Number and Algebra

Index laws

100

What is an index?

x²

200

What is index law 1?

a² + a³ = a⁵

300

What is index law 2?

a¹⁰ / a⁴ = a⁶

400

What is 7¹² x 7¹¹

7^{12 + 11}

= 7²³

500

What is 2¹⁵ / 2³

= 2 ^{15 -3}

= 2¹²

Solve for x

100

x + 3 = 7

x + 3 = 7

- 3        - 3

x = 4

200

2x + 10 = 40

2x + 10 = 40

- 10          - 10

2x = 30

/2     /2

x = 15

300

4x + 3x = 42

4x + 3x = 42

(4 + 3)x = 42

7x = 42

/7     /7

x = 6

400

3(5x - 2) = 54

3(5x - 2) = 54

15x - 6 =54

+6         +6

15x = 60

/15     /15

x = 4

500

(8x - 12x² )/ 2x = 16

(8x - 12x² ) / 2x = 16

4 - 6x = 16

-4          -4

-6x = 12

/-6    /-6

x = -2

Expand

100

2(x + 3) 

= 2x + 6

200

3 (x + 4)

3x + 12

300

4x (x + 10)

4x² + 40x

400

5x (3x - 7x²) 

15x² - 35x³

500

4 (x + 7) + 3 (x - 7)

= (4x + 28) + (3x-21)

= 4x + 3x + 28 - 21

=7x+ 7

Factorise

100

What is the HCF of 10 and 15

5

200

What is the HCF of 24 and 36

12

300

2x + 12

2 (x + 6)

400

5x + 25

5 (x + 5)

500

9x² + 18x + 12xy

3x (3x + 6 +4y)

Fractions, Decimals and Percentages

100

What is 1/2 + 1/2

= 1

200

Convert 10% to a fraction

10/100

300

Convert 1/100 to a percentage

1%

400

Convert 0.05 to a percentage

0.05 x 100 = 5 

5%

500

Convert 2.5/50 to a decimal

=0.05