Functions - Prior Knowledge Review

Solving linear equations

100

Find x

3x+2=9x-10

x=2

200

Find y

2y-6=5y+7

y=-13/3

300

Find x

4(2x-3)=3(5x+6)

x=-30/7

400

Find x

(3x+4)/(x+9) = 1/2

x=1/5

500

Find x

12/x + 8 = 5

x=-4

Factoring

100

Fully factor the following

9x+27

9(x+3)

200

Fully factor the following

8x²+12x

4x(2x+3)

300

Fully factor the following

x²-x-30

(x+5)(x-6)

400

Fully factor the following

6x²-7x-24

(2x+3)(3x-8)

500

Fully factor the following

3ac-ad+6bc-2bd

(a+2b)(3c-d)

Solving quadratics

100

Solve the following for x

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

x=-3 or x=5

200

Solve the following for x

x²-3x-10=0

x=-2 or x=5

300

Solve the following for x

x²-8x+15=0

x=5 or x=3

400

Solve the following for x

2x²-5x-3=0

x=-1/2 or x=3

500

Solve the following for x

3x²+2=7x

x=1/3 or x=2

Exponents

100

Simplify fully

x² * x⁵

x⁷

200

Simplify fully

(x³*x^-5)/x^-4

x²

300

Simplify fully

(3x⁴)²

9x⁸

400

Simplify fully

(2x³y⁸)⁵

32x¹⁵y⁴⁰

500

Simplify fully

(3a²b⁹)²/(2a^-3b^-2)³

(9a¹³b²⁴)/8

Systems of equations

100

Solve the system of equations

3x + 2y = 22
4x - 2y = 6

x=4, y=5

200

Solve the system of equations

5x + 6y = 9
4x - 2y = 14

x=3, y=-1

300

Solve the system of equations

4x - 3y = 12
2x + 2y = 13  

x=4.5, y=2

400

Solve the system of equations

4x + 6y = 6
2x + 9y = -5

x=3.5, y=-4/3

500

Solve the system of equations

2x + 5y = -1
6x - y = 5

x=0.75, y=-0.5