Year 10 Maths Higher Tier Revision

Simplifying expressions

Gather all similar expressions together: Group all letters

4a+a-7d+6d= 5a-d

4a+a2-a=3a+a2     You can't add 4a and a2, so they are separate, just as you can't add a2 and a3.

Indices

a2 x a3=a5          a4 / a2=a2          (a2)3=a6

a-2 x a3=a           a-4 / a2=a-6        (a-2)3=a-6

a2 x a-3=a-1        a4 / a-2=a6         (a2)-3=a-6

a-2 x a-3=a-5       a-4 / a-2=-2         (a-2)-3=a6

3 to the power of -3= 1/27 (3x3x3=27 reciprocal)

25 to the power of 1/2=5 (square root of 25)

27 to the power of 2/3= 9 (cube root of 27=3 square it)

Expanding brackets

single brackets- times the term on the outside of the bracket by the terms on the inside of the bracket. eg 3(a+2)=3a+6

Double brackets- FOIL

F irst: Multiply the first term in each bracket

O utside: Multiply the terms on the outside of the expression

I  nside: Multiply the terms on the inside of the expression

L ast: Multiply the last term in each bracket

THEN SIMPLIFY EG: (3a+2)(2a+6)

F      O      I     L

6a2  18a   4a   12

6a2+18a+4a+12= 6a2+22a+12

Factorising Brackets

Single Brackets- Look for a common factor and put it outside the brackets. Put the unique terms inside the brackets eg: 18a+12=6(3a+2)

Double Brackets- ax2+bx+c

If a=1, you can factorise using a sum and product approach.

Eg: x2+12x+35, you need…