**Formula Sheet**

Foundation Tier

**Area of trapezium** = ½ (a + b) h

**Volume of prism** = area of cross-section x length

This worksheet contains a sample of practice questions based on the 2013 GCSE Foundation Level syllabus. Calculators may be used.

**Key stage:** KS 4

**Curriculum topic:** GCSE Practice Papers

**Curriculum subtopic:** Selection of Topics for Calculator Practice

**Difficulty level:**

**Formula Sheet**

Foundation Tier

**Area of trapezium** = ½ (a + b) h

**Volume of prism** = area of cross-section x length

Place these numbers against an appropriate description.

8 9 10 36 37 40

## Column A | ## Column B |

a square number | 8 |

a cube number | 37 |

a prime number | 9 |

a factor of 20 | 36 |

a multiple of 8 | 40 |

a multiple of 6 | 10 |

The heights in centimetres of ten seedlings were measured as follows.

Work out the range of these heights.

*(Just write the number)*

1.28, 1.47, 1.89, 1.8, 2.09, 2.5, 1.7, 1.18, 0.16, 2.21

Find the value of the following when a = -3

4a^{2} - 3a

Kate goes shopping with two £20 notes.

She buys a coffee for £3.20 and lunch for £8.55.

Then she buys a jacket in the sale.

Jacket Sale

Normal Price £28

10% off all prices in the SALE

How much money does she have left?

The perimeter of a square is 62 cm.

Calculate its area in cm^{2} to 3 sig. figs.

*(Just write the number)*

Match the following measurements.

## Column A | ## Column B |

45 cm | 45 cm |

45 mm | 4.5 m |

450 cm | 0.45 cm |

0.45 m | 4.5 cm |

0.045 m | 4.5 cm |

4.5 mm | 450 mm |

Increase 140 by 25%.

What is the mathematical name of this shape:

The formula for the cost of buying a car on credit is:

Cost of buying car = 36 x Monthly payment + Deposit

Find the monthly payment when the cost of buying the car is £12000 and the deposit is £499.80.

Jack drove 250 miles, measured correct to the nearest 10 miles.

What is the least distance Jack could have driven?

*(Just write the number)*

Work out:

4^{2} + 4^{3} |

4^{4} |

Look at this diagram, which is to have two lines of reflective symmetry.

Which squares should be yellow?

A

B

C

D

E

F

G

H

I

J

K

L

M

Look at this diagram, which shows a rectangle ABCD, which is to be rotated through 90º anticlockwise about the point D to give the rectangle A'B'C'D'.

Write down the coordinates of B'.

Work out the size of the missing angle shown below.

*(Just write the number)*

**(Diagram not drawn accurately)**

Solve:

5x + 8 = 45

*(Just write the value of x)*

A, B, C, D and E are five points on a circle centred at O.

Match the letters to the parts of the circle.

## Column A | ## Column B |

AB | radius |

OC | diameter |

DE | arc |

Curved part DE | chord |

The diagram shows an irregular pentagon.

Work out the perimeter of the rectangle in cm when x = 6.

*(Just write the number)*

A piece of wood is 240 cm long.

It is cut into three pieces in the ratio 3 : 4 : 5.

Work out the length of the shortest piece in cm.

*(Just write the number)*

Work out the following to 3 decimal places:

√596 |

6 + 1.98^{2} |

A circle of diameter 14 cm is shown in the diagram.

Work out the area of the circle in cm^{2} to 3 sig. figs.

The pie chart shown below shows the results of a survey about favourite crisp flavours.

168 children voted.

Work out how many children voted for Cheese and Onion flavoured crisps.

Use Pythagoras' Theorem to calculate the value of x in this right-angled triangle.

Give your answer to 1 decimal place.

*(This is not drawn accurately)*

Look at this timetable.

At what time does the 1510 London Euston train get to Coventry?

*(Just write four digits)*

Simplify:

y^{2} + 2y^{2} + 3y^{2}

5y^{2}

6y^{2}

5y^{6}

6y^{6}

3y^{6}

The diagram shows the code of a padlock.

The code is a letter followed by a single digit number (e.g. B3).

What is the probability that I will not be able to open the padlock when I select a code at random?

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

- ANSWERS

- Question 1

Place these numbers against an appropriate description.

8 9 10 36 37 40

CORRECT ANSWER

## Column A | ## Column B |

a square number | 9 |

a cube number | 8 |

a prime number | 37 |

a factor of 20 | 10 |

a multiple of 8 | 40 |

a multiple of 6 | 36 |

EDDIE SAYS

36 is the only multiple of 6 in the list, so the square number is 9.

- ANSWERS

- Question 2

The heights in centimetres of ten seedlings were measured as follows.

Work out the range of these heights.

*(Just write the number)*

1.28, 1.47, 1.89, 1.8, 2.09, 2.5, 1.7, 1.18, 0.16, 2.21

CORRECT ANSWER

2.34

EDDIE SAYS

Tallest - shortest = 2.5 - 0.16 = 2.34

- ANSWERS

- Question 3

Find the value of the following when a = -3

4a^{2} - 3a

CORRECT ANSWER

45

EDDIE SAYS

4 × (-3) × (-3) - 3 × (-3) = 36 - -9 = 36 + 9 = 45

- ANSWERS

- Question 4

Kate goes shopping with two £20 notes.

She buys a coffee for £3.20 and lunch for £8.55.

Then she buys a jacket in the sale.

Jacket Sale

Normal Price £28

10% off all prices in the SALE

How much money does she have left?

CORRECT ANSWER

£ 3.05

£3.05

£3.05

EDDIE SAYS

She starts with £40.

After coffee and lunch, she has £40 - 3.20 - 8.55 = £28.25

Jacket costs £28 - 2.80 = £25.20

She has £28.25 - 25.20 = £3.05 left.

After coffee and lunch, she has £40 - 3.20 - 8.55 = £28.25

Jacket costs £28 - 2.80 = £25.20

She has £28.25 - 25.20 = £3.05 left.

- ANSWERS

- Question 5

The perimeter of a square is 62 cm.

Calculate its area in cm^{2} to 3 sig. figs.

*(Just write the number)*

CORRECT ANSWER

240

EDDIE SAYS

Side length = 62 ÷ 4 = 15.5 cm

Area = 15.5 × 15.5 = 240.25 cm²

Area = 15.5 × 15.5 = 240.25 cm²

- ANSWERS

- Question 6

Match the following measurements.

CORRECT ANSWER

## Column A | ## Column B |

45 cm | 450 mm |

45 mm | 4.5 cm |

450 cm | 4.5 m |

0.45 m | 45 cm |

0.045 m | 4.5 cm |

4.5 mm | 0.45 cm |

EDDIE SAYS

100 cm = 1 m

10 mm = 1 cm

10 mm = 1 cm

- ANSWERS

- Question 7

Increase 140 by 25%.

CORRECT ANSWER

175

EDDIE SAYS

¼ of 140 = 35

140 + 35 = 175

140 + 35 = 175

- ANSWERS

- Question 8

What is the mathematical name of this shape:

CORRECT ANSWER

cone

- ANSWERS

- Question 9

The formula for the cost of buying a car on credit is:

Cost of buying car = 36 x Monthly payment + Deposit

Find the monthly payment when the cost of buying the car is £12000 and the deposit is £499.80.

CORRECT ANSWER

£ 319.45

£319.45

£319.45

EDDIE SAYS

On the calculator, we type 12000 - 499.80 = ÷ 36 =

- ANSWERS

- Question 10

Jack drove 250 miles, measured correct to the nearest 10 miles.

What is the least distance Jack could have driven?

*(Just write the number)*

CORRECT ANSWER

245

EDDIE SAYS

Anything less than 245 would have been rounded to less than 250, e.g. 244 rounds down to 240.

- ANSWERS

- Question 11

Work out:

4^{2} + 4^{3} |

4^{4} |

CORRECT ANSWER

0.3125

EDDIE SAYS

4^{2} + 4^{3} = 16 + 64 = 80

80 ÷ 4 to the power 4 = 0.3125

80 ÷ 4 to the power 4 = 0.3125

- ANSWERS

- Question 12

Look at this diagram, which is to have two lines of reflective symmetry.

Which squares should be yellow?

CORRECT ANSWER

A

C

K

C

K

EDDIE SAYS

Reflect the yellow square in both lines of symmetry.

- ANSWERS

- Question 13

Look at this diagram, which shows a rectangle ABCD, which is to be rotated through 90º anticlockwise about the point D to give the rectangle A'B'C'D'.

Write down the coordinates of B'.

CORRECT ANSWER

(10,8)

(10, 8)

(10, 8)

EDDIE SAYS

A will be at (10, 10) and B will be 2 units below A.

- ANSWERS

- Question 14

Work out the size of the missing angle shown below.

*(Just write the number)*

**(Diagram not drawn accurately)**

CORRECT ANSWER

137

EDDIE SAYS

360° - 90° - 104° - 29° = 137°

- ANSWERS

- Question 15

Solve:

5x + 8 = 45

*(Just write the value of x)*

CORRECT ANSWER

7.4

EDDIE SAYS

Subtract 8 from both sides to get:

5x = 37

Divide both sides by 5 to get:

x = 7.4

5x = 37

Divide both sides by 5 to get:

x = 7.4

- ANSWERS

- Question 16

A, B, C, D and E are five points on a circle centred at O.

Match the letters to the parts of the circle.

CORRECT ANSWER

## Column A | ## Column B |

AB | diameter |

OC | radius |

DE | chord |

Curved part DE | arc |

- ANSWERS

- Question 17

The diagram shows an irregular pentagon.

Work out the perimeter of the rectangle in cm when x = 6.

*(Just write the number)*

CORRECT ANSWER

144

EDDIE SAYS

Perimeter = 7x + 2x + 5x + 4x + 6x = 24x

When x = 6, 24x = 144 cm

When x = 6, 24x = 144 cm

- ANSWERS

- Question 18

A piece of wood is 240 cm long.

It is cut into three pieces in the ratio 3 : 4 : 5.

Work out the length of the shortest piece in cm.

*(Just write the number)*

CORRECT ANSWER

60

EDDIE SAYS

3 + 4 + 5 = 12 shares

12 shares ≡ 240cm, so 1 share ≡ 240 ÷ 12 = 20 cm

3 shares ≡ 3 × 20 = 60 cm

12 shares ≡ 240cm, so 1 share ≡ 240 ÷ 12 = 20 cm

3 shares ≡ 3 × 20 = 60 cm

- ANSWERS

- Question 19

Work out the following to 3 decimal places:

√596 |

6 + 1.98^{2} |

CORRECT ANSWER

2.461

EDDIE SAYS

On the calculator, type:

√596 ÷ (6 + 1.98 squared) = 2.460899886...

√596 ÷ (6 + 1.98 squared) = 2.460899886...

- ANSWERS

- Question 20

A circle of diameter 14 cm is shown in the diagram.

Work out the area of the circle in cm^{2} to 3 sig. figs.

CORRECT ANSWER

154

EDDIE SAYS

Radius is half the diameter = 7 cm

Area = πr² = 49 × π = 153.9cm²

Area = πr² = 49 × π = 153.9cm²

- ANSWERS

- Question 21

The pie chart shown below shows the results of a survey about favourite crisp flavours.

168 children voted.

Work out how many children voted for Cheese and Onion flavoured crisps.

CORRECT ANSWER

70

EDDIE SAYS

360° ≡ 168 children

1° ≡ 168 ÷ 360 children

150° ≡ 168 ÷ 360 × 150 children

1° ≡ 168 ÷ 360 children

150° ≡ 168 ÷ 360 × 150 children

- ANSWERS

- Question 22

Use Pythagoras' Theorem to calculate the value of x in this right-angled triangle.

Give your answer to 1 decimal place.

*(This is not drawn accurately)*

CORRECT ANSWER

4.9

EDDIE SAYS

x² + 5² = 7²

x² + 25 = 49

x² = 49 - 25 = 24

x = √24 = 4.898979...

x² + 25 = 49

x² = 49 - 25 = 24

x = √24 = 4.898979...

- ANSWERS

- Question 23

Look at this timetable.

At what time does the 1510 London Euston train get to Coventry?

*(Just write four digits)*

CORRECT ANSWER

1614

EDDIE SAYS

Use the second column of times.

- ANSWERS

- Question 24

Simplify:

y^{2} + 2y^{2} + 3y^{2}

CORRECT ANSWER

6y^{2}

EDDIE SAYS

one y² and two more y² and three more y² makes 6y² in total

i.e. collect like terms.

i.e. collect like terms.

- ANSWERS

- Question 25

The diagram shows the code of a padlock.

The code is a letter followed by a single digit number (e.g. B3).

What is the probability that I will not be able to open the padlock when I select a code at random?

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

CORRECT ANSWER

7/8

EDDIE SAYS

There are 8 combinations:

A1, A2, A3, A4

B1, B2, B3, B4

Only one of these will be correct, and so 7 out of 8 are incorrect.

A1, A2, A3, A4

B1, B2, B3, B4

Only one of these will be correct, and so 7 out of 8 are incorrect.

---- OR ----

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