Year 10 Adv Half Yearly Revision

Index Laws

100

Simplify:

11t^-3

11 / t³

200

(p³m⁵)⁶

p¹⁸m³⁰

300

(3 / x)^-3

x³ / 27

400

10a¹⁰b³  x  5a²b⁶

 50a²⁰b¹⁸

500

(4p^-3h²)²  /   (-2p⁶h⁵)²

4p^-18h^-6

Algebraic Fractions

100

(4t / 3)  +  (t / 9)

13t / 9

200

(m+6) / 5    +   (m+2) / 3

4(2m+7) / 15

300

5p / 4r   x   8r / 15p

4 / 5

400

8y / 5 divided by 32y² / 3g

3g / 20y

500

5mn/2d  x  4d/n  x  1/15mn

2 / 3n

Factorising

100

Factorise:

36d²+24d

6d(6d+4)

200

Factorise:

3px + 2qx + 3py + 2qy

(x+y)(3p+2q)

300

Factorise:

100 - 49n²

(10-7n)(10+7n)

400

Factorise:

c² - 10c + 25

(c-5)(c-5)

500

Factorise:

15u² - 7u - 4

(5u-4)(3u+1)

Equations

100

Solve:

(2y-1) / 5 = (y+1) / 4

y = 3

200

Solve:

8(n+1) / 3  + 2 = 4

n = -1/4

300

Solve:

x² - 3x -10 = 0

x = 5 and x = -2

400

Make y the subject:

(y+3)/5 = 4m/3

y = 20m/3  - 3

500

The average of m and n is A = (m+n)/2. If two numbers have an average of 28 and one of them is 13, find the other number.

The other number is 43.

Inequalities & Logs

100

8 - 5a < 3

a > 1

200

Evaluate:

log₃243

5

300

(5+w)/-3 > 2

w < -11

400

Write in logarithmic form.

5²=25

log₅25 = 2

500

3(3x+4)>6(1-2x)

x > -6/21