TT1 revision set 1

Factors and primes

100

List the first five prime numbers.

2, 3, 5, 7, 11

200

Write 84 as a product of prime factors.

84=2²x3x7

300

Write 456 as a product of prime factors.

456=2³x3x19

400

Given the following numbers and their prime factors, find their HCF:

360=2³x3²x5

144=2⁴x3²

HCF=2³x3²

 =72

500

Given the following numbers and their prime factors, find their LCM:

132=2²x3x11

126=2x3²x7

LCM=2²x3²x7x11

 =2772

Indices

100

Write the answer to this calculation in index form.

12⁸ ÷ 12⁵

12³

200

Solve ∛729 + 5²

∛729 + 5²

=9 + 25

=34

300

Solve

(3⁴)⁵ ÷ 3²⁰

3⁰ or 1

400

Solve x³ + 216 = 0

x³ + 216 = 0

x³ = -216

x = ∛ -216

x = -6

500

Given that 1936 = 2⁴ x 11²,

write √1936 as a product of prime factors.

√1936 = 2² x 11

Expressions and equations

100

Solve -42 ÷ 7

-6

200

Solve 46 - (6 + 3) x 4

46 - (6 + 3) x 4

=46 - 9 x 4

=46 - 36

=10

300

Find the value of x, given

x ÷ 5 - 9 = 2

x ÷ 5 - 9 = 2

x ÷ 5 = 2 + 9

x ÷ 5 = 11

x = 11 x 5

x = 55

400

Solve 4x² + 5x - 18 when x = -3

4x² + 5x - 18

= 4(-3)² + 5(-3) - 18

= 4(9) + 5(-3) - 18

= 36 - 15 - 18

= 3

500

Given that a triangle has a base of 4y and a height of 3y, write an expression for the area of the triangle.

Area of triangle = 3y x 4y x 1/2

= 12y² x 1/2

= 6y²

Expanding and factorising

100

Expand 2a(3 - b)

6a - 2ab

200

Expand -6h(4k - 7h)

-24kh + 42h²

300

Factorise 45n³ + 30n

15n(3n² + 2)

400

Factorise 6xy - 22y² + 18yz

2y(3x - 11y + 9z)

500

Simplify b(3b + 5c) - 2c(6b - 4c)

b(3b + 5c) - 2c(6b - 4c)

=3b² + 5bc - 12bc + 8c²

=3b² - 7bc + 8c²

Inequalities and rounding

100

List all integers of x for the inequality -3 ≤ x < 2

-3, -2, -1, 0, 1

200

Round 5643 to 1s.f.

6000

300

Round 2.0455 to 2s.f.

2.0

400

Given that 1 kilometer = 0.621371192 miles, find the distance in miles for 6 kilometers rounded to 3s.f.

0.621371192 x 6 = 3.728227153

= 3.73 miles

500

Given that the gravitational acceleration on Earth, g_Earth is 9.80665 m/s² and the gravitational acceleration on Mars is one third of Earth's, find g_Mars rounded to 3s.f.

g_Mars = 9.80665 ÷ 3

= 3.268883333

= 3.27 m/s² (3s.f.)