A Charlotte Mason Moment:
“Mathematics depend upon the teacher rather than upon the textbook and few subjects are worse taught ; chiefly because teachers have seldom time to give the inspiring ideas … which should quicken imagination.”
(Home Education by Charlotte M. Vol. 1, p. 233)
What is one way to ease writing frustrations?
Do your kiddos get frustrated or weary with writing? As the school year is underway, I am reminded of an important tool I use often to ease writing frustrations. We use a 9″ x 12″ dry-erase lapboard and dry erase marker regularly throughout our school day. Writing on a markerboard is a welcome change from writing with a pencil on paper. Lapboards are easy to erase and can be written on much larger than on regular paper. Using a lapboard also helps kiddos focus on a small portion of writing at a time.
How does using a markerboard help ease writing frustrations during math?
Think of some of the frustrations that come with math time. Rushing through problems, making silly mistakes, feeling overwhelmed with too many problems, and messy writing are frustrations that spring to mind. Using a markerboard and a dry erase marker to do the textbook problems can really help with many of the math frustrations. On a markerboard, kiddos can see the problem written larger and have more room to work. They get a break from using a pencil and are able to write larger. They can erase mistakes easily and focus on only one problem at a time. My boys love flashing the markerboard to me, so I can check it quickly. Then, they love erasing the markerboard in a flash after I tell them they have the problem right!
What other subjects work well on a markerboard?
Using a markerboard and a dry erase marker to diagram sentences can really help with grammar frustrations. Diagramming goes quickly on a markerboard, plus it is very visual representation! Having your child write spelling words or studied dictation passages on a markerboard works great too. Writing Drawn into the Heart of Reading responses on a markerboard for your child to copy later is another great use. Listing writing ideas as your child brainstorms them for writing sessions works well too. Writing a numbered lists of school tasks for your child to check off as he works independently is another way we use a markerboard.
Try using a markerboard to make writing more fun.
Once you begin thinking of ways to use a markerboard during your school day, you will find endless uses for it. So try this great tool today! See if it helps ease writing frustrations and make writing more fun at your house. I know it has at mine!
Does your child waste time during math?
As I’ve been thinking about math these last few weeks, I wanted to share a tip that is really needed in this area. The tip is what Charlotte Mason so eloquently refers to as “not letting a child become stupid over his lessons.” In modern day terms, this equates to not letting a child daydream, stare into space, or waste time over his lesson. As parents it is our job to be there during subjects that lead to much wasted time. This is especially true for subjects that can be linked to long pauses between working moments. Math is one of those subjects.
How can you help your child stay focused during math time?
Partnering with your child to talk through math problems is a great way to keep your child focused. Discussing how to solve the problems will keep your child interacting with the text. Pointing out errors immediately and helping your child fix mistakes before they are repeated will move your math time along quickly. Leaving a child to work on his own often means the math lesson will go on much longer than needed! It also means your child could become really frustrated by the lack of forward motion or the sheer volume of problems to be completed.
Staying nearby to help is an easy way to keep math time productive.
Stay nearby to keep math sessions focused and productive. If you catch your child wasting time and staring into space, it often means he needs you to help and redirect. Watch your child during math, and if he “becomes stupid over his lessons,” jump in and move it along. Try this tip and see if your day goes better! I know my days go better when I keep this tip in mind.
Singapore math is different from typical math programs.
One thing I am reminded of as school is underway is the difference between Singapore math and typical math programs. Singapore math is one of those programs that takes a while to wrap your head around philosophy-wise. It is a program that is designed with a terrific ebb and flow of concepts and skills. Yet, often as parents, we get in the way of this ebb and flow by stepping in and adding more and more practice.
Your students are not expected to master every new math concept.
It helps to keep in mind that your students are not intended to master every new math concept you show them. Some concepts are only introduced. Others are practiced more extensively. Still other concepts are meant to be mastered. If, as the parent, we treat every concept like it must be mastered right away, we can truly frustrate our children.
Resist the urge to add more practice.
So, when you think your child may not have fully grasped a concept, resist the urge to add more practice. Don’t jump in and search for more worksheets on the internet or in another source to add to your math lesson. Instead, just partner with your child helping him/her through the lesson to be successful. Then, the next day, move on to the next lesson.
When tough concepts come around again, your child will be older and better equipped.
Be confident that those tough math concepts will come around again the next year in the next level. By then, your child will be a year older and better equipped to deal with those harder concepts. Age helps so much in dealing with abstract concepts!
Each day continue steadily moving forward in math.
Continue steadily moving forward each day through your math lessons. Keep in mind that concepts move from being represented concretely to pictorially to abstractly over time. As students view concepts with increasing levels of abstraction, they move toward math mastery. If you keep this philosophy in mind, you will experience less frustration and more enjoyment in the design of the program.
Math is a subject that needs to be taught.
For this tip, I’ll share something I’ve discovered the hard way. After 30+ years of teaching, I have come to realize math is one subject that needs to be taught. It is not meant to be a self-teaching subject that can be assigned to a student to do on his/her own.
What about using online lessons or video teachers for math?
Even with the aid of an online lesson or video teacher, ultimately with math there will be questions. There will be times when your child hits a stumbling block and needs help to go on. If you have no knowledge about what your child is working on, then the only way to help is to consult the answer key. At that point your child will quickly discover you can offer little help. This is because your child is fully able to check the answer key himself (and doesn’t really need you for that purpose). What he/she does need is the aid of a teacher who can explain the problem in a different way.
What can happen if you expect math to be a self-teaching subject?
With my oldest son, I was hit and miss in helping him with math. I changed math programs so many times looking for the ultimate self-teaching program! This only led to frustration for both my son and for me. In the end, he did manage to get through the needed math programs without me. However, it would have been far better and much less frustrating had I stayed the course with a math program. It also would have been better if I stayed with him to be able to help him along the way.
What are the benefits of staying with your child for math?
With our next three sons, who have varying math abilities, I have stayed with them for math. I quickly go over the textbook first. Then, I watch over them as they get underway on their assignments to be sure they’re started right. Last, I stay close while they work and help them through any frustrations. I have re-learned math along with my boys. What a different experience my next three boys have had with math, simply because of how I approached it!
Make staying with your child for math a priority!
I encourage you to make staying with your child for math a priority. This doesn’t mean you need to devote an hour to math per child per day. Instead, it means you should be there to teach 5-15 min. at the beginning of the lesson. Next, guide your student for another 5-10 minutes. Then, check-in closely while your child works. If you can’t find the time to be present for math, consider assigning another mathematical child in your family to help. Partner with your child to be successful in math. It will reap untold benefits whether your child is mathy or not!


Algebra is type of math where we use letters alongside numbers. The main feature is it allows to write rules and formulas in a general way. By using letters we can define rules for any number not particular number. We can determine the unknowns by equating them with knowns. It's a unique tool for solving puzzles and many everyday life problems
Arithmetic is type of math where numbers are subjected to different operations- addition, substraction, multiplication and division. Its the elementary branch of mathematics involving counting as well as different representation of numbers- decimals, fractions and percentages
Statistics is the type of math that helps in collection, organization, displaying, analysis, interpretation and presentation of information or data.
Geometry is a branch of mathematics that deals with problems of shape, size, relative position of figures, and the properties of space.
it involves the concepts of point, line plane, distance, angle surface, curve and few other advance topics.
Probability is a likelihood of the event occurance. It is a type of maths that looks at information/data to predict the occurance of event between 0 and 1.
Exam style question arranged by topic and grade
What are we waiting for...
Pick the topic you want to revise or try some exam question to test your mettle!


OR gate is one of the basic logic gates used in Boolean algebra and electronic circuits. This logic gate gives a HIGH output (1) result if one or more inputs to the gate are HIGH (1). Again, a LOW (0) output results, if all inputs to the gate are LOW (0).
Let’s consider an OR gate with two inputs A and B that generate output Q. The output, Q of this Logic OR Gate returns “0” value when both A and B inputs are at a logic level “0”. In other words if A= 0 , B=1 or A=1 , B= 0 or A=1 and B=1 , OR gate gives logic level “1” output.
The logic or Boolean expression for a digital logic OR gate is that for Logical Addition which is denoted by a plus (+) symbol, giving us the Boolean expression as follows:
Q = A + B ; Q = A OR B
There are two symbols of OR operation and a truth table to prove OR operation as follows.
SET theory is also helpful to explain this gate. A and B are two set can be used to define Union set. Q ∈ A ∪ B . According to OR operation A ∪ B is true if A is true, or if B is true, or if both A and B are true.
We can use an electric parallel switch circuit to explain OR function. Let’s consider an electric bulb as an output Q where two parallel switches A and B are inputs. If either switch A or B is ON, or both switches A and B are ON then Q is ON. In other words if both switches A and B are OFF then Q is OFF.
For the construction of OR gate, we can use RTL Resistor-transistor switches connected together as shown below. The inputs are connected directly to the transistor bases. For the OR logic, the transistors are in parallel and the output is driven high if either transistor is saturated “ON”.
OR from NAND and NOR gate
OR logic can also be made from NAND or NOR gates. With two one-input NAND gate and one two-input NAND gate is in combined, we can easily construct an effective OR gate.
Two NOR gate with one is two-input and the other is one-input in combined, we can construct OR gate effectively.
If OR gate is not available, NAND or NOR gate in combination can be alternative of OR gate. Yes, OR logic gate is possible, since NAND or NOR gate is an universal gate. The image is given below.
OR gate IC
OR gate IC behaves as OR logic gate. There are some or gate IC. The most commonly used OR gate IC is IC7432. It is made with four independent positive logic OR gates in a 14-pin DIP package of two parallel rows.
Some OR gate IC are as follows:
- 7432 -OR gate IC
- CD 4071 – Dual-Input OR IC
- CD 4072 Dual 4-input OR Logic IC
- CD 4075 Triple 3-input OR Logic IC
- CD 4072B CMOS Dual 4-Input OR Logic IC
- 74LS32 – Quad 2-input OR Logic IC
For example, we consider OR gate IC 7432. Four OR gates have been placed in this IC as following the image.


Mathematics Biology Interdisciplinary
The complexities of the biological sciences make interdisciplinary involvement essential, and the increasing use of mathematics in biology is inevitable as biology becomes more quantitative and as biology and biotechnology become more important in the coming decades. The mathematical biology major seeks to prepare graduates to address problems arising from this new and rich area of interaction. This major will prepare them for success in professions in the biotechnology sector, either in academia or in the commercial world.
Graduates with a mathematical biology major will be able to
- Understand and construct mathematical proofs.
- Solve significant biological problems using mathematical methods and appropriate technology.
- Develop and understand mathematical models in the biological sciences.


If you want to be a great mathematician, it is very important that you know which universities are the best on this topic. In this article we will try to answer the question to how you can study applied mathematics in the United States and which are the best universities to study this program.
The universities in the United States have the best rankings in regards to the best universities in the world. The following is a list of the best options to study Mathematics in the United States.
1. Florida International University (FIU): It is one of the biggest public universities in the United States and it is located in Miami. It has two main campuses: Modesto A. Maidique Campus (MMC) and Biscayne Bay Campus (BBC). It has a library with more than a million books, equipped gyms, pools, different sports fields, and more than 31 restaurants. It also has more than 1200 professors and 5400 employees.
Its international student body comes from more than 120 countries. The TOEFL or IELTS is an important requirement if your first language is not English. It also has the Office of International students and Scholar Services (ISSS) that provides support to international students.
The Degree Program in Mathematical Sciences emphasizes in the study of applied mathematics. In order to be accepted to the Program, students must have met all lower division requirements included CLAST (College Level Academic Skills Test) and completed 60 semester hours.
In order to obtain more specific information visit https://mathstat.fiu.edu/academic-programs/undergrad-programs/bs-in-math/
2. State University of New York Plattsburgh: Also known as SUNY Plattsburgh; it is a 4 year public liberal arts college located in Plattsburgh, New York. It was founded in 1889 and it has more than 5500 students of whom almost 400 are international students from 70 different countries.
It offers a 4 year Bachelor’s degree in Math allowing students to be prepared to work in the financial and entrepreneurial areas. The Global Education Office gives support to international students with regards to immigration and visa, employment opportunities, programs, among others.
3. University of North Alabama: Founded in 1831. Also known as UA or Bama. It is a public university located in Tuscaloosa, Alabama.
It has a Mathematics Department that offers a B.S in Mathematics. This program includes calculus, geometry, differential equations, linear algebra, applied statistics, applied mathematics, Intro to analysis and Numerical analysis. It also started offering online courses.
4. Arkansas University: Public University located in Fayetteville, Arkansas. It has a very good international reputation and it has more than 27 thousand students of whom 2000 are international students from more than 120 countries.
This University offers a B.S, B.A and Master’s Degree in Mathematics and it is considered a research university. The math program prepares students to follow careers in research, actuarial science and industry and secondary education. The department is committed to a high level of mathematics instruction preparing its students to continue their graduate studies in whichever area they like the most.
5. University of California Los Angeles (UCLA): Founded in 1919 and located in Los Angeles, California, it is considered one the best universities in the United States and the world. According to the Shanghai Jiao Tong ranking, UCLA is the 8th best university in the world in mathematics. It has more than 4000 professors and nearly 43 thousand students.
The UCLA Department of Mathematics offers different mathematical approaches. Those interested in theory can study pure mathematics while those that like engineering can choose to study applied mathematics. Those that prefer can also find a program in Mathematics of computation Major which is designed for those students interested in the mathematical theory and the applications of computing.
The University of California has 10 campuses: Berkeley, Davis, Irvine, Los Angeles, Merced, riverside, San diego, Sa Francisco, Santa Barbara and Santa Cruz.
6. Massachusetts Technological Institute (MIT): private Research University founded in 1861. It has more than 1000 professors and approximately 12000 students. It is among the best five universities in the world. It has a great reputation in careers such as science, robotics, engineering and mathematics.
The Department of Mathematics was created in 1933 and it offers the option of specializing in General Mathematics, Applied Mathematics, Theoretical Mathematics or Mathematics with a Computer Science degree. Although it has a basic study plan for all the mathematics area each one has its one particular requirements.
The opportunity of studying applied mathematics in the United States is a unique experience that will enrich you as person and will allow you to be part of the best universities in the world. The best researchers and Nobel prize winners in science have been in these universities.
Contact us at email@example.com and choose the best universities in the United States and the world to study applied mathematics.


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Enter all the cash flows, the interest rate per period and the number of periods in the appropriate fields. To enter data, click on the appropriate field (not the button) and type the value.
It is very important that the sign of any cash inflow be the opposite of the sign of all cash outflows.
It does not matter which is which, but they must be entered with the opposite signs.
You can enter the interest rate either as a decimal or as a percentage. In other words, you can enter the interest rate as .065 or 6.5.
When you have entered all the needed information, click on the button of the desired answer.
Suppose you want to find the price of this bond: Par value = 1000, coupon= 100 per semi annual period, maturity = 10 periods; yield to maturity (interest rate = 9.5% a period).
Enter the following data in any order: PMT = 100, FV = 1000, i = 9.5, n = 10 and click the PV button. Answer = 1031.39.
Suppose you want to find the yield to maturity on the same bond given its price. Enter the following data in any order: PMT = 100, FV = 1000, PV = - 1031.39, n = 10 and click the i button. Answer = .095.


Last Saturday I joined a group of children and youth from Luckysummer and Kariobangi for a game of ultimate Frisbee at the Nairobi arboretum. It’s the first competitive game of any kind I have ever participated in. My participation in the game was actually very good to the amazement of many of my friends.
But this post is not about that. It is about what goes in one’s mind to enable them to catch a disc that is at them. For one to catch the disc the brain has to solve complex math problems and it does this in real time and without them knowing it is doing it.
The disc is thrown. You run to catch it. To do this you need to solve some incredibly complex problems. You have to see the disc. You have to recognize it. You then have to combine two different images that are slightly offset from each other in order to calculate where the disc is in three dimensional space. You have to compare several observations of the disc’s position as it changes over time to calculate how fast it is moving. You have to calculate the force of gravity and how it will cause the discs’s path to curve. Then you must compute a path that you can take that will cause you to intersect the discs’s path through space at the time the disc will be arriving in the space you occupy. You must compute how quickly to move your hand and how far, in order to line it hand to intersect with the s discs’s path.
This is hard. It requires real-time computation on an extraordinarily complex level. This complex calculation is done at the same time as you are constantly computing the forces of gravity on your body and the correct counteracting forces of your muscles just to hold you upright. And you must do all these calculations nearly instantly, while constantly monitoring the ball’s flight and adjusting for wind or other disturbances in its flight trajectory.


This post is part of a series in which I try to explain everything I learned at GDC ’09. In it, I over Jim Van Verth‘s talk on affine transformations. I had hoped to get this post done a week ago, but I wasn’t confident in my understanding of the subject matter, so I took some time to research it independently. So, caveat lector: although I’m a math guy, I’m not a 3D graphics expert. I linked to the references I used at the end of this article, and I encourage you to take a look at some of them. However, the fact that I learned this recently could be a good thing; it’s always easier to teach things you just learned. People who’ve known a thing for years have totally internalized it and don’t know what it was like to hear it for the first time.
What is an affine transformation?
It’s a way of changing the size, shape, and/or position of an object in a 2D or 3D scene. Affine transforms are not the only kinds of transforms; they have some special properties.
- If three points were on a line before an affine transform, they will still be collinear after it.
- The same holds true for four points on a plane.
- If two lines were parallel before an affine transform, they will be afterwards.
An affine transformation is a function that takes a vector or point and returns another vector or point. To transform an entire shape, just apply it to all the vectors and points in the shape.
I struggled with deciding when to introduce equations in this article. I decided to put them at the end, so that I can motivate them with concepts first. The trade-off is that it’s going to sound a little weird when I talk about composing transforms, because I’ll have to split it between the two sections. Luckily, they’re both pretty short..
Why use affine transforms?
Objects in a 3D scene are stored in memory somewhere with their own local coordinate system. To be in the right relative positions when the scene is rendered, they need to be moved, rotated, and sometimes scaled.
What kinds of affine transformations are there?
Translations, rotations, scales, reflections, and shears. All but shears are easy to imagine and describe, which is convenient because shears are “the bad one” that usually only happen by accident.
- A translation move objects around without rotating them or changing their sizes. It’s a rigid body transform, meaning it could be performed on a rigid object, like a brick, in the real world.
- A scale increase or decrease the size of objects. It can just make an object bigger, or stretch it in just one direction, or any combination of those. It’s not a rigid body transform, because you can’t stretch bricks.
- A rotation does just what you’d think; rotates an object. It’s a rigid body transform. It only rotates objects around the origin; to rotate objects around other points, you have to first translate the object, rotate it, then translate it back. I’ll go into that later.
- A reflection is a mirror-image. It swaps left and right or up and down. It’s not a rigid body transform. Another way to think of it is as a negative scale; it’s what you’d get if you squash something down to zero and stretch it back out again in the other direction.
- A shear is a non-uniform translation. When you apply one to an object, the effect is visually similar to slanting. It’s not a rigid body transform. You rarely want these in computer graphics.
How do you compose them?
By applying one and then applying the next. There are only two things to say about composing before looking at the math. First is that order matters; for example, if you’re applying a scale and a rotation both, and you apply them in the wrong order, you can end up with a shear. Second, composing transforms is the tool that lets you rotate around a point other than the origin. You do this by translating until that point is the origin, applying the desired rotation, and then applying the inverse of the original translation.
How does the math work?
Affine transforms can be represented in more than one way. I’m only going to show the one I think is easiest. In fact, the method I present is not the standard, as many readers have pointed out. I only picked it to make this material as approachable as possible, which will make learning the other methods easier later. For more on this, see the Van Verth presentation and the wikipedia page in the references. That said, here’s how an affine transform’s function looks to mathematicians:
T(x) = Ax + y
x is the point you’re transforming, represented as a column vector.
y define the affine transform;
A is a matrix and
y is another column vector. Here’s what that looks like in 3 dimensions:
In this example, I filled in all the numbers in the matrix
A and the vector
y at random. Intelligently generated transforms have a specific form for each type.
Translating an object by
a units along the x axis,
b units along the y axis, and
c units along the z axis:
Scaling a an image by a factor of
a in the x direction, a factor of
b in the y direction, and a factor of
c in the z direction:
Rotating an image degrees around the x axis:
Rotating an image degrees around the y axis:
Rotating an image degrees around the z axis:
Reflecting an image across the x axis:
Reflecting an image across the y axis:
Reflecting an image across the z axis:
How do you compose them? (with math!)
Same answer as before: apply one, then apply the other. And, as above, order matters. Let’s take a look at one. Suppose I want to apply two transforms:
Ax + y and then
Bx + z. It would look like this:
B(Ax + y) + z
Let’s compose a scale that increases an object’s size by a factor of 2:
and a rotation by 90 degrees about the z axis:
Here’s the composition:
- Jim Van Verth’s powerpoint presentation on affine transformations from GDC
- Wikipedia’s entry on transform matrices
- Wikipedia on affine transforms
- Diana Gruber’s presentation on rotation matrices from Xtreme Game Developers Conference in 2000
Every GDC article I write has the goal of helping us do a better job at IMVU. Since I want my articles to be relevant to a wider audience, I’m separating out the IMVU tie-ins. What follows is the IMVU-centric section of this post, which won’t be relevant to everyone. For the rest of you, please enjoy the fuzzy kitten.
At IMVU, we’ve already got this pretty well licked. 3D rendering is our core product! Maybe we could get me involved in it, though, now that I’ve spent all this time studying it. Affine transforms are not nearly all there is to 3D rendering, though, so maybe we should wait until I finish studying and writing about the rest of the math involved. Also, I’m not the only programmer we have who is not a 3D graphics guru, so we could simply use this article as education.


Phone Number: 719-852-5984 ext 3114
Room Number: 114
Daily Schedule & Classroom Calendars
1st Period - 6th Grade Math (7:50-8:57)
2nd Period - 6th Grade Math (9:00-9:57)
3rd Period -6th Grade Math (10:00-10:57)
4th Period - ILP - IXL Math Intervention (11:00-11:50)
5th Period - Lunch/Fitness (11:53-12:30)
6th Period - Plan (12:33-1:30)
7th Period - 6th Grade Math (1:33-2:30)
8th Period - 6th Grade Math (2:33-3:30)
9th Period -Elective (3:34-4:05)
Times Available for Assistance
Mrs. Gibbs is almost always available from 4:00pm - 4:45pm.
I am Mrs. Gibbs and I teach Math at the Middle School. I am married to Danny Gibbs, who is a mechanic at a shop in Del Norte, Colorado. I am originally from Kansas City, Missouri (hence my favorite teams), but moved to a small town in Eastern Colorado called Cheyenne Wells during my middle school years. It was Adams State that brought me to the valley.
I love to hike, ski, fish, travel, watch NFL games (GO CHIEFS!), and MLB games (GO ROYALS!).
I received my undergraduate degree from Adams State University in 2012, and received my Masters of Education in the Spring of 2015 in Culturally and Linguistically Diverse Education through the Boettcher Teacher Residency Program.
I taught Language Arts at the Middle School for 4 years before making the leap to 6th grade Math in 2017. I have loved and enjoyed being a part of the transition from Elementary to Middle School for these students. I have always had a passion for teaching and helping students succeed and learn. It was a teacher during my middle school years that was an inspiration to me and really took the time to get to know her students and show that she cared, which led me to want to teach. I want to make a difference in these children's lives and if I can say that they truly learned while they were in my class, I'd say that is a success!
Middle School Volleyball


By Brooke Guiton
Are you interested in driving your business profitability?
One of the most effective ways to do so is to focus on your break-even point.
What is my break-even point?
Your break-even point is the point at which your business generates sufficient sales to equal your total costs. This is the point before you commence earning profit (before tax).
Why know your break-even point?
How do you calculate your break-even point?
The break-even point is calculated by the following formula:
Break-even point = fixed costs/(1 – variable costs/total sales)
Fixed costs (or overhead expenses) are costs incurred regardless of the amount of sales you make e.g. rent, advertising and salaries.
Variable costs are costs that can directly be traced to a sale e.g. costs you paid your supplier, commissions etc. These costs will vary depending on your level of sales.
It is best explained by way of an example:
Kate’s flower shop made sales of $52,000, variable costs (flowers) were $31,200 and all other overheads (rent and salaries) were $15,600.
To calculate Kate’s break-even point we calculate the following formula:
Break-even point = Overhead expenses/(1-(cost of goods sold/total sales)
Break-even point = $15,600/(1-($31,200/$52,000)
Break-even point = $39,000
Kate needs to generate sales totalling $39,000 before she reaches her break-even point and starts generating profit.
If you would like assistance calculating your break-even point or increasing the profitability of your business, please contact your WDF team.


Version 1.1.015th April 2015
HSL_MI29: MPGMRES: an extension of GMRES which allows multiple preconditioners
This package solves the \(n\times n\) unsymmetric linear system \(A x = b\) using the iterative method restarted MPGMRES, otherwise known as
MPGMRES(m) is itself a generalization of the standard right-preconditioned generalized minimal residual method with restarts (
GMRES(m)) that allows the user to employ multiple preconditioners at each iteration.
MPGMRES comes in two variants: complete and selective. Complete
MPGMRES finds the approximation which minimizes the 2-norm of the residual over some space, termed the multi-Krylov space, which is defined by the choice of preconditioners. This search space grows exponentially with the iteration number, and so this version is generally to be avoided in practice, but useful in diagnostics. A selective version of
MPGMRES finds an approximation to the solution in some subspace of the full multi-Krylov space, the dimension of which will grow only linearly with the iteration number. The use of both variants is supported in this package.
Reverse communication is used for preconditioning operations and matrix-vector/matrix-matrix products with \(A\).


In Years 5 to 8 Maths is taught by specialist teachers in well-resourced classrooms.
Our aim is to build confidence and competence with numbers using an approach that is enjoyable, relevant and meaningful. We recognise the ability to solve problems in different contexts and to apply Maths throughout the curriculum and in daily life.
We encourage pupils to think creatively, to take risks and to see that making mistakes is an opportunity to learn. At the same time we emphasise the importance of methodical, systematic and accurate work.
We base our learning on the 11+ and 13+ ISEB syllabus. We provide a sound grounding in the mechanical skills necessary to tackle exams without allowing the examination syllabus to be restrictive. We enjoy the creative side of Maths which incorporates many activities such as making straw models, creating interesting patterns using line design, constructing polyhedra and other 3D shapes, drawing the Golden Ratio and designing Islamic patterns.
Our classes are set in ability groups to enable differentiation and allow each child to enjoy the fun and play of Maths at his or her own level. We participate in the Primary and Junior Maths Challenges and some of our pupils progress to complete the Maths Olympiad.
The department enjoys a sound academic record at both Common Entrance and Scholarship level.
Year 6 Pupil “My Maths experience has been one of the best things about the school. We do loads of different topics and get a huge variety of learning. Also, if you don’t understand anything, the teacher will go over it again.”
“Since I came to St Andrew’s my Maths knowledge has expanded masses. Our teachers teach in a fun and exciting way. Maths is really fun here.”


A level Mathematics is a highly valued and useful course, which is suited to students who enjoy problem-solving, algebra and numeracy. This course extends your knowledge from GCSE Mathematics through exploring many fascinating areas of pure and applied mathematics.
In the first year you will start by studying the foundation topics, building on GCSE Mathematics, such as surds, straight lines and quadratics. You will then move on to pure topics such as calculus and logarithms, statistics topics such as numerical measures and hypothesis testing, and mechanics topics such as kinematics and Newton’s laws of motion.
In the second year you will further your understanding of pure topics met in the first year, such as trigonometry and calculus, and will study new ones such as sequences and numerical methods. You will also extend your understanding of statistical distributions and more realistic contexts in mechanics through consideration of friction and moments.
Over the two years you will greatly develop your problem-solving skills in a variety of pure and applied contexts.
What do I need to study A Level Mathematics?
At least 6, preferably at least 7, at GCSE Mathematics
A real interest and enjoyment in the study of Mathematics
Things to know….
At the end of this two-year course you will have three external examinations to give you your A level grade.
During the course you will have plenty of practice tests and mock examinations to ensure you are fully prepared for the final examinations.
Extra help is available from teachers and fellow students in drop-in sessions.
Loreto Sixth Form College
Chichester Road South


Maths Week 2014 takes place from October 11th-19th. Maths week is celebrated all over Ireland, with over 200,000 participants last year. Already this year almost 50,000 participants have signed up on www.mathsweek.ie to take part in special maths activities and join in lots of different maths games and challenges. According to the website, Maths Week ‘promotes awareness, appreciation and understanding of maths through a huge variety of events and activities.’
Running alongside maths week is the very popular initiative ‘Developing Maths Eyes’, which started in Tallaght in 2011 and which has extended over the years into other communities. The project went international in 2013 and has now been replicated in many countries. Aimed at every member of the community, it was based on addressing the fact that traditional methods of teaching maths have resulted in a ‘maturing population’ who do not appreciate the maths around them in everyday life. Some children too, despite being taught in a more interactive way, often don’t make the link between the maths they learn in the classroom and the real world. Terry Maguire, who developed the idea, says,
“Everyone has maths eyes – they just need them to be opened.”
Our school self-evaluation this year focuses on maths and a large part of our work will be on helping children see maths around them and make connections between the maths they learn in school and maths in the real world. As a school we participate in Maths Week every year, and this year again the children will take part in activities that will help to ‘open maths eyes’. There are many activities that can be done at home too, and which might help to open the maths eyes of adults into the bargain! For younger children, why not have an ‘iwalk’, asking children to find as many regular shapes as they can, or spot all the different places and situations where numbers are used. What about organising a Maths Treasure Hunt (older children might enjoy thinking up clues) or Maths Trail? (some templates are available on www.haveyougotmathseyes.com).
What about some practical maths experiments? We are told that we waste 6 litres of water a minute from leaving a tap running while brushing teeth. Most young children have no conception of how much this is. Why not have them fill a container with 6 litres and have a look (it can then be used to water the plants!). What about maths in the supermarket? Children who don’t enjoy shopping but have to ‘tag along’ might enjoy a supermarket ‘maths checklist’. Some children might like to keep a maths diary for a week and report back on all the different situations they found which featured maths in some form. The maths week website, www.mathsweek.ie, has lots of ideas and suggestions such as,
- Have a Maths Puzzle Day at home
- Design a Maths Maze
- Explore the maths in art
- Code Breaking for the Young Secret Agent
- Become a Maths Magician
- Discover some ‘maths heroes’ from the past.
To make it more interesting, you can take a digital photo of any of your activities and upload it to the maths week website.
The ‘Maths Eyes’ initiative is not just for children, it’s for all learners, young and not so young. It helps us all to become more aware, to look at things in a new way, to make connections and links. One of the street workshops held in Tallaght last year during Maths Week helped people understand issues in relation to water conservation – a very timely activity!
If you would like more information on the Maths Eyes initiative, or just some motivation to get into maths action, check out the website
www.haveyougotmathseyes.com or join Maths Eyes on facebook.
There is a list of websites under the tab ‘Activities for Primary Schools’ on the maths week website.
One maths website that has proved very popular is www.mangahigh.com. This is a games based site which provides a wealth of challenges to all maths lovers. This site is recommended by Maths Week Ireland as a great way to get pupils to practise their maths, in particular their problem solving ability.
Another popular site is
This easy to navigate website has maths games that are linked to the different strands of the maths curriculum. Learning as it should be – through enjoyment!
Enjoy maths week!


Have them give the new course instructions to a partner to determine if they can sail to the new spot. The important to remember that vector addition is commutative so that resultants are exactly the same. Log In Join Us. Fascinate students with facts about bugs. Round your answer to the nearest tenth. There was an error cancelling the draft. This worksheet help you to understand. When two vectors are added, the result is also a vector. Explain why it is not possible to add a scalar to a vector. Review their answers to gauge their mastery of the subject. Analyze each vector diagram and fill in the diagram below. What is the net force on the ball? Printable Worksheets Browse our categories to find the worksheet you are looking for or use search option on the top to search for any worksheet you need. Learn GCSE Maths for Free Free online GCSE video tutorials, notes, exam style questions, worksheets, answers for all topics in Foundation and Higher GCSE. While these conditions may be reminiscent of how we test subspaces, they really are quite different, so do not confuse the two. The concept of the vector subtraction is used to describe the difference of physical quantities which have a magnitude and a direction associated with them. Ask students to come up with approximate distances. This may negatively impact your site and SEO. Click on the link and you can have one for FREE! BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. The various lines represent paths taken by different people walking in a city. We add the first vector to the negative of the vector that needs to be subtracted. The content is suitable for the Edexcel, OCR and AQA exam boards. Remember the resultant vector must have both magnitude and direction.
Just enter the two vectors in the vectors subtraction calculator and submit to know the difference. Just like scalars which can have positive or negative values, vectors can also be positive or negative. The whole procedure can take a few seconds. The basics when combining two vectors that act at a right angle to each other you are able to use some basic geometry to find the magnitude and direction of the resultant. Numbers online worksheet for Beginners, elementary. When you add two vectors, it is as if you took the vectors and placed them end to end and created a new vector running from the starting point to the end point. Create worksheets tests and quizzes for pre calculus trigonometry with math analysis. You can take them everywhere and even use them while on the go as long as you have a stable connection to the internet. For example, consider the addition of the same three vectors in a different order. More generally, can two vectors with different magnitudes ever add to zero? Teachers Pay Teachers is an online marketplace where teachers buy and sell original educational materials. When you are trying to balance the chemical equations you should remember that. Draw it or two or click on vectors adding vectors shown on vectors can help? It is a good idea to carry an. Log in to your registered account. The lecture series: short term advance.
We send out for each of graphical vectors worksheet and the length of the path she needs to ground. After she walks along the vector you described in the previous step, what will her displacement be? Asked by Wiki User. Every vector is determined by two points. You must show all your working out. Try using your email address instead. What is the magnitude of his displacement? Examples of such quantities are velocity and acceleration. We show students how perform this will column and row vectors. Vectors This video prepares you for vectors in GCSE Maths. In this activity, students are given a graph and three vectors. Under something to each time after each other vector is a rough sketch of many fields to answers graphically find the vectors form the forces can check your experimental, then at its. These problems can vary from learners who do not know the correct format for. This web page is designed to provide some additional practice with the use of scaled vector diagrams for the addition of two or more vectors. Mobile devices like smartphones and tablets are in fact a ready business alternative to desktop and laptop computers. Analytical methods of vector addition and subtraction employ geometry and simple trigonometry rather than the ruler and protractor of graphical methods. Graphic addition permits one to see why mental addition is possible and why algebraic addition through components works so nicely. How long does it take to get to the destination? Your session has expired or you do not have permission to edit this page. Please contact phethelp colorado. Past papers, exam questions by topic, revision notes, worksheets and solution banks. Grouped by level of study. Your browser sent a request that this server could not understand.
Pictorally, the sum is the diagonal of the parallelogram formed by adding them in either order. Kinematics in Two Dimensions: An Introduction and Vector Addition and Subtraction: Graphical Methods. Adding or subtracting vectors can be as easy as adding two numbers if they are in component form. The page was successfully unpublished. It is one of my favorite subjects in math. Girl Kicking Soccer Ball Silhouette Svg. Draw net force vector on the ring below. Label the forces and use equality marks on the force vectors. We send out a monthly email of all our new free worksheets. Vector addition worksheet ahs vectors and trig worksheets. It take them to the vectors adding graphically using yumpu now! The three vectors are drawn below, along with the vector sum. Addition and adding worksheet on this case, and the vectors! Keep in mind that sometimes an. The actual distance traveled by the ship is the resulting vector from the sum of the three movement vectors each month. The magnitude of vector is the size of a vector often representing force or velocity. Place the vectors head to tail retaining both their initial magnitude and direction. More useful would be go three miles south a quantity having both size magnitude and direction is called a vector. We offer you free printable worksheets to use at home and also in the classroom. How much will a doctor with a physical disability and annual net income of around Rs. The same resultant R is obtained regardless of the order in which the vectors are added. If you have any suggestions or questions please contact me using the Contact Us page. You need a modern browser or flash to view this video. For lower grades, do the wind correction part of the activity together as a class. Remember that for this relationship to work, the units must match. We use vectors to, for example, describe the velocity of moving objects.
Addition of Vectors This file contains five slides that students can use to practice adding vectors. STEM Cases, Handbooks and the associated Realtime Reporting System are protected by US Patent No. How would they represent this graphically? Also in basketball match, this is the same. Free for commercial use High Quality Images. Sorry, no products matched your selection. Round your answers to the nearest tenth. There might be too much traffic or a configuration error. Here is a nine problem worksheet that will allow your students to practice calculating the area of a parallelogram. We could not want your device to create a sheet of vector worksheet kidz activities of distinguishing between vectors and measure both vectors is, reading and adding vectors graphically? We describe some settings in which vectors are used. It easy enough pieces of vectors analytically in the genotype or flash to trigonometry questions mark to two alleles together as adding vectors worksheet answers graphically. We use lots of large diagrams and grids to help the students visualize the vector concept. The best lab you can do to teach your students how to add multiple vectors by graphical and analytic method. The student directions on the worksheet state: Show all your work for the problems below. Vector subtraction calculator to find the resultant vector by finding the difference between two vectors. This new vector is the sum of the original two. One such operation is the addition of vectors. Vectors In this section there are interactive resources on Vectors. Each time one measurement ended, the next measurement would begin.
We are working in one dimension so this arrow would be drawn on top of the first vectors to the left. Department of teaching experience develops outstanding women of school questionnaire. As long as you are consistent, the final answer will be correct regardless of the system you choose. VECTORS Materials required for examination Items included with question papers Ruler graduated in centimetres and Nil millimetres, protractor, compasses, pen, HB pencil, eraser. Write a formula relating acceleration down an incline, the angle of the incline, and acceleration due to gravity. You work energy power of measurement in and worksheet answers graphically? How Excel Handles Matrix Math. Graphing inverse functions worksheet with answers pdf. Use vectors to understand directions, distances and times associated with movement and speed. Name: Add the following vectors together to give the resultant vector. Addition of vectors can be expressed by a diagram. To add or subtract two vectors, add or subtract the corresponding components. In this worksheet with this file attached in a, adding worksheet form or contact me. Ap physics c practice problems.
Vectors and vector addition: A scalar is a quantity like mass or temperature that only has a magnitude. Please choose from rain forests to x and adding vectors graphically worksheet answers to show the. STEM curriculum for educators everywhere. Check that your answer is reasonable. What living things can vectors graphically? We will never sell or rent your email. Click here to search the whole site. Interactive worksheets organised into engaging, vectors adding graphically worksheet answers on the angle between them together are looking at selected is being applied to see that has revision notes when combining two. You have any worksheet answers are summarized below as that you created in conjunction with answers on laws governing motion. Hot Wheels Vector Art Svg. The following triangles, adding vectors graphically worksheet answers graphically using the pythagorean theorem and spaces vectors! All about Cazoom Maths Worksheets. Download, customize and print the. Take the next vector and draw it starting at the arrowhead of the previous vector. Students will develop an understanding of the relationships among technologies and the connections between technology and other fields of study. The rules for adding vectors together are unique to vectors and cannot be used when adding scalars together. The clockwise direction is considered negative. We recommend using the latest version of Chrome, Firefox, Safari, or Edge. Heldt gives his students an article to read and questions to answ.


This article is a comprehensive guide to understanding what torque is with the help of worked examples. Torque is the measurement of the force that propels something into rotation around a point. Consider a seized-up nut and a wrench.
It would be difficult to get the nut loose with a shorter wrench. This process will be much simpler if you use a long wrench.
This is due to the torque of the object. For example, using the formula for torque, we calculate that 0.3 meters times 90 newtons is 27-newton meters of torque. This is if a 30 cm wrench is used and 90 newtons of force are applied. The result would be 0.6 meters x 90 N = 54 N.m if you applied the same 90 newtons of power to a wrench that was 60 centimeters long.
We can see that utilizing the longer wrench results in more force acting on the nut, according to this straightforward formula. We can alter the speed and torque by varying the size. A high gear gives high speed by low torque, while a low gear gives low speed but tremendous torque.


Oct 06, 2015 · I have a project, and I have to find 3 facts about things that involve positive numbers less than one-millionth. For example, like the weight of something that's less than one-millionth or a number of species that are less than one-millionth. I don't even know. Can someone give me three facts because I kept searching and searching and i couldn't find anything.
Number activities for preschoolers don't have to be boring and just worksheets, make them fun so your preschooler will love math! I love math. Im a nerd, yes. But I love anything to do with numbers. I really do hope I can pass this along to my kids by making learning activities about numbers and counting fun for them and not a chore. By The Numbers Trivia Quiz and Fun Facts 0-10Category:0-10. Quiz #380,044. 10 trivia questions, rated Easy. By kyleisalive. Use the clues provided to identify the numbers. All you need to do is count to ten. Start Match Quiz. Match items on
Number 2 is obviously one of the biggest numbers in numerology and comes directly after 1 and is followed by 3. This special number is incredibly important in our world so why not completely geek out with these incredible 10 facts all about number 2? Read More Facts About the Number Seven That are Purely Amazing This was a compilation of some interesting facts about the number 7. Numbers are infinite, and each is believed to have a significance of its own. Each number is magical in its own right. Now check if the magical number seven, or any other, has affected you in any way. For a fact, some numbers keep repeating in our lives.
PDF, 1.56 MB. Preview. Send-to-Kindle or Email . Please login to your account first; Need help? Please read our short guide how to send a book to Kindle. Save for later . Post a Review . You can write a book review and share your experiences. From one to a billion:10 awesome but totally random facts Sep 21, 2014 · Sun 21 Sep 2014 04.00 EDT. Last modified on Wed 20 Sep 2017 07.07 EDT. 36. 36. 1. One. It doesnt get better than Number One. Its the average number
Fun Facts About Numbers 4 and 5. Greek philosopher and mathematician Pythagoras believed that all things are numbers.. Racking your brain what he meant? We will help you reveal the hidden symbolism and meaning the numbers 4 and 5! Welcome to the world of numbers! Share on Facebook. Funbers 10, 11 and 12 TOM ROCKS MATHSAug 03, 2017 · The fun facts about numbers that you didnt realise youve secretly always wanted to know 10 TEN. We did it! We finally reached double figures! The fact that 10 is the first number in our system of counting that has two digits tells us that we count in base ten. We start with 0, 1, 2, and keep going until we reach 9.
New from the Naked Mathematician, Tom Crawford, is the Funbers series in partnership with the BBC. Each 3-minute episode looks at a number more closely than anyone ever really should, to tell you the fun facts that you didnt realise youve secretly always wanted to know Beginning with 0, the series has now reached the  Funbers! Fun facts about numbers that you didnt realise New from the Naked Mathematician, Tom Crawford, is the Funbers series in partnership with the BBC. Each 3-minute episode looks at a number more closely than anyone ever really should, to tell you the fun facts that you didnt realise youve secretly always wanted to know Beginning with 0, the series has now reached the
Hindu-Arabic numerals, system of number symbols that originated in India and was later adopted in the Middle East and Europe. List of Number Activities Learning 4 KidsPeg-A-Number-Facts:Peg-A-Number Fact is a fun maths game that allows kids to practise basic numbers sums and encourage the use of strategies to solve maths problems. Read more.. Make Your Own Solid Numbers :Combining science and learning numbers together in the one activities.
A symbol for a binary number is made up of these two bit symbols. The position of the bit symbols shows how big the number is. For example, the number 10 in the binary number system really means 1 times 2 plus 0, and 101 means 1 times four (=4) plus 0 times two (=0) plus 1 times 1 (=1). The binary number 10 is the same as the decimal number 2. Number did you knowsNumber did you knows. Did you know 11% of people are left handed. Did you know a bear has 42 teeth. Did you know 8% of people have an extra rib. Did you know 85% of plant life is found in the ocean. Did you know the Hawaiian alphabet has 13 letters. Did you know armadillos have 4 babies at a time and are all the same sex.
This is an attempt to give a count-down of the top ten coolest numbers.Lets first admit that this is a highly subjective orderingone persons 14.38 is anothers 2 6.The astute (or probably simply awake) reader will notice, for example, a definite bias toward numbers interesting to a number Fun Facts:Facts and superstitions about NumbersFun and interesting facts starting from zero:0 - Zero was not even considered a number for the Ancient Greeks. However, they also questioned whether 1 was a number. 1 The number 1 is NOT prime number, as many people believe. It is also the exact amount of butler schools in the US and the number of public telephones in Kabul.


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Statistical Models for the Analysis and Design of Digital
Statistical power depends on the significance criterion used in the test, the magnitude of the effect of interest in the population, and the sample size used to the detect the effect. This video is the first in a series of videos related to the basics of power analyses.All materials shown in the video, as well as content from the other vid Se hela listan på idatassist.com Se hela listan på cxl.com As the lower statistical power of an experiment leads to invalid conclusions about the result, the experiments are desired to have a minimum threshold of power. Generally, it is expected to be 80% or more. Power of 80% means there is an 80% chance of detecting an effect that exists (and in turn 20% probability of observing Type 2 error). Statistical power is equal to 1-β where beta is the type II error, or the false negative rate of the test procedure.
av S Lydersen · 2019 · Citerat av 1 — Denne typen feilslutning kalles «the power approach paradox» (2). «Observert styrke» og konfidensintervall. Andre former for retrospektiv project Ulf is the nutritionist in the team that digest anything from design of clinical trials and statistical power calculations to intestinal hormone response. av D Berglind · Citerat av 2 — (40 individuals per group) provides 80% power to detect a between-group difference of 10 min of daily MVPA. Statistical Analyses. Participant's Sök jobb som Power Systems Integration Engineer (HWEE) - Wireless Power Division på Apple. Läs om rollen och ta reda på om den passar describe and discuss statistical methods to construct load profiles, load forecasting and reliability.
It is hard to underestimate the importance of studies being well-powered. I would say that when assessing the quality of an empirical study, having adequate power is one of the most crucial aspects. Kontrollera 'statistical power' översättningar till svenska.
OtaStat: Statistisk lexikon svenska-engelska - Aalto Math
Each one serves a purpose. Sure, knowing when to post on Facebook is important, but it’s not the be-all and end-all of running a Facebook page with maximum impact and engageme Statistics is broken into two groups: descriptive and inferential.
Energy and Power Measurement » Gammadata - Improving
2015-4-28 2021-2-16 · Statistical power, or sensitivity, is the likelihood of a significance test detecting an effect when there actually is one. A true effect is a real, non-zero relationship between variables in a population. An effect is usually indicated by a real difference between groups or a correlation between variables. 2009-3-16 · Statistical Power is the probability (1-β) of rejecting null hypothesis when it is false, and this null hypothesis should be rejected in order to avoid Type II error. Therefore, one needs to keep the Statistical Power correspondingly high, as the higher our Statistical Power, the … Statistical power is defined as the probability of number 4 occurring. Instinctively, you can imagine that this depends on the size of your sample, the actual (unobserved) difference in the population (appropriately normalized), and the standard of certainty at which you reject the null hypothesis (alpha).
2. Probabilities. I. Title.
to assist you with the operation an d maintenance of the Power-PRO™ XT Cot. to Karlstad Centralstation Bet on IFK Lulea v Vasalunds IF with Paddy Power™. Sollentuna - detailed statistical head to head preview and odds comparison. In the NUTS codes of Sweden (SE), the three levels are: Level, Subdivisions, #. NUTS 1, LANDS (Swedish: LANDSDELAR), 3. NUTS 2, National Areas With the return of great power competition, the United States needs every You have a business question: Let's say you need to run statistical forecasts or run a Power-PRO XT 6500 medical equipment pdf manual download.
The power is calculated before the research is carried out by entering the effect size, the significance level and the desired statistical pwer in the program G*Power. Then, the required sample size is calculated. G*Power is a free power analysis program for a variety of statistical tests. We present extensions and improvements of the version introduced by Faul, Erdfelder, Lang, and Buchner (2007) in the domain of correlation and regression analyses.
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Statistical Power Analysis - Kevin R. Murphy - inbunden
Therefore, one needs to keep the Statistical Power correspondingly high, as the higher our Statistical Power, the fewer Type II errors we can expect. 2021-02-16 · Statistical power, or sensitivity, is the likelihood of a significance test detecting an effect when there actually is one. A true effect is a real, non-zero relationship between variables in a population. An effect is usually indicated by a real difference between groups or a correlation between variables.


The main aim of 7 Up Down is to correctly predict the total of two standard game dice. It is the ultimate dice game, and we have it on Card Games App. You can bet on three options which are known as 7 Down, Lucky 7, and 7 Up.
For dice games lovers we have a great offer. This is the game Over/Under 7. Bets are placed on the probability of a number falling below, above or equal to 7. In total, the options are 36. Six of them form the number 7 and those are – one and six; two and five; three and four and, respectively, four and three; five and two or six and one.
If you choose to bet on the probability of a number falling over 7, you win if the sum of the sides of the dice is 8, 9, 10, 11 or 12. Choosing the option of 7, gives the chance to reap rich rewards.
This game is extremely easy and all you need to play it, is luck. You can have fun and win with Under / over 7 (also called “7-up-7-down”) .
This is a game of two dices. It is an easy game based on probability and statistics. If you follow the pattern for long, then you have high winning probability. The gameplay is fairly simple and all you have to do is predict the sum of numbers on the dices. Winning is a matter of following the pattern.
7 Up Down: The Ultimate Dice Game Rules
- You can bet on the total being below 7, exactly 7, or above 7.
- Above and below 7 gives pay out double the bet amount.
- Exactly 7 gives payout 5 times the bet amount.
- When the dice result opened, gold dice bonus will randomly appears, and all the players betted in this round will win (win money = the amount betted*sum of the two dices’ points)
Try your luck or test your observation skills! This is once in a lifetime opportunity to earn money while having fun! Play with your friends and enjoy the loot!


Final trial examination
The final trial examinations include 90 closed-ended questions in 3 subjects (Native Language, English, Mathematics) as per the second stage of the final exams for 9th graders. The total score is 210. The exam duration is 2 hours and 15 minutes.
11th graders are given 85 questions. The exam duration is 3 hours.
Native language - 2 texts for reading and understanding (literary, non fiction), 10 questions for each text (5 open + 5 closed-ended) and 10 closed-ended questions on grammar. Total: 30 tasks
Mathematics - 7 open-ended questions to be solved with step by step explanation + 5 open-ended standard questions + 13 closed-ended questions.
Total: 25 tasks
Foreign language – 1. Listening text (non fiction or dialogue) - 6 tasks (3 open + 3 written closed-ended);
2. 8 tasks for reading comprehension text (non fiction or fiction) (4 closed + 4 written open-ended);
3. 16 closed-ended questions on grammar. Total: 30 tasks
Admission trial examination
The 3-hour trial exam includes tasks for 4 specialty groups.
Group I: Mathematics, Physics, Chemistry
Group II: Mathematics, Geography, History
Group III: Azerbaijani (Russian), History, Literature
Group IV: Chemistry, Biology, Physics
Group V: Azerbaijani (Russian), Mathematics, Foreign language
Applicants will be given 30 test questions in each subject (22 closed + 8 open-ended).
Three of the open-ended questions are situational or text-based tasks that require a written response. Other open-ended questions include calculation, selection, chronology, and matching.
Fill in the following fields


Each year, BRICKsters begin their journey with the arts with this months-long project. Beginning with a simple piece of wood, students sand for smooth edges then prime and paint their color of choice.Next, the students receive a design template. From here, they must measure, erase, and measure again and mark where each and every one of their hundreds of nails must go on the board. At this point, students are learning math skills, patience and focus.When each place is marked, the students begin nailing…and nailing….and nailing! After boxes and boxes of nails and many lessons in concentration, the students are taught how to string their prjects using colors of their choice. The result is a beautiful project they can keep forever.
Below are the final projects of the 2012 BRICKsters.


Mathematics is about the logical study of pattern in shape and number. In a complex world, professionals, managers, researchers etc. need to have analytical minds to solve difficult problems. Mathematics is the tool that allows you to do this. Competence in mathematics is highly regarded and valued in industry and commerce. Graduates in all subjects average 10% extra pay within 5 years if they have A level mathematics, in comparison with those who do not. There is no coursework element in the A2 mathematics course. There are also no specific synoptic papers in mathematics.
For the A level you will study three modules with exams being taken at the end of the year 13.
Module P1 (a two hour paper worth 100 marks)
Core: covers algebra and functions, coordinate geometry, sequence and series, exponentials and
logarithms, vectors, trigonometry , differentiation and integration.
Module P2 (a two hour paper worth 100 marks)
Core: covers proof, algebra and functions, coordinate geometry, sequences and series, further
trigonometry, further differentiation, further integration, numerical methods and vectors.
Module SM (a two hour paper worth 100 marks)
Statistics: covers statistical sampling, data presentation and interpretation, probability, statistical
distribution and hypothesis.
Mechanics: covers kinematics, forces and Newton’s laws and moments.
You can study mathematics at university, perhaps in combination with another subject. Many university courses in science, engineering, computing and economics insist on A level mathematics as an entrance requirement. It also gives a positive advantage in many other areas of study such as geography and psychology.


Power to x (PTX or Power-to-X) facts
Power to X in 2023
Power-to-X (PTX) refers to a group of technologies that use renewable energy, such as solar or wind power, to produce a range of different energy carriers that can be stored, transported, and used as fuels or chemicals. The "X" in PTX represents the variable nature of the products that can be produced, which can include hydrogen, synthetic fuels, and chemicals.
PTX technologies typically involve converting renewable electricity into a different form of energy or chemical using various conversion processes, such as electrolysis, gasification, or synthesis. For example, in the case of power-to-hydrogen (PTH), renewable electricity is used to split water molecules into hydrogen and oxygen gas through electrolysis. The hydrogen can then be stored or transported for use in fuel cells or other applications.
Other examples of PTX include power-to-methane (PTM), power-to-liquids (PTL), and power-to-chemicals (PTC), each of which involves a different conversion process to produce a different energy carrier or chemical. These technologies have the potential to play an important role in transitioning to a low-carbon economy, as they offer a way to store and transport renewable energy in a more flexible and versatile manner.
Power to X in the math world "Power to x" refers to an expression in mathematics that represents a base number raised to the power of an exponent. In other words, it is a way of multiplying a number by itself multiple times. The base number is the number being raised to a certain power, while the exponent is the number that tells us how many times the base number should be multiplied by itself.
The notation for power to x is typically written as "x^n", where x is the base number and n is the exponent. For example, 2^3 (read as "two to the power of three") means 2 multiplied by itself three times, which equals 8 (2 x 2 x 2 = 8). Similarly, 5^2 (read as "five to the power of two") means 5 multiplied by itself twice, which equals 25 (5 x 5 = 25).
Power to x has many applications in mathematics, science, engineering, and other fields. It can be used to represent exponential growth or decay, calculate compound interest, model population growth, and much more. It is also a fundamental concept in algebra and calculus, where it is used to solve equations and analyze functions.
In terms of how it works, power to x follows the basic rules of arithmetic. For example, when you multiply two numbers with the same base, you can add their exponents. So, 2^3 multiplied by 2^4 would be equal to 2^(3+4) which is equal to 2^7 or 128. There are also rules for dividing, adding, and subtracting numbers with exponents that are based on the properties of logarithms. PTX can refer to several different things depending on the context:
PTX (Power to X): As explained earlier, power to x (PTX) refers to an expression in mathematics that represents a base number raised to the power of an exponent.
PTX (Parallel Thread Execution): PTX is a low-level parallel programming language used in NVIDIA GPUs for implementing CUDA kernels. It is used to write device code that can be executed in parallel by multiple threads, which enables high-performance computing for tasks such as scientific simulations, machine learning, and image processing.
PTX (Pentatonix): PTX is also the acronym for the American a cappella group Pentatonix, which is composed of five vocalists who cover a variety of songs and genres.
PTX (Peripheral T-cell Lymphoma, Not Otherwise Specified): PTX is a type of cancer that affects the T-cells, which are part of the immune system. It is a rare subtype of non-Hodgkin's lymphoma and can present with a variety of symptoms, including enlarged lymph nodes, fever, night sweats, and weight loss. Treatment options may include chemotherapy, radiation therapy, and stem cell transplant.


First derivative of a function what is the graphical meaning of the first derivative of a function in calculus a graphical interpretation of the derivative of a function based on the difference quotient is explored interactively using an applet. Calculus i here are the notes for my calculus i course that i teach here at lamar university despite the fact that these are my “class notes”, they should be accessible to anyone wanting to learn calculus i or needing a refresher in some of the early topics in calculus. Indefinite integrals an indefinite integral has the form when evaluated, an indefinite integral results in a function (or family of functions) an indefinite integral of a function f(x) is also known as the antiderivative of f a function f is an antiderivative of f on an interval i, if f'(x) = f(x) for all x in i.
The fundamental theorem of calculus for line integral by learnonline through ocw 2856 views the line integral for work done around a curve is discussed in this video lecture. While it is possible to learn and perfect calculus, sometimes it is just not possible to deliver on time as expected the reason could be lack of time or a necessity to shore up performance as the learner perfects their ability in calculus. A tutorial introduction to the lambda calculus raul rojas freie universit at berlin version 20, 2015 abstract this paper is a concise and painless introduction to the -calculus. Lambda calculus is a framework developed by alonzo church in 1930s to study computations with functions function creation − church introduced the notation λxe to denote a function in which ‘x’ is a formal argument and ‘e’ is the functional body these functions can be of without names and single arguments.
I have a love/hate relationship with calculus: it demonstrates the beauty of math and the agony of math education calculus relates topics in an elegant, brain-bending manner. 4: predicate calculus: language predicates so far the most basic constituents into which we have analysed sentences have been sentences. Learn differential calculus for free—limits, continuity, derivatives, and derivative applications full curriculum of exercises and videos.
I preface this book is a revised and expanded version of the lecture notes for basic calculus and other similar courses o ered by the department of mathematics, university of hong kong, from the ﬁrst semester of the academic. There are two components to calculus one is the measure the rate of change at any given point on a curve this rate of change is called the derivative the simplest example of a rate of change of a function is the slope of a line. Three dimensional space this is the only chapter that exists in two places in my notes when i originally wrote these notes all of these topics were covered in calculus ii however, we. Calculus is all about changes sam and alex are traveling in the car but the speedometer is broken no, sam not our average for the last minute, or even the last second, i want to know our speed right now i can't calculate it sam i need to know some distance over some time, and you are.
Calculus ii notes feb 13, 2009 by pauls online math notes tweet several examples and tutorials dealing with integral calculus several examples and tutorials dealing with integral calculus military families the official provider of online tutoring and homework help to the department of defense check eligibility. Calculus is the theory of two fundamental operations on functions, differentiation and integration differentiation is a theory to compute the rate of change of functions, called the derivative, and integration is a theory to compute the area under curves specified by functions. Algebra review the material in this tutorial is reprinted with permission of the authors and publisher of how to ace calculus by colin adams, abigail franklin, and joel hass here we will list some of the most common mistakes that we see on exams. Calculus i or needing a refresher in some of the early topics in calculus i’ve tried to make these notes as self contained as possible and so all the information needed to read through them is either from an algebra or trig class or contained in other sections of the.
Dormant for almost a decade, the problem of the week is back with a vengeance for the 2011-2012 school year each saturday morning, a new problem and its complete solution will be posted here the problems range in difficulty, but they are tuned to the ap calculus ab school year in other words, the content continue reading problem of the week. Calculus for beginners and artists chapter 1 why study calculus chapter 2 numbers chapter 3 linear functions chapter 4 quadratics and derivatives of functions chapter 5 rational functions and the calculation of derivatives chapter 6 exponential functions, substitution and the chain rule chapter 7 trigonometric functions and their derivatives. Loading sos math on cd sale only $1995 works for pcs, macs and linux books we like.
C alculus tutorial-1 differential c alculus introduction calculus is divided into two parts: differential calculus and integral calculusthere is also a related subject-- differential equations. Tutorial for calculus¶ this sage document is one of the tutorials developed for the maa prep workshop “sage: using open-source mathematics software with undergraduates” (funding provided by nsf due 0817071) it is licensed under the creative commons attribution-sharealike 30 license ()this tutorial has the following sections. Our topic of discussion in this section is one-sided limits, which builds upon the preceding lesson on continuitycreate a new worksheet called 03-one-sided limits the basis of one-sided limits is that when a function jumps suddenly from one value to another, it often is not possible to describe the function's behavior with a single limit. Cbse maths, maths class 12 , class 11 maths, iit jee maths, iit jee calculus, ncert calculus, ncert maths 12, ncert class 12 maths, iit jee maths books, iit jee maths syllabus, iit jee maths paper.


It’s not that hard to comprehend. If X= disagreement, and Y= hate, X cannot equal Y check the math, it’s impossible. If Z= anger, then XZ is disagreement times anger, which may equal Y, hate. But Z, anger, cannot equal Y, hate. Same with being alone, A, and loneliness, B. In math, one variable cannot equal the other, therefore A cannot equal B. Now, with depression, C, AC can equal B, but C cannot equal B. Just because you’re alone, doesn’t make you lonely. Just because you disagree doesn’t mean you hate each other. It’s been proven. Do the math.
(Sorry for the spelling errors)


Some like math, some don’t. However, you can never deny the fact that learning is vital. It is really an essential part of the world. One of the common reasons students would say when asked why math is their least favorite subject is that it cannot be used in the actuality of life. But if you look from a deeper perspective, you can actually benefit and use it in daily life, which can end up totally changing your life. Math is actually everywhere—engineering, science, and technology.


In this talk we will give an introduction to maximally hypoelliptic differential operators. This is a class of differential operators generalizing elliptic operators and includes operators like Hormander’s sum of squares. We will present our work where we define a principal symbol and show that maximally hypoellipticity is equivalent to invertibility of our principal symbol generalizing the classical regularity theorem for elliptic operators.
We will also give a topological index formula for maximally hypoelliptic differential operators using our symbol. Explicit examples of index computations will be included at the end.
This talk is based on joint work with Androulidakis and Yuncken.


Modern Cosmology -
Part III: The Friedmann Universe
Jacobs University Bremen
Alexander Friedmann lived much of his life in Saint Petersburg. He fought in World War I (on behalf of Imperial Russia) as a bomber and later lived through the Russian Revolution of 1917. Friedmann obtained his degree in St. Petersburg State University (1910), became a lecturer in St.-Petersburg State College of Mines, and a professor in Perm State University in 1918.
He discovered the expanding-universe solution to the general relativity field equations in 1922, which was corroborated by Edwin Hubble's observations in 1929. Friedmann's 1924 papers, including "Über die Möglichkeit einer Welt mit konstanter negativer Krümmung des Raumes" (On the possibility of a world with constant negative curvature of space) published by the German physics journal Zeitschrift für Physik (Vol. 21, pp. 326-332), demonstrated that he had command of all three Friedmann models describing positive, zero and negative curvature respectively, a decade before Robertson and Walker published their analysis.
|1. Einstein's Equations
The Einstein field equations (EFE) or Einstein's equations are a set of ten equations in Albert Einstein's theory of general relativity which describe the fundamental interaction of gravitation as a result of spacetime being curved by matter and energy. First published by Einstein in 1915 as a tensor equation, the EFE equate spacetime curvature (expressed by the Einstein tensor) with the energy and momentum within that spacetime (expressed by the stress-energy tensor).
Although the Einstein field equations were initially formulated in the context of a four-dimensional theory, some theorists have explored their consequences in n dimensions. The equations in contexts outside of general relativity are still referred to as the Einstein field equations. The vacuum field equations define Einstein manifolds.
|2. Friedmann-Robertson-Walker Universe
The Friedmann equations are a set of equations in physical cosmology that govern the expansion of space in homogeneous and isotropic models of the universe within the context of general relativity. They were first derived by Alexander Friedmann in 1922 from Einstein's field equations of gravitation for the Friedmann-Lemaitre-Robertson-Walker metric and a fluid with a given mass density and pressure. The equations for negative spatial curvature were given by Friedmann in 1924.
|3. The Lambda CDM Universe
Einstein's field equations are not used in deriving the general form for the metric: it follows from the geometric properties of homogeneity and isotropy. However, determining the time evolution of the expansion factor a(t) does require Einstein's field equations together with a way of calculating the density, also called the cosmological equation of state. The main results of the FLRW model without considering the cosmological constant were first derived by the Soviet mathematician Alexander Friedmann in 1922 and 1924. Although his work was published in the prestigious physics journal Zeitschrift für Physik, it remained relatively unnoticed by his contemporaries. Friedmann was in direct communication with Albert Einstein, who, on behalf of Zeitschrift für Physik, acted as the scientific referee of Friedmann's work. Eventually Einstein acknowledged the correctness of Friedmann's calculations, but failed to appreciate the physical significance of Friedmann's predictions.
Caption: The Universe of galaxies is expanding. According to the Big Bang theory, the Universe emerged from an extremely dense and hot state (singularity). Space itself has been expanding ever since, carrying galaxies with it, like raisins in a rising loaf of bread.These equations are the basis of the standard big bang cosmological model including the current LCDM model. Because the FLRW model assumes homogeneity, some popular accounts mistakenly assert that the big bang model cannot account for the observed lumpiness of the universe. In a strictly FLRW model, there are no clusters of galaxies, stars or people, since these are objects much denser than a typical part of the universe. Nonetheless, the FLRW model is used as a first approximation for the evolution of the real, lumpy universe because it is simple to calculate, and models which calculate the lumpiness in the universe are added onto the FLRW models as extensions. Most cosmologists agree that the observable universe is well approximated by an almost FLRW model, i.e., a model which follows the FLRW metric apart from primordial density fluctuations. As of 2010, the theoretical implications of the various extensions to the FLRW model appear to be well understood, and the goal is to make these consistent with observations from COBE and WMAP.
|Exercises III - Solutions
|Ex_3 - Sol||Midterm Review Key Knowledge||Key Knowledge||SCP Union2 Supernova Data||SNe Ia Data||Lecture Notes: Part III
|LN: Part III|