Algebra Revision

Factorisation

100

x² + x - 30

1 (x² + x -30)

200

8p - 6q +10r

2 (4p - 3q + 5r)

300

m²n + mn² + m²n²

mn (m + n + 1)

400

72x + 36y - 18z

18 (4x + 2y - z)

500

1 - t⁴

(1 +t²) ((1 + t)(1 - t)) 

Rearranging formula (making "x" the subject)

100

m = 5x²

x = √5/m

200

a = nx²/9

x = √9a/n

300

y = cube root of x/a

x = ay³

400

1/x + 1/y = 1/t

x = t/y 

500

a = y + t/p + x²

x = √pa-py/t

Linear Equations

100

12 = 20 + 2x

x = -4

200

3(p + 4) = 21

p = -3

300

4(x -5) = 7(2x - 5)

x = 2/3

400

1/2 (4x + 6 - 8) = 1/3 (18x + 9)

x = -1

500

x(x + 2) = x(x + 5) + 3

x = -1

Simultaneous Equations

100

2x + 2y = 16

x - 3y = 4

y = 3

x = 13

200

4x + y = 23

x + y = 8

y = 3

x = 5

300

2y + 3x = 6

x = 4y + 16

y = -3

x = 4

400

3x + 2y = 22

2x + 2y = 18

y = 5

x = 4

500

4.4x - 4.8y = 2.2

0.8y + 2.4y = 4

y = -1.1

x = 1.7

Quadratics

100

x² - 6x - 27

(9 , -3)

200

x² - 15x + 56

(8 , 7)

300

x² + 9x - 36

(3/2 , -21/2)

400

x² - 18x + 45

(15 , 3)

500

4x² + 7x - 13

(1.129 , -2.879)