Maths Rules & Methods (Y9 T1)

1) Write down (x ) (x )

2) Find 2 number that add to make the X value and multiply to make the number value

eg. 3 & 2 for 5x & 6

3) Insert these into the brackets and check the signs are correct

eg. (x + 3) (x + 2)

4) If you have been asked to solve, make each bracket equal zero and solve

eg. x + 3 = 0 -> x = - 3, x + 2 = 0 -> x = -2

1) Rearrange - 3x squared + 7x - 6 = 0
2) Write in brackets with first number in a bracket - (3x ) (x ) = 0
3) Find number pairs that multiply to give the end number - 1,6 & 2,3
4) Try each pair until one multiplies it give the X number - (3x 2) (x 3) = 9x, 2x = 7x (-)
5) Fill in the signs - (3x - 2) (x + 3)
6) Check by expanding brackets - 3x squared + 9x - 2x - 6 = 3x squared + 7x - 6
7) If required, solve by making each bracket equal 0 - 3x - 2 = 0, x = 2/3, x + 3 = 0, x = -3

1) Rearrange into standard format - x squared + 8x + 5

2) Write the initial bracket in the format of (x + b/2) squared - (x + 4) squared

3) Multiply out brackets to find what needs to be added or subtracted - x squared + 8x + 16 - difference between 5 and 16 = 11

4) Write in this number after bracket - (x + 4) squared - 11

5) If required, solve by writing equals the last number - (x + 4) squared = 11

6) Square root both sides - x + 4 = +/- square root 11 - x = -4 +/- square root 11

7) Write out both solutions - x = -4 + square root 11 & x = -4 - square root 11