In this assessment, you'll review your understanding of various topics across key stage 3. May take approximately 45 minutes to complete but take all the time you need.

In this assessment, students will review their comprehension of various topics across key stage 3. May take approximately 45 minutes to complete.

**Key stage:** KS 3

**Curriculum topic:** End of Key Stage Assessments

**Curriculum subtopic:** Starter Assessments

**Difficulty level:**

Work out:

840.3 + 8.403 + 84.03

Work out:

74.32 × 8.4

Work out:

78.39 × 8.7 ÷ 0.3

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.)*

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?

1 663 893

2

3

4

5

6

8

9

10

11

Round the following number to 2 decimal places.

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. |

Subtract these numbers, written in **standard form**.

3.1 × 10^{2 }- 3.1 × 10^{-2}

Write your answer as a **decimal**.

Work out:

7 | ÷ | 5 | |

40 | 20 |

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

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

29.1 × 41.9 |

57.8 |

You may use a calculator for this question.

At this year's annual fete, Jack sold **476 **hotdogs, which is a **12% increase** compared to **last **year.

How many hotdogs did he sell in total in the two years, i.e **this **year and **last **year?

Work out the nth term in this sequence:

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

n + 3

3n + 1

4n + 3

4n + 7

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} |

Simplify:

a(-3a + 1) - 2a(a - 3)

-5a^{2} + 7a

-5a^{2} - 5a

-a^{2} - 5a

Solve the inequality:

6x + 4 ≤ -20

x < 3

x ≥ 4

x ≤ -4

x < -4

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

*(Just write the number.)*

Select the correct **HCF (Highest Common Factor) **of these two algebraic expressions:

7p^{5}q^{4}r and 21pq^{6}r^{6}

7pq^{4}r

14pq^{4}r

21pq^{4}r

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

a | + | b |

2 | 8 |

Multiply out the two brackets and simplify:

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

8x^{2} - 12x - 36

8x^{2} + 36x - 12

State the gradient of a line which is **perpendicular **to the line with equation:

y = 4 - 7x

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

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.)*

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.)*

Convert the following area into one measured in** cm ^{2}**.

12.6 m^{2}

*(Just write the number.)*

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

Calculate its **exterior 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.

The formula for the volume of a sphere, V, in terms of its radius, r, is:

V = 4/3πr^{3}

A **sphere **has a **volume **of **1000 cm ^{3}**.

Calculate its **radius in cm **and its **surface area in cm ^{2}**.

Give your answers to 3 sig. figs.

*(Just write the number.)*

answers | |

radius | |

surface area |

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**.

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, find the height of this isosceles triangle in metres to** 3 sig. figs**.

*(Just write the number.)*

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 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**.

These two fair spinners are spun and the two scores are **added **together.

Use a sample-space diagram to answer the question.

What is the **probability **of getting a **total score of 5**?

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

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

A

B

C

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

You may use a calculator for this question.

This table shows the masses of children in a Year 9 class at school.

Estimate the **total **mass in kg** **of all the children in the class.

Mass (m kg) | Frequency |
---|---|

40 ≤ m < 45 | 2 |

45 ≤ m < 50 | 5 |

50 ≤ m < 55 | 9 |

55 ≤ m < 60 | 3 |

60 ≤ m < 65 | 1 |

- 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:

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

Work out:

78.39 × 8.7 ÷ 0.3

CORRECT ANSWER

2273.31

EDDIE SAYS

Use long multiplication to work out 7839 × 87.

Then divide the answer by 1000 to get 681.993.

Then multiply both numbers by 10 to give 6819.93 ÷ 3.

Then divide the answer by 1000 to get 681.993.

Then multiply both numbers by 10 to give 6819.93 ÷ 3.

- ANSWERS

- Question 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.)*

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 5

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 6

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

1 663 893

CORRECT ANSWER

3

9

11

9

11

EDDIE SAYS

2: ends in odd digit.

3: digit sum is 36, which is divisible by 3.

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

5: does not end in 0 or 5.

6: not divisible by 2.

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

9: digit sum is 36, which is divisible by 9.

10: does not end in 0.

11: compare alternate digit sums which are both 18.

3: digit sum is 36, which is divisible by 3.

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

5: does not end in 0 or 5.

6: not divisible by 2.

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

9: digit sum is 36, which is divisible by 9.

10: does not end in 0.

11: compare alternate digit sums which are both 18.

- 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

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 9

Subtract these numbers, written in **standard form**.

3.1 × 10^{2 }- 3.1 × 10^{-2}

Write your answer as a **decimal**.

CORRECT ANSWER

309.969

EDDIE SAYS

3.1 × 10^{2} = 310

3.1 × 10^{-2} = 0.031

310 - 0.031 = 309.969

3.1 × 10

310 - 0.031 = 309.969

- 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

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 12

You may use a calculator for this question.

At this year's annual fete, Jack sold **476 **hotdogs, which is a **12% increase** compared to **last **year.

How many hotdogs did he sell in total in the two years, i.e **this **year and **last **year?

CORRECT ANSWER

901

EDDIE SAYS

476 ÷ 1.12 = 425

425 + 476 = 901

425 + 476 = 901

- ANSWERS

- Question 13

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 14

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 15

Simplify:

a(-3a + 1) - 2a(a - 3)

CORRECT ANSWER

-5a^{2} + 7a

EDDIE SAYS

-3a^{2} + a - 2a^{2} + 6a

- ANSWERS

- Question 16

Solve the inequality:

6x + 4 ≤ -20

CORRECT ANSWER

x ≤ -4

EDDIE SAYS

6x ≤ -24

- ANSWERS

- Question 17

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 18

Select the correct **HCF (Highest Common Factor) **of these two algebraic expressions:

7p^{5}q^{4}r and 21pq^{6}r^{6}

CORRECT ANSWER

7pq^{4}r

EDDIE SAYS

The HCF of 7 and 21 is 7.

Choose the smaller of the powers of each letter.

Choose the smaller of the powers of each letter.

- ANSWERS

- Question 19

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 20

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 21

State the gradient of a line which is **perpendicular **to the line with equation:

y = 4 - 7x

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

CORRECT ANSWER

1/7

EDDIE SAYS

The gradient of the given line is -7.

A perpendicular line will have gradient 1/7, so that the gradients of the two lines multiply to give -1.

A perpendicular line will have gradient 1/7, so that the gradients of the two lines multiply to give -1.

- ANSWERS

- Question 22

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 23

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 24

Convert the following area into one measured in** cm ^{2}**.

12.6 m^{2}

*(Just write the number.)*

CORRECT ANSWER

126000

126 000

126 000

EDDIE SAYS

There are 100 × 100 = 10 000 cm^{2} in 1 m^{2}.

- ANSWERS

- Question 25

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

Calculate its **exterior angle**.

*(Just write the number.)*

CORRECT ANSWER

45

EDDIE SAYS

360 ÷ 8

- ANSWERS

- Question 26

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 27

You may use a calculator for this question.

The formula for the volume of a sphere, V, in terms of its radius, r, is:

V = 4/3πr^{3}

A **sphere **has a **volume **of **1000 cm ^{3}**.

Calculate its **radius in cm **and its **surface area in cm ^{2}**.

Give your answers to 3 sig. figs.

*(Just write the number.)*

CORRECT ANSWER

answers | |

radius | |

surface area |

EDDIE SAYS

Radius = ³√ [(3 × 1000) ÷ (4 × π)]

Surface area = 4 × π × r^{2}

Do not round off the radius to find the surface area.

Surface area = 4 × π × r

Do not round off the radius to find the surface area.

- ANSWERS

- Question 28

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 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, find the height of this isosceles triangle in metres to** 3 sig. figs**.

*(Just write the number.)*

CORRECT ANSWER

13.4

EDDIE SAYS

height = 2.6/tan11º

- ANSWERS

- Question 31

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 32

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 33

These two fair spinners are spun and the two scores are **added **together.

Use a sample-space diagram to answer the question.

What is the **probability **of getting a **total score of 5**?

*(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

1 | 2 | 3 | 4 | |
---|---|---|---|---|

1 | 2 | 3 | 4 | 5 |

2 | 3 | 4 | 5 | 6 |

3 | 4 | 5 | 6 | 7 |

4 | 5 | 6 | 7 | 8 |

The probability of getting a total of 5, P(5) = 4/16 = 1/4.

- ANSWERS

- Question 34

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.

- ANSWERS

- Question 35

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.

- ANSWERS

- Question 36

You may use a calculator for this question.

This table shows the masses of children in a Year 9 class at school.

Estimate the **total **mass in kg** **of all the children in the class.

Mass (m kg) | Frequency |
---|---|

40 ≤ m < 45 | 2 |

45 ≤ m < 50 | 5 |

50 ≤ m < 55 | 9 |

55 ≤ m < 60 | 3 |

60 ≤ m < 65 | 1 |

CORRECT ANSWER

1030

EDDIE SAYS

Total is (2 × 42.5) + (5 × 47.5) + (9 × 52.5) + (3 × 57.5) + (1 × 62.5) = 1030 kg

---- OR ----

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