gcse mathematics · gcse mathematics formulae: higher tier volume of a prism = area of cross...

NameFor Edexcel

GCSE MathematicsPaper 3I (Non-Calculator)

Higher TierTime: 1 hour and 45 minutes

Materials requiredRuler, protractor, compasses,pen, pencil, eraser.Tracing paper may be used.

Instructions and Information for CandidatesWrite your name in the box at the top of the page.Answer all the questions in the spaces provided in this question paper.The marks for each question and for each part of a question are shown in brackets.The total number of marks for this paper is 100. There are 21 questions in this paper.Calculators must not be used.

Advice to CandidatesShow all stages in any calculation.Work steadily through the paper. Do not spend too long on one question.If you cannot answer a question, leave it and attempt the next one.Return at the end to those you have left out.

Written by Shaun ArmstrongOnly to be copied for use in the purchaser's school or college

EH3I © Churchill Maths Limited

GCSE Mathematics

Formulae: Higher Tier

Volume of a prism = area of cross section × length

Volume of sphere = 43 πr3 Volume of cone = 1

3 πr2hSurface area of sphere = 4πr2 Curved surface area of cone = πrl

In any triangle ABC The Quadratic EquationThe solutions of ax2 + bx + c = 0where a ≠ 0, are given by

x = −b±b2−4ac 2a

Sine Rule asin A =

bsin B =

csinC

Cosine Rule a2 = b2 + c2 – 2bc cos A

Area of triangle = 12 ab sin C


sectioncross

length

rl h

r

c B

C

A

b a

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Q1

Q2

Answer ALL TWENTY ONE questions.

Write your answers in the spaces provided.

You must write down all the stages in your working.

You must NOT use a calculator.

1. Estimate the value of

89.730.1 × 5.92

…………………………

(Total 3 marks)

2. Change 2.4 m2 to cm2.

………………………… cm2

(Total 2 marks)


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Q3

3. Alex, Beth and Clive are all collecting football cards.

The ratio of the number of cards Alex has to the number Beth has is 2 : 1The ratio of the number of cards Beth has to the number Clive has is 3 : 2

Beth has 45 cards.

(a) Work out how many cards Alex, Beth and Clive have between them.

…………………………(3)

(b) Work out the ratio

number of cards Alex has : number of cards Clive has

Give your answer in its simplest form.

…………………………(1)

(Total 4 marks)


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Q4

4. (a) Solve 18x = 3

x = ……………………(2)

(b) Solve 19 + 2y = 15

y = ……………………(2)

(c) Expand and simplify (a + b)(a + 3b)

………………………………(2)

(Total 6 marks)


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Q5

5. Martin wants to buy some new clothes.

He buys a shirt which usually costs £24 but has been reduced by 14 in a sale.

(a) Work out the cost of the shirt in the sale.

£ ……………………(2)

He also buys a jacket which costs £80 plus 17 12 % VAT.

(b) Work out the total cost of the jacket.

£ ……………………(3)

(Total 5 marks)


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Q6

Q7

6. (a) Work out 53 – 112

…………………………(2)

(b) Find the value of x such that

3x = 93

x = ……………………(2)

(Total 4 marks)

7. Convert 45 metres per second into kilometres per hour.

………………………… km/h

(Total 3 marks)


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Q8

8. (a) Diagram NOTaccurately drawn

Find the size of an interior angle of a regular hexagon.

°…………………

(2)

(b) Diagram NOTaccurately drawn

A child is playing with pieces of plastic in the shape of different regular polygons.She finds that a square, a regular hexagon and one other piece fit together at a point as shown.

Work out how many sides the third piece has.

…………………(3)

(Total 5 marks)


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Q9

1 2 43 5–1

1

3

2

4

5

6

–5 –4 –3 –2 –1 O x

y

A (0, 6)

C (0, –1)

B (2, 2)

7

9.

A is the point (0, 6).B is the point (2, 2).C is the point (0, –1).

Find an equation of the straight line that is parallel to AB and passes through C.

…………………………

(Total 3 marks)


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Q10

A

CB

D

10.

The diagram is a scale drawing of a rectangular wall-hanging ABCD.The scale of the diagram is 2 cm represents 1 m.

(a) Use the diagram to find the actual width (AD) of the wall-hanging.

……………………… m(2)

(b) The wall-hanging is made up of pieces of different materials.One of these pieces covers the region that is

nearer to AB than BCand more than 4 m from D.

On the diagram, shade the region covered by this piece of material.

(3)(Total 5 marks)


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Q11

16 cm

12 cm

11. Diagram NOTaccurately drawn

The diagram shows a rhombus.

The diagonals of the rhombus have lengths of 12 cm and 16 cm.

(a) Find the area of the rhombus.State the units of your answer.

……………………………(3)

(b) Find the length of one side of the rhombus.

………………………… cm(2)

(Total 5 marks)


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Q12

12. A primary school has 180 pupils who all come from 4 villages.

This accurate pie chart gives information about the number of pupils from each village.

There are 74 pupils from Monton.

(a) Use the pie chart to find the number of pupils from each of the other villages.

Nelvy …………………

Oxber …………………

Pudney …………………(3)

The governers of the school want to look at the work of a stratified sample of 40 pupils according to the village they come from.

(b) Calculate the number of pupils from Monton that should be in the sample.

…………………………(2)

(Total 5 marks)


Pudney

Oxber

Monton

Nelvy

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Q13

13. Solve the simultaneous equations

2p – 3q = 215p + 2q = 5

p = ……………………

q = ……………………

(Total 4 marks)


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Q14

l cm

r cm14. Diagram NOTaccurately drawn

The shape in the diagram is made up of a square of side l cm and 4 semicircles of radius r cm.

(a) Find a formula for the perimeter of the shape, P cm, in terms of l and r.

…………………………(3)

(b) The area of the shape, A cm2, is given by the formula

A = l 2 + 2πr2

Make r the subject of this formula.

r = ……………………(3)

(Total 6 marks)


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Q15

15. (a) Simplify

(i) y10 × y –5

……………………

(ii) (5a5b)2

……………………(3)

(b) Solve the inequality 2t + 11 ≤ 7t – 4

…………………………(3)

(c) Factorise x2 + 4x + 3

…………………………(2)

(Total 8 marks)


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Q16

16. A group of 50 students each had to choose to play one outdoor sport and one indoor sport.

The outdoor sport had to be rugby or hockey.The indoor sport had to be badminton or squash.

The table gives information about the sports the students chose.

At the start of one lesson a student is picked at random to get the keys to the cupboard.

(a) Write down the probability that this student had chosen to play badminton.

……………………(2)

At the end of an outdoor lesson two students are picked to check the equipment.One of these is picked at random from those doing rugby and the other at random from those doing hockey.

(b) Work out the probability that both students picked had also chosen to play squash.

……………………(3)

(Total 5 marks)


Badminton Squash

Hockey

Rugby 10

12

20

8

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Q17

a

b

A

C

B

O

X

E D


OABCDE is a regular hexagon.

OA = a and OE = b.

X is the point on AE such that AX : XE = 1 : 2

(a) Find, in terms of a and b, the vectors

(i) AE…………………………

(ii) OX

…………………………

(iii) OB

…………………………(5)

(b) Hence, explain why OXB is a straight line.

………………………………………………………………………………………

………………………………………………………………………………………(2)

(Total 7 marks)


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Q18

Time (t minutes)10 15 2520 305

Frequencydensity

O

18. The incomplete histogram and table show information about how long it took 50 contestants to complete a puzzle in a competition.

Time (t minutes) Frequency

5 ≤ t < 10 8

10 ≤ t < 12

12 ≤ t < 14

14 ≤ t < 20 15

20 ≤ t < 30 8

(a) Use the histogram to complete the table.(2)

(b) Use the table to complete the histogram.(2)

(Total 4 marks)


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Q19

Q20

8 cm

19. Express

4 − 22

as simply as possible with a rational denominator.

…………………………

(Total 3 marks)


The diagram shows a solid square prism.

The length of the prism is 8 cm.The volume of the prism is 72 cm3.

Find the surface area of the prism.

………………………… cm2

(Total 5 marks)


y

xO

y = 4

P (x, y)

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The diagram shows the line y = 4 and the locus of the point P (x, y).

The locus of P is defined as follows:

The distance of the point P from the origin, O, is equal to the distance of the point P from the line y = 4.

(a) Show that the locus of P is the curve with equation 8y = 16 – x2

(4)


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Q21

(b) Find, using algebra, the coordinates of the points where the straight line y = x – 4 intersects the curve 8y = 16 – x2

……………………………………………(4)

(Total 8 marks)

TOTAL FOR PAPER: 100 MARKS

END


gcse mathematics · gcse mathematics formulae: higher tier volume of a prism = area of cross...

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