MrJacksonMaths Higher Non Calculator Paper J

Name

For Edexcel

GCSE MathematicsPaper 3G (Non-Calculator)

Higher TierTime: 1 hour and 45 minutes

Materials required

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

Instructions and Information for Candidates

Write 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 23 questions in this paper.Calculators must not be used.

Advice to Candidates

Show 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 Armstrong

Only to be copied for use in the purchaser's school or college

EH3G 09 © 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 πr2h

Surface area of sphere = 4πr2 Curved surface area of cone = πrl

In any triangle ABC The Quadratic Equation

The solutions of ax2 + bx + c = 0where a ≠ 0, are given by

x = −b± b2−4ac

2a

Sine Rule a

sin A =

bsin B

= c

sinC

Cosine Rule a2 = b2 + c2 – 2bc cos A

Area of triangle = 12 ab sin C


sectioncross

length

r

l h

r

c B

C

A

b a

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Q1

Q2

Answer ALL TWENTY THREE 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. Solve 3(x – 2) = 5x + 8

x = ……………………

(Total 3 marks)

2. (a) Simplify

(i) r2 × r5

……………………

(ii) 4a + b + 2a – 2b

………………………(2)

(b) Work out the value of 5p + 2q when p = 3 and q = 4.5

……………………(2)

(Total 4 marks)


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Q3

3. Nabeel wants to find out how often people send text messages.

He plans to ask 50 people who have mobile phones this question.

“How many text messages have you sent?”

(a) Write down two reasons why this is not a good question.

First reason …………………………………………………………………………

………………………………………………………………………………………

Second reason ………………………………………………………………………

………………………………………………………………………………………(2)

(b) Design a better question that Nabeel could use.You should include response boxes.

(2)

(Total 4 marks)


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Q4

4. Anne has a pack of cards which each have a picture of a shape.The shape on each card can be a triangle, a square, a pentagon or a hexagon.

Anne picks one of the cards at random.

The table shows the probability that her card has a picture of a square or a picture of a pentagon.

Shape Triangle Square Pentagon Hexagon

Probability 0.45 0.25

(a) Write down the probability that her card does not have a picture of a pentagon.

……………………(1)

There are 200 cards in the pack.

(b) How many of the cards have a picture of a square?

……………………(2)

The probability that her card has a picture of a triangle is the same as the probability that it has a picture of a hexagon.

(c) How many of the cards have a picture of a triangle?

……………………(2)

(Total 5 marks)


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Q5

Q6

5. A library has 600 history books.

15% of these books are paperbacks.

(a) Work out 15% of 600.

………………………(2)

192 of the history books have been borrowed in the last six months.

(b) Work out 192 as a percentage of 600.

…………………… %(2)

(Total 4 marks)

6. Use the information that

46 × 173 = 7958

to find the value of

(a) 4.6 × 17.3

………………………(1)

(b) 4600 × 0.173

………………………(1)

(c) 79 580 ÷ 4.6

………………………(1)

(Total 3 marks)


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Q7

109°

32°

T

P

Q

R

S

141°

7. Diagram NOTaccurately drawn

Sally says that the lines PQ and ST are parallel.

Is Sally correct?You must show working to justify your answer.

(Total 3 marks)


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Q8

8. A group of people each choose one of three desserts.Some information about their choices is shown in the table.

A female is picked at random.

(a) Find the probability that she chose the ice cream.Give your answer as a fraction in its simplest form.

……………………(2)

A male is to be picked at random.

The probability that he chose the fruit bowl is 14 .

(b) Work out how many males chose the fruit bowl.

……………………(3)

(Total 5 marks)


Ice cream Fruit bowlCake

Female

Male 28

21

20

30 19

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Q9

9. Ann opens a bank account and pays in £100.She then pays in another £5 each week.

(a) Write down an expression for the total amount, in pounds, that Ann will have paid into her account after n weeks.

…………………………(2)

Emma opens a bank account at the same time as Ann and pays in £40.She then pays in another £8 each week.

(b) Work out how many weeks it will take for Emma to have paid the same amount in total into her account as Ann.

…………………………(3)

(Total 5 marks)


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Q10

O 1 2 43 5 6 7 8 x–1–2

1

2

4

3

5

6

7

8

y

–1

–2

10. (a) List all the possible integer values of n such that

–4 < n ≤ 2

………………………………(2)

(b) On the grid below, show by shading the region which satisfies all three of these inequalities.

x > 2 y < 6 y > x

Label the region R.

(3)

(Total 5 marks)


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Q11

Q12

11. (a) Work out

34 × 5

6

Give your answer as a fraction in its simplest form.

……………………(2)

(b) Work out

2 – 23

47

……………………(3)

(Total 5 marks)

12. (a) Expand 2y(y2 + 4y)

……………………………(2)

(b) Expand and simplify (p + 1)(p – 3)

……………………………(2)

(Total 4 marks)


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Q13

A

C

E

B

D

7 cm

12.8 cm

3.1 cm

14 cm


AB is parallel to CD.The straight lines AD and BC intersect at E.AB = 7 cm.CD = 14 cm.AE = 3.1 cm.CE = 12.8 cm.

(a) Work out the length of DE.

………………………… cm(2)

(b) Work out the length of BE.

………………………… cm(2)

(Total 4 marks)


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Q14

O

39°

A

C

D

B14. Diagram NOT

accurately drawn

A, B, C and D are points on the circumference of a circle, centre O.AOB is a diameter of the circle.Angle ABC = 39°.

(a) (i) Write down the size of angle AOC.

°……………………

(ii) Give a reason for your answer.

…………………………………………………………………………………

…………………………………………………………………………………(2)

(b) (i) Write down the size of angle ADC.

°……………………

(ii) Give a reason for your answer.

…………………………………………………………………………………

…………………………………………………………………………………(2)

(Total 4 marks)


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Q15

15. Solve the simultaneous equations

x – y = 5

3x – 4y = 13

x = ……………………

y = ……………………

(Total 3 marks)

16. 60 people were asked to estimate the time between two bells ringing.The results are shown in the table.

Estimated time (t s) Frequency

20 ≤ t < 30 3

30 ≤ t < 40 10

40 ≤ t < 50 22

50 ≤ t < 60 17

60 ≤ t < 70 8

(a) Complete the cumulative frequency table.

Estimated time (t s) Cumulative Frequency

20 ≤ t < 30

20 ≤ t < 40

20 ≤ t < 50

20 ≤ t < 60

20 ≤ t < 70

(1)


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Q16

20 30 5040 60 700

10

30

20

40

50

60

CumulativeFrequency

Estimated time (t s)

(b) On the grid, draw a cumulative frequency graph for your table.

(2)

(c) Use your graph to estimate the median time estimated by the people.

……………………… s(1)

The actual time between the bells was 53 s.

(d) Use your graph to estimate how many people estimated a time of more than 53 s.

………………………(1)

(Total 5 marks)


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Q17

17. (a) Write in standard form

(i) 32 000 000

…………………………

(ii) 0.000 067

…………………………

(iii) 120

…………………………(3)

(b) Work out an estimate for the value of

(1.93 × 106) ÷ (9.82 × 1010)

Give your answer in standard form.

…………………………(3)

(Total 6 marks)


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Q18

Q19

160°6 cm

A B

O

18. (a) Evaluate

(i) (23)2

………………………

(ii) 932

………………………(3)

(b) Rationalise the denominator of 15

5

Give your answer in its simplest form.

………………………(2)

(Total 5 marks)


OAB is a sector of a circle, centre O.Angle AOB = 160°.The radius of the sector is 6 cm.

Find the area of the sector.Give your answer in terms of π and state the units of your answer.

…………………………

(Total 4 marks)


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Q20

2a

6b

X

L

N

M

OY


OLMN is a trapezium with LM parallel to ON.

OL = 2a, LM = 6b, and ON = 8b.

X is the midpoint of OM.Y is the midpoint of ON.

(a) Express, in terms of a and b,

(i) OM…………………………

(ii) OX…………………………

(2)

(b) Use vectors to show that XY is parallel to MN.

(4)

(Total 6 marks)


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Q21

y

x

P

O

y

x

1

–1

90O

180 360270

21. (a) On the grid, sketch the graph of y = – sin x° for 0 ≤ x ≤ 360.

(2)

(b) Here is a sketch of part of the graph of y = 3 cos x° – 1.

Write down the coordinates of P.( …… , …… )

(2)

(Total 4 marks)


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Q22

22. Solve the equation

x2 – 2x – 7 = 0

Give your answers in the form a + b 2 , where a and b are integers.

…………………………………………

(Total 4 marks)


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Q23

–6

–4

O

–2

2

4

6

y

–2 2 4 6 x–6 –4

23. (a) On the grid below, draw the graphs of

x2 + y2 = 36

and y = 2x + 4

(3)

(b) Use your graphs to estimate the solutions of the simultaneous equations

x2 + y2 = 36

y = 2x + 4

x = …………………… y = ……………………

or x = …………………… y = ……………………(2)

(Total 5 marks)

TOTAL FOR PAPER: 100 MARKS

END


MrJacksonMaths Higher Non Calculator Paper J

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