GCSE UNIT 2 Foundation
... Recognise the equations of straight line graphs Notice that all equations that look like this (y = ax + b) will make a straight line: y = 3x + 1 y= 2x + 4 y =6 – 3x y = 2x + 1 y = -0.5x – 3 The gradient of the line is the number in front of the ‘x’ The place that the line cuts the vertical (y axis) ...
... Recognise the equations of straight line graphs Notice that all equations that look like this (y = ax + b) will make a straight line: y = 3x + 1 y= 2x + 4 y =6 – 3x y = 2x + 1 y = -0.5x – 3 The gradient of the line is the number in front of the ‘x’ The place that the line cuts the vertical (y axis) ...
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... 5x – 5 = 2(x + 1) + 3x – 7 5x – 5 = 2x + 2 + 3x – 7 5x – 5 = 5x – 5 Both sides of the equation are identical. This equation will be true for every x that is substituted into the equation. The solution is “all real numbers.” The equation is called an identity. ...
... 5x – 5 = 2(x + 1) + 3x – 7 5x – 5 = 2x + 2 + 3x – 7 5x – 5 = 5x – 5 Both sides of the equation are identical. This equation will be true for every x that is substituted into the equation. The solution is “all real numbers.” The equation is called an identity. ...
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... all xQ such that p(x 0 ) = 0. Letting p(x) = 1 + x + x2 + x3 + xh , we see that p(ar) is the cyclotomic polynomial (x5 - I) / (x - 1 ) 9 which has four complex zeros equal to the complex fifth roots of unity. Let 0 denote any of these roots. Since p(0) = 0 9 it suffices to show that q(Q) = 0 9 where ...
... all xQ such that p(x 0 ) = 0. Letting p(x) = 1 + x + x2 + x3 + xh , we see that p(ar) is the cyclotomic polynomial (x5 - I) / (x - 1 ) 9 which has four complex zeros equal to the complex fifth roots of unity. Let 0 denote any of these roots. Since p(0) = 0 9 it suffices to show that q(Q) = 0 9 where ...
Chapter Two: Numbers and Functions Section One: Operations with
... Think about the graphs of the previous three problems. How can we tell by looking at a graph is something is a function? If one point is directly over another, this means that an x-value is paired with multiple y’s. This would not be a function. Therefore, if a vertical line can be drawn anywhere on ...
... Think about the graphs of the previous three problems. How can we tell by looking at a graph is something is a function? If one point is directly over another, this means that an x-value is paired with multiple y’s. This would not be a function. Therefore, if a vertical line can be drawn anywhere on ...
Review for June Exam #2
... 30. A school field has the dimensions shown. a) Calculate the length of one lap of the track. b) If Amanda ran 625 m, how many laps did she run? c) Calculate the area of the field. 31. A right triangle’s legs are 20 cm and 48 cm. What is the area of the square whose side length is equal to the hypot ...
... 30. A school field has the dimensions shown. a) Calculate the length of one lap of the track. b) If Amanda ran 625 m, how many laps did she run? c) Calculate the area of the field. 31. A right triangle’s legs are 20 cm and 48 cm. What is the area of the square whose side length is equal to the hypot ...
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... It may be seen that Figure lb is the usual Pascal array with power of 2 multipliers. Indeed the Pth term In the nth row, where O^r^ri is given by 2n~rl ...
... It may be seen that Figure lb is the usual Pascal array with power of 2 multipliers. Indeed the Pth term In the nth row, where O^r^ri is given by 2n~rl ...
Lecture 01
... Now the terms in the square brackets will cancel each other out leaving behind the two terms (n+1)! and 1!, which corresponds with the first solution. Bounding Summations With this method, it is necessary to find a term that is either greater than or less than the term being evaluated. This new ter ...
... Now the terms in the square brackets will cancel each other out leaving behind the two terms (n+1)! and 1!, which corresponds with the first solution. Bounding Summations With this method, it is necessary to find a term that is either greater than or less than the term being evaluated. This new ter ...
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... mom has agreed to pay half the cost (and all the sales tax). The shoes that Teri likes are normally $30 a pair but are on sale for 13 off. How much money does Teri need to buy the shoes? $10 ...
... mom has agreed to pay half the cost (and all the sales tax). The shoes that Teri likes are normally $30 a pair but are on sale for 13 off. How much money does Teri need to buy the shoes? $10 ...
WRITING EQUATIONS FOR WORD PROBLEMS (THE 5-D PROCESS) 1.1.3 Math Notes
... problems with the 5-D Process can be time consuming and it may be difficult to find the correct solution if it is not an integer. The patterns developed in the 5-D Process can be generalized by using a variable to write an equation. Once you have an equation for the problem, it is often more efficie ...
... problems with the 5-D Process can be time consuming and it may be difficult to find the correct solution if it is not an integer. The patterns developed in the 5-D Process can be generalized by using a variable to write an equation. Once you have an equation for the problem, it is often more efficie ...
Elementary mathematics
Elementary mathematics consists of mathematics topics frequently taught at the primary or secondary school levels. The most basic topics in elementary mathematics are arithmetic and geometry. Beginning in the last decades of the 20th century, there has been an increased emphasis on problem solving. Elementary mathematics is used in everyday life in such activities as making change, cooking, buying and selling stock, and gambling. It is also an essential first step on the path to understanding science.In secondary school, the main topics in elementary mathematics are algebra and trigonometry. Calculus, even though it is often taught to advanced secondary school students, is usually considered college level mathematics.