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 11/end of Key Stage 4 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:

3 - 0.3^{2}

Is the following number rational or irrational?

√3

rational

irrational

You may use a calculator for this question.

Select the recurring decimal which is equal to:

4 |

33 |

1.

2.

3.

Work out, without a calculator:

√9 × 3^{3}

Work out:

7 | - | 5 | + | 7 |

15 | 6 | 10 |

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

Place these numbers in **ascending **order of size:

35% 1/3 3/10 √0.16 0.7^{3}

## Column A | ## Column B |

1 (smallest) | 3/10 |

2 | 1/3 |

3 | 35% |

4 | √0.16 |

5 (largest) | 0.7 ^{3} |

Round this number to **3 significant figures**:

5212.5

Add together:

4 × 10^{6} + 6 × 10^{4}

1 × 10^{24}

4.06 × 10^{6}

4.6 × 10^{6}

Rearrange the following equation so that it is in the form y = ...

2y - 4x = 8

y = 4 + 2x

y = 4 - 2x

y = 2x - 4

Rearrange the following formula to make h the subject.

A = ½bh

h = ½Ab

h = 2A/b

h = ½A/b

h = 2Ab

Solve the following equation for x:

2x + 3(x - 1) = 32

*(Just write the number.)*

Factorise the following quadratic expression.

x^{2} - 8x + 16

(x - 4) (x - 4)

(x - 2) (x - 8)

(x - 1) (x - 9)

(x + 16) (x - 1)

Is this an equation with one solution, an equation with no solutions or an identity?

3x + 12 = 3(x + 4)

equation with one solution

equation with no solutions

identity

Select the correct equation which is represented by **graph B**.

y = x²

y = 2x²

y = x + 2

y = 2x

y = x³ + 2

Divide the following expression by 2.

4x^{4} - 6x^{3} + 10x^{2} - 2x

8x^{6} - 2x^{3} + 5x^{2} - x

2x^{4} - 3x^{3} + 5x^{2} - x

2x^{4} - 12x^{2} + 3x^{} - 1

Choose the equation which represents a line with a **gradient of 3** that passes through the point **(3, -1)**.

3x + y = 10

y - 3x = -10

y + 3x = 10

y = -3x + 8

Select all the possible equations represented by the red line shown below.

y = 4x - 5

x = 4y - 5

y + 5 = 4x

y = ¼x - 5

y = 5x - 5

Find the **smallest integer **that satisfies the inequality:

15 - 5x ≤ 2(1 - x)

You may use a calculator for this question.

William invests £50 000 at 3% compound interest p.a.

He makes no further withdrawals or investments.

How much is his investment worth in pounds after five years?

*(Just write the number with 2 decimal places.)*

Given that y is **directly proportional** to x and that** x = 8 when y = 192**,

find the value of **y** when **x = 25**.

Given that y is **inversely proportional** to x and that** x = 8 when y = 3**,

find the value of **y** when **x = 6**.

You may use a calculator for this question.

Look at the function:

**f(t) = 3 ^{t} + 10**

Work out** f(5)**.

Look at this graph.

Is it **exponential**, **quadratic **or **linear**?

exponential

quadratic

linear

ABCDEFGH is a **cuboid**.

Select the coordinates of **F**.

(3, 5, 2)

(3, 5, -2)

(-2, 5, 3)

You may use a calculator for this question.

Calculate the **volume **(in cm^{3}) of a cone with **radius R equal to 2 cm** and **height H equal to 6 cm**.

*(Write your answer to 1 dp and just write the number.)*

ABCD is a quadrilateral.

M and N are the midpoints of AB and BC respectively.

Select an expression, in terms of* p, q, r* and

You may use a calculator for this question.

Calculate the **perimeter **of this right-angled triangle to 3 sig. figs.

Using one of the triangles shown below, state the value of:

cos 45°

2/√3

1

√2

1/√3

1/√2

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.)*

The tangent SU touches the circle, with centre C, at T.

Calculate the **angle TUP** in degrees.

*(Just write the number.)*

ABC is a triangle, inside which is inscribed a circle.

The circle touches the triangle at the points P, Q and R.

AB = 23 and BQ =11.

Calculate the length** AP**.

A money bag contains 20 × £1 coins, 25 × 50p coins, 10 × 10p coins and 5 × 2p coins.

What is the **probability **that a coin selected at random is a **50p coin**?

*(Write your answer as a fully reduced fraction, e.g. 4/7.)*

Two fair dice are thrown and the results are shown in this sample space diagram.

What is the **probability **that the two dice will show the **same numbers**?

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

A spinner was spun and the score was noted down before it was spun again.

The experiment was repeated several times.

The results were as follows.

Score | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|

Frequency | 19 | 22 | 21 | 23 | 24 | 25 | 18 | 22 |

Calculate the expected probability of spinning a seven next.

*(Give your answer as a fraction in its lowest terms in the form a/b.)*

The probability that it will rain at the weekend is** 6/24**.

What is the **probability **that it will **not rain** at the weekend?

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

Which of these statistical measures could be used to measure the **spread **of a set of data?

average

mean

median

mode

range

Look at these scatter graphs.

Match each situation to the most likely scatter graph.

**A**** **

**B**

**C**

## Column A | ## Column B |

Outside Temperature and No. of Ice Creams Sold | B |

Shoe Size and Maths Test Marks | A |

Distance Travelled and Petrol Left in the Tank | C |

You may use a calculator for this question.

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

Estimate the mean height of all the children in the class to the nearest cm.

*(Just write the number.)*

The marks of 20 children in a maths test are represented on a Stem and Leaf Diagram as shown below.

Work out the median mark.

Stem |
Leaf |

0 | 7 7 9 |

1 | 1 2 4 4 4 4 7 |

2 | 1 3 3 3 9 |

3 | 0 4 5 |

4 | 4 8 |

- ANSWERS

- Question 1

Work out:

3 - 0.3^{2}

CORRECT ANSWER

2.91

EDDIE SAYS

0.3 × 0.3 = 0.09

3 - 0.09 = 2.91

3 - 0.09 = 2.91

- ANSWERS

- Question 2

Is the following number rational or irrational?

√3

CORRECT ANSWER

irrational

EDDIE SAYS

It cannot be written as a fraction, so it is irrational.

- ANSWERS

- Question 3

You may use a calculator for this question.

Select the recurring decimal which is equal to:

4 |

33 |

CORRECT ANSWER

1.

EDDIE SAYS

4 ÷ 33 = 0.1212121212...

The 1 and the 2 recur.

The 1 and the 2 recur.

- ANSWERS

- Question 4

Work out, without a calculator:

√9 × 3^{3}

CORRECT ANSWER

81

EDDIE SAYS

√9 = 3

3^{3} = 27

3 × 27 = 81

3

3 × 27 = 81

- ANSWERS

- Question 5

Work out:

7 | - | 5 | + | 7 |

15 | 6 | 10 |

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

CORRECT ANSWER

1/3

EDDIE SAYS

LCM of 15, 6 and 10 is 30.

14/30 - 25/30 + 21/30 = 10/30 = 1/3

14/30 - 25/30 + 21/30 = 10/30 = 1/3

- ANSWERS

- Question 6

Place these numbers in **ascending **order of size:

35% 1/3 3/10 √0.16 0.7^{3}

CORRECT ANSWER

## Column A | ## Column B |

1 (smallest) | 3/10 |

2 | 1/3 |

3 | 0.7 ^{3} |

4 | 35% |

5 (largest) | √0.16 |

EDDIE SAYS

3/10 = 0.3

1/3 = 0.33333...

0.7^{3} = 0.343

35% = 0.35

√0.16 = 0.4

1/3 = 0.33333...

0.7

35% = 0.35

√0.16 = 0.4

- ANSWERS

- Question 7

Round this number to **3 significant figures**:

5212.5

CORRECT ANSWER

5210

EDDIE SAYS

5212.5 is between 5210 and 5220, but is closer to 5210.

- ANSWERS

- Question 8

Add together:

4 × 10^{6} + 6 × 10^{4}

CORRECT ANSWER

4.06 × 10^{6}

EDDIE SAYS

4 × 10^{6} = 4 000 000

6 × 10^{4} = 60 000

4 000 000 + 60 000 = 4 060 000 = 4.06 × 10^{6}

6 × 10

4 000 000 + 60 000 = 4 060 000 = 4.06 × 10

- ANSWERS

- Question 9

Rearrange the following equation so that it is in the form y = ...

2y - 4x = 8

CORRECT ANSWER

y = 4 + 2x

EDDIE SAYS

2y - 4x = 8

2y = 8 + 4x

y = 4 + 2x

2y = 8 + 4x

y = 4 + 2x

- ANSWERS

- Question 10

Rearrange the following formula to make h the subject.

A = ½bh

CORRECT ANSWER

h = 2A/b

EDDIE SAYS

Double both sides and then divide by b.

- ANSWERS

- Question 11

Solve the following equation for x:

2x + 3(x - 1) = 32

*(Just write the number.)*

CORRECT ANSWER

7

EDDIE SAYS

2x + 3x - 3 = 32

5x = 35

x = 7

5x = 35

x = 7

- ANSWERS

- Question 12

Factorise the following quadratic expression.

x^{2} - 8x + 16

CORRECT ANSWER

(x - 4) (x - 4)

EDDIE SAYS

We look for factor pairs that multiply to give 16 and add to give -8.

These are -4 and -4.

Factorise x² - 4x - 4x + 16 in pairs.

These are -4 and -4.

Factorise x² - 4x - 4x + 16 in pairs.

- ANSWERS

- Question 13

Is this an equation with one solution, an equation with no solutions or an identity?

3x + 12 = 3(x + 4)

CORRECT ANSWER

identity

EDDIE SAYS

3(x + 4) simplifies to 3x + 12 so this is true for all values of x.

- ANSWERS

- Question 14

Select the correct equation which is represented by **graph B**.

CORRECT ANSWER

y = x²

EDDIE SAYS

This is the basic y = x² parabolic curve.

- ANSWERS

- Question 15

Divide the following expression by 2.

4x^{4} - 6x^{3} + 10x^{2} - 2x

CORRECT ANSWER

2x^{4} - 3x^{3} + 5x^{2} - x

EDDIE SAYS

4x^{4} |
- | 6x^{3} |
+ | 10x^{2} |
- | 2x^{} |

2^{} |
2^{} |
2^{} |
2^{} |

- ANSWERS

- Question 16

**gradient of 3** that passes through the point **(3, -1)**.

CORRECT ANSWER

y - 3x = -10

EDDIE SAYS

y = mx + c is the equation and we know that the gradient m = 3.

Put x = 3 and y = -1 into y = 3x + c, to get -1 = 3 × 3 + c.

-1 = 9 + c gives c = -10.

Equation is y = 3x - 10 or y - 3x = -10.

Put x = 3 and y = -1 into y = 3x + c, to get -1 = 3 × 3 + c.

-1 = 9 + c gives c = -10.

Equation is y = 3x - 10 or y - 3x = -10.

- ANSWERS

- Question 17

Select all the possible equations represented by the red line shown below.

CORRECT ANSWER

y = 4x - 5

y + 5 = 4x

y + 5 = 4x

EDDIE SAYS

It crosses the y-axis at -5 and has a gradient of 4 (1 to the right and 4 up).

So y = mx + c becomes y = 4x - 5.

y + 5 = 4x is a rearrangement of this.

So y = mx + c becomes y = 4x - 5.

y + 5 = 4x is a rearrangement of this.

- ANSWERS

- Question 18

Find the **smallest integer **that satisfies the inequality:

15 - 5x ≤ 2(1 - x)

CORRECT ANSWER

5

EDDIE SAYS

15 - 5x ≤ 2(1 - x)

15 - 5x ≤ 2 - 2x

15 - 2 ≤ 5x - 2x

13 ≤ 3x

3x ≥ 13

x ≥ 13/3 = 4.33333...

15 - 5x ≤ 2 - 2x

15 - 2 ≤ 5x - 2x

13 ≤ 3x

3x ≥ 13

x ≥ 13/3 = 4.33333...

- ANSWERS

- Question 19

You may use a calculator for this question.

William invests £50 000 at 3% compound interest p.a.

He makes no further withdrawals or investments.

How much is his investment worth in pounds after five years?

*(Just write the number with 2 decimal places.)*

CORRECT ANSWER

57963.70

57 963.70

57 963.70

EDDIE SAYS

50 000 × 1.03^{5}

- ANSWERS

- Question 20

Given that y is **directly proportional** to x and that** x = 8 when y = 192**,

find the value of **y** when **x = 25**.

CORRECT ANSWER

600

EDDIE SAYS

y = kx

192 = 8k

k = 192 ÷ 8 = 24

y = 24x

y = 24 × 25 = 600

192 = 8k

k = 192 ÷ 8 = 24

y = 24x

y = 24 × 25 = 600

- ANSWERS

- Question 21

Given that y is **inversely proportional** to x and that** x = 8 when y = 3**,

find the value of **y** when **x = 6**.

CORRECT ANSWER

4

EDDIE SAYS

y = k/x

3 = k/8

k = 3 × 8 = 24

y = 24/x

y = 24 ÷ 6 = 4

3 = k/8

k = 3 × 8 = 24

y = 24/x

y = 24 ÷ 6 = 4

- ANSWERS

- Question 22

You may use a calculator for this question.

Look at the function:

**f(t) = 3 ^{t} + 10**

Work out** f(5)**.

CORRECT ANSWER

253

EDDIE SAYS

3^{5} = 243

243 + 10 = 253

243 + 10 = 253

- ANSWERS

- Question 23

Look at this graph.

Is it **exponential**, **quadratic **or **linear**?

CORRECT ANSWER

exponential

EDDIE SAYS

This is an exponential curve.

A quadratic would be parabolic.

A linear graph would be straight.

A quadratic would be parabolic.

A linear graph would be straight.

- ANSWERS

- Question 24

ABCDEFGH is a **cuboid**.

Select the coordinates of **F**.

CORRECT ANSWER

(3, 5, -2)

EDDIE SAYS

3 along the x-axis.

5 along the y-axis.

-2 along the z-axis.

5 along the y-axis.

-2 along the z-axis.

- ANSWERS

- Question 25

You may use a calculator for this question.

Calculate the **volume **(in cm^{3}) of a cone with **radius R equal to 2 cm** and **height H equal to 6 cm**.

*(Write your answer to 1 dp and just write the number.)*

CORRECT ANSWER

25.1

EDDIE SAYS

Vol = 1 ÷ 3 × π × 2² × 6

- ANSWERS

- Question 26

ABCD is a quadrilateral.

M and N are the midpoints of AB and BC respectively.

Select an expression, in terms of* p, q, r* and

CORRECT ANSWER

EDDIE SAYS

This is the same as M to B and then B to N, which is half of p and then half of -s.

- ANSWERS

- Question 27

You may use a calculator for this question.

Calculate the **perimeter **of this right-angled triangle to 3 sig. figs.

CORRECT ANSWER

26.5

EDDIE SAYS

a² + 7² = 11²

a² + 49 = 121

a² = 121 - 49 = 72

a = √72 = 8.49

Perimeter = 8.49 + 7 + 11 = 26.49 = 26.5

a² + 49 = 121

a² = 121 - 49 = 72

a = √72 = 8.49

Perimeter = 8.49 + 7 + 11 = 26.49 = 26.5

- ANSWERS

- Question 28

Using one of the triangles shown below, state the value of:

cos 45°

CORRECT ANSWER

1/√2

EDDIE SAYS

In the yellow triangle, cos 45° = adj/hyp = 1/√2.

- ANSWERS

- Question 29

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 30

You may use a calculator for this question.

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

*(Just write the number.)*

CORRECT ANSWER

41.8

EDDIE SAYS

θ = sin^{-1}(6/9)

- ANSWERS

- Question 31

The tangent SU touches the circle, with centre C, at T.

Calculate the **angle TUP** in degrees.

*(Just write the number.)*

CORRECT ANSWER

48

EDDIE SAYS

The tangent SU and the diameter PT meet at right angles,

so ∠PTU = 90°

∠TUP = 180° - 90° - 42° = **48°**

- ANSWERS

- Question 32

ABC is a triangle, inside which is inscribed a circle.

The circle touches the triangle at the points P, Q and R.

AB = 23 and BQ =11.

Calculate the length** AP**.

CORRECT ANSWER

12

EDDIE SAYS

BP = BQ = 11

AP = AB - BP = 23 - 11 = 12

AP = AB - BP = 23 - 11 = 12

- ANSWERS

- Question 33

A money bag contains 20 × £1 coins, 25 × 50p coins, 10 × 10p coins and 5 × 2p coins.

What is the **probability **that a coin selected at random is a **50p coin**?

*(Write your answer as a fully reduced fraction, e.g. 4/7.)*

CORRECT ANSWER

5/12

EDDIE SAYS

There are 60 coins in the bag.

P(50p coin) = 25/60 = 5/12

P(50p coin) = 25/60 = 5/12

- ANSWERS

- Question 34

Two fair dice are thrown and the results are shown in this sample space diagram.

What is the **probability **that the two dice will show the **same numbers**?

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

CORRECT ANSWER

1/6

EDDIE SAYS

There are 6 doubles out of 36.

6/36 reduces to 1/6.

6/36 reduces to 1/6.

- ANSWERS

- Question 35

A spinner was spun and the score was noted down before it was spun again.

The experiment was repeated several times.

The results were as follows.

Score | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|

Frequency | 19 | 22 | 21 | 23 | 24 | 25 | 18 | 22 |

Calculate the expected probability of spinning a seven next.

*(Give your answer as a fraction in its lowest terms in the form a/b.)*

CORRECT ANSWER

3/29

EDDIE SAYS

It is not stated that this is a fair spinner, so you must use the results.

The experiment is carried out 19 + 22 + 21 + 23 + + 24 + 25 + 18 + 22 = 174 times.

18/174 reduces to 3/29.

The experiment is carried out 19 + 22 + 21 + 23 + + 24 + 25 + 18 + 22 = 174 times.

18/174 reduces to 3/29.

- ANSWERS

- Question 36

The probability that it will rain at the weekend is** 6/24**.

What is the **probability **that it will **not rain** at the weekend?

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

CORRECT ANSWER

3/4

EDDIE SAYS

1 - 6/24 = 1 - 1/4 = 3/4

- ANSWERS

- Question 37

Which of these statistical measures could be used to measure the **spread **of a set of data?

CORRECT ANSWER

range

EDDIE SAYS

The range is the greatest value - least value, which is a measure of how spread out the data is.

- ANSWERS

- Question 38

Look at these scatter graphs.

Match each situation to the most likely scatter graph.

**A**** **

**B**

**C**

CORRECT ANSWER

## Column A | ## Column B |

Outside Temperature and No. of Ic... | A |

Shoe Size and Maths Test Marks | C |

Distance Travelled and Petrol Lef... | B |

EDDIE SAYS

A shows a positive correlation. The higher the temperature, the more ice creams are sold.

B shows a negative correlation. The further the distance, the less petrol there is remaining in the tank.

C shows no correlation. There is no connection between shoe size and marks gained in a test.

B shows a negative correlation. The further the distance, the less petrol there is remaining in the tank.

C shows no correlation. There is no connection between shoe size and marks gained in a test.

- ANSWERS

- Question 39

You may use a calculator for this question.

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

Estimate the mean height of all the children in the class to the nearest cm.

*(Just write the number.)*

CORRECT ANSWER

136

EDDIE SAYS

The total estimated height of all the children is (2 × 117.5) + (6 × 127.5) + (5 × 132.5) + (4 × 137.5) + (3 × 142.5) + (2 × 147.5) + (3 × 152.5) = 3392.5 cm.

There are 2 + 6 + 5 + 4 + 3 + 2 + 3 = 25 children in the class.

Mean height = 3392.5 ÷ 25 = 135.7 cm

There are 2 + 6 + 5 + 4 + 3 + 2 + 3 = 25 children in the class.

Mean height = 3392.5 ÷ 25 = 135.7 cm

- ANSWERS

- Question 40

The marks of 20 children in a maths test are represented on a Stem and Leaf Diagram as shown below.

Work out the median mark.

Stem |
Leaf |

0 | 7 7 9 |

1 | 1 2 4 4 4 4 7 |

2 | 1 3 3 3 9 |

3 | 0 4 5 |

4 | 4 8 |

CORRECT ANSWER

19

EDDIE SAYS

With 20 people, we are looking for the 10th and 11th mark when placed in order. These are 17 and 21, the mean of which is 19.

---- OR ----

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