Maths GCSE Higher Tier Unit 2

Revision Booklet

Name:

This booklet contains past paper questions by topic

1. Integers and Decimals

2. Factors and Multiples

3. Laws of Indices

4. Standard Form

5. Fractions

6. Percentages

7. Ratio and Scale

8. Algebra

9. Angles and Triangles

10. Formulae

11. Perimeter and Area

12. Polygons

13. Sequences

14. Volume

15. Linear Graphs

16. 3D Shapes

17. Compound Measures

Module U2/1(H) Integers and Decimals

1. Work out

(i) 2 × 3 + 4 ……………………….

(ii) 10 – 2 × 5 ……………………….

(iii) 16 ÷ (2 × 4) ………………………. (Total 3 marks)

2. (a) Work out £3.75 × 24

£ ..................................... (3)

(b) Divide £135 by 20

£ ..................................... (3)

(Total 6 marks)

3. Use the information that

322 × 48 = 15 456

to find the value of.......

(a) 3.22 × 4.8 .............................. (1)

(b) 0.322 × 0.48 ..................................... (1)

(c) 15 456 ÷ 4.8 ..................................... (1)

(Total 3 marks)

5. Work out an estimate for the value of 523.0

31279.5

........................................... (Total 3 marks)

6. Work out an estimate for the value of 8.92.3

637

…………………….. (Total 2 marks)

8. Work out 25.6 × 1.6 You must show all your working.

.......................................... (Total 3 marks)

9. Work out 147.6 ÷ 0.24

You must show all your working.

..................................... (Total 3 marks)

Module U2/2(H) Factors and Multiples

2. (a) Express 108 as the product of powers of its prime factors.

......................... (3)

4. (a) Find the Highest Common Factor of 75 and 90.

…………………………… (2)

(b) Find the Lowest Common Multiple of 75 and 90.

…………………………… (2)

(Total 4 marks)

7. The number 40 can be written as 2m

× n, where m and n are prime numbers.

Find the value of m and the value of n.

m = …………………

n = …………………. (Total 2 marks)

Module U2/3(H) Laws of Indices

1. Write as a power of 5

(i) 54 × 5

2

…………………….

(ii) 59 ÷ 5

6

……………………. (Total 2 marks)

3. (a) Simplify x5 ÷ x

2

…………………………… (1)

(b) Simplify

2w4y × 3w

3y

2 ……………………………

(2)

(Total 3 marks)

4. 75 × 7

6 = 7

3 × 7

k

Find the value of k.

k = …………… (Total 2 marks)

5. Simplify fully

(i) (p3)3

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

(ii) 3

54 23

q

qq

................................. (Total 3 marks)

9. Work out

(i) 40

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

(ii) 4–2

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

(iii) 2

3

16

................................. (Total 3 marks)

Module U2/4(H) Standard Form

1. Write in standard form

(a) 456 000 ……………………… (1)

(b) 0.00034 ……………………… (1)

(c) 16 × 107

……………………… (1)

(Total 3 marks)

(b) Work out the value of (7 × 104) × (3 × 10

5)

Give your answer in standard form.

......................................... (2)

(Total 3 marks)

(b) Work out 5–

3

108

104

Give your answer in standard form.

..................................... (2)

(Total 4 marks)

10. Work out the value of (2 × 104) + (7 × 10

3)

Give your answer in standard form.

..................................... (Total 2 marks)

Module U2/5(H) Fractions

1. Anil sold his car for £600.

He put £250 of the £600 in a bank account.

Write £250 as a fraction of £600.

Give your answer as a fraction in its simplest form.

…………………………… (Total 2 marks)

2.

Young Person’s RAILCARD

3

1 off normal price

Lisa uses her railcard to buy a ticket. She gets 3

1 off the normal price of the ticket.

The normal price of the ticket is £24.90. Work out how much Lisa pays for the ticket.

£ .................................. (Total 3 marks)

3. Work out 7

1

5

2

.................... (Total 2 marks)

4. Work out the value of 13

2 + 2

4

3

Give your answer as a fraction in its simplest form.

…………… (Total 3 marks)

6. (a) Write these fractions in order of size.

Start with the smallest fraction.

12

7

3

2

6

5

4

3

................................................................ (2)

8. Convert the recurring decimal 92.0 to a fraction.

……………………………… (Total 2 marks)

10. (a) Change 11

3 to a decimal.

……………………. (1)

Module U2/6(H) Percentages

1. Work out 70% of £340

£ .......................................... (Total 2 marks)

2. Mary scored 14 out of 20 in a test.

Find 14 out of 20 as a percentage.

.......................... % (Total 2 marks)

3. There are 800 students at Prestfield School.

45% of these 800 students are girls.

(a) Work out 45% of 800

.......................... (2)

There are 176 students in Year 10.

(b) Write 176 out of 800 as a percentage.

......................% (2)

(Total 4 marks)

6. Mr Brown buys a garden spade.

The spade costs £20 plus 17½% VAT.

Garden spade

£20 + 17½ % VAT

Calculate the total cost of the spade.

£ ....................................... (3)

7. Ben bought a car for £12 000.

Each year the value of the car depreciated by 10%.

Work out the value of the car two years after he bought it.

£ …………………. (Total 3 marks)

Module U2/7(H) Ratio and scale

2. Sidra and Gemma share £48 in the ratio 5 : 3

Work out how much more money Sidra gets than Gemma gets.

£ ................................. (Total 3 marks)

4. Lillian, Max and Nazia share a sum of money in the ratio 2 : 3 : 5

(a) What fraction of the money does Max receive?

..................................... (2)

Nazia receives £60

(b) Work out how much money Lillian receives.

£ ..................................... (3)

(Total 5 marks)

6. 3 metres of ribbon cost £1.26.

Work out the cost of 5 metres of the same ribbon.

£ ………………………… (Total 2 marks)

7. This is a recipe for making Spaghetti Carbonara for 4 people.

Spaghetti Carbonara

Ingredients for 4 people

400 g of spaghetti

120 g of bacon

2 tablespoons of oil

4 eggs

50 g of cheese

Bill is making Spaghetti Carbonara for 6 people.

Work out the amount he needs.

........................ g of spaghetti

........................ g of bacon

........................ tablespoons of oil

........................ eggs

........................ g of cheese (Total 3 marks)

8. Picture NOT accurately drawn

A model of a space shuttle is made to a scale of 2 centimetres to 1 metre.

The length of the space shuttle is 24 metres.

(a) Work out the length of the model.

Give your answer in centimetres.

………………………cm (2)

The height of the model is 10 centimetres.

(b) Work out the height of the space shuttle.

Give your answer in metres.

………………………m (2)

(Total 4 marks)

Module U2/8(H) Algebra

1. (a) Simplify a + a + a + a ..................... (1)

(b) Simplify 3 × b × 4 ..................... (1)

(c) Simplify completely 4a + 5b – 2a + b ..................................... (2)

(d) Factorise x2 – 6x .....................

(2)

(Total 6 marks)

2. (a) Simplify a × a × a ............................ (1)

(b) Expand 5(3x – 2) ........................................ (1)

(c) Expand 3y(y + 4) ........................................ (2)

(d) Expand and simplify 2(x – 4) + 3(x + 2)

............................ (2)

(e) Expand and simplify (x + 4)(x – 3)

........................................ (2)

(Total 8 marks)

3. (a) Expand and simplify

(x – 6)(x + 4)

…………………………… (2)

(b) Factorise completely

12x2 – 18xy

…………………………… (2)

(Total 4 marks)

(b) Expand and simplify (2x + 5)(3x – 4)

....................................................... (2)

(c) Factorise x2 + 7x + 10

....................................................... (2)

(Total 6 marks)

6. Factorise x2 5x 14

………………………… (Total 2 marks)

(b) Simplify fully xx

xx

2

652

2

..................................... (2)

(Total 6 marks)

Module U2/9(H) Angles and triangles

1.

x°

y°

126°

P Q

RDiagram accurately drawn

NOT

PQ is a straight line.

(a) Work out the size of the angle marked x°.

..............................° (1)

(b) (i) Work out the size of the angle marked y°.

..............................°

(ii) Give reasons for your answer.

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

................................................................................................................... (3)

(Total 4 marks)

(b)

D

F

E

G

62º yº

64º

Diagram NOT accurately drawn

DE is parallel to FG.

(i) Find the size of the angle marked y°.

..........................°

(ii) Give a reason for your answer.

............................................................................................................................... (Total 2 marks)

Module U2/10(H) Formulae

1. P = 4k – 10

P = 50

(a) Work out the value of k.

..................................... (2)

y = 4n – 3d

n = 2

d = 5

(b) Work out the value of y.

..................................... (2)

(Total 4 marks)

2. Work out the value of 4

)3–(qp when p = 2 and q = –7

........................ (Total 3 marks)

5. Find the value of

t2 – 4t when t = 3

…………………………… (Total 2 marks)

7. Pat plays a game with red cards and green cards.

Red cards are worth 5 points each.

Green cards are worth 3 points each.

Pat has r red cards and g green cards.

His total number of points is N.

Write down, in terms of r and g, a formula for N.

………………………….. (Total 3 marks)

Module U2/11(H) Perimeter and Area

1.

9cm

12cm

5cm

7cm

Diagram NOT accurately drawn

Work out the area of the shape.

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

(Total 4 marks)

2.

Diagram NOT accurately drawn

The diagram shows a rectangle inside a triangle. The triangle has a base of 12 cm and a height

of 10 cm. The rectangle is 5 cm by 3 cm.

Work out the area of the region shown shaded in the diagram.

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

(Total 3 marks)

6.

Work out the surface area of the triangular prism. State the units with your answer.

……………………. (Total 4 marks)

Module U2/12(H) Polygons

1.

120º 140º

58º

a

Diagram NOT accurately drawn

Work out the size of the angle a.

........................................° (Total 2 marks)

4.

Diagram accurately drawn

NOT

Calculate the size of the exterior angle of a regular hexagon.

................................... (Total 2 marks)

5. The size of each exterior angle of a regular polygon is 40°.

Work out the number of sides of the regular polygon.

..................................... (Total 2 marks)

Module U2/13(H) Sequences

1. Here are the first four terms of a number sequence.

2 7 12 17

(a) Write down the 6th term of this number sequence.

............................................ (1)

The nth term of a different number sequence is 4n + 5

(b) Work out the first three terms of this number sequence.

............ ............ ............ (2)

(Total 3 marks)

5. Here are the first five terms of a number sequence.

3 7 11 15 19

(a) Write down an expression, in terms of n, for the nth term of this sequence.

.......................................... (2)

Adeel says that 319 is a term in the number sequence.

(b) Is Adeel correct?

You must justify your answer.

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

..................................................................................................................................... (2)

(Total 4 marks)

Module U2/16(H) Volume

1. A cuboid has

a volume of 40 cm3

a length of 5 cm

a width of 2 cm

(a) Work out the height of the cuboid.

...................... cm (2)

(b)

100 cm 20 cm

20 cm

100 cm

Diagrams accurately drawn

NOT

200 cm

50 cm

A carton measures 200 cm by 100 cm by 100 cm.

The carton is to be completely filled with boxes.

Each box measures 50 cm by 20cm by 20 cm.

Work out the number of boxes which can completely fill the carton.

..................................... (3)

(Total 5 marks)

3. The diagram shows a wedge in the shape of a triangular prism.

10 cm15 cm2

Diagram accurately drawn

NOT

The cross section of the prism is shown as a shaded triangle.

The area of the triangle is 15 cm2.

The length of the prism is 10 cm.

Work out the volume of the prism.

.......................... (Total 3 marks)

Module U2/17(H) Linear Graphs

1. (a) Complete the table of values for y = 3x + 1

x –3 –2 –1 0 1 2

y –8 –2

(2)

(b) On the grid, draw the graph of y = 3x + 1

x

y

8

7

6

5

4

3

2

1

–1

–2

–3

–4

–5

–6

–7

–8

–9

–3 –2 –1 O 1 2

(2)

(Total 4 marks)

3. A straight line has equation y = 5 – 3x

(a) Write down the gradient of the line. ……………………….. (1)

(b) Write down the coordinates of the point where the line crosses the y axis.

(…… , ……) (1)

(Total 2 marks)

Module U2/18(H) 3-D Shapes

1. The diagram shows a solid triangular prism.

Diagram NOT

accurately drawn

Write down

(i) the number of faces ..................

(ii) the number of edges ..................

(iii) the number of vertices .................. (Total 3 marks)

Module U2/19(H) Compound measures

1. What is 1.5 kilograms in grams?

15 grams 150 grams 1.500 grams 1500 grams 1050 grams

A B C D E (Total 1 mark)

2. Jade measured the length of a line as 54 mm.

What is this length in centimetres?

54 cm 540 cm 5400 cm 5.4 cm 0.54 cm

A B C D E (Total 1 mark)

4. An aeroplane flies from Liverpool to Prague, a distance of 1200 km.

The aeroplane takes 4 hours.

Work out the average speed of the aeroplane.

……………………. km/h (Total 2 marks)

5. The distance from Bristol to Leeds is 216 miles.

(a) Cara drove the 216 miles in 4 hours 30 minutes.

Calculate her average speed.

State the units of your answer.

.................. .................. (4)