In this worksheet, you will find 40 questions that include many of the **level 1** 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 1 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 1** 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:

840.3 + 8.403 + 84.03

Work out:

14.3 × 8.4

In a room of people:

½ of them wear glasses.

¼ of them wear contact lenses.

The rest have perfect eyesight.

What **percentage **have perfect eyesight?

*(Just write the number.)*

Is the following number divisible by 11?

42 141

yes

no

Think about the list of

Multiples of 10.

Is this list **finite **or **infinite**?

finite

infinite

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

## Column A | ## Column B |

1 sig. fig. | 4230 |

2 sig. figs. | 4200 |

3 sig. figs. | 4000 |

Round the following number to 2 decimal places.

Write the following number in standard form:

8051

80.51 × 10^{2}

8.051 × 10^{2}

8.051 × 10^{3}

Work out:

15 | + | 5 | |

40 | 20 |

*(Give your answer as a fraction, reduced to its lowest terms, e.g. 3/10.)*

Work out:

7 | ÷ | 5 | |

40 | 20 |

*(Give your answer as a fraction, reduced to its lowest terms, e.g. 3/10.)*

Match the fractions to their decimal equivalents.

## Column A | ## Column B |

1/10 | 0.1 |

1/2 | 0.75 |

1/4 | 0.5 |

3/4 | 0.25 |

Work out:

0.024 ÷ 0.04

Work out:

( | 1 | )^{3} |

4 |

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

Round each of these numbers to 1 significant figure to work out an approximate answer to:

389 × 19.5

Work out:

12% of 35

Find the **original **price of a television in pounds, sold for £350 after a 50% reduction in a sale.

*(Just write the number.)*

You may use a calculator for this question.

Jane sells **110 cakes** on Monday.

She sells **132 cakes **on Tuesday.

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

*(Just write the number.)*

Work out the nth term in this sequence:

4, 7, 10, 13, 16 ...

n + 3

3n + 1

4n + 3

4n + 7

What is the sum of the angles shown in this triangle?

*(Just write the expression. No need to include the degrees sign.)*

Simplify:

(5a + 1) - (5a - 1)

Simplify:

2a^{3} × 3a^{2}

6a^{5}

5a^{6}

6a^{6}

Multiply out the brackets and simplify:

3x - 8(1 - 4x)

-8 - 29x

35x - 8

x - 8

Simplify:

(b^{3})^{2}

b^{9}

b^{32}

b^{6}

Solve for a:

6a - 2 = 2a - 22

a = -6

a = 24

a = -5

Solve the inequality:

6x + 4 ≤ -20

x < 3

x ≥ 4

x ≤ -4

x < -4

Work out the value of the following expression when** a = -16** and **b = 72**.

a | + | b |

2 | 8 |

Find the gradient of the red line.

*(If it is not a whole number, write it as a fraction in the form a/b.)*

Look at this grid.

What are the coordinates of** G** after it has been **reflected in the y-axis**?

*(Write your answer in the form (a, b) using brackets and a comma between the coordinate numbers.)*

A sum of money** **is shared in the ratio **5:3** between two people, A and B.

If A gets **£95**, how much does B get in £?

*(Just write the number.)*

John sets off on a car journey at 08:15.

He travels at an **average speed of 85 km/h** and arrives at his destination at 10:45.

Find the **distance **he travelled 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.)*

You may use a calculator for this question.

Find the **volume **of this cylinder in cm^{3} to the nearest whole number.

Remember that the **volume **= **base area × height**.

*(Just write the whole number.)*

A **regular **polygon has** 8** **sides**.

Calculate its **exterior angle**.

*(Just write the number.)*

You may use a calculator for this question.

Use Pythagoras' Theorem to calculate the length of the hypotenuse, c, in the following right-angled triangle.

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

In relation to the angle θ, label the sides correctly in this right-angled triangle.

## Column A | ## Column B |

adjacent | b |

opposite | a |

hypotenuse | c |

Which trigonometric ratio is used to calculate the angle θº ?

sin

cos

tan

One fair coin and one fair die are thrown.

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

In how many outcomes is there a **tail **and an **even **number?

The following table shows the numbers of right- and left-handed children in a class of 30 children.

Boys | Girls | Total | |
---|---|---|---|

Right | 10 | 12 | 22 |

Left | 5 | 3 | 8 |

Total | 15 | 15 | 30 |

What is the **probability **that a child chosen at random is a **right-handed girl**?

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

Work out the **mean**, **mode**, **median **and **range **of the following set of numbers:

3, 15, 3, 12, 4.5

answers | |

mean | |

mode | |

median | |

range |

Which line is the line of best fit on this scatter graph?

A

B

C

- ANSWERS

- Question 1

Work out:

840.3 + 8.403 + 84.03

CORRECT ANSWER

932.733

EDDIE SAYS

Line up the decimal points, and add the digits in columns.

- ANSWERS

- Question 2

Work out:

14.3 × 8.4

CORRECT ANSWER

120.12

EDDIE SAYS

Use long multiplication to work out 143 × 84.

Then divide the answer by 100.

Then divide the answer by 100.

- ANSWERS

- Question 3

In a room of people:

½ of them wear glasses.

¼ of them wear contact lenses.

The rest have perfect eyesight.

What **percentage **have perfect eyesight?

*(Just write the number.)*

CORRECT ANSWER

25

EDDIE SAYS

¼ of the people in the room have perfect eyesight.

¼ of 100 = 25.

¼ of 100 = 25.

- ANSWERS

- Question 4

Is the following number divisible by 11?

42 141

CORRECT ANSWER

yes

EDDIE SAYS

Add alternate digits.

4 + 1 + 1 = 6

2 + 4 = 6, which matches.

4 + 1 + 1 = 6

2 + 4 = 6, which matches.

- ANSWERS

- Question 5

Think about the list of

Multiples of 10.

Is this list **finite **or **infinite**?

CORRECT ANSWER

infinite

EDDIE SAYS

Finite lists have a set number of items.

Infinite lists go on for ever.

Lists of multiples go on for ever, because you can always find the next multiple.

Infinite lists go on for ever.

Lists of multiples go on for ever, because you can always find the next multiple.

- ANSWERS

- Question 6

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

CORRECT ANSWER

## Column A | ## Column B |

1 sig. fig. | 4000 |

2 sig. figs. | 4200 |

3 sig. figs. | 4230 |

EDDIE SAYS

1 sig. fig: 4225 is between 4000 and 5000 but nearer to 4000.

2 sig. figs: 4225 is between 4200 and 4300 but nearer to 4200.

3 sig. figs: 4225 is between 4220 and 4230 but 'nearer' to 4230, as halfway numbers always round up.

2 sig. figs: 4225 is between 4200 and 4300 but nearer to 4200.

3 sig. figs: 4225 is between 4220 and 4230 but 'nearer' to 4230, as halfway numbers always round up.

- ANSWERS

- Question 7

Round the following number to 2 decimal places.

CORRECT ANSWER

42.26

EDDIE SAYS

42.259 is between 42.25 and 42.26, but it is nearer to 42.26.

- ANSWERS

- Question 8

Write the following number in standard form:

8051

CORRECT ANSWER

8.051 × 10^{3}

EDDIE SAYS

Fix the decimal point after the first digit, then count how many times you must multiply by 10 to get up to 8051.

- ANSWERS

- Question 9

Work out:

15 | + | 5 | |

40 | 20 |

*(Give your answer as a fraction, reduced to its lowest terms, e.g. 3/10.)*

CORRECT ANSWER

5/8

EDDIE SAYS

15/40 + 10/40 = 25/40 = 5/8

- ANSWERS

- Question 10

Work out:

7 | ÷ | 5 | |

40 | 20 |

*(Give your answer as a fraction, reduced to its lowest terms, e.g. 3/10.)*

CORRECT ANSWER

7/10

EDDIE SAYS

Turn second fraction upside down and multiply.

7/40 × 20/5

Reduce to get 7/10.

7/40 × 20/5

Reduce to get 7/10.

- ANSWERS

- Question 11

Match the fractions to their decimal equivalents.

CORRECT ANSWER

## Column A | ## Column B |

1/10 | 0.1 |

1/2 | 0.5 |

1/4 | 0.25 |

3/4 | 0.75 |

EDDIE SAYS

1/10 = 0.1

1/2 = 5/10 = 0.5

1/4 = 25/100 = 0.25

3/4 = 75/100 = 0.75

1/2 = 5/10 = 0.5

1/4 = 25/100 = 0.25

3/4 = 75/100 = 0.75

- ANSWERS

- Question 12

Work out:

0.024 ÷ 0.04

CORRECT ANSWER

0.6

EDDIE SAYS

Multiply both numbers by 100 to get:

2.4 ÷ 4 = 0.6

2.4 ÷ 4 = 0.6

- ANSWERS

- Question 13

Work out:

( | 1 | )^{3} |

4 |

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

CORRECT ANSWER

1/64

EDDIE SAYS

1/4 × 1/4 × 1/4

- ANSWERS

- Question 14

Round each of these numbers to 1 significant figure to work out an approximate answer to:

389 × 19.5

CORRECT ANSWER

8000

EDDIE SAYS

400 × 20 = 8000

- ANSWERS

- Question 15

Work out:

12% of 35

CORRECT ANSWER

4.2

EDDIE SAYS

0.12 × 35 = 4.2

- ANSWERS

- Question 16

Find the **original **price of a television in pounds, sold for £350 after a 50% reduction in a sale.

*(Just write the number.)*

CORRECT ANSWER

700

EDDIE SAYS

In a 50% sale, prices are halved.

350 ÷ 0.5 = 350 × 2 = 700

350 ÷ 0.5 = 350 × 2 = 700

- ANSWERS

- Question 17

You may use a calculator for this question.

Jane sells **110 cakes** on Monday.

She sells **132 cakes **on Tuesday.

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

*(Just write the number.)*

CORRECT ANSWER

20

EDDIE SAYS

Actual increase = 132 - 110 = 22

% increase = 22 ÷ 110 × 100 = 20

% increase = 22 ÷ 110 × 100 = 20

- ANSWERS

- Question 18

Work out the nth term in this sequence:

4, 7, 10, 13, 16 ...

CORRECT ANSWER

3n + 1

EDDIE SAYS

Common difference is 3.

Add 1 to adjust.

Add 1 to adjust.

- ANSWERS

- Question 19

What is the sum of the angles shown in this triangle?

*(Just write the expression. No need to include the degrees sign.)*

CORRECT ANSWER

10a+70

10a + 70

70+10a

70 + 10a

10a + 70

70+10a

70 + 10a

EDDIE SAYS

5a + 3a + 30 + 2a + 40 = 5a + 3a + 2a + 30 + 40 = 10a + 70

- ANSWERS

- Question 20

Simplify:

(5a + 1) - (5a - 1)

CORRECT ANSWER

2

EDDIE SAYS

5a + 1 - 5a + 1

- ANSWERS

- Question 21

Simplify:

2a^{3} × 3a^{2}

CORRECT ANSWER

6a^{5}

EDDIE SAYS

2 × 3 × a × a × a × a × a

- ANSWERS

- Question 22

Multiply out the brackets and simplify:

3x - 8(1 - 4x)

CORRECT ANSWER

35x - 8

EDDIE SAYS

3x - 8 + 32x

- ANSWERS

- Question 23

Simplify:

(b^{3})^{2}

CORRECT ANSWER

b^{6}

EDDIE SAYS

b^{3} × b^{3}

Add the indices.

Add the indices.

- ANSWERS

- Question 24

Solve for a:

6a - 2 = 2a - 22

CORRECT ANSWER

a = -5

EDDIE SAYS

6a - 2a = 2 - 22

4a = -20

a = -5

4a = -20

a = -5

- ANSWERS

- Question 25

Solve the inequality:

6x + 4 ≤ -20

CORRECT ANSWER

x ≤ -4

EDDIE SAYS

6x ≤ -24

- ANSWERS

- Question 26

Work out the value of the following expression when** a = -16** and **b = 72**.

a | + | b |

2 | 8 |

CORRECT ANSWER

1

EDDIE SAYS

-8 + 9

- ANSWERS

- Question 27

Find the gradient of the red line.

*(If it is not a whole number, write it as a fraction in the form a/b.)*

CORRECT ANSWER

5

EDDIE SAYS

5 up for every 1 to the right.

- ANSWERS

- Question 28

Look at this grid.

What are the coordinates of** G** after it has been **reflected in the y-axis**?

*(Write your answer in the form (a, b) using brackets and a comma between the coordinate numbers.)*

CORRECT ANSWER

(-2,3)

(-2, 3)

(-2, 3)

EDDIE SAYS

The x-coordinate changes its sign from 2 to -2.

The y-coordinate stays at 3.

The y-coordinate stays at 3.

- ANSWERS

- Question 29

A sum of money** **is shared in the ratio **5:3** between two people, A and B.

If A gets **£95**, how much does B get in £?

*(Just write the number.)*

CORRECT ANSWER

57

EDDIE SAYS

There are £95 in 5 bags, so each bag contains £95 ÷ 5 = £19.

B gets 3 bags, i.e. 3 × £19 = £57.

B gets 3 bags, i.e. 3 × £19 = £57.

- ANSWERS

- Question 30

John sets off on a car journey at 08:15.

He travels at an **average speed of 85 km/h** and arrives at his destination at 10:45.

Find the **distance **he travelled in **km**.

*(Just write the number.)*

CORRECT ANSWER

212.5

EDDIE SAYS

His journey is 2½ hours long.

85 × 2 = 170

½ of 85 = 42.5

170 + 42.5 = 212.5

85 × 2 = 170

½ of 85 = 42.5

170 + 42.5 = 212.5

- 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

113.1

EDDIE SAYS

Area = π × r^{2} = π × 36 = 113.097...

- ANSWERS

- Question 32

You may use a calculator for this question.

Find the **volume **of this cylinder in cm^{3} to the nearest whole number.

Remember that the **volume **= **base area × height**.

*(Just write the whole number.)*

CORRECT ANSWER

283

EDDIE SAYS

π × 3² × 10 = 282.74...

- ANSWERS

- Question 33

A **regular **polygon has** 8** **sides**.

Calculate its **exterior angle**.

*(Just write the number.)*

CORRECT ANSWER

45

EDDIE SAYS

360 ÷ 8

- ANSWERS

- Question 34

You may use a calculator for this question.

Use Pythagoras' Theorem to calculate the length of the hypotenuse, c, in the following right-angled triangle.

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

CORRECT ANSWER

10.4

EDDIE SAYS

Work out 3^{2} + 10^{2} = 109.

√109 = 10.440...

√109 = 10.440...

- ANSWERS

- Question 35

In relation to the angle θ, label the sides correctly in this right-angled triangle.

CORRECT ANSWER

## Column A | ## Column B |

adjacent | b |

opposite | a |

hypotenuse | c |

EDDIE SAYS

a is opposite the angle θ.

b is next to or adjacent to the angle θ.

c is the longest side.

b is next to or adjacent to the angle θ.

c is the longest side.

- ANSWERS

- Question 36

Which trigonometric ratio is used to calculate the angle θº ?

CORRECT ANSWER

sin

EDDIE SAYS

sin θ = opposite / hypotenuse

- ANSWERS

- Question 37

One fair coin and one fair die are thrown.

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

In how many outcomes is there a **tail **and an **even **number?

CORRECT ANSWER

3

EDDIE SAYS

T2, T4, T6

- ANSWERS

- Question 38

The following table shows the numbers of right- and left-handed children in a class of 30 children.

Boys | Girls | Total | |
---|---|---|---|

Right | 10 | 12 | 22 |

Left | 5 | 3 | 8 |

Total | 15 | 15 | 30 |

What is the **probability **that a child chosen at random is a **right-handed girl**?

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

CORRECT ANSWER

2/5

EDDIE SAYS

12/30 reduces to 2/5.

- ANSWERS

- Question 39

Work out the **mean**, **mode**, **median **and **range **of the following set of numbers:

3, 15, 3, 12, 4.5

CORRECT ANSWER

answers | |

mean | |

mode | |

median | |

range |

EDDIE SAYS

Mean = (3 + 15 + 3 + 12 + 4.5) ÷ 5 = 37.5 ÷ 5 = 7.5

Mode is most frequently occuring.

Median is middle of ordered list: 3, 3,**4.5**, 7.5, 12.

Range = largest - smallest = 15 - 3 = 12

Mode is most frequently occuring.

Median is middle of ordered list: 3, 3,

Range = largest - smallest = 15 - 3 = 12

- ANSWERS

- Question 40

Which line is the line of best fit on this scatter graph?

CORRECT ANSWER

C

EDDIE SAYS

The line C goes through the most points and follows the general direction of the points.

---- OR ----

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