In this worksheet, you will find 40 questions that include many of the **level 3** 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 3 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 3** 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!

Is the following number rational or irrational?

5 - √12

rational

irrational

Write the following recurring decimal as a fraction in its lowest terms.

*(Write your answer as a reduced fraction in the form a/b.)*

Work out, without a calculator:

12^{2/}^{3} × 18^{2/3}

Work out:

7 | - | 5 | ÷ | 7 |

15 | 6 | 8 |

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

You may use a calculator for this question.

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

45.5% 5/11 4.5 × 10^{-1} 0.1936^{½} (¾)^{3}

## Column A | ## Column B |

1 (smallest) | 45.5% |

2 | 4.5 × 10 ^{-1} |

3 | 0.1936 ^{½} |

4 | 5/11 |

5 (largest) | ¾ ^{3} |

You may use a calculator for this question.

Find the **greatest **and **least **possible **areas **in cm^{2} of the floor of a rectangular room with measurements:

**268 cm by 322 cm**

*(Just write the number with no spaces between the numbers.)*

answers (cm^{2}) | |

least area | |

greatest area |

Simplify by rationalising the denominator of this fraction, giving your answer as a surd in the form a√b, where a and b are integers and b is as small as possible, or if the answer is a whole number, just state the whole number.

(√20)/4

½√5

(√5)/4

Subtract:

2.5 × 10^{-5} - 6.35 × 10^{-4}

-3.85 × 10^{-1}

3.85 × 10^{-9}

-6.1 × 10^{-4}

Rearrange the following equation so that it is in the form** ax + by = c**,

where a ≥ 0, a, b and c are integers and the HCF of a, b, and c is 1.

4¾y = 4 - 2¼x

2x + 4y = 19

9x + 19y = 16

2¼x + 4¾y = 4

Solve the following equation for x:

4x - 5 | = | 5x - 4 |

7 | 11 |

*(Just write the number.)*

Factorise the following quadratic expression.

18x^{2} - 87x + 14

(6x - 2) (3x - 7)

(3x - 2) (6x + 7)

(6x - 1) (3x - 14)

(2x - 7) (9x - 2)

Use the quadratic formula to solve for x, giving your answers to 3 sig. figs.

17x + 21 = 3x^{2}

x = 6.70

x = -4.04

x = 6.71

x = -1.04

Find **all **the x-intercepts of the graph with the following equation:

(i.e. where the line crosses the x-axis)

y = 8x^{2} - 10x - 3

(1½, 0)

(-1½, 0)

(-4, 0)

(-¼, 0)

Divide the following expression by 4x^{3}.

40x^{7} + 36x^{6} - 16x^{4} - 20x^{3}

10x^{4} + 9x^{3} - 4x^{} - 5

36x^{5} + 9x^{2} - 4x^{} - 5x

10x^{4} + 9x^{2} -12x^{} - 5

Find the equation of the line **perpendicular **to** 2x + 9y + 10 = 0**, which passes through **(1, 5)**.

2y - 9x - 1 = 0

2y + 9x + 1 = 0

9y - 2x = 1

Solve the following simultaneous equations:

18 - y^{2} = x^{2}

y = 6 - x

solutions | |

x | |

y |

Choose the function which fits the following results:

f(-1) = -24.8

f(3/2) = (√5)^{3} - 25

f(2) = 0

f(x) = 5^{x} - 25

f(x) = 5^{x} + 5

f(x) = 25^{x} - 5

Select the correct equation of the circle shown below:

y^{2} + x^{2} = 4.5

y = x² = 4.5

x^{2} + y^{2} = 20.25

Simplify the following equation to one that is quadratic:

2 | + | 1 | = | 7 |

2x - 1 | 4x + 3 |

56x² + 4x - 26 = 0

56x² - 24x - 10 = 0

56x² - 4x + 10 = 0

You may use a calculator for this question.

Kate invests £65 000 at 8.5% **compound **interest **p.a**.

Jack invests £65 000 at 8.5% **simple **interest **p.a**.

Neither of them touch their money for ten years.

How much **more **interest does Kate earn in pounds in **ten years**?

*(Just write the number.)*

3 painters take 2 days to paint a wall.

How many days would it take 4 painters to paint 2 similar walls?

*(Just write the number.)*

You may use a calculator for this question.

The population of a certain species is expected to fall by x% each year.

After 10 years the population is halved.

Calculate** x** to 1 decimal place.

You may use a calculator for this question.

Look at the function **f(t) = 3 ^{t}**.

By what percentage does it change in the interval between t = 5 and t = 7?

*(Just write the number.)*

Look at this graph.

What is the equation of the blue line?

y = 5/x + 3

y = 5/x - 3

x = 5/y + 3

x = 5/y - 3

Calculate the **total surface area** (in cm^{2}) of a cone with **radius R equal to 3 cm** and **height H equal to 7 cm**.

Select the correct answer.

(3√58 + 9)π

3√58π

183π

(3√58 + 3)π

You may use a calculator for this question.

The diagram shows a **4 cm × 5 cm × 10 cm cuboid***.*

Calculate the **perimeter **of triangle **ACG**.

*(Just write the number to 3 sig. figs.)*

You may use a calculator for this question.

The diagram below shows a Christmas tree with base at A and top at T.

The distance **AC **is 28 metres.

The angle of elevation of T from C is 35°.

The angle of elevation of T from B is 12°.

Calculate the distance, **BC **in metres.

*(Just give your answer as a number to 1 decimal place.*)

You may use a calculator for this question.

In triangle PQR, which is not drawn to scale,

PQ = 12 cm, PR = 22 cm, and ∠QPR = 35º.

Calculate the length **QR **in cm** **to 3 sig. figs.

*(Just write the number.)*

You may use a calculator for this question.

In triangle PQR, which is not drawn to scale,

PQ = 8 cm, PR = 11 cm and ∠PQR = 111°.

Use the sine rule to find ∠QPR to 1 dp.

*(Just write the number.)*

In triangle PQR, which is not drawn to scale,

PQ = 6 cm, PR = 12 cm and ∠QRP = 30°.

**Without** the use of a calculator, find **∠QPR.**

*(Just write the number.)*

In triangle ABC above,

**a** = 6.2 cm

**b** = 7 cm

**∠BCA** = 125º

Calculate the triangle's area in cm^{2} to 3 sig. figs.

*(Just write the number.)*

The diagram shows a circle, centre C and three points A, B and P on the circumference.

Calculate the angle ∠**ABC**.

*(Just write the number.)*

A money bag contains 22 × £1 coins, 21 × 50p coins, 6 × 10p coins and 5 × 2p coins as well as a number of 20p coins.

The **probability **that a 20p coin is selected at random is **1/4**.

Calculate the number of **20p coins** in the bag.

Two fair tetrahedral dice are thrown. Each is numbered from 1 to 4.

What is the **probability **that **at least one die **will show** a 4**?

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

There are 16 red balls and 4 white balls in a bag.

Fatima randomly chooses 2 balls, removing each in turn from the bag.

What is the probability of choosing one of each colour?

*(Give your answer as a reduced fraction in the form a/b.)*

A number between 380 and 440 is chosen at random.

What is the probability that it is **between 385 and 425**?

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

From the information in the box plot diagrams, match how each distribution is skewed or if it is symmetrical.

## Column A | ## Column B |

symmetrical | B |

positively skewed | C |

negatively skewed | A |

Find the **interquartile range **of the following set of data:

12 4 17 12 10 18 2 31 13

You may use a calculator for this question.

Over the course of five days, there were the following number of empty seats at a theatre.

12 seats, 14 seats, 10 seats, 20 seats, 24 seats

Calculate the** standard deviation** in the number of empty seats to 3 sig. figs.

You may use a calculator for this question.

The following histogram shows the distribution of the lengths of adverts on one television channel during a particular day.

Work out how many TV adverts have been surveyed in **total**.

- ANSWERS

- Question 1

Is the following number rational or irrational?

5 - √12

CORRECT ANSWER

irrational

EDDIE SAYS

√12 is a non-recurring decimal.

- ANSWERS

- Question 2

Write the following recurring decimal as a fraction in its lowest terms.

*(Write your answer as a reduced fraction in the form a/b.)*

CORRECT ANSWER

15/37

EDDIE SAYS

Three digits recur, so 405 over 999, which reduces.

Divide top and bottom by 27 or by 9 and 3 in stages.

Divide top and bottom by 27 or by 9 and 3 in stages.

- ANSWERS

- Question 3

Work out, without a calculator:

12^{2/}^{3} × 18^{2/3}

CORRECT ANSWER

36

EDDIE SAYS

(12 × 18)^{1/3}

= 216^{1/3}

=^{3}√216

= 6

6² = 36

= 216

=

= 6

6² = 36

- ANSWERS

- Question 4

Work out:

7 | - | 5 | ÷ | 7 |

15 | 6 | 8 |

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

CORRECT ANSWER

-17/35

EDDIE SAYS

First work out 5/6 ÷ 7/8 = 5/6 × 8/7 = 20/21.

Then work out 7/15 - 20/21 = 49/105 - 100/105 = -51/105 = -17/35.

Then work out 7/15 - 20/21 = 49/105 - 100/105 = -51/105 = -17/35.

- ANSWERS

- Question 5

You may use a calculator for this question.

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

45.5% 5/11 4.5 × 10^{-1} 0.1936^{½} (¾)^{3}

CORRECT ANSWER

## Column A | ## Column B |

1 (smallest) | ¾ ^{3} |

2 | 0.1936 ^{½} |

3 | 4.5 × 10 ^{-1} |

4 | 5/11 |

5 (largest) | 45.5% |

EDDIE SAYS

0.75^{3} = 0.421875

0.1936^{½} = √0.1936 = 0.44

4.5 × 10^{-1} = 0.45

5/11 = 0.4545...

45.5% = 0.455

0.1936

4.5 × 10

5/11 = 0.4545...

45.5% = 0.455

- ANSWERS

- Question 6

You may use a calculator for this question.

Find the **greatest **and **least **possible **areas **in cm^{2} of the floor of a rectangular room with measurements:

**268 cm by 322 cm**

*(Just write the number with no spaces between the numbers.)*

CORRECT ANSWER

answers (cm^{2}) | |

least area | |

greatest area |

EDDIE SAYS

Smallest possible dimensions are 267.5 by 321.5.

Largest possible dimensions are 268.5 by 322.5.

Largest possible dimensions are 268.5 by 322.5.

- ANSWERS

- Question 7

CORRECT ANSWER

(√20)/4

EDDIE SAYS

4/80 reduces to 1/20.

Multiply top and bottom by √20.

Remember 20 = 4 × 5.

Multiply top and bottom by √20.

Remember 20 = 4 × 5.

- ANSWERS

- Question 8

Subtract:

2.5 × 10^{-5} - 6.35 × 10^{-4}

CORRECT ANSWER

-6.1 × 10^{-4}

EDDIE SAYS

2.5 × 10^{-5} = 0.000025

6.35 × 10^{-4} = 0.000635

0.000025 - 0.000635 = -0.00061 = -6.1 × 10^{-4}

6.35 × 10

0.000025 - 0.000635 = -0.00061 = -6.1 × 10

- ANSWERS

- Question 9

Rearrange the following equation so that it is in the form** ax + by = c**,

where a ≥ 0, a, b and c are integers and the HCF of a, b, and c is 1.

4¾y = 4 - 2¼x

CORRECT ANSWER

9x + 19y = 16

EDDIE SAYS

4¾y = 4 - 2¼x

2¼x + 4¾y = 4

Multiply by 4 to get:

9x + 19y = 16

2¼x + 4¾y = 4

Multiply by 4 to get:

9x + 19y = 16

- ANSWERS

- Question 10

Solve the following equation for x:

4x - 5 | = | 5x - 4 |

7 | 11 |

*(Just write the number.)*

CORRECT ANSWER

3

EDDIE SAYS

Multiply each side by 77 to get:

11(4x - 5) = 7(5x - 4)

44x - 55 = 35x - 28

9x = 27

x = 3

11(4x - 5) = 7(5x - 4)

44x - 55 = 35x - 28

9x = 27

x = 3

- ANSWERS

- Question 11

Factorise the following quadratic expression.

18x^{2} - 87x + 14

CORRECT ANSWER

(6x - 1) (3x - 14)

EDDIE SAYS

We look for factor pairs that multiply to give 252 and add to give -87.

These are -84 and -3.

Factorise 18x² - 84x - 3x + 14 in pairs.

These are -84 and -3.

Factorise 18x² - 84x - 3x + 14 in pairs.

- ANSWERS

- Question 12

Use the quadratic formula to solve for x, giving your answers to 3 sig. figs.

17x + 21 = 3x^{2}

CORRECT ANSWER

x = 6.71

x = -1.04

x = -1.04

EDDIE SAYS

-3x^{2} + 17x + 21 = 0

a=-3 b=17 c=21

a=-3 b=17 c=21

- ANSWERS

- Question 13

Find **all **the x-intercepts of the graph with the following equation:

(i.e. where the line crosses the x-axis)

y = 8x^{2} - 10x - 3

CORRECT ANSWER

(1½, 0)

(-¼, 0)

(-¼, 0)

EDDIE SAYS

When y = 0,

8x² - 10x - 3 = 0

(2x - 3)(4x + 1) = 0

x = -¼, 1½

8x² - 10x - 3 = 0

(2x - 3)(4x + 1) = 0

x = -¼, 1½

- ANSWERS

- Question 14

Divide the following expression by 4x^{3}.

40x^{7} + 36x^{6} - 16x^{4} - 20x^{3}

CORRECT ANSWER

10x^{4} + 9x^{3} - 4x^{} - 5

EDDIE SAYS

40x^{7} |
+ | 36x^{6} |
- | 16x^{4} |
- | 20x^{3} |

4x^{3} |
4x^{3} |
4x^{3} |
4x^{3} |

- ANSWERS

- Question 15

Find the equation of the line **perpendicular **to** 2x + 9y + 10 = 0**, which passes through **(1, 5)**.

CORRECT ANSWER

2y - 9x - 1 = 0

EDDIE SAYS

Rearrange 2x + 9y + 10 = 0 to read 9y = -2x - 10 and then y = -2/9x - 10/9.

This line has a gradient of -2/9, so a perpendicular line will have gradient 9/2, i.e. y = 9/2x + c.

Put in the coordinates (1, 5) to get 5 = 9/2 + c, which gives c = 1/2.

Equation of perpendicular line is y =9/2x + 1/2 or 2y = 9x + 1.

This line has a gradient of -2/9, so a perpendicular line will have gradient 9/2, i.e. y = 9/2x + c.

Put in the coordinates (1, 5) to get 5 = 9/2 + c, which gives c = 1/2.

Equation of perpendicular line is y =9/2x + 1/2 or 2y = 9x + 1.

- ANSWERS

- Question 16

Solve the following simultaneous equations:

18 - y^{2} = x^{2}

y = 6 - x

CORRECT ANSWER

solutions | |

x | |

y |

EDDIE SAYS

Substitute for y to get:

18 - (6 - x)^{2} = x^{2}

18 - (36 - 12x + x^{2}) = x^{2}

-18 + 12x - x^{2} = x^{2}

2x^{2} - 12x + 18 = 0

x^{2} - 6x + 9 = 0

(x - 3)^{2} = 0

x = 3

y = 3

18 - (6 - x)

18 - (36 - 12x + x

-18 + 12x - x

2x

x

(x - 3)

x = 3

y = 3

- ANSWERS

- Question 17

Choose the function which fits the following results:

f(-1) = -24.8

f(3/2) = (√5)^{3} - 25

f(2) = 0

CORRECT ANSWER

f(x) = 5^{x} - 25

EDDIE SAYS

5^{-1} - 25 = 0.2 - 25

5^{3/2} - 25 = (√5)³ - 25

5^{2} - 25 = 25 - 25

5

5

- ANSWERS

- Question 18

Select the correct equation of the circle shown below:

CORRECT ANSWER

x^{2} + y^{2} = 20.25

EDDIE SAYS

Radius = 4.5 units

Equation is x^{2} + y^{2} = 4.5^{2} = 20.25.

Equation is x

- ANSWERS

- Question 19

Simplify the following equation to one that is quadratic:

2 | + | 1 | = | 7 |

2x - 1 | 4x + 3 |

CORRECT ANSWER

56x² + 4x - 26 = 0

EDDIE SAYS

Multiply everything by (2x - 1) and by (4x + 3).

Cancel matching brackets, top and bottom.

2(4x + 3) + 1(2x - 1) = 7(2x - 1)(4x +3)

2(4x + 3) + 1(2x - 1) = 7(8x² + 2x - 3)

8x + 6 + 2x - 1 = 56x² + 14x - 21

0 = 56x² + 14x - 21 - 10x - 5

0 = 56x² + 4x - 26

Cancel matching brackets, top and bottom.

2(4x + 3) + 1(2x - 1) = 7(2x - 1)(4x +3)

2(4x + 3) + 1(2x - 1) = 7(8x² + 2x - 3)

8x + 6 + 2x - 1 = 56x² + 14x - 21

0 = 56x² + 14x - 21 - 10x - 5

0 = 56x² + 4x - 26

- ANSWERS

- Question 20

You may use a calculator for this question.

Kate invests £65 000 at 8.5% **compound **interest **p.a**.

Jack invests £65 000 at 8.5% **simple **interest **p.a**.

Neither of them touch their money for ten years.

How much **more **interest does Kate earn in pounds in **ten years**?

*(Just write the number.)*

CORRECT ANSWER

26713.92

26 713.92

26 713.92

EDDIE SAYS

Kate's interest = 65 000 × 1.085^{10} - 65 000 = 81 963.92

Jack's interest = 65 000 × 0.085 × 10 = 55 250

81 963.92 - 55 250 = 26 713.92

Jack's interest = 65 000 × 0.085 × 10 = 55 250

81 963.92 - 55 250 = 26 713.92

- ANSWERS

- Question 21

3 painters take 2 days to paint a wall.

How many days would it take 4 painters to paint 2 similar walls?

*(Just write the number.)*

CORRECT ANSWER

3

EDDIE SAYS

1 painter would take 6 days to paint a wall, so 12 days to paint 2 walls.

4 painters would take ¼ of 12 days.

4 painters would take ¼ of 12 days.

- ANSWERS

- Question 22

You may use a calculator for this question.

The population of a certain species is expected to fall by x% each year.

After 10 years the population is halved.

Calculate** x** to 1 decimal place.

CORRECT ANSWER

6.7

EDDIE SAYS

(1 - x/100)^{10} = 0.5

Work out the 10th root of 0.5 = 0.933.

x/100 = 1 - 0.933 = 0.066967...

x = 6.6967

Work out the 10th root of 0.5 = 0.933.

x/100 = 1 - 0.933 = 0.066967...

x = 6.6967

- ANSWERS

- Question 23

You may use a calculator for this question.

Look at the function **f(t) = 3 ^{t}**.

By what percentage does it change in the interval between t = 5 and t = 7?

*(Just write the number.)*

CORRECT ANSWER

800

EDDIE SAYS

3^{5} = 243

3^{7} = 2187

Actual increase = 2187 - 243 = 1944

% increase = 1944 ÷ 243 × 100 = 800

3

Actual increase = 2187 - 243 = 1944

% increase = 1944 ÷ 243 × 100 = 800

- ANSWERS

- Question 24

Look at this graph.

What is the equation of the blue line?

CORRECT ANSWER

y = 5/x + 3

EDDIE SAYS

This is the exponential curve y = 5/x shifted up 3 units.

Test out different values, e.g. when x = 5, y = 1 + 3 = 4.

Test out different values, e.g. when x = 5, y = 1 + 3 = 4.

- ANSWERS

- Question 25

Calculate the **total surface area** (in cm^{2}) of a cone with **radius R equal to 3 cm** and **height H equal to 7 cm**.

Select the correct answer.

CORRECT ANSWER

(3√58 + 9)π

EDDIE SAYS

Slant length = √(3² + 7²) = √58

Curved Surface Area = π × 3 × √58

Base Area = π × 3² = 9π

Total Area = 3√58π + 9π = (3√58 + 9)π

Curved Surface Area = π × 3 × √58

Base Area = π × 3² = 9π

Total Area = 3√58π + 9π = (3√58 + 9)π

- ANSWERS

- Question 26

You may use a calculator for this question.

The diagram shows a **4 cm × 5 cm × 10 cm cuboid***.*

Calculate the **perimeter **of triangle **ACG**.

*(Just write the number to 3 sig. figs.)*

CORRECT ANSWER

27.6

EDDIE SAYS

Use Pythagoras' Theorem to get:

AC² = 4² + 10² = 16 + 100 = 116

AC = √116

AG² = 4² + 5² + 10² = 16 + 25 + 100 = 141

AG = √141

Perimeter = √116 + √141 + 5 = 27.64467...

AC² = 4² + 10² = 16 + 100 = 116

AC = √116

AG² = 4² + 5² + 10² = 16 + 25 + 100 = 141

AG = √141

Perimeter = √116 + √141 + 5 = 27.64467...

- ANSWERS

- Question 27

You may use a calculator for this question.

The diagram below shows a Christmas tree with base at A and top at T.

The distance **AC **is 28 metres.

The angle of elevation of T from C is 35°.

The angle of elevation of T from B is 12°.

Calculate the distance, **BC **in metres.

*(Just give your answer as a number to 1 decimal place.*)

CORRECT ANSWER

64.2

EDDIE SAYS

tan35° = AT/AC

AT = 28tan35° = 19.6058...

AB = AT/tan12° = 19.6058 ÷ tan12° = 92.238...

BC = AB - AC = 92.238 - 28 = 64.238...

AT = 28tan35° = 19.6058...

AB = AT/tan12° = 19.6058 ÷ tan12° = 92.238...

BC = AB - AC = 92.238 - 28 = 64.238...

- ANSWERS

- Question 28

You may use a calculator for this question.

In triangle PQR, which is not drawn to scale,

PQ = 12 cm, PR = 22 cm, and ∠QPR = 35º.

Calculate the length **QR **in cm** **to 3 sig. figs.

*(Just write the number.)*

CORRECT ANSWER

14.0

EDDIE SAYS

Use the cosine rule to get QR² = 12² + 22² - 2 × 12 × 22 × cos 35°.

- ANSWERS

- Question 29

You may use a calculator for this question.

In triangle PQR, which is not drawn to scale,

PQ = 8 cm, PR = 11 cm and ∠PQR = 111°.

Use the sine rule to find ∠QPR to 1 dp.

*(Just write the number.)*

CORRECT ANSWER

26.2

EDDIE SAYS

11 | = | 8 |

sin 111° | sin ∠QRP |

∠QPR = 180° - 111° - ∠QRP

- ANSWERS

- Question 30

In triangle PQR, which is not drawn to scale,

PQ = 6 cm, PR = 12 cm and ∠QRP = 30°.

**Without** the use of a calculator, find **∠QPR.**

*(Just write the number.)*

CORRECT ANSWER

60

EDDIE SAYS

6 | = | 12 |

sin 30° | sin ∠PQR |

You should know that sin 30° = 0.5.

So sin ∠PQR = 1, which means that ∠PQR = 90°.

This is a right-angled triangle.

- ANSWERS

- Question 31

In triangle ABC above,

**a** = 6.2 cm

**b** = 7 cm

**∠BCA** = 125º

Calculate the triangle's area in cm^{2} to 3 sig. figs.

*(Just write the number.)*

CORRECT ANSWER

17.8

EDDIE SAYS

Area = ½ × 6.2 × 7 × sin125°

- ANSWERS

- Question 32

The diagram shows a circle, centre C and three points A, B and P on the circumference.

Calculate the angle ∠**ABC**.

*(Just write the number.)*

CORRECT ANSWER

53

EDDIE SAYS

∠ACB = 2∠APB so a = 74°

Triangle ACB is isosceles.

∠ABC = (180° - 74°) ÷ 2 = 106° ÷ 2 = 53°

Triangle ACB is isosceles.

∠ABC = (180° - 74°) ÷ 2 = 106° ÷ 2 = 53°

- ANSWERS

- Question 33

A money bag contains 22 × £1 coins, 21 × 50p coins, 6 × 10p coins and 5 × 2p coins as well as a number of 20p coins.

The **probability **that a 20p coin is selected at random is **1/4**.

Calculate the number of **20p coins** in the bag.

CORRECT ANSWER

18

EDDIE SAYS

Let n be the number of 20p coins.

n/(22 + 21 + 6 + 5 + n) = 1/4

n/(54 + n) = 1/4

Multiply both sides by 4 and by (54 + n) to get:

4n = (54 + n)

3n = 54

n = 18

n/(22 + 21 + 6 + 5 + n) = 1/4

n/(54 + n) = 1/4

Multiply both sides by 4 and by (54 + n) to get:

4n = (54 + n)

3n = 54

n = 18

- ANSWERS

- Question 34

Two fair tetrahedral dice are thrown. Each is numbered from 1 to 4.

What is the **probability **that **at least one die **will show** a 4**?

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

CORRECT ANSWER

7/16

EDDIE SAYS

List out all 16 possibilities.

7 of these have at least one 4.

7 of these have at least one 4.

- ANSWERS

- Question 35

There are 16 red balls and 4 white balls in a bag.

Fatima randomly chooses 2 balls, removing each in turn from the bag.

What is the probability of choosing one of each colour?

*(Give your answer as a reduced fraction in the form a/b.)*

CORRECT ANSWER

32/95

EDDIE SAYS

16/20 × 4/19 + 4/20 × 16/19

- ANSWERS

- Question 36

A number between 380 and 440 is chosen at random.

What is the probability that it is **between 385 and 425**?

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

CORRECT ANSWER

2/3

EDDIE SAYS

440 - 380 = 60

425 - 385 = 40

Probability = 40/60 = 2/3

425 - 385 = 40

Probability = 40/60 = 2/3

- ANSWERS

- Question 37

CORRECT ANSWER

## Column A | ## Column B |

symmetrical | B |

positively skewed | A |

negatively skewed | C |

EDDIE SAYS

In A, the median is nearer to the lower quartile, so it is positively skewed.

In B, the median is in the middle, so it is symmetrical.

In C, the median is nearer to the upper quartile, so it is negatively skewed.

In B, the median is in the middle, so it is symmetrical.

In C, the median is nearer to the upper quartile, so it is negatively skewed.

- ANSWERS

- Question 38

Find the **interquartile range **of the following set of data:

12 4 17 12 10 18 2 31 13

CORRECT ANSWER

10.5

EDDIE SAYS

First place the numbers in order to get:

2, 4, 10, 12, 12, 13, 17, 18, 31

Upper Quartile is the Median of 13, 17, 18, 31, which is 17.5.

Lower Quartile is the Median of 2, 4, 10, 12, which is 7.

Interquartile Range is 17.5 - 7 = 10.5.

2, 4, 10, 12, 12, 13, 17, 18, 31

Upper Quartile is the Median of 13, 17, 18, 31, which is 17.5.

Lower Quartile is the Median of 2, 4, 10, 12, which is 7.

Interquartile Range is 17.5 - 7 = 10.5.

- ANSWERS

- Question 39

You may use a calculator for this question.

Over the course of five days, there were the following number of empty seats at a theatre.

12 seats, 14 seats, 10 seats, 20 seats, 24 seats

Calculate the** standard deviation** in the number of empty seats to 3 sig. figs.

CORRECT ANSWER

5.22

EDDIE SAYS

Step 1

Mean = (12 + 14 + 10 + 20 + 24) ÷ 5 = 80 ÷ 5 = 16

Step 2

(12 - 16)^{2} = (-4)^{2} = 16

(14 - 16)^{2} = (-2)^{2} = 4

(10 - 16)^{2} = (-6)^{2} = 36

(20 - 16)^{2} = (4)^{2} = 16

(24 - 16)^{2} = (8)^{2} = 64

Step 3

Mean of 16, 4, 36, 16 and 64 = (16 + 4 + 36 + 16 + 64) ÷ 5 = 136 ÷ 5 = 27.2

Variance = 27.2

Standard Deviation = √27.2 =

- ANSWERS

- Question 40

You may use a calculator for this question.

The following histogram shows the distribution of the lengths of adverts on one television channel during a particular day.

Work out how many TV adverts have been surveyed in **total**.

CORRECT ANSWER

113

EDDIE SAYS

We add up all the frequencies to get:

(0.8 × 10) + (2.4 × 5) + (2.8 × 15) + (3.3 × 10) + (1.2 × 15)

= 8 + 12 + 42 + 33 + 18 = 113

(0.8 × 10) + (2.4 × 5) + (2.8 × 15) + (3.3 × 10) + (1.2 × 15)

= 8 + 12 + 42 + 33 + 18 = 113

---- OR ----

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