Year 10 Math- Term 1 2023

Index Laws

100

Simplify:

a² x a⁴ = 

Answer:

a²⁺⁴ = a⁶

200

Simplify:

m⁷ divide m⁵

Answer:

m^7-5 = m²

300

Simplify:

3a²b x 4ab³ =

Answer:

12a³b⁴

400

Simplify:

(a³)⁴

Answer:

a^3x4 = a¹²

500

Simplify:

4x²y⁵ divide 8xy²

Answer:

1/2 xy³

or 

xy³/2

Negative Indices

100

Express each of the following using positive indices:

b^-4

Answer:

1/b⁴

200

Express each of the following using positive indices:

5/x^-3

Answer:

5x³

300

Express each of the following using positive indices:

3x^-4y²

Answer:

3y²/x⁴

400

Express each of the following using positive indices:

2a³b² /a⁵b³

Answer:

2/a²b

500

Express each of the following using positive indices:

4m^-2n³ / 8m⁵n^-4

Answer:

n⁷/2m⁷

Inequalities

100

Solve the following inequalities:

3x > 30

Answer:

x > 10

200

Solve the following inequalities:

x/2 < 20

Answer:

x < 40

300

Solve the following inequalities:

3x + 4 > 13

Answer:

x > 3

400

Solve the following inequalities:

3x + 5 > 20 

Answer:

x > 5

500

Solve the following inequalities:

x/9 + 6 < 4 

Answer:

x < -18

Solving Linear Equations

100

Solve the following linear equation:

x - 5 = 3

Answer: 

x =8

200

Solve the following equations:

4x + 5 = 17

Answer:

x = 3

300

Solve the following equations:

2x + 7 = 13

Answer:

 x = 3

400

Solve the following equations:

3(2x + 5) = 4x

Answer:

x = -15/2

500

Solve the following linear equations:

4x-2/3 = 3x-1/2

Answer:

x = -17/4

Simultaneous Equations

100

Solve these pairs of simultaneous equations using the method of substitution:

2x + y = −7 and y = x + 2

Answer:

(-3, -1)

200

Solve these pairs of simultaneous equations using the method of substitution:

2x + y = 1 and y = x − 5

Answer:

x = 2, y = −3 

300

Solve these pairs of simultaneous equations using the method of substitution:

2x − 3y = −8 and y = x + 3

Answer:

(-1, 2)

400

Solve these pairs of simultaneous equations using the method of substitution:

y = −3x + 2 and y = 7x − 8.

Answer:

(1, -1)

500

Solve these pairs of simultaneous equations using the method of substitution:

3x − 2y = −9 and y = x + 4

Answer:

x = −1, y = 3