GCSE Mathematics - the "Life Cloud · GCSE Mathematics Formulae: Higher Tier ... 0 10 20 30 40 50 60 Weight in grams 7. The box plot gives information about the distribution of the

Name

For Edexcel

GCSE MathematicsPaper 3D (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 24 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

EH3D 09 Page 1 © 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

Answer ALL TWENTY FOUR 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. Here is a list of ingredients for making 12 pancakes.

Work out how much of each ingredient is needed to make 18 pancakes.

…………………………. eggs

…………………… ml of milk

…………………… g of butter

………………. g of plain flour

(Total 3 marks)


Ingredients2 eggs

250 ml of milk

50 g of butter

110 g of plain flour

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Q2

Number of pages

Time to read

(hours)

0

2

6

4

8

10

100 150 250200 300 350 400

2. Lisa records how long it takes her to read each book that she buys.

The scatter graph shows these times plotted against the number of pages in each book.

(a) Describe the correlation between the time it takes Lisa to read a book and the number of pages the book has.

…………………………(1)

Lisa buys a book with 260 pages.

(b) Use the graph to estimate how long it will take Lisa to read this book.

…………………… hours(2)

(Total 3 marks)


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Q3

Q4

3. A is the point (–1, 7)B is the point (2, 5)

B is the midpoint of AC.

Find the coordinates of C.

( …… , …… )

(Total 2 marks)

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

5, 8, 11, 14, 17

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

…………………………(2)

(b) Explain why 81 will not be a term in this sequence.

………………………………………………………………………………………

………………………………………………………………………………………

………………………………………………………………………………………(2)

(Total 4 marks)


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Q6

Q5

5. Rhodri is carrying out a survey about attitudes to pollution.

(a) Give one reason why he should not do the survey outside a bicycle shop.

………………………………………………………………………………………

………………………………………………………………………………………(1)

(b) One of his questions is

“Do you agree that it is better to travel to London on the train than by car?”

Give one reason why this is not a good question.

………………………………………………………………………………………

………………………………………………………………………………………(1)

(Total 2 marks)

6.

Sox is a cat.

When he was five weeks old he weighed 400 grams.Over the following week his weight increased by 20%.

(a) Work out Sox's weight when he was six weeks old.

…………………… grams(2)

As an adult cat, Sox weighs 3.2 kg.

(b) Work out 400 grams as a percentage of 3.2 kg.

……………………… %(3)

(Total 5 marks)


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Q7

Q8

0 10 3020 40 50 60Weight in grams

7. The box plot gives information about the distribution of the weights of fish in a pond.

(a) Write down the median weight of the fish.

…………………… g(1)

(b) Work out the interquartile range of the weights of the fish.

…………………… g(2)

(Total 3 marks)

8. v = 2t 2 – 7

t = 3

(a) Work out the value of v.

v = ……………………(2)

R = 4x + 3y

R = 9y = –5

(b) Work out the value of x.

x = ……………………(3)

(Total 5 marks)


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Q9

9. Dale makes his own pizzas.He always has a topping of ham, beef, chicken or pepperoni.The table shows the probability that he will have a ham, beef or chicken topping.

Topping Ham Beef Chicken Pepperoni

Probability 0.1 0.25 0.45

(a) Work out the probability that Dale has a pepperoni topping.

……………………(2)

In a year, Dale will make 60 pizzas.

(b) Work out an estimate for the number of times in a year that Dale will have a pizza with a beef topping.

………………………(2)

(Total 4 marks)


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Q10

10.

(a) Reflect triangle P in the line y = 4.Label this image Q.

(2)

(b) Rotate triangle P 90° clockwise about O.Label this image R.

(2)

(c) Enlarge triangle P by scale factor 3, centre O.Label this image S.

(2)

(Total 6 marks)


1 2 43 5 x

y

–2 –1 6 87 9

–3

–2

–1

O

7

9

8

1

2

4

3

5

6

P

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Q11

Q12

11.

The diagram shows a shaded semicircle of radius 4 cm, centre O.

Draw the locus of all points that are 2 cm from the edge of the semicircle.

(Total 3 marks)

12. Solve the equation

x − 34

+ x2

= 3

x = ……………………

(Total 4 marks)


O

Q14

Q13

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13. (a) Work out the mean of these five numbers.

2 2 3 6 7

………………………(2)

(b) Using your answer to part (a), or otherwise, write down the mean of each of these groups of five numbers.

(i) 32 32 33 36 37

………………………

(ii) 612 612 613 616 617

………………………(2)

(Total 4 marks)

14. (a) Expand and simplify r(r2 – 2) + 2r

…………………………(2)

(b) Find the value of p and the value of q such that for all values of x,

x2 + 4x – 1 = (x + p)2 + q

p = …………………

q = …………………(3)

(Total 5 marks)


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Q15

a

c

D

A

C

BOE

15. Diagram NOTaccurately drawn

OABC is a rhombus.

OA = a.

OC = c.

D is the midpoint of AC.E is the midpoint of BD.

Express the vector OE in terms of a and c.

…………………………

(Total 3 marks)


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Q16

1 2 3 5 6 x–1–4 –3 –2

4

3

5

6

7

8

y

–1

–2

O 4

1

2

16. The shaded region on the grid below shows all the points which satisfy all three of these inequalities.

x ≤ a y ≥ b y ≤ cx + d

Write down the values of the integers a, b, c and d.

a = …………………

b = …………………

c = …………………

d = …………………

(Total 3 marks)


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Q17

6 cm x cm

x cm

9 cm


The diagram shows two candles which have the same volume.

One is a hemisphere of radius 6 cm.The other is a cuboid of height 9 cm which has a square base of side x cm.

Find the value of x in terms of π.Give your answer in its simplest form.

x = …………………………

(Total 4 marks)


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Q18

10 cm12 cm

A B


Two cylinders, A and B, are mathematically similar.

The height of cylinder A is 10 cm.The height of cylinder B is 12 cm.The total surface area of cylinder A is 200 cm2.

Work out the total surface area of cylinder B.

………………………… cm2

(Total 3 marks)


y

x

1

–190

O180 360270

y

x

1

–190

O180 360270

y

x

1

–190

O180 360270

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19. Here is a sketch of the graph of y = cos x° for 0 ≤ x ≤ 360.

On each copy of this diagram, add a sketch of the graph indicated for 0 ≤ x ≤ 360.

(a) y = 2 cos x°

(1)

(b) y = cos (x + 60)°

(1)


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Q19

y

x

1

–190

O180 360270

Q20

(c) y = 1 + cos ( 12 x)°

(2)

(Total 4 marks)

20. (a) Change 512 to a decimal.

………………………(2)

(b) Convert the recurring decimal 0. 5̇ 4̇ to a fraction.Give your answer in its simplest form.

………………………(3)

(Total 5 marks)


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Q21

21. A company has 400 employees.

The table gives some information about the employees.

The manager of the company wants to carry out a survey of employees' views about working hours.

She decides to take a sample of 40 employees, stratified by both gender and whether or not they have children.

Find the number of employees in each sub-group that should be in the sample.

Female, children …………………

Female, no children …………………

Male, children …………………

Male, no children …………………

(Total 4 marks)


Children No children

Male

Female 156

129

47

68

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Q22

y

xO

A (–2, –2)

B (1, 7)

C

L1

L2


The diagram shows the straight lines L1 and L2.

The line L1 passes through the points A (–2, –2) and B (1, 7) and crosses the y-axis at the point C.

The line L2 is perpendicular to L1 and also crosses the y-axis at the point C.

Find the equation of line L2.

…………………………

(Total 5 marks)


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Q23

23. (a) Evaluate

(i) 2 –3

……………………

(ii) 6413

……………………

(iii) 49

32

……………………(4)

(b) (i) Express 12 in the form m 3 , where m is an integer.

……………………

(ii) Rationalise the denominator of 1

12

Give your answer in the form 3n

, where n is an integer.

……………………(4)

(Total 8 marks)


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Q24

A C

E

B

D F

23

x + 2

x2 – 7

x


Triangles ABC and DEF are mathematically similar.

Angle ABC = angle DEF.Angle ACB = angle DFE.

All measurements are in centimetres.

(a) Show that 2x2 – 3x – 20 = 0

(3)

(b) Solve the equation 2x2 – 3x – 20 = 0

x = …………… or x = ……………(3)

(c) Find the length of AC.

………………… cm(2)

(Total 8 marks)

TOTAL FOR PAPER: 100 MARKS

END


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GCSE Mathematics - the "Life Cloud · GCSE Mathematics Formulae: Higher Tier ... 0 10 20 30 40 50 60 Weight in grams 7. The box plot gives information about the distribution of the