In this worksheet, you will find 40 questions that include many of the **level 2** topics that you have learned this year.

Work through the questions carefully.

Calculators may **not **be used *unless *the question says that you may use one.

Good luck!

This is a level 2 revision exercise to help prepare for Year 9/end of Key Stage 3 tests.

In this worksheet, you will find 40 questions that include many of the **level 2** topics that you have learned this year.

Work through the questions carefully.

Calculators may **not **be used *unless *the question says that you may use one.

Good luck!

Work out:

8403 - 8.403

Work out:

74.32 × 8.4

Which of these sequences will be the first to pass 1000?

A: 3 31 59 87 ...

B: 3 6 9 12 ...

C: 3 9 27 81 ...

A

B

C

By which of the given numbers is the following number divisible?

314 550

2

3

4

5

6

8

9

10

11

Select all the **irrational **numbers in this list.

0

π

√7

⅓

Round the following number to 1, 2 and 3 significant figures.

*(Don't leave any space between the numbers.)*

answers | |

1 sig. fig. | |

2 sig. figs. | |

3 sig. figs. |

Round the following number to 1, 2 and 3 decimal places.

answers | |

1 dp | |

2 dp | |

3 dp |

Write the following number in standard form:

0.000201

2.01 × 10^{-3}

2.01 × 10^{4}

2.01 × 10^{-4}

Work out:

15 | - | 5 | |

40 | 24 |

*(Give your answer as a fraction, reduced to its lowest terms, e.g. 7/10.)*

Work out:

15 | ÷ | 18 | |

40 | 24 |

*(Give your answer as a fraction, reduced to its lowest terms, e.g. 7/10.)*

Match the fractions to their decimal equivalents.

## Column A | ## Column B |

6/8 | 0.375 |

1/8 | 0.75 |

4/8 | 0.75 |

9/12 | 0.125 |

3/8 | 0.5 |

Work out:

29.694 ÷ 0.0021

Work out:

( | 1 | )^{7} |

2 |

*(Write your answer in its lowest terms in the form a/b.)*

Round each of these numbers to **1 sig. fig.** to work out an approximate answer to:

29.1 × 41.9 |

57.8 |

Find the **original **price of a television in pounds, sold for **£320** after a **20%** reduction in a sale.

*(Just write the number.)*

Jane sells **120 cakes** on Monday.

She sells **102 cakes **on Tuesday.

What is the** percentage decrease **in sales from Monday to Tuesday?

*(Just write the number without the % sign.)*

Work out the nth term in this sequence and write the formula in the answer box:

-2, 5, 12, 19, 26 ...

Find the first **5 terms** in the sequence given by the formula:

**T _{n} =**

where **n** is the position of the term in the sequence.

value | |

T_{1} | |

T_{2} | |

T_{3} | |

T_{4} | |

T_{5} |

Form an equation from the angles shown in this triangle and solve it to find the value of **a**.

*(Just write the number.)*

Simplify:

(-3a + 1) - (a - 3)

Simplify:

2a^{3}b × 3a^{4}b^{3}

5a^{7}b

6a^{7}b^{3}

6a^{7}b^{4}

Multiply out the two brackets and simplify:

(2x - 6)(4x + 6)

8x^{2} - 12x - 36

8x^{2} + 36x - 12

Simplify:

(p^{3}q^{4})^{7}

p^{10}q^{11}

p^{21}q^{11}

p^{21}q^{28}

Solve for a:

a -16 - 2a = a - 21 + 3a

*(Just write the value of a as a number.)*

Solve simultaneously:

6x + y = 16

3x + y = 10

answers | |

x | |

y |

Solve the following equation:

a | - | a | = | 14 |

3 | 12 |

*(Just write the value of a.)*

State the gradient of the line with equation:

y = 4 - 7x

Use the graph to select the best estimate for the solution to the simultaneous equations:

**y = 2x - 2**

**y = -1 - x**

x = 0.3, y = 1.3

x = 3.3, y = -1.3

x = 0.3, y = -1.3

A sum of money** **is shared in the ratio **7:5** between two people, A and B.

If A gets **£84**, how much money is there in total in £?

*(Just write the number.)*

A plane flies from London to Rome at an average speed of 668 km/h. The flying time is 2¼ hours.

Find the distance travelled by the plane in km.

*(Just write the number.)*

You may use a calculator for this question.

Find the **area **in **cm ^{2 }**of a circle of

*(Just write the number to 1 decimal place.)*

A **regular **polygon has **18 sides**.

Calculate its **interior **angle.

*(Just write the number.)*

You may use a calculator for this question.

Find the **surface area **of this cylinder in **cm ^{2} **to

*(Just write the number.)*

You may use a calculator for this question.

Use Pythagoras' Theorem to calculate the length of the side, **a**, in the following right-angled triangle.

Give your answer to **3 sig. figs**.

You may use a calculator for this question.

Using trigonometry, calculate the side length* x* to **3 sig. figs**.

You may use a calculator for this question.

Using trigonometry, calculate the angle θº to **3 sig. figs**.

*(Just write the number.)*

Two fair dice are thrown.

Make a list of the possible outcomes on a piece of paper.

Start your list like this:

1 1

1 2

1 3

1 4

1 5

1 6

2 1

2 2

2 3

2 4... etc.

What is the **probability **of getting **two even **numbers?

*(Write your answer with the / symbol, e.g. 2/3 and remember to reduce your fraction to its lowest terms.)*

The tree diagram shows the probabilities that my bus is on time or late on Friday and Saturday.

Buses are usually late on Saturdays because it is market day.

Calculate the **probability **that it will be **on time on one day and late on the other**.

You may use a calculator for this question.

This table shows the number of pets owned by children in a Year 9 class at school.

Find the **mean** number of pets owned by a child.

Number of pets | 0 | 1 | 2 | 3 |
---|---|---|---|---|

Frequency | 11 | 8 | 3 | 8 |

*(Give your answer to 1 decimal place.)*

This chart shows the heights of children in a Year 9 class at school.

Find the **median **class.

110 cm to 115 cm

115 cm to 120 cm

120 cm to 125 cm

125 cm to 130 cm

130 cm to 135 cm

135 cm to 140 cm

140 cm to 145 cm

145 cm to 150 cm

150 cm to 155 cm

- ANSWERS

- Question 1

Work out:

8403 - 8.403

CORRECT ANSWER

8394.597

EDDIE SAYS

Change 8403 to 8403.000.

Line up the decimal points and subtract the digits in columns, borrowing if necessary.

Line up the decimal points and subtract the digits in columns, borrowing if necessary.

- ANSWERS

- Question 2

Work out:

74.32 × 8.4

CORRECT ANSWER

624.288

EDDIE SAYS

Use long multiplication to work out 7432 × 84.

Then divide the answer by 1000.

Then divide the answer by 1000.

- ANSWERS

- Question 3

Which of these sequences will be the first to pass 1000?

A: 3 31 59 87 ...

B: 3 6 9 12 ...

C: 3 9 27 81 ...

CORRECT ANSWER

C

EDDIE SAYS

C shows the powers of 3, which increase very quickly.

The next number is 243, then 729.

The next number will be more than 1000.

The next number is 243, then 729.

The next number will be more than 1000.

- ANSWERS

- Question 4

By which of the given numbers is the following number divisible?

314 550

CORRECT ANSWER

2

3

5

6

9

10

3

5

6

9

10

EDDIE SAYS

2: ends in even digit.

3: digit sum is 18, which is divisible by 3.

4: last two-digit number is**not** divisible by 4.

5: ends in 0 or 5.

6: divisible by 2 and by 3.

8: last three-digit number is**not** divisible by 8.

9: digit sum is 18, which is divisible by 9.

10: ends in 0.

11: compare alternate digit sums which are**different**.

3: digit sum is 18, which is divisible by 3.

4: last two-digit number is

5: ends in 0 or 5.

6: divisible by 2 and by 3.

8: last three-digit number is

9: digit sum is 18, which is divisible by 9.

10: ends in 0.

11: compare alternate digit sums which are

- ANSWERS

- Question 5

Select all the **irrational **numbers in this list.

CORRECT ANSWER

π

√7

√7

EDDIE SAYS

0 and ⅓ are rational because they can be written as fractions.

π and √7 are never-ending, non-recurring decimals.

π and √7 are never-ending, non-recurring decimals.

- ANSWERS

- Question 6

Round the following number to 1, 2 and 3 significant figures.

*(Don't leave any space between the numbers.)*

CORRECT ANSWER

answers | |

1 sig. fig. | |

2 sig. figs. | |

3 sig. figs. |

EDDIE SAYS

1 sig. fig: 37255 is between 30000 and 40000 but nearer to 40000.

2 sig. figs: 37255 is between 37000 and 38000 but nearer to 37000.

3 sig. figs: 37255 is between 37200 and 37300 but nearer to 37300.

2 sig. figs: 37255 is between 37000 and 38000 but nearer to 37000.

3 sig. figs: 37255 is between 37200 and 37300 but nearer to 37300.

- ANSWERS

- Question 7

Round the following number to 1, 2 and 3 decimal places.

CORRECT ANSWER

answers | |

1 dp | |

2 dp | |

3 dp |

EDDIE SAYS

1 dp: 37.2595 is between 37.2 and 37.3 but nearer to 37.3.

2 dp: 37.2595 is between 37.25 and 37.26 but nearer to 37.26.

3 dp: 37.2595 is between 37.259 and 37.260 but nearer to 37.260.

2 dp: 37.2595 is between 37.25 and 37.26 but nearer to 37.26.

3 dp: 37.2595 is between 37.259 and 37.260 but nearer to 37.260.

- ANSWERS

- Question 8

Write the following number in standard form:

0.000201

CORRECT ANSWER

2.01 × 10^{-4}

EDDIE SAYS

Fix the decimal point after the first non-zero digit, then count how many times you must divide by 10 to get back to 0.000201. The index will be negative.

- ANSWERS

- Question 9

Work out:

15 | - | 5 | |

40 | 24 |

*(Give your answer as a fraction, reduced to its lowest terms, e.g. 7/10.)*

CORRECT ANSWER

1/6

EDDIE SAYS

45/120 - 25/120 = 20/120 = 1/6

- ANSWERS

- Question 10

Work out:

15 | ÷ | 18 | |

40 | 24 |

*(Give your answer as a fraction, reduced to its lowest terms, e.g. 7/10.)*

CORRECT ANSWER

1/2

EDDIE SAYS

Turn second fraction upside down and multiply.

15/40 × 24/18

Reduce to get 3/8 × 4/3 = 4/8 = 1/2.

15/40 × 24/18

Reduce to get 3/8 × 4/3 = 4/8 = 1/2.

- ANSWERS

- Question 11

Match the fractions to their decimal equivalents.

CORRECT ANSWER

## Column A | ## Column B |

6/8 | 0.75 |

1/8 | 0.125 |

4/8 | 0.5 |

9/12 | 0.75 |

3/8 | 0.375 |

EDDIE SAYS

6/8 = 3/4 = 0.75

1/8 = 1.000 ÷ 8 = 0.125

4/8 = 1/2 = 0.5

9/12 = 3/4 = 0.75

3/8 = 3.000 ÷ 8 = 0.375

1/8 = 1.000 ÷ 8 = 0.125

4/8 = 1/2 = 0.5

9/12 = 3/4 = 0.75

3/8 = 3.000 ÷ 8 = 0.375

- ANSWERS

- Question 12

Work out:

29.694 ÷ 0.0021

CORRECT ANSWER

14140

14 140

14 140

EDDIE SAYS

Multiply both numbers by 10 000 to get:

296 940 ÷ 21

Use long division, or divide by 3 and 7 to get the answer.

296 940 ÷ 21

Use long division, or divide by 3 and 7 to get the answer.

- ANSWERS

- Question 13

Work out:

( | 1 | )^{7} |

2 |

*(Write your answer in its lowest terms in the form a/b.)*

CORRECT ANSWER

1/128

EDDIE SAYS

2^{7} = 128

- ANSWERS

- Question 14

Round each of these numbers to **1 sig. fig.** to work out an approximate answer to:

29.1 × 41.9 |

57.8 |

CORRECT ANSWER

20

EDDIE SAYS

30 × 40 = 1200

1200 ÷ 60 = 20

1200 ÷ 60 = 20

- ANSWERS

- Question 15

Find the **original **price of a television in pounds, sold for **£320** after a **20%** reduction in a sale.

*(Just write the number.)*

CORRECT ANSWER

400

EDDIE SAYS

320 ÷ 0.8 = 400

- ANSWERS

- Question 16

Jane sells **120 cakes** on Monday.

She sells **102 cakes **on Tuesday.

What is the** percentage decrease **in sales from Monday to Tuesday?

*(Just write the number without the % sign.)*

CORRECT ANSWER

15

EDDIE SAYS

Actual decrease = 120 - 102 = 18

% decrease = 18 ÷ 120 × 100 = 15

% decrease = 18 ÷ 120 × 100 = 15

- ANSWERS

- Question 17

Work out the nth term in this sequence and write the formula in the answer box:

-2, 5, 12, 19, 26 ...

CORRECT ANSWER

7n-9

7n - 9

7n - 9

EDDIE SAYS

Common difference is 7.

Subtract 9 to adjust.

Subtract 9 to adjust.

- ANSWERS

- Question 18

Find the first **5 terms** in the sequence given by the formula:

**T _{n} =**

where **n** is the position of the term in the sequence.

CORRECT ANSWER

value | |

T_{1} | |

T_{2} | |

T_{3} | |

T_{4} | |

T_{5} |

EDDIE SAYS

T_{1} = 5 × 1^{2} = 5 × 1 = ** 5**

T_{2} = 5 × 2^{2} = 5 × 4 = ** 20**

T_{3} = 5 × 3^{2} = 5 × 9 = ** 45**

T_{4} = 5 × 4^{2} = 5 × 16 = ** 80**

T_{5} = 5 × 5^{2} = 5 × 25 = ** 125**

T

T

T

T

- ANSWERS

- Question 19

Form an equation from the angles shown in this triangle and solve it to find the value of **a**.

*(Just write the number.)*

CORRECT ANSWER

20

EDDIE SAYS

60 - a + 3a + 30 + 4a - 30 = 180

60 + 6a = 180

6a = 120

a = 20

60 + 6a = 180

6a = 120

a = 20

- ANSWERS

- Question 20

Simplify:

(-3a + 1) - (a - 3)

CORRECT ANSWER

-4a+4

-4a + 4

4-4a

4 - 4a

-4a + 4

4-4a

4 - 4a

EDDIE SAYS

-3a + 1 - a + 3

- ANSWERS

- Question 21

Simplify:

2a^{3}b × 3a^{4}b^{3}

CORRECT ANSWER

6a^{7}b^{4}

EDDIE SAYS

2 × 3 × a × a × a × a × a × a × a × b × b × b × b

- ANSWERS

- Question 22

Multiply out the two brackets and simplify:

(2x - 6)(4x + 6)

CORRECT ANSWER

8x^{2} - 12x - 36

EDDIE SAYS

2x(4x + 6) - 6(4x + 6) = 8x^{2} + 12x - 24x - 36

- ANSWERS

- Question 23

Simplify:

(p^{3}q^{4})^{7}

CORRECT ANSWER

p^{21}q^{28}

EDDIE SAYS

p^{3}q^{4} × p^{3}q^{4} × p^{3}q^{4} × p^{3}q^{4} × p^{3}q^{4} × p^{3}q^{4} × p^{3}q^{4}

p^{3} × p^{3} × p^{3} × p^{3} × p^{3} × p^{3} × p^{3} × q^{4} × q^{4} × q^{4} × q^{4} × q^{4} × q^{4} × q^{4}

p

- ANSWERS

- Question 24

Solve for a:

a -16 - 2a = a - 21 + 3a

*(Just write the value of a as a number.)*

CORRECT ANSWER

1

EDDIE SAYS

-16 - a = 4a - 21

-a - 4a = -21 + 16

-5a = -5

a = 1

-a - 4a = -21 + 16

-5a = -5

a = 1

- ANSWERS

- Question 25

Solve simultaneously:

6x + y = 16

3x + y = 10

CORRECT ANSWER

answers | |

x | |

y |

EDDIE SAYS

Subtract the equations to get:

3x = 6

x = 2

y = 10 - 3x = 10 - 6 = 4

3x = 6

x = 2

y = 10 - 3x = 10 - 6 = 4

- ANSWERS

- Question 26

Solve the following equation:

a | - | a | = | 14 |

3 | 12 |

*(Just write the value of a.)*

CORRECT ANSWER

56

EDDIE SAYS

Multiply both sides by the denominator 12.

4a - a = 168

3a = 168

a = 168 ÷ 3 = 56

4a - a = 168

3a = 168

a = 168 ÷ 3 = 56

- ANSWERS

- Question 27

State the gradient of the line with equation:

y = 4 - 7x

CORRECT ANSWER

-7

- 7

- 7

EDDIE SAYS

The gradient is m, when in the form y = mx + c.

The coefficient of x is -7 here.

The coefficient of x is -7 here.

- ANSWERS

- Question 28

Use the graph to select the best estimate for the solution to the simultaneous equations:

**y = 2x - 2**

**y = -1 - x**

CORRECT ANSWER

x = 0.3, y = -1.3

EDDIE SAYS

- ANSWERS

- Question 29

A sum of money** **is shared in the ratio **7:5** between two people, A and B.

If A gets **£84**, how much money is there in total in £?

*(Just write the number.)*

CORRECT ANSWER

144

EDDIE SAYS

There are £84 in 7 bags, so each bag contains £84 ÷ 7 = £12.

In total, there are 12 bags, i.e. 12 × £12 = £144.

In total, there are 12 bags, i.e. 12 × £12 = £144.

- ANSWERS

- Question 30

A plane flies from London to Rome at an average speed of 668 km/h. The flying time is 2¼ hours.

Find the distance travelled by the plane in km.

*(Just write the number.)*

CORRECT ANSWER

1503

EDDIE SAYS

668 × 2¼ = 668 + 668 + 668 ÷ 4 = 668 + 668 + 167

- ANSWERS

- Question 31

You may use a calculator for this question.

Find the **area **in **cm ^{2 }**of a circle of

*(Just write the number to 1 decimal place.)*

CORRECT ANSWER

37.4

EDDIE SAYS

Radius = 6.9 ÷ 2 = 3.45 cm

Area = π × r^{2} = π × 3.45^{2} = 37.3928...

Area = π × r

- ANSWERS

- Question 32

A **regular **polygon has **18 sides**.

Calculate its **interior **angle.

*(Just write the number.)*

CORRECT ANSWER

160

EDDIE SAYS

180 - 360 ÷ 18 = 180 - 20

- ANSWERS

- Question 33

You may use a calculator for this question.

Find the **surface area **of this cylinder in **cm ^{2} **to

*(Just write the number.)*

CORRECT ANSWER

245

EDDIE SAYS

Two circles and a rectangle.

The base of the rectangle is the circumference of the circle.

2 × π × 3² + 6 × π × 10

The base of the rectangle is the circumference of the circle.

2 × π × 3² + 6 × π × 10

- ANSWERS

- Question 34

You may use a calculator for this question.

Use Pythagoras' Theorem to calculate the length of the side, **a**, in the following right-angled triangle.

Give your answer to **3 sig. figs**.

CORRECT ANSWER

5.66

EDDIE SAYS

a = √(9^{2} - 7^{2}) = √32 = 5.6568...

- ANSWERS

- Question 35

You may use a calculator for this question.

Using trigonometry, calculate the side length* x* to **3 sig. figs**.

CORRECT ANSWER

31.3

EDDIE SAYS

x = 12 × tan69°

- ANSWERS

- Question 36

You may use a calculator for this question.

Using trigonometry, calculate the angle θº to **3 sig. figs**.

*(Just write the number.)*

CORRECT ANSWER

38.9

EDDIE SAYS

θ = cos^{-1}(7/9)

- ANSWERS

- Question 37

Two fair dice are thrown.

Make a list of the possible outcomes on a piece of paper.

Start your list like this:

1 1

1 2

1 3

1 4

1 5

1 6

2 1

2 2

2 3

2 4... etc.

What is the **probability **of getting **two even **numbers?

*(Write your answer with the / symbol, e.g. 2/3 and remember to reduce your fraction to its lowest terms.)*

CORRECT ANSWER

1/4

EDDIE SAYS

Out of 36 outcomes, 9 have two even numbers.

2 2, 2 4, 2 6

4 2, 4 4, 4 6

6 2, 6 4, 6 6

2 2, 2 4, 2 6

4 2, 4 4, 4 6

6 2, 6 4, 6 6

- ANSWERS

- Question 38

The tree diagram shows the probabilities that my bus is on time or late on Friday and Saturday.

Buses are usually late on Saturdays because it is market day.

Calculate the **probability **that it will be **on time on one day and late on the other**.

CORRECT ANSWER

0.56

EDDIE SAYS

0.8 × 0.6 + 0.2 × 0.4 = 0.48 + 0.08 = 0.56

- ANSWERS

- Question 39

You may use a calculator for this question.

This table shows the number of pets owned by children in a Year 9 class at school.

Find the **mean** number of pets owned by a child.

Number of pets | 0 | 1 | 2 | 3 |
---|---|---|---|---|

Frequency | 11 | 8 | 3 | 8 |

*(Give your answer to 1 decimal place.)*

CORRECT ANSWER

1.3

EDDIE SAYS

Total no. of pets = 0 × 11 + 1 × 8 + 2 × 3 + 3 × 8 = 8 + 6 + 24 = 38

Total no. of children = 11 + 8 + 3 + 8 = 30

Mean = 38 ÷ 30 = 1.266666...

Total no. of children = 11 + 8 + 3 + 8 = 30

Mean = 38 ÷ 30 = 1.266666...

- ANSWERS

- Question 40

This chart shows the heights of children in a Year 9 class at school.

Find the **median **class.

CORRECT ANSWER

130 cm to 135 cm

EDDIE SAYS

No. of children in class = 1 + 3 + 7 + 5 + 4 + 3 + 1 = 24

We need to find the 12th and 13th child in order of height.

They will both be in the 130 cm to 135 cm group, because the first 11 children are in the first 3 groups shown.

We need to find the 12th and 13th child in order of height.

They will both be in the 130 cm to 135 cm group, because the first 11 children are in the first 3 groups shown.

---- OR ----

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