NameFor Edexcel

GCSE MathematicsPaper 3J (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 25 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

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GCSE Mathematics

Formulae: Higher Tier

Volume of a prism = area of cross section length

Volume of sphere = 43 pir3 Volume of cone = 13 pir

2hSurface area of sphere = 4pir2 Curved surface area of cone = pirl

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

x = b b24ac

2a

Sine Rule asin A = b

sin B = c

sinC

Cosine Rule a2 = b2 + c2 2bc cos A

Area of triangle = 12 ab sin C

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sectioncross

length

rl h

r

c B

C

A

b a

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Q1

D

CBA24

Answer ALL TWENTY FIVE 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. Diagram NOTaccurately drawn

In the diagram, ABC is a straight line and AB = AD = BD.Angle BCD = 24.

Find the size of angle BDC.

(Total 3 marks)

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Q2

Q3

2. Input Output

n + 4 3 3(n + 4)

The diagram shows that if you are given a number, n, add 4 to it and multiply the result by 3, the number obtained is given by the expression 3(n + 4).

Write in expressions for the output in each of these diagrams.

(a) Input Output

n 2 5

(2)

(b) Input Output

n + 1 4

(2)(Total 4 marks)

3. On one day, 78 of the workers at an office arrive on time and 1

10 arrive late.The rest of the workers are absent.

Calculate the fraction of workers who are absent.Give your answer as a fraction in its simplest form.

(Total 3 marks)

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Q4

LeaveBlank

4. Janice has a dice with sides numbered from 1 to 6.Her dice is biased.

She rolls it 200 times and gets the following results.

Score 1 2 3 4 5 6

Frequency 31 29 51 24 45 20

(a) Estimate the probability of getting a 6 when the dice is rolled once.

(1)

(b) Describe what Janice could do to get a better estimate of the probability of rolling a 6 when the dice is rolled once.

(1)

(c) How many times should Janice expect to get a 4 if she rolls her dice 300 times?

(2)

(Total 4 marks)

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Q5

Q6

5. (a) Factorise completely 3ab + 6b2

(2)

(b) Expand 4(7y + 2)

(1)

(c) Expand and simplify x(x 5) + 4(x 1)

(2)

(Total 5 marks)

6. (a) Use the information that

11 19 = 209

to find the value of

(i) 0.11 19

(ii) 20 900 1.9

(2)

(b) Use the information that

11 19 = 209

to find the Highest Common Factor (HCF) of 66 and 418.

(2)

(Total 4 marks)

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LeaveBlank

Q7

0

5

15

10

20

Hours of sunshine1 2 43 5 6

Maximumtemperature

(C)

05

7. The scatter graph shows the number of hours of sunshine and the maximum temperature for eight cities on the same day.

(a) Describe the relationship between the maximum temperature and the number of hours of sunshine.

(1)

Another city had 3.5 hours of sunshine on the same day.

(b) Use the graph to estimate the maximum temperature in the city.

C(2)

(Total 3 marks)

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Q8

Q9

A

C

B

28

8. Find an expression, in terms of n, for the nth term of each sequence.

(a) 1, 5, 9, 13, 17, ...

(2)

(b) 18, 16, 14, 12, 10, ...

(2)

(Total 4 marks)

9. Diagram NOTaccurately drawn

A, B and C are points on a circle.AB is a diameter of the circle.Angle BAC = 28.

(a) Find the size of angle ABC.

(1)

(b) Give reasons for your answer.

(2)

(Total 3 marks)

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Q10

10. A shop starts selling a new camera.

The shop is open 6 days a week.The table gives information about daily sales of the camera over the first 2 weeks.

Number of sales Number of days

3 4

4 3

5 2

6 1

7 2

(a) For these data. write down

(i) the mode,

(ii) the median,

(iii) the range.

(3)

After 3 weeks, the shop has a total of 90 sales of the camera.

(b) Work out the mean number of sales per day of the camera in the third week.

(4)

(Total 7 marks)

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Q11

A

x

B

y

O

11. Diagram NOTaccurately drawn

The diagram is a sketch.

A is the point (10, 4).B is the point (4, 6).

Find the distance of the midpoint of AB from O.Give your answer in the form k 2 , where k is an integer.

(Total 5 marks)

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Q12

P R

Q

12 cm

M

L N9 cm

6 cm8.1 cm

12. Diagram NOTaccurately drawn

Triangles LMN and PQR are similar.Angle LMN = Angle PQR.Angle LNM = Angle PRQ.LM = 8.1 cm.LN = 9 cm.MN = 6 cm.PR = 12 cm.

Work out the length of

(a) QR,

cm(2)

(b) PQ.

cm(2)

(Total 4 marks)

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Q13

Q14

13. The table shows some expressions.p, q, and r represent lengths.

p + q pr pqr p + qr p(q + r) pqr r

Tick () the boxes underneath the two expressions which could represent areas.

(Total 2 marks)

14. (a) Factorise 9 x2

(2)

(b) Solve y4 + 3 y1

2 = 3

y = (4)

(Total 6 marks)

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Q15

1 2 43 6 7

3

4

1

1

2

3

2 1 O x

y

5

2

15.

Find the equation of the straight line drawn on the grid.

(Total 3 marks)

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LeaveBlank

Q16

Q17

16. (a) Solve the inequality 2x + 5 > 12

(2)

(b) Solve the simultaneous equations

3a + 4b = 3a 2b = 21

a =

b = (3)

(Total 5 marks)

17. (a) Calculate 5% of 8.2 1012

(2)

(b) Work out (4.2 1021) (3 108)

(3)

(Total 5 marks)

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Q18

D

AC

B

O

18. Diagram NOTaccurately drawn

ABCD is a parallelogram.

O is the point such that

OA = 3p, OB = 2p + q, and OC = 4p + 3q.

Find, in terms of p and q, the vectors

(a) BA

(2)

(b) OD

(2)

(Total 4 marks)

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Q19

Q20

19. A tin of spaghetti weighs 250 gramscorrect to the nearest gram.

A cardboard tray weighs 120 gramscorrect to the nearest 10 grams.

A full tray carries 12 tins of spaghetti.Two full trays are weighed.

Find the maximum difference between the weights of the two full trays.

g

(Total 4 marks)

20. (a) Find the value of

(i) 1612

(ii) 16 14

(3)

(b) Expand and simplify

(2 + 3 )(4 3 )

Give your answer in the form p + q 3 , where p and q are integers.

(2)

(Total 5 marks)

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Q21

y

xO

y

xO

y

xO

y

xO

y

xO

y

xO

Graph A Graph B Graph C

Graph D Graph E Graph F

21.

Each of these equations is represented by one of the sketch graphs above.

Write down the letter of the correct graph for each equation.

(i) y = x3 2Graph

(1)

(ii) y = 2xGraph

(1)

(iii) x2 + y2 = 4Graph

(1)(Total 3 marks)

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LeaveBlank

Q22Attendance (A)

400 800 16001200 20000

22. A basketball club recorded the attendance at each of its home games in one season.

The results are shown in the table.

Attendance (A) Frequency

0 A < 1000 3

1000 A < 1200 6

1200 A < 1400 5

1400 A < 1600 4

1600 A < 2000 4

Draw a histogram for this information.

(Total 3 marks)

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LeaveBlank

Q23

3 cm

4 cm

Q24

23. Diagram NOTaccurately drawn

The radius of the base of a cone is 4 cm.The height of the cone is 3 cm.

Work out the curved surface area of the cone.Give your answer as a multiple of pi.

cm2

(Total 3 marks)

24. The probability that it will rain on Monday is x where x < 0.5The probability that it will rain on Tuesday is 2x.

Given that the probability that it rains on exactly one of these two days is 0.5, find the value of x.

x =

(Total 5 marks)

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Q25

E

OA

CD

B25. Diagram NOT

accurately drawn

A, B and C are points on a circle, centre O.DCE is the tangent to the circle at C.

Prove that angle ABC = angle ACD.

(Total 3 marks)

TOTAL FOR PAPER: 100 MARKS

END

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