Maths Revision - 07/12/21

Factorising-: 

Making an expanded expression into an expression that involves brackets

Eg1 

35x - 56v + 14

- First, find the HCF (which is 7)
-Then find any like variable (no, there are not)

So the value outside of the brackets is 7: 

-After that, divide everything in the brackets by 7

= 7(5x - 8v + 2)

Note: If there are indices, add an extra of the same variable INSIDE the brackets. Eg: 5x(x - 5) = 5x2 - 25x

Algebraic Fractions-: 

Fractions that involve algebraic features such as variables

Eg1

2x/4 + 4x/10 = ?

-As normal we need to make the denominators the same

-To do that we first find the LCM (which is 20)

So we multiply 2x and 4 by 5 & 4x and 10 by 2

2x/4 + 4x/10 = 10x/20 + 8x/20

Then we add the numerators and KEEP THE DENOMINATORS THE SAME to get:

18x/20 which can be simplified to 9x/10

Change the subject of formulae-:

Eg1

Change the subject of this formulae to x:

a) y(6zx-3c) = 2v - f

-First, we have to expand the equation

6zxy - 3cy = 2v - f 

- We have to get rid of the "least attached" by moving this to the other side. However, when doing so, the operation will be inversed.

= 6zxy = 2v - f + 3cy

- Now, we could get rid of the rest by dividing by 6zy

= x = 2v - f +3cy / 6zy

Finding the gradient and y-intercept in an equation-:

Gradient - How steep a line plotted on a graph is

y-intercept - Where the line intersects the y-axis

Eg1

  Q1: a)  y = 2x + 1

m (gradient) = 2         c (y-intercept) = 1

A pattern emerges the gradient will always be equal to how many x's there are: y = 5x - 6 and the y-intercept will always be equal to the part after - y = 5x - 6

       Finding the gradient and y-intercept in a graph-:

Q1) a) Find the gradient of this line

-First what we need to do is select any 2 points on the line then connect them up to form a right-angled triangle

-Count how many squares the sides of the triangle take

-Divide the numbers together to get the gradient!

To find y-intercept to see where the line intercepts the y-axis (in this case it is -1)

Finding the midpoint of two coordinates-:

Finding the midpoint means finding the middle of two points

Eg1

a) Find the midpoint of (2,8) and (1,4)

- To quickly find the midpoint, add the two numbers together and then divide by 2

2 + 1 = 3

=3/2

=1.5

- Do the same with the other pair...

8 + 4 = 12

=12/2

=6

And so the answer is (1.5,6)