pre public examination march 2017 gcse mathematics … · pre public examination march 2017 gcse...

Pre Public Examination March 2017 GCSE Mathematics (AQA style) Higher Tier Paper 3H

Name ……………………………………………………………… Class ………………………………………………………………

TIME ALLOWED 1 hour 30 minutes

INSTRUCTIONS TO CANDIDATES

• Answer all the questions. • Read each question carefully. Make sure you know what you have

to do before starting your answer. • You are permitted to use a calculator in this paper. • You may use the π button on your calculator or you may take the

value of π to be 3.142. • Do all rough work in this book.

INFORMATION FOR CANDIDATES

• The number of marks is given in brackets at the end of each question or part question on the Question Paper.

• You are reminded of the need for clear presentation in your answers. • The total number of marks for this paper is 80. © The PiXL Club Limited 2017 This resource is strictly for the use of member schools for as long as they remain members of The PiXL Club. It may not be copied, sold nor transferred to a third party or used by the school after membership ceases. Until such time it may be freely used within the member school. All opinions and contributions are those of the authors. The contents of this resource are not connected with nor endorsed by any other company, organisation or institution.

Que

stio

n

Mar

k

out

of

1 1

2 1

3 1

4 1

5 5

6 2

7 3

8 4

9 1

10 3

11 6

12 4

13 5

14 3

15 5

16 2

17 2

18 2

19 2

20 3

21 4

22 8

23 3

24 3

25 6

Total 80

© The PiXL Club Limited page 2

There are no questions printed on this page

DO NOT WRITE ON THIS PAGE ANSWER IN THE SPACES PROVIDED


Answer all questions in the spaces provided 1 Which of these numbers is the biggest? Circle your answer. [1 mark] 4 × 10−4 4 × 10−5 5 × 10−5 5 × 10−4. 2 The first term of a Fibonacci type sequence is 3. The second term of the same sequence is n. What is the fourth term in the sequence? Circle your answer. [1 mark] n + 3 2n + 3 3n 5n + 6 3 A pyramid has six faces. How many edges does it have? Circle your answer. [1 mark] 6 7 10 12 4 Which of these ratios are always equivalent to 2 : 4 ? Circle both the correct answers. [1 mark]

2x : 4x x + 2 : x + 4 2x : x

4:

2xx


5 Mary sells hot drinks at a cafeteria. She records the numbers of hot drinks that she sells on each of the twelve days. She also

records the temperature at midday on each of those days. She displays her data on the scatter diagram. The data for one of the days is missing. 5 (a) On one day, the temperature at midday was 22°C, and Mary sold 40 hot drinks. Show this information on the scatter diagram. [1 mark] 5 (b) The diagram shows a negative correlation. Describe the relationship between the temperature at midday and the number of hot

drinks Mary sells. [1 mark]

10 12 14 16 18 20 22 24 26 0

50

100

150

Temperature at midday (°C)

Num

ber o

f hot

drin

ks s

old

S


5 (c) Use the diagram to estimate the number of hot drinks Mary could expect to sell on a day when the temperature at midday is 18°C.

[2 marks]

5 (d) The point representing the data for one day is labelled S. Describe what you think happened on this day. [1 mark]

Answer


6 Solve the equation 7x + 4 = 3x − 10. [2 marks]

7 (a) Find the value of

15.7 + 8.22.38 × 4.19 .

Write down all the numbers on your calculator display. [2 marks]

7 (b) Round your answer to 7 (a) to three significant figures. [1 mark]

Answer

Answer

Answer


8 8 (a) Which of the following is a pair of alternate angles? Circle your answer. [1 mark] a and b a and c b and c b and d 8 (b) Find the size of the angle marked a. [3 marks]

Answer

°

a

b

c d

125°

40°


9 A solid is made using 1cm cubes. The front elevation, side elevation and plan view of the solid are each drawn on 1cm grids. How many 1cm cubes are used to make the solid? Circle your answer. [1 mark] 6 7 9 10

You may use the isometric grid below to help work out your answer.


plan view front elevation side elevation


10 Jonathan runs a lucky dip stall.

Lucky Dip

Tickets cost 50p each

If the number of the ticket ends with a 5, you win £1.50

If the number on the ticket is a multiple of 100, you win £20

There are 600 tickets, numbered from 1 to 600. Jonathan sells all the tickets. Does Jonathan make a profit? Tick a box. Yes. No. You must show how you obtain your answer. [3 marks]


11 The lengths of 50 earthworms were measured. The results are given in the table.

Length, x cm Midpoint Frequency

0 < x ≤ 10 23

10 < x ≤ 20 18

20 < x ≤ 30 8

30 < x ≤ 40 1

Total = 50

11 (a) Which class interval contains the median length of the earthworms? Circle your answer. [1 mark] 0 < x ≤ 10 10 < x ≤ 20 20 < x ≤ 30 30 < x ≤ 40


11 (b) Calculate an estimate for the mean length of an earthworm. [3 marks]

11 (c) You are now told that one of the earthworms in the sample is 40cm long. How does this change the estimate you obtained in 11 (b) ? Tick a box. It increases my estimate. It decreases my estimate. It does not change my estimate. Give a reason for your answer. You do not need to make any further calculations. [2 marks]

Answer

cm


12 I see this sign on the motorway while I am on holiday in Spain. Madrid 420 km I know that my car does an average of 56 miles on one gallon of fuel. When it is full, my car’s fuel tank holds 10.5 gallons of fuel. The tank is two thirds full. The car’s manual says I should never allow the amount of fuel in the tank to fall below

20% of the tank’s capacity. Do I have enough fuel to reach Madrid? Tick a box. Yes, I have enough fuel. No, I need more fuel. You may use this conversion: 5 miles = 8 kilometres You must show how you obtain your answer. [4 marks]


13

Not drawn accurately In the diagram, PQ is perpendicular to QR. P is at the point ( 0 , 2 ). Q is at the point ( 6 , 0 ). R lies on the y axis. 13 (a) Find the equation of the line passing through the points P and Q. [2 marks]

13 (b) Find the equation of the line passing through the points Q and R. [3 marks]

Answer

Answer

P ( 0 , 2 )

Q ( 6 , 0 )

y

x

R


14 Solve the simultaneous equations 2a − 3b = 13 4a + 5b = 4. [3 marks]

Answer a =

b =


15 The Venn diagram shows information about the numbers of trees in a forest. ξ = trees in the forest. A = trees with red berries. B = trees that shed their leaves in winter. There are 750 trees in the forest. 15 (a) The ratio of the number of trees with red berries to the number of trees that shed their leaves in winter is 3 : 5. Complete the Venn diagram. [3 marks] 15 (b) A tree with red berries is chosen at random. What is the probability that it sheds its leaves in winter? [2 marks]

Answer

A B ξ

180 60


16 Calculate the size of the angle marked y in this diagram. Not drawn accurately [2 marks]

17 In a sale, all prices are reduced by 35%. What was the original price of a jacket that is reduced to £104 in the sale? [2 marks]

Answer

°

Answer £

y

6cm

11cm


18 Find all the integers that satisfy the inequality 2 < 3x + 8 ≤ 15. [2 marks]

19 A function is defined as f(x) = x3 + 5. Find f−1(x). [2 marks]

Answer

Answer


20 Not drawn accurately The diagram shows a circle, centre O. A, C and D are points on the circumference of the circle. The line AB is a tangent to the circle. Find the size of angle CDA, marked x on the diagram. Give reasons for each stage of your working out. [3 marks]

Answer

°

26°

A

D

C

B

O

x


21 (a) You are told that y is inversely proportional to x2. Which of the following graphs represents the relationship between x and y? Circle the correct letter. [1 mark] 21 (b) You are now also told that y = 52 when x = 2. Find the value of y when x = 4. [3 marks]

Answer

y

x

A y

x

B

y

x

C y

x

D


22 The area of this trapezium is 24cm2. The lengths of three of its sides are given, in terms of x, on the diagram. Not drawn accurately 22 (a) Show that 3x2 + 5x − 16 = 0. [2 marks] 22 (b) Find the perimeter of the trapezium. Give your answer to three significant figures. [6 marks]

Answer

cm

3x

2x + 5

x


23 You are told that 5 is a solution of the equation

x

xx25

2+= .

Use the iterative formula

n

nn x

xx

25

21 +=+ ,

with 1x = 2.5, to find the value of 5 to three decimal places. [3 marks]

Answer


24 Alan wants to store his collection of DVDs. He measures the thickness of a DVD case to be 1.5cm, to the nearest millimetre. He sees a shelf in a shop that is 40cm long, to the nearest centimetre. What is the greatest number of DVD cases that Alan can be sure the shelf will hold? [3 marks]

Answer


25 Not drawn accurately PQR is a triangle. The length of PQ is 7cm. The length of QR is 9cm. The size of angle QRP is 35°. Find the area of triangle PQR. [6 marks]

Answer

cm2

R 35°

7cm

9cm

Q

P


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pre public examination march 2017 gcse mathematics … · pre public examination march 2017 gcse...

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