppose that a number of people never think about it. Many take it for granted. But that entire road system had to go through a conceptual process in someone’s brain, then transferred to a paper and computer plan, and finally transferred into reality with the aid optical and mechanical layout equipment controlling heavy equipment around massive but precise amounts of dirt, fabricating complex pieces of steel which all must fit together tightly like a jigsaw puzzle. What wonder of science makes this possible? Mathematics does!
Perhaps you have taken an Algebra course where you learned to graph and plot complex curves with names like hyperbola or parabola, spirals of various types, or just more simple shapes like triangles, rectangles or parallelograms. Perhaps you advanced to 3 dimensional graphing, where various geometric shapes are represented by mathematical functions. In the highway construction world, everything you see being built is defined on paper and in a computer by such mathematical functions. And construction engineering is only the tip of the iceberg. In a continuation of this blog, we will go over a simple street and curve design to show how the lines and functions which you l may have already learned to plot in coordinate geometry in your Algebra class.


The kindergarten children develop and use mathematical thinking, concepts, skills and language during their play and everyday activities in the same way that they develop their language skills- through imitation, experimentation and negotiation. Mathematical language and thinking emerge in an organic, fluid and social way as they explore, construct, interact with and make sense of their world.
Tuesday is bread roll baking day, and the children are involved with weighing, measuring, counting, making shapes, using fractions:
‘Mine is twice as big as yours.’ ‘I have cut mine in half.’ ‘Pass me the knife, I want to make a star on top.’ ‘They are too close together, there won’t be room when they are cooked.’ ‘I can see that it is a pint of water. It is the same as Daddy’s pint glass’.
During indoor free-play the children enjoy construction. Playing (alone and collaboratively) with wooden blocks involves working with ideas around shapes, space and patterns. Designing, building and operating a bookshop is even more complex:
‘How many are we?’ ‘How many racks can we have each?’ ‘How many all together?’ ‘How much do the books cost?’ ‘What shall we use for money?’ ‘The wooden blocks are worth a hundred, the smaller ones can be ten, conkers five and the shells one.’ ‘How many more conkers do we need?’ ‘How many do we need so we can have 4 each?’
Handwork helps to develop mathematical thinking as well as fine motor skills: ‘My finger-knitting is wider than yours, that is why it is shorter.’ ‘Mine is longer because I started before you.’ ‘Mine is as tall as the school.’ ‘We measured mine, it is as long as the hallway.’ ‘My sandpaper is rougher, look, the sand is bigger.’ ‘Yes, but mine has more sand.’ ‘Look, the numbers on the back tell you which has bigger sand.’
Snack time provides mathematical opportunities too: counting children, adding two teachers, placing the right amount of chairs and boards, discussing the snack: ‘I have more than you.’ ‘Mine is longer.’ ‘I have more left because I ate it slowly.’ ‘I have 36 raisins.’ ‘I have more.’ All the children start to count their raisins. They count together to 100. Conversation might turn to animals- Which are the fastest? What do tigers eat? How may sheep could seven tigers kill? ‘One tiger could kill one sheep, two could kill three, three could kill four, four could kill six, five could kill seven, six could kill nine, and seven could eat ten, because they couldn’t kill half a sheep’. Or Space- ‘How long would it take to get to the moon?’ ‘A bigger rocket would be slower than a smaller rocket, so it would take longer, it would take a year, a small rocket would take a week.’
During outside play there is more construction: the children use levers, judging weight, length, space. ‘If we put this plank here, it will make it high enough’, ‘Try this one, it is longer so it will reach’. They dig tunnels, deeper, to the middle of the earth. They run and skid- faster, further, longer. And ask questions- ‘How many short gnomes would have to stand on each other’s shoulders to reach the top of the gate post, if a gnome was as tall as my two fists on top of each other?’
During the course of the morning, like true mathematicians, the children work alone or collaborate, developing and testing their theories, developing language alongside concepts, naturally, without any interaction or intervention from the teacher. They use cardinal and ordinal numbers, positional language, explore direction, distance, speed, temperature, time, magnitude, shape, fractions and geometry. They actively look for, notice and construct relationships, organizing them into concepts that will later become regarded as mathematics.


Learning math has never been this much fun
It can be quite a challenge to get your child interested in learning math. At a young age, match can appear to be quite complicated, difficult and even boring! However, it’s extremely important that your child get a strong grasp on simple math concepts early and easily
Turn math class and math homework into the most fun and interactive part of the day with the Light N’ Strike Math game – the game where math, timing and hand-eye coordination come together to create an environment of achievement and fun!
How it works
The Light N’ Strike Math game works by allowing your child to dictate play and figure out answers for themselves. Unlike calculators or flash cards, Light N’ Strike Math puts your child in control of their actions!
Select the equation you want to practice: addition, subtraction, multiplication or division. And then choose from one of 3 skill levels. The easy-to-read display screen will then feature a math problem for you to solve.
And that’s where the fun begins! Use the included soft mallet to strike the numbers that correspond with the question when they are lit up. For example, if the question on the screen is 5+7, you would hit the number 1 when it is lit up, followed by the number 2 to create the answer 12. When you think you’ve got the right answer, strike the enter key with your mallet and see if you’re correct!
Learning and fun come together
With the Light N’ Strike Math game, your child will hone their mental math skills and reasoning abilities in a fun and interactive format that encourages education and achievement.
With easy to read buttons, bright lights and fun sounds, the Light N’ Strike Math game will soon become your child’s favorite toy to play. Durable enough to handle whatever can be thrown at it, you can use and play Light N’ Strike math with or without the included rubber mallet.


Humans are inherently risk averse. When offered a coin toss with a reward of $10,000 for heads but a loss of $10,000 for tails, most people would decline. They would likely agree to pay a significant sum to avoid the gamble, despite the expected value of the gamble being zero.
When economists describe the preferences of a person, they often build in some form of risk aversion. A risk averse person will always prefer a sum with certainty than a gamble with that expected value. One way that economists do this is by describing the preferences of a person as logarithmic. This means that the level of utility that an individual gets from, say, a sum of money increases at a diminishing rate. They might value an increase in their wealth from $1 to $10 the same as an increase from $10 to $100. These preferences then shape the choices that the person makes. For example, they might value of 50-50 gamble between $1 and $100 at only $10, despite the expected value of the gamble being slightly above $50.
Beyond the extensive research on preferences in the behavioural economics literature, the use of logarithmic preferences to approximate decision-making has some support in empirical work on how we view numbers in our minds. In 2008, Stanislas Dehaene and colleagues made a useful contribution to this area through their examination of whether our mental mapping of numbers was inherent or trained.
First, some background. As noted by the authors, there have been a number of experiments that showed that children mapped numbers to space in a logarithmic fashion. They noted that:
When asked to point toward the correct location for a spoken number word onto a line segment labeled with 0 at left and 100 at right, even kindergarteners understand the task and behave nonrandomly, systematically placing smaller numbers at left and larger numbers at right. They do not distribute the numbers evenly, however, and instead devote more space to small numbers, imposing a compressed logarithmic mapping. For instance, they might place number 10 near the middle of the 0-to-100 segment.
This logarithmic view of the world does not last. Between first and fourth grade children start to move from logarithmic to a more linear mapping of numbers. This transition is most pronounced across small numbers, and moves to higher numbers as they age. Some logarithmic mapping persists for very large numbers.
Dehaene and colleagues contributed to this picture through their examination of whether the move from logarithmic to linear mapping was a result of formal schooling or a natural process of brain maturation. To study this, they undertook some number-mapping exercises with the Mundurucu, an Amazonian group with little access to education or other instruments that may affect their perception of numbers (such as maps and rulers).
To test how they map numbers, the participants were given a line with one dot at one end and 10 or 100 dots at the other. They were then given a number of dots between either one and 10 or one and 100 and were asked to place them at the proper place on the line.
This exercise showed that logarithmic mapping persisted into adulthood for the Mundurucu. This was even the case for numbers between one and ten. These findings suggest that it is the experience of children who receive formal education in mathematics that shifts their mental mapping to a linear way. This could be through either through the formal education itself or some other cultural cause.
This study raises a number of implications for the way people’s risk preferences are formed. If people perceive quantities in a logarithmic fashion, they will tend to be risk averse. As they move to a more linear way of mapping numbers, this could coincide with a reduction in risk aversion. Does the education of children in mathematics tend to increase their risk tolerance through changing the way they see numbers?
This could be argued to have a number of follow-on effects. A reduction in risk aversion would naturally see an increase in risk taking activity. They will weight the possibility of great wealth higher and be willing to accept the risk of a larger loss to make it. An economy full of people with a greater risk tolerance could have more entrepreneurial activity, greater wealth (with some unlucky losers) and a larger tendency to chase wealth.
From a historical perspective, the questions become more interesting. Could the increasing degree of education over the last few hundred years have been training children to be more risk seeking in their activities? If so, could we argue that an environmental cue is part of the reason modern economies look the way they do?
An additional implication from the study is the manner in which large numbers are dealt with. From a logarithmic scale, large numbers appear closer together. If functioning with large numbers in an accurate fashion is important (for example, if it matters whether I pay you $100 or $110), the shift to a linear way of thinking will reap some important dividends. This is not so much a question of risk aversion but the ability to differentiate when numbers get large.


Students exhibit a wide range of mathematical skills and aspirations. Some students may need to develop the mathematical skills necessary to function in daily life. Other students may seek to address more challenging mathematics to prepare them for the highest-level courses in Year 11 and Year 12.
Mathematics is a compulsory subject in Years 7 -10. For this reason, Stage 5 has been expressed in terms of the three sub-stages, Stage 5.1, Stage 5.2 and Stage 5.3. As well as studying the Stage 5.1 content, the majority of students will study some or all of the Stage 5.2 content. Similarly, as well as studying the Stage 5.2 content, some students will study some or all of the Stage 5.3 content. The Stage 5.3 course is the highest level of mathematics studied in years 7-10. Movement between the sub-stages is possible, and all decisions are made on case by case basis.


Artificial neural networks- a tool for clinical decision: a computerised mathematical model for understanding and predicting complex and chaotic dynamics in complex biological systems. A type of artificial intelligence that attempts to imitate the way a human brain works. Rather than using a digital model, in which all computations manipulate zeros and ones, a neural network works by creating connections between processing elements, the computer equivalent of neurons. The organization and weights of the connections determine the output. Neural networks are particularly effective for predicting events when the networks have a large database of prior examples to draw on.


Spheres and orbs in Copernicus
Question 1: Using an 8.5x11 inch sheets of graph paper and a compass, draw Copernicus' cosmic scheme to scale using the figures indicated below. Label the spherical shell -- or orb -- corresponding to each object, in the correct order. (Ptolemy's figures from Exercise 5 are given for comparison.)
Question 2: On the sheet provided, figures 2A and 2B show Ptolemy's Almagest model for the sun and for the moon, with the corresponding three-dimensional orb models. Figures 2C and 2D show Copernicus's models for the moon and for an outer planet. What would the corresponding orb models look like?


Cluster analysis Documentation
This program is under development. Check your results carefully.
The Python script 'clusterana.py' is used to extract more detailed
information from the data produced by the script
program requires a completed or partly completed run of clusterstat.py.
The program reads the restart file generated by clusterstat to extract
the system information. In particular, the script allows to check the
accuracy of the cluster expansion under consideration or negligence of
To start calculating the clusters type:
Possible options can be obtained with
Purpose: Statistical analysis for the cluster expansion
of a potential surface.
Usage: clusterana [-deb -ver -h -? ] inputfile.inp
-deb Run in debug mode (more detailed logging).
-D <name> The name directory of a clusterstat run.
-ver Print version info.
-h -? Print this help text.
Further analysis of data produced by statistical analysis program
'clusterstat'. This requires an (at least partly) completed run
of 'clusterstat'. The system information is obtained from the restart
file of 'clusterstat'.
The input needed by clusterana in general follows the rules
of the usual MCTDH input. The input is organized in three sections:
||What is to be done.
||Specification of the expansion terms. (optional)
||modification of the coordinate ranges (optional).
Example inputs can be found in
|name = S
||The 'name' directory of the previous clusterstat run and
directory to which output files are written.
|steps = I (,I1)
||The number of Monte-Carlo steps to be processed. If one value
is given, the first I steps
are read, if two numbers are given, steps
I1 are read.
Default: all steps will be processed.
|logminmax = I (,I1)
||Enable logging of the set of samples with the smallest and
lowest values concerning the true potential, the approximated potential
and the difference between them.
The first number denotes the maximum number of samples to be logged,
the second, if given, the minimum number of samples to be skipped
before the next sample can be logged. This can be used to avoid logging
of all samples when the random walker is in a certain region of the PES
that produces large errors etc.
|count-samples = R,R1 (,S)
||Count the number of samples for which the contribution of a
cluster is NOT in the region between R and R1. S is a unit, i.e.,
one of "cm-1", "eV", "meV", "au",
"kcal/mol" or "kJ/mol".
|densities = S (,S1)
|| Calculate 1D and/or 2D densities (histograms) for the
coordinate vectors of the random walker. S and S1 can be one of "1D"
and "2D". If "1D" is set, all one-dimensional densities are calculated,
if "2D" is set, all two-dimensional densities are calculated. Requires
|bins = I
||The number of bins used in the
calculation of the densities.
|outunit = S
||Unit in which the output is
written. Default: same as used in the clusterstat run.
||Allow overwriting of existing files in the 'name' directory.
Similar to option -w in the command line.
||Write order-dependent and reference-dependent cumulative mean
error of the cluster expansion to file.
||Write order-dependent and
reference-dependent cumulative root-mean-square error of the cluster
expansion to file.
||Calculate the auto-correlation
of the trajectory of the random walker to file
(to check the quality of the random walk).
||Write detailed statistics for
each cluster to file.
The EXPANSION-SECTION if given, is used to define which of the clusters
calculated in the clusterstat run are to be used to
PES. Only the clusters specified here will be included in the
mean and RMS values as specified in the RUN-SECTION.
For a detailed description on defining the cluster-expansion see
the documentation of clusterstat.
The COORDINATES-SECTION can be used to alter the range of the
the random walker. All samples for which the walker has left the
are ignored (except for calculation of the auto-correlation function).
range can be specified in two ways. On possibility is the definition of
as in the documentation of
clusterstat. A second possibility is providing a function
tests if the walker is an a certain region. In this case the
COORDINATES-SECTION may only contain two keywords:
|user-source = S
||The path (relative or absolute) to the module containing the
routine which tests the coordinate vector. See
using the 'user-source' keyword.
|routine = S
||Name of the routine provided by
the module given with 'user-source' which is used to test the
The routine specified above receives a NumPy array (type float) containing
a coordinate vector and must return
True or False, indicating the validity of the sample
belonging to the coordinate vector. If True is returned the
sample is assumed to be valid and included in the statistics, otherwise
the sample is skipped.
The output generated by clusterana are a number of ASCII
different types of data. The following files are generated:
The log file containing time stamp and messages sent through the
String representation of the original input. This file is reproduced
from already processed input and is not merely a copy of the original
Detailed statistics for all clusters, one cluster per line. If more
than one reference point is used the numbers in this file represent the
weighted sum over all reference points. The file is organized in up to
6 columns. The first column contains the tuple specifying the cluster,
the second and third column its mean contribution and root-mean-square
value. If count-samples is given in the RUN-SECTION, the number of
samples below and above the range specified with count-samples
are given in columns four and
five, respectively. If the cluster had been excluded from the cluster
expansion, this is flagged in the last column.
The last two lines of this files contain estimated of the overall
error of the cluster-expansion.
Same as statistics, but for one reference point only, where <i>
denotes the number of the reference point. The numbers given in these
files do not incorporate weighting factors. These files are only
generated if more then one reference point is used.
If logminmax is set in the RUN-SECTION this file contains the
coordinate vectors and energies of the samples that produced the
largest absolute numbers for the true potential (<suffix>
= "exact"), the approximated potential (<suffix>
= "approx") and their difference (<suffix> =
"delta"). If count-samples is set in the RUN-SECTION also the most
relevant clusters are listed.
Same as samples_largest_<suffix> but for the smallest
For each sample (one sample a line) the first column contains the
difference between the exact potential and the approximated potential
(Vexact - Vapprox).
The second column contains the exact potential
and the third column the approximated potential.
For each sample (one sample per line) the summed contribution of all
clusters of a certain order to the approximated potential. The file is
organized in columns. The first column contains all contributions from
the zeroth order clusters, the second column the contribution from all
first order clusters, etc.
The n-th line contains the mean of the first n lines of file curr_order_ana
The n-th line contains the root-mean-square of the first n lines of
For each sample (one sample per line) the order-dependent error of the
approximation. All clusters in the expansion up to a certain order are
summed and subtracted from the exact potential. The file is organized
in columns. The first column contains the exact potential minus all
zeroth order contribution. The second column contains the exact
potential minus all zeroth and first order contributions, and so on.
The n-th line contains the mean of the first n lines of file curr_error_order_ana.
The n-th line contains the root-mean-square of the first n lines of
For each sample (one sample per line) the weighted contribution of the
expansion around the reference points of the approximation. The n-th
column contains the contribution of the expansion around the n-th
The n-th line contains the mean of the first n line in file curr_ref_ana.
The n-th line contains the root-mean-square of the first n line in file
For each sample (one sample per line) the weighted exact potential
minus the weighted
approximation.. All clusters around the n-th reference point are summed
and subtracted from the weighted exact potential. the n-th column
contains the result for the n-th reference point.
The n-th line of this file contains the mean of the first n lines of
The n-th line of this file contains the root-mean-square of the first n
lines of file curr_error_ref_ana


Holt homework help - Put aside your concerns, place your task here and receive your top-notch project in a few days Use this service to order. Homework help holt algebra 2 Name. Publisher, Holt McDougal Littell. Homework help online holt. Homework Help and Answers: Go math homework help common app essay prompt 5 buy paper mache houses.
Apply for the needed guidance on the website Allow us to help with your Bachelor. Homework help on demand every order is double-checked by the webs best professionals. Students are encouraged to use the textbook online resources to get help. ENotes Homework Help is a way for educators to help students understand their school work. Click your Geometry textbook below for homework help. For parents, it offers advice on how to help with homework and access to games.
Holt hjem homework a. We provide holt homework help is of a need to gather data. For you out very. All kinds of homework help. Holt McDougal Collections; 7th Grade: Geometry Burger, et al. Geometry Larson, et al. Geometry - Concepts and Skills Larson, et al. Geometry Jurgensen, et al. Geometry Charles, et al. Geometry Bass, et al. Algebra 2 Carter, et al. Algebra 2 Holliday, et al. Algebra 2 Burger, et al. Algebra 2 Larson, et al.
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With math class, students also need to write out examples of math problems. Examples used during class are often the same type of problems in the daily homework. Try to review notes immediately after school. Draw boxes around key words or phrases.
Write all of the boxed words and phrases in the left hand recall section. This helps students remember the key subjects covered in each class period. Students can also put key formulas and equations in the left hand column. This will make finding pertinent information easier when trying to complete math homework. The Cornell method, as described above, is helpful for students of all ages, but can be tailored to suit the needs of middle school students.
Students who still have difficulties completing their assignment after reading through their notes should look to their math textbook for guidance. Most textbooks have examples of each type of question that a student will be asked to complete in the chapter homework. When a student has troubles with a particular question, it is recommended that they review the sample problems provided in the chapter to see the procedures that were used to find the solution.
Sometimes middle school students fail to understand the sample problems provided in their class notes and textbook. When this happens, they should consult the advice of their friends or family. Students often forget that their older siblings or parents once studied similar topics and faced similar difficulties in their middle school math classes. While a middle schooler should never expect others to complete their homework for them, they can ask questions on how to complete a problem.
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Holt McDougal Mathematics - Grade 7. Get the exact Holt McDougal Mathematics - Grade 7 help you need by entering the page number of your Holt McDougal Mathematics - Grade 7 textbook below.
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WEDNESDAY, AUGUST 26: Ittay Weiss, University of the South Pacific, will discuss "Weak fibrations
and a metric formalism for topology". At CCNY; tea 3:15pm, talk 4pm, NAC 4/205. For more information, contact Ralph
ABSTRACT: Continuity spaces give rise to a category of (generalized) metric space which is equivalent to the category of topological spaces. Classical topological spaces and continuity spaces are thus different models of the same thing, and which models are better depends on the question at hand. I will present a simple machinery cast in the language of fibrations, resulting in a mechanism that converts metric constructions into topological ones, or into uniform ones. Two main special cases recover (in the uniform case) and generalize (in the topological case) recent work on discrete homology and discrete homotopy of metric spaces.
THURSDAY, OCTOBER 15: Michael Mislove, Department of Computer Science, Tulane University, will
speak on "From Haar to Lebesgue via Domain Theory". At Queensboro Community College, Science Building; tea 12:30-1 pm,
Room 231, talk 1-2 pm, Room 212. For more information, contact Francis Jordan,
ABSTRACT: This talk starts with the almost classic result of SchmidtÕs that the canonical map from the middle-third Cantor set to the unit interval maps Haar measure to Lebesgue measure. The Haar measure in question is defined by viewing the Cantor set as an infinite product of two-point groups. We show that there is a broad generalization of this result:
Theorem: Any compact, perfect, totally disconnected metric group admits a mapping onto the unit interval that sends Haar measure to Lebesgue measure.
The Haar measure here can be taken to be the unique left-invariant probability measure that such a group possesses. We use the lexicographic order on such a group, realized as a subset of an infinite product of finite groups, to describe how the mapping from the group to the unit interval gives a representation of real numbers in [0,1] in the group. This is joint work with Will Brian.
For more information, contact:
CCNY: R. Kopperman (845-915-0914), S. Popvassilev (646-257-7197)
College of Staten Island (718-982-3626): P. R. Misra
Baruch College (646-312-4136): A. Todd
LIU C. W. Post Center (516-299-2447): S. Andima
Medgar Evers College, (718-270-6416): H. Pajoohesh
Queensborough Community College, (718-281-5291): F. Jordan


There are four graphs; a histogram, a box plot, an average value per time-of-day, and an average value per day-of-week.
A histogram is a graphical display of frequencies, shown as bars. It shows what proportion of cases fall into each of several categories. In this case, it shows how many values have fallen into each of ten ranges, starting with 1-9, then 10-19, 20-29, and so forth.
John Tukey described the Box Plot in 1977 as an efficient method for displaying a data summary. It visually summarizes the median, the upper and lower quartiles, and the minimum and maximum data values. The filled box itself contains the middle 50% of the data. The right edge (hinge) of the box indicates the 75th percentile of the data set, and the lower hinge indicates the 25th percentile. The range of the middle two quartiles is known as the inter-quartile range. The line inside the box indicates the median value of the data. If the median line within the box is not equidistant from the hinges, then the data is skewed. The ends of the horizontal lines or "whiskers" indicate the minimum and maximum data values, unless outliers are present in which case the whiskers extend to a maximum of 1.5 times the inter-quartile range. The points outside the ends of the whiskers are outliers or suspected outliers.
Values per Time-of-Day
This is a custom chart allowing you to view the average value for each of the 24 hours in a day. This might be useful for a variable that changes a lot during a typical day. For example, if you are tracking hunger, you might expect the hours before lunch and dinner to have the highest average value. Or, stress might be generally higher during working hours.
Values per Day-Of-Week
This is a custom chart allowing you to view the average value for each of the 7 days in a week. This can be useful for detecting factors that are dependent on the day; for example, your stress levels just might be lower on weekends. The first day of the week for this chart is Sunday.
Copyright 2009 by Mike Berro. All rights reserved.


If you ask, let's say, a football player: "How many goals did you score last season?" the guy would know the number. If you ask me as an investor, you know, what was being your performance last year, I would know that number, and if anyone mentioned sustainability in asking, "What's your CO2 footprint of your institution? Scope 1, 2 and 3, last year, accumulated and break me down and most importantly, which assumption did you use in order to calculate the number?" If he can't explain the workings, the math, then you know he's a liar. It's as simple as that.


WHAT DOES THE TERM CARD ODDS EXACTLY MEAN?
If you have not already noticed, probability is an immense factor in Texas Hold 'em. E.g., there are 2,598,960 possible hands in a 52card deck but only 4 Royal Flushes. If the ordinary serious poker player is dealt out 100,000 hands in their lifespan, they will never hold (on the first five cards) more than 4 percent of all the possible hands. And in all likelihood a lot less.
Working out straight card combinings for the purpose of this text are called Card Odds (you will be introduced to additional kinds of odds later). Card Odds can expose a lot of quite interesting data.
For instance, how many pat straight flushes will you see in your lifetime? To find out that number, the likely amount of hands that could be dealt during your lifetime is counted on by the following computation: 10 complete poker hands / hr. x 5 hrs. / game x 50 games / yr. x 40 yrs. / poker life = l00,000 hands of poker per lifetime.
This is a pretty aggressive approximation, as most people will never come close to this number of complete hands in Texas Holdem. Based on this level of play, the number of pat (on the first five cards) poker hands that you should get during your lifespan is calculated from the card odds and tabularized as follows:
Cards Dealt Number of Pat Hands
No pair 50,000 One pair 40,00 Two pair 5,000 Three of a kind 2,000 Straight
400 Flush 200 Full house 170 Four of a kind 25 Straight flush 1.4 Royal straight flush 0.15
So statistically, you should see a pat straight flush on your first five cards once or twice during your lifetime. Most intermediate poker players will never see even one. Card players often talk of having a ‘hot streak’ or a ‘run’. Mathematically, ‘stripes’ do not exist. But imagine you did have an astonishing run of cards one evening. What would the odds be of having five back-to-back straight flushes in a row?
Royal Flush 4 .0000015391
Other Straight Flush 36 .0000138517
Four of a kind 624 .0002400960
Full House 3,744 .0014405762
Flush 5,108 .0019654015
Straight 10,200 .0039246468
Three of a kind 54,912 .0211284514
Two Pairs 123,552 .0475390156
One Pair 1,098,240 .4225690276
Nothing 1,302,540 .5011773940
Total 2,598,960 1.0000000000
In every 1.7x1024 deals . . . or once in every 700,000,000,000,000,000,000 years. You would have to study those cards in the dark though, because our sun will be long gone by that time.
Up to now we know that the real Rounders use card odds to make playing decisions. A determination made without taking into account card odds makes poker a hazarding game. The probabilities of finishing a flush or a straight, the probability of getting an over card (face card), the percentage of times you are going to flop a card to match your pocket pair - are all highly significant factors in Texas Hold’em. Knowledge of these statistics is key to winning.
Here are some other more common probabilities that you should know about:
You need one more heart to make your flush on the turn or river - 35% Probability of hitting an open-ended straight draw (i.e. 4 straight cards, need one on either end to hit on turn or river)- 31.5%
Chance of being dealt suited cards: 23.5%
Probability of hitting a three or four of a kind at the flop when you hold a pocket pair: 11.8%
Chance you will hit a pair at the flop, holding two unpaired cards in the pocket: 32.4%
Probability of being dealt AA: .45%
Probability of no one holding a particular card, by amount of players, presuming you do not have that card, by number of overall players.
2 - 84.5%
3 - 70.9%
4 - 59%
5 - 48.6%
6 - 39.7%
7 - 32.1%
8 - 25.6%
9 - 20.1%
10 - 15.6%
Chance someone else does not have an ace, assuming you do hold an ace, by total number of players:
2 - 88.2%
3 - 77.5%
4 - 67.6%
5 - 58.6%
6 - 50.4%
7 - 43%
8 - 36.4%
9 - 30.5%
10 - 25.3%
make your hand). Suppose you are holding 6c 7d and the flop comes 9s 10h Kc.
In this example you need an 8 to make the straight. Since there are four 8’s in the deck of cards, you have 4 outs.
Calculating the odds with one card to come is comparatively straightforward.
When you are anticipating drawing to the inside straight, you have four outs. There are a total of 46 unknown cards (52 minus the 2 cards in your hand minus the 3 cards for the flop and the 1 turn card). 42 of the cards do not build your hand and four do. 42:4 or 10.5:1 = about 9%. We opt to use the percentage as it assists when calculating Pot Odds (to come later).
To estimate the appropriate odds with two cards to come, you must first find out the total number of two-card combinations getable after the flop. The easiest formula to calculate this is by multiplying the amount of cards available for the turn (47) by the number of cards available for the river (46) and dividing that number by 2 (because a card can't match itself). 47*46/2 = 1081.
A certain number of these 1081 two card combinations will have eights in them. To determine odds properly, you need to estimate two more figures.
One of the four eights can appear on the turn. And if one does, on that point will be three left for the river. If you multiply 4 by 3 and divide by 2 (because a card can't match itself) you see that there are six unique pairing of 8s.
have at least one eight in them and as many as two eights. Out of 1081 possible two card combinations on the turn and river, 178 of those combinations help us make our hand. Subtract 178 from 1081 to find
the number of combinations that don't make the straight (1081-178=903). The odds against making a straight by the river are: 903:178, or 20%.
Learn About Odds, Permutations And Return On Investment (ROI)
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Map scale is the relationship between a unit of length on a map and the corresponding length on the ground. You can find an explanation of the different types of scales you will see on maps at http://www.sfei.org/it/gis/map_interpretation/maps-and-scales.
Half-way down that page is a section on finding area measurement from scale, etc. This is useful if you need to figure out what area on a paper map represents what area on the surface of the earth. For example, you might need to figure out how many square inches of the map you are looking at represents 50 square miles on the surface of the earth.
You can also also Google "map scale converters" to find some handy online tools.
The Knight Reference desk has a few rulers available if you need to measure distances on a map.


The Jenks optimization method, also called the Jenks natural breaks classification method, is a data classification method designed to determine the best arrangement of values into different classes. This is done by seeking to minimize each class’s average deviation from the class mean, while maximizing each class’s deviation from the means of the other groups. In other words, the method seeks to reduce the variance within classes and maximize the variance between classes.
1. Wikiepedia Contributors (2013) Jenks Natural Breaks Optimization URL: http://en.wikipedia.org/wiki/Jenks_natural_breaks_optimization [accessed: 5 November 2013].


MiRitH (from MinRank-in-the-Head) is a project in collaboration between the Technology Innovation Institute of Abu Dhabi (UAE) and the Politecnico di Torino (Italy).
MiRitH is a Digital Signature Scheme (DSS) whose security is based on the hardness of solving the MinRank problem. MiRitH has been submitted to the NIST Call for Additional Digital Signature Schemes for the Post-Quantum Cryptography Standardization Process (https://csrc.nist.gov/projects/pqc-dig-sig) . The scheme allows high flexibility in the parameters choice and several trade-offs between signature size and sign/verification time.
Informally, the MinRank problem asks to find a non-trivial low-rank linear combination of some given matrices over a finite field. The construction of MiRitH starts from an MPC-in-the-Head (MPCitH) Zero-Knowledge Proof of Knowledge (ZKPoK) of a solution to the MinRank problem, which is then used to construct a 5-pass identification scheme, which in turn is converted into a non-interactive signature scheme via the Fiat-Shamir transform.
MiRitH is built on top of the MinRank-based signature scheme proposed by Adj, Rivera-Zamarripa, and Verbel [ARZV], which introduced a Multi-Party Computation (MPC) protocol P to verify solutions to the MinRank problem using the Kipnis--Shamir modeling and checking that a triple of shared matrices (Z, X, Y) satisfies Z = X.Y.
MiRitH introduces two optimizations over [ARZV], namely:
More details can be found in the technical specifications document.
As an example, for several variants of MiRitH, we report key/signature sizes and constant-time AVX2 implementation benchmarks on an 11th Gen Intel(R) Core(TM) i7-1165G7 @ 2.80GHz (Turbo Boost disabled). Other variants of the scheme and related performances can be found in the specifications document.
This numbers are dependent on the eXtended Keccak Code Package (XKCP) compiled with AVX2 enabled (https://github.com/XKCP/XKCP).
|Set||Variant||Public key [bytes]||Secret key [bytes]||Signature (avg) [bytes]||KeyGen[Clock Cycles]||Sign [Clock Cycles]||Verify [Clock Cycles]|


Next week in Topic the children will be looking at the work of different artists who created seaside scenes, such as J.M.W Turner and they will be creating their own seaside scene, using a range of medium such as collage, oil pastels and paint. They will be learning about different weather patterns in Science and will be looking at how the weather has changed through the Spring season, as they have been recording this on a daily weather chart. Towards the end of the week, they will be writing a recipe for how to make a picnic sandwich and will be writing an apology letter for Mr Grinling, from the pesky seagulls who ate all of his lunch!
In Maths the children will be exploring money and will be finding out about the values of different British coins and notes. They will be comparing, sorting and ordering them and finally using addition to find the total value of a group of coins.
Our last day of school before the half term holiday is Friday 24th May.


10. In geography and astronomy, the elevation and azimuth (or quantities very close to them) are called the latitude and longitude, respectively; and the radial distance is usually replaced by an altitude (measured from a central point or from a sea level surface). 11. Spherical coordinates are useful in analyzing systems that have some degree of symmetry about a point, such as volume integrals inside a sphere, the potential energy field surrounding a concentrated mass or charge, or global weather simulation in a planet's atmosphere. A sphere that has the Cartesian equation x2 + y2 + z2 = c2 has the simple equation r = c in spherical coordinates. 12.


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When math makes sense, kids leap way ahead. Mathnasium’s specially trained math instructors will teach your child how to understand math in an individual setting. Our unique approach enables us to effectively explain math concepts well and lend a helping hand to every student.
Every day, students around the world attend Mathnasium learning centers to boost their math skills. We are highly specialized; we teach only math. Members usually attend two or three times a week for about an hour. Our goal is to significantly increase your child’s math skills, understanding of math concepts, and overall school performance, while building confidence and forging a positive attitude toward the subject.
Our approach is to use sophisticated techniques to determine, with great accuracy, what a student knows and does not know. Next, we tailor-make a personalized and prescriptive learning program. Each student follows the program with the help of specially trained Mathnasium math tutors who provide instruction—and lots of warm encouragement. For proof of progress, we rely on the student’s report card, independent tests, and parent testimony to measure the speed and magnitude of improvement in math skills, numerical thinking, and attitude. Multiple independent studies have found Mathnasium to be effective 100 percent of the time, increasing student performance on standards-based tests in 20 sessions or fewer. Student skills jumped at least a grade level and in most cases, multiple grade levels.
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