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GCSE Foundation

Mathematics

Half - Term

Revision

S outham College

Mathematics Department

Name: ..............................................

PRIME FACTORISATION

1. (a) Express the following numbers as products of their prime factors.

(i) 60 (ii) 150

............................... ...............................

(4 marks)

(b) Find the highest common factor (HCF) of 60 and 150

...............................

(1 mark)

(c) Find the lowest common multiple (LCM) of 60 and 150

...............................

(1 mark)

1. Express 36 as a product of its prime factors.

...............................

(2 marks)

2. Express 42 as a product of its prime factors.

...............................

(2 marks)

3. Write 24 as a product of its prime factors.

...............................

(2 marks)

4. Write 550 as a product of its prime factors.

...............................

(2 marks)

5. (a) Write 48 as a product of its prime factors.

...............................

(2 marks)

(b) Find the Highest Common Factor (HCF) of 48 and 56.

...............................

(4 marks)

6. (a) Write 60 as a product of its prime factors.

...............................

(2 marks)

(b) Find the Lowest Common Multiple (LCM) of 60 and 75.

...............................

(4 marks)

ERROR INTERVALS

1. The weight, 𝑤, of a suitcase is 14 kg, correct to the nearest kilogram.

Write down an inequality to show the error interval for 𝑤.

............................... ≤ 𝑤 < ...............................

(2 marks)

2. Katy drove for 238 miles, correct to the nearest mile.

(a) Write down an error interval for the number of miles (𝑚) driven.

............................... ≤ 𝑚 < ...............................

(2 marks)

Katy used 27.3 litres of petrol, to the nearest tenth of a litre.

(b) Write down an error interval for the number of litres (𝑙) used.

..............................................................

(2 marks)

3. The number, 𝑧, rounded to two significant figures, is 5800.

Write down the error interval for 𝑧.

..............................................................

(2 marks)

1. The length, 𝑙, of a piece of wood is 123 mm, correct to the nearest mm.

Write down an inequality to show the error interval for 𝑙.

............................... ≤ 𝑙 < ...............................

(2 marks)

2. A number, 𝑛, is rounded to 2 decimal places. The result is 4.76

Using inequalities, write down the error interval for 𝑛.

..............................................................

(2 marks)

3. The number 𝑥, rounded to one decimal place, is 5.7

(a) Write down an error interval for 𝑥.

..............................................................

(2 marks)

The number 𝑦, rounded to two decimal places, is 7.36

(b) Write down the error interval for 𝑦.

..............................................................

(2 marks)

The number 𝑧, rounded to two significant figures, is 8300

(c) Write down the error interval for 𝑧.

..............................................................

(2 marks)

CHALLENGE

4. The perimeter of a square is 48 cm to the nearest centimetre.

Work out the error interval of the length, 𝑙, of a side of this square.

..............................................................

(2 marks)

PERCANTAGES

Percentage increase A ticket to a theme park costs £35 plus 20% VAT.

Work out the total cost of the ticket.

...............................

(2 marks)

Percentage decrease A set of tyres normally costs £500.

In a sale there is a 30% discount.

Work out the sale price if the set of tyres.

...............................

(2 marks)

Reverse percentages The normal price if a television is reduced by 30% in a sale.

The sale price if the television is £350.

Work out the normal price if the television.

...............................

(3 marks)

1. Glen buys four tickets for a concert.

Each ticket costs £54.

Glen also has to pay a booking fee.

The booking fee is 5% of the total price of the tickets.

Work out the total amount Glen has to pay.

...............................

(2 marks)

2. Ria is going to buy a caravan.

The total cost of the caravan is £7000 plus VAT at 20%.

Ria pays a deposit of £3000.

She pays the rest of the total cost in 6 equal monthly payments.

Work out the amount of each monthly payment.

...............................

(4 marks)

3. Two shops, Mega Bathrooms and Bathroom Mart, each have a sale.

Sally wants to buy some bathroom units.

The units have a normal price of £1500.

Sally wants to buy the units as cheaply as possible.

Which shop should she buy the units from?

You must show all your working.

(4 marks)

4. In a sale normal prices are reduced by 20%.

A washing machine has a sale price of £464.

By how much is the normal price of the washing machine reduced?

...............................

(3 marks)

5. Kristen buys a laptop.

She gets a discount of 30% off the normal price.

Kristen pays £480 for the laptop.

Work out the discount.

...............................

(3 marks)

SIMPLE AND COMPOUND INTEREST

Simple Interest (a) Harry invests £5000 for 3 years.

He gets simple interest of 4% per year.

Work out the total interest Harry gets.

...............................

(2 marks)

(b) Jane invests £300 at a simple interest rate of 4.5% per year.

At the end of each year Jane gives the interest to charity.

Work out the least number of years it will take for the total amount given to

the charity to be greater than £50.

...............................

(2 marks)

Compound interest (a) Charlie invests £1200 at 3.5% per annum compound interest.

Work out the value of Charlie’s investment after 3 years.

...............................

(2 marks)

(b) £3000 is invested for 3 years at 3.8% per annum compound interest.

Work out the total interest earnt over 2 years.

...............................

(2 marks)

Depreciation Martin bought a computer for £1200.

At the end of each year the value of the computer is depreciated by 20%.

Work out the value of the computer after 4 years.

...............................

(2 marks)

Jack has £15 000 in a savings account for 3 years.

He finds information about two savings accounts.

Jack wants to have as much money as possible in his savings account at the end of the 3

years.

Which of these two savings account should he choose?

(4 marks)

1. Tom invested £1000 for 2 years with Bettabank.

He got 2.5% simple interest each year.

Jay invested £1000 for 2 years with Moneyplus.

She got a total of £60 interest for the 2 years.

Show that Jay got the better investment.

...............................

(2 marks)

2. £500 is invested at a simple interest rate of 3% per year.

After how many years is the total interest £60?

...............................

(2 marks)

3. Franz invests £2500 for 2 years at 3½% per annum compound interest.

Work out the value of his investment at the end of 3 years.

...............................

(2 marks)

4. £4000 is invested for 2 years at 5% per annum compound interest.

Work out the total interest earned over the 2 years.

...............................

(2 marks)

4. The value of a caravan when new is £15 000.

Its value depreciates 8% each year.

Work out value of the car after 3 years.

...............................

(2 marks)

5. The value of a car depreciates by 25% each year.

At the end of 2013 the value of the car was £4800.

Work out the value of the car at the end of 2015.

...............................

(2 marks)

CHALLENGE

6. Mrs Bell buys a house for £60 000. In the first year, the value of the house increases by 16%.

In the second year, the value of the house decreases by 4% of its value at the beginning of

that year.

Work out the value of the house after the 2 years.

...............................

(3 marks)

CHANGING THE SUBJECT OF A FORMULA

1. Make 𝑥 the subject of the formula 𝑦 = 5𝑥 − 3

...............................

(2 marks)

2. Make ℎ the subject of the formula 𝑥 = 5ℎ + 8

...............................

(2 marks)

2. Make 𝑔 the subject of the formula

𝑡 =𝑔 + ℎ

10

...............................

(2 marks)

3. Make 𝑝 the subject of this formula.

𝑞 =𝑝

𝑟+ 𝑡

...............................

(2 marks)

1. Make 𝑣 the subject of the formula 𝑇 = 4𝑣 + 3

...............................

(2 marks)

2. Make ℎ the subject of the formula 𝐺 = 3ℎ − 5

...............................

(2 marks)

3. Make 𝑎 the subject of the formula

𝑓 =𝑎 + 1

2

...............................

(2 marks)

4. Make 𝑡 the subject of the formula

𝑦 =𝑡

3− 2𝑎

...............................

(2 marks)

SIMULTANIOUSE EQUATIONS

1. Solve the simultaneous equations 3𝑥 + 𝑦 = −4 3𝑥 − 4𝑦 = 6

𝑥 =............................... 𝑦 =...............................

(3 marks)

2. Solve the simultaneous equations 4𝑥 + 𝑦 = 25 𝑥 − 3𝑦 = 16

𝑥 =............................... 𝑦 =...............................

(3 marks)

3. Make ℎ the subject of the formula 3𝑥 − 2𝑦 = −5 2𝑥 − 4𝑦 = 2

𝑥 =............................... 𝑦 =...............................

(3 marks)

1. Solve the simultaneous equations 𝑥 + 𝑦 = 5

𝑥 − 3𝑦 = 1

𝑥 =............................... 𝑦 =...............................

(3 marks)

2. Solve the simultaneous equations 4𝑥 + 𝑦 = 10 𝑥 − 5𝑦 = 13

𝑥 =............................... 𝑦 =...............................

(3 marks)

3. Solve the simultaneous equations 2𝑥 + 3𝑦 = 10 4𝑥 − 𝑦 = −1

𝑥 =............................... 𝑦 =...............................

(3 marks)

4. Solve the simultaneous equations 𝑥 + 3𝑦 = 12 5𝑥 − 𝑦 = 4

𝑥 =............................... 𝑦 =...............................

(3 marks)

5. Solve the simultaneous equations 2𝑥 + 5𝑦 = 16 5𝑥 − 2𝑦 = 11

𝑥 =............................... 𝑦 =...............................

(3 marks)

6. Solve the simultaneous equations 3𝑥 + 2𝑦 = 11 2𝑥 − 5𝑦 = 20

𝑥 =............................... 𝑦 =...............................

(3 marks)

AVERAGES FROM TABLES 1

The table shows information about the number of goals scored by a football team in

their last 20 matches.

Number of Goals Frequency

0 8

1 6

2 3

3 1

4 2

(a) Write down the modal number of goals.

(1 mark)

(b) Find the median number of goals.

(1 mark)

(c) Work out the range.

(2 marks)

(d) Work out the mean number of goals.

(3 marks)

Sarah had 10 boxes of sweets. She counted the number of sweets in each box.

The table gives information about her results.

Number of sweets Frequency

15 2

16 3

17 4

18 1

(a) Write down the modal number of sweats in a box.

(1 mark)

(b) Find the median number of sweets in a box.

(1 mark)

(c) Work out the range

(2 marks)

(d) Work out the mean.

(3 marks)

AVERAGES FROM TABLES 2

The table shows information about the numbers of minutes 40 children take to get to

school.

Number of minutes (𝒎) Frequency Midpoint

0 < 𝑚 ≤ 10 13 5

10 < 𝑚 ≤ 20 16

20 < 𝑚 ≤ 30 8

30 < 𝑚 ≤ 40 3

(a) Write down the modal class interval.

(1 mark)

(b) Work out an estimate for the mean number of minutes.

(4 marks)

1. The table shows information about the weight, in kilograms, of some children

Weight (𝒘 kg) Frequency

60 < 𝑤 ≤ 65 6

65 < 𝑤 ≤ 70 7

70 < 𝑤 ≤ 75 10

75 < 𝑤 ≤ 80 2


(1 mark)

(b) Work out an estimate for the mean weight.

(4 marks)

2. The table shows information about the total amounts, in pounds, some people spent in a

supermarket.

Total amount (£𝑻) Frequency

0 < 𝑇 ≤ 20 7

20 < 𝑇 ≤ 40 10

40 < 𝑇 ≤ 60 13

60 < 𝑇 ≤ 80 5

80 < 𝑇 ≤ 100 5


(1 mark)

(b) Work out an estimate for the mean amount spent.

(4 marks)

FREQUENCY POLYGONS

Helen went on 35 flights in a hot air balloon last year.

The table gives some information about the length of time, t minutes, of each flight.

Length of time (𝒕 minutes) Frequency

0 < 𝑡 ≤ 10 6

10 < 𝑡 ≤ 20 9

20 < 𝑡 ≤ 30 8

30 < 𝑡 ≤ 40 7

40 < 𝑡 ≤ 50 5

On the grid below, draw a frequency polygon for this information.

(1 marks)

2. The grouped frequency table gives information about the heights of 30 students.

Height (h cm) Frequency

130 < h ≤ 140 1

140 < h ≤ 150 7

150 < h ≤ 160 8

160 < h ≤ 170 10

170 < h ≤ 180 4

(2) Write down the modal class interval.

…............................

(1 mark)

This incorrect frequency polygon has been drawn for the information in the table.

(a) Write down two things wrong with this incorrect frequency polygon.

1. ……………………………………………………………………………………………………………………………………………………………………………………..

2. …………………………………………………………………………………………………………………………………………………………………………………….

(2 marks)

2. The table gives information about the temperature, T °C, at noon in a town for 50 days.

Temperature (𝑻°C) Frequency

8 < 𝑇 ≤ 12 6

12 < 𝑇 ≤ 16 8

16 < 𝑇 ≤ 20 13

20 < 𝑇 ≤ 24 21

24 < 𝑇 ≤ 28 2

Draw a frequency polygon for the information in the table.

(1 marks)

3. The frequency table gives information about the heights of some people.

Height (h cm) Frequency

160 < h ≤ 165 2

165 < h ≤ 170 5

170 < h ≤ 175 10

175 < h ≤ 180 21

180 < h ≤ 185 16

185 < h ≤ 190 4

Draw a frequency polygon for this information.

(2 marks)

PYTHAGORAS ’ THEOREM

Pythagoras’ theorem is a really useful rule. You can use it to find the length of a missing side

in a right-angled triangle.

1. Work out the length of the missing side.

Give your answer correct to 1 decimal place.

…………………………………………………….

2. Work out the length of the missing side.


…………………………………………………….

6.5 cm

8.3 cm

4 cm

x cm

11 cm

x cm

1. Work out the length AB.

Give your answer correct to 3 significant figures.

…………………………………………………….

(3 marks)

2. Work out the length of LM.


…………………………………………………….

(3 marks)

14 cm

12 cm

A

B

C

N

M

L

9 cm

6 cm

3.

ABC is a right-angled triangle.

AC = 25 cm

BC = 7 cm

(a) Work out the length AB.

…………………………………………………….

(3 marks)

(b) Work out the area of the triangle.

…………………………………………………….

(2 marks)

25 cm

7 cm

B

C

A

PROBLEM SOLVING WITH PYTHAGORAS

1. ABCD is a trapezium.

A square has the same perimeter as this trapezium.

Work out the area of the square.


…………………………………………………….

(5 marks)

2.

ABC is a right-angled triangle.

A, B and C are points on the circumference of a circle centre O.

AB = 5 cm

BC = 8 cm

AOC is a diameter of the circle.

Calculate the circumference of the circle.


…………………………………………………….

(4 marks)

1. Here is part of a field.

This part of the field is in the shape of a trapezium.

A farmer wants to put a fence all the way around the edge of this part of the field.

The farmer has 50m of fence.

Does he have enough fence?

You must show all your working.

(5 marks)

2. A frame is made from wire.

The frame is in the shape of a rectangle, 30 cm by 20 cm.

The two diagonals of the rectangle are also made from wire.

Calculate the total length of wire needed to make the frame and the diagonals.


........................................................... cm

(4 marks)

3. ABCDE is a pentagon.

Work out the area of ABCDE.

........................................................... cm2

(4 marks)

4. Here is a triangular prism.

Work out the volume of the prism.


........................................................... cm3

(5 marks)

5. The diagram shows a square ABCD inside a circle.

The points A, B, C and D lie on the circle.

The radius of the circle is 6 cm.

Work out the total area of the shaded regions.


........................................................... cm2

(4 marks)

SOHCAHTOA

Finding a side

1. Calculate the value of 𝑥. Give your answer correct to 3 significant figures.

........................................ cm

2. Work out the length of CB. Give your answer correct to 3 significant figures.

........................................ cm

3. Work out the angle marked 𝑥.


........................................°

7.3 cm

52 °

A

C B

8.7 cm

𝑥

4.5 cm

4. Work out the value of 𝑦.


........................................°

Grade 4

1. Work out the length of BC.


........................................ cm

(3 marks)

𝑦

21.4 cm

15.7 cm

8.2 cm

2. Calculate the length of YZ.

Give your answer correct to 3 significant figures

........................................ cm

(3 marks)

3. Calculate the value of 𝑥.

Give your answer correct to 3. Significant figures

........................................°

(3 marks)

4. Calculate the value of 𝑥.

Give your answer correct to 3. Significant figures

........................................°

(3 marks)

Grade 5

5. The diagram shows a quadrilateral ABCD.

Calculate the length of CD.

Give your answer correct to 3 significant figures

........................................ cm

(5 marks)

6. ABCD is a trapezium.

Work out the size of angle CDA.

Give your answer to 1 decimal place.

........................................ °

(5 marks)

southam - wordpress.com...2019/05/02 · 1.glen buys four tickets for a concert. each ticket costs...

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