Year 10 Maths

Factorisation

100

x²-10 = 90

+/- 10

200

5x² = 20

+/- 2

300

( x - 1 )² = 9

+/- 4

400

(x + 2)² = 0

-2

500

1/3 (2x + 3)² = 2

= - (3 + sqrt(6))/2

Null Factor

100

2a = 0

a = 0

200

(x - 1)(x- 3) = 0

x = 1, 3

300

2(x - 3)² = 0

x = 3

400

(3x + 1)(2x - 5) = 0

x = -1/3, 5/2 

500

ax(x - b) = 0

x = 0, b

Completing the square

100

x² + 2x = 5

(x + 1)² = 6

200

x² + 2x + 4 = 0

no real solutions

300

x² - 4x + 1 = 0

x = 2 +/- Sqrt(3)

400

x² - 5x + 6 = 0 

x = 3 or 2

500

x² + 5x - 2 = 0

x = (-5 +/- sqrt(33))/2

Quadratic Formula

100

x² + 6x + 8 = 0

x = -2, -4

200

x² + x - 5 = 0

x = (-1 +/- sqrt(31))/2

300

x² - 4x + 5 = 0

no real solution

400

x² - 4x -5 = 0

x = -1, 5

500

x + 1/(x + 2) = 4

x = 1 +/- 2*sqrt(2) 

Problem solving

100

The sum of a number and its square is 110. Find the number.

Number is either -11 or 10.

200

When 24 is subtracted from the square of a number, the result is five times the original number.

number is -3 or 8

300

the sum of two number is 6, and the sum of their square is 28. Find these numbers exactly.

3 +/- sqrt (5)

400

Two numbers differ by 7, and the sum of their squares is 29.

-2 and 5 OR -5 and 2

500

A rectangle has length 4cm greater than its widthm and its area is 96cm². What is the width?

8cm