Math Revision

Algebraic Fractions

100

Simplify:

5x/6 + 2x/6

=7x/6

200

Simplify:

7x/3 - x/2

11x/6

300

Simplify:

3b/5 x 2b/3

=6b²/15 

=2b²/5

400

Simplify:

7/2x ÷ 3/5x

=35/6

500

Simplify:

13x/11 - 7x/3

=-38x/33

Index Laws

100

Evaluate the following:

a³ x a³

=a⁶

200

Evaluate the following:

10a⁷ ÷ 2a⁵

=5a²​​​​

300

Evaluate the following:

(a⁷)³

=a²¹

400

Evaluate the following:

c^-7

= 1 / c^-7

500

Evaluate the following:

30x⁸ ÷ 5x³

=6x⁵

Expanding

100

Expand:

a(3a+6)

=3a²+6a

200

Expand and simplify:

(4a-2)(3a+3)

=12a²+6a-6

300

Expand and simplify:

(5x-2) (3x+5)

=15x²+19x-10

400

Expand and simplify:

b(3-2b) + 2(b²- 4)

=3b-8

500

Expand:

(x - 2)(x + 6)(x - 3)

x³ - x² - 24x + 36

Factorising

100

Factorising the following expression:

3x+6

3(x+2)

200

Factorising the following expression:

10x²+20x

=10x(x+2)

300

Factorise the following quadratic:

x²+8x+12

(x + 6)(x + 2)

400

Factorise the following quadratic:

x²-12x-27

=(x-9)(x-3)

500

Factorise: 

6x² - 7x - 3

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

Substitution / Equations

100

Substitute and calculate the following expression, given a = 3, b = 2

3a+5b

=19

200

Substitute and calculate the following expression, given a=4, b=3

b²+3a

=21

300

Solve for x:

(x+5)+6=20

x=9

400

Solve for a:

5(a+2)=20

a=2

500

9(2a - 3) = 3(2a + 7)

a = 4