Algebra Summary

Factors

1. Highest Common Factor     Example: 9xy2 - 6x2y2 + 3xy = 3xy(3y - 2xy +1)
2. Grouping                                Example: 2c2 - 4cd - c + 2d = 2c(c - 2d) - 1(c - 2d)
=(c - 2d)(2c - 1)
3. Quadratic Factor                  Example: x2 - 7x + 12 = (x - 4)(x - 3)
4. Difference of two squares  Formula: x2 - y2 = (x + y)(x - y)

Example: 9x2 - 25y2 = (3x + 5y)(3x - 5y)

Simplify

This instruction can mean:

1. Add like terms                         Example: 3x - 2x2 + 6x + 10x2 - 5x = 4x = 8x2

2. Expand (multiply) brackets    Example: (2x - 3)(x + 4) = 2x(x + 4) - 3(x + 4)
= 2x2 + 8x -3x -12 = 2x2 + 5x - 12

3. Divide                                       Example: 6x3 - x2 - 33x - 28 ÷ 3x + 4

4. Express as a single fraction    Example:

 1 1 1 1 x2 - 9 x2 - x - 6 (x - 3)(x + 3) (x - 3)(x + 4)

 1(x + 2) - 1(x + 3) -1 (x - 3)(x + 3)(X + 2) (x - 3)(x + 3)(x+ 2)

5. Cancel

Example:

 4x2 - y2 (2x + y)(2x - y) 2x - y 2xy + y2 y(2x + y) y

Substitution

This means that you should replace certain letters by the numbers you are given.

Example: if x = 9 find the value of

Replacing x by 9:

Manipulating Formula

The instruction given in this case is usually express x in terms of y and z (obviously the letters change). Be very careful that you "do the same thing to both sides of the equation". Remember to "get rid" of something by "doing the opposite to both sides".

Example:      If , express a in terms of b and c.

Example:      Express a  in terms of b  and c  where   .

Solving Equations

1.        Linear                 Example:
(has x’s and numbers)

2.        Fractional linear Example:
(has x’s and numbers and fractions)

3.        Linear simultaneous  Example:

(has x’s and y’s)

Solving Inequalities

1.        Linear inequalities

Treat like equations but multiplying or dividing by a minus number reverses the inequality sign.

Example:  Solve

## Note

Algebra appears on Paper 1 in Question 1 (usually 40 or 50 marks), Question 3 (50 marks) and Question 6 (20/30 marks)

That’s a total of about 130 out of 600 marks or 22% just for Algebra!

Read and practice the methods on these sheets and then practice exam questions.