# Advantages and Disadvantages of Private Tuition

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UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level

* 0 2 1 5 8 3 0 0 9 3 *

MATHEMATICS (SYLLABUS D) Paper 1 Candidates answer on the Question Paper. Additional Materials: Geometrical instruments

4024/12
May/June 2013 2 hours

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. DO NOT WRITE IN ANY BARCODES.

Answer all questions. If working is needed for any question it must be shown in the space below that question. Omission of essential working will result in loss of marks. ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER.

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The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 80.

This document consists of 20 printed pages.
DC (SLM/SW) 64206/2 © UCLES 2013

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2 ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER. 1 Evaluate (a) 4 2 – , 7 5 For Examiner’s Use

(b) 5 2 ‘ � 8 3

Answer

�������������������������������������������� [1]

2

Answer �������������������������������������������� [1] A bag contains red counters and blue counters� On each counter there is either an odd or an even number� The table shows the number of counters of each type� Odd Red Blue 6 5 Even 9 3

(a) Find the fraction of the counters that are blue�

(b) Find the ratio of odd to even numbers�

Answer �������������������������������������������� [1]

Answer ������������������� : �������������������� [1]

© UCLES 2013

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3 3 (a) Write these lengths in order of size, starting with the shortest� 500 m 5 cm 50 km 500 mm For Examiner’s Use

Answer ������������������������ shortest (b) Convert 41�6 cm2 to mm2�

������������������������

������������������������

������������������������

[1]

4 A line has equation 3y = 2 – x � (a) Find the gradient of the line�

Answer ����������������������������������� mm2 [1]

(b) The line passes through the point (5, k)� Find the value of k�

Answer �������������������������������������������� [1]

Answer k = �������������������������������������� [1]

© UCLES 2013

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4 5 The diagram shows the regions A to I�
y 5 4 3 2 1 0 A B D F 1 G 2 3 E H 4 I 5 x C
For Examiner’s Use

Give the letter of the region defined by each set of inequalities� (a) x > 0, y > 0, y < 1 and y < 4 – 2x

(b) y > 1, y < x – 2 and y < 5 – x

Answer �������������������������������������������� [1]

Answer �������������������������������������������� [1]

© UCLES 2013

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5 6 The diagram shows triangle A�
y 7 6 5 4 A 3 2 1 –7 –6 –5 –4 –3 –2 –1 0 –1 –2 –3 –4 1 2 3 4 5 6 7 x For Examiner’s Use

(a) Reflect triangle A in the line x = 1� Label the image B� (b) Rotate
triangle A through 90° clockwise about the point (–1, 3)� Label the image C�

[1] [1]

© UCLES 2013

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6 7 The diagram shows a scale used to measure the water level in a river� For Examiner’s Use

m 2.0 1.5 1.0 0.5 0 –0.5 –1.0 –1.5 –2.0 –2.5

June

The table shows the reading, in metres, at the beginning of each month� Month Reading (m) January 0�8 February 1�2 March 1�3 April 0�5 May –0�1 June July –1�9

(a) The diagram shows the water level at the beginning of June� Complete the table with the June reading� (b) Work out the difference between the highest and lowest levels shown in the table� [1]

Answer ����������������������������������������m [1] (c) The August reading was 0�4 m higher than the July reading� Work out the reading in August�

Answer ����������������������������������������m [1]

© UCLES 2013

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7 8 (a) James thinks of a two-digit number� It is a cube number� It is an
even number� What is his number? For Examiner’s Use

(b) Omar thinks of a two-digit number� It is a factor of 78� It is a prime number� What is his number?

Answer �������������������������������������������� [1]

(c) Write down an irrational number between 1 and 2�

Answer �������������������������������������������� [1]

9

Answer �������������������������������������������� [1] (a) Write 0�004 075 1 correct to two significant figures�

(b) 131 lies between two consecutive integers� Complete the inequality below with these integers�

Answer �������������������������������������������� [1]

Answer ������������ 1 131 1 ������������� [1] (c) Add brackets to the statement below to make it correct�

3 × 2 + 1 2 = 49

[1]

© UCLES 2013

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8 10  = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} A = {odd numbers} B = {multiples of
3} (a) Complete the Venn diagram to illustrate this information� For Examiner’s Use

A

B

[1] (b) Find the value of n (A B)�

(c) List the elements of the set A B9�

Answer �������������������������������������������� [1]

11

Answer �������������������������������������������� [1] A photo is 10 cm long� It is enlarged so that all dimensions are increased by 20%� (a) Find the length of the enlarged photo�

Answer �������������������������������������� cm [1] (b) Find the ratio of the area of the enlarged photo to the area of the original photo� Give your answer in the form k : 1�

© UCLES 2013 4024/12/M/J/13

Answer ����������������������������������� : 1 [2]

9 12 The diagram below shows triangle ABC� (a) Construct the perpendicular bisector of AB� (b) Shade the region inside the triangle containing points that are closer to A than to B and more than 6 cm from C� [1] [2] For Examiner’s Use

A

B

C

© UCLES 2013

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10 13 A=e 2 3 o -2 0 B=e -2 -3 4 o 1
For Examiner’s Use

(a) Find A – B �

(b) Find A–1 �

Answer

[1]

Answer

[2]

© UCLES 2013

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11 14 (a) Sofia earns \$7�60 for each hour she works� She starts work at 7�45 a�m� and finishes at 4�30 p�m� She stops work for half an hour for lunch� How much does she earn for the day? For Examiner’s Use

(b) Marlon earns \$1500 each month� He pays rent of \$525 each month�

Answer \$ ������������������������������������������ [2]

Find the amount he pays in rent as a percentage of his earnings�

Answer ����������������������������������������% [1]

© UCLES 2013

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12 15 P is directly proportional to the square of Q� When P = 9, Q = 6� (a) Find the formula for P in terms of Q� For Examiner’s Use

(b) Find the values of Q when P = 25�

Answer P= �������������������������������������� [1]

16 (a) Evaluate 4–2 �

Answer Q=�������������� or ������������������ [2]

(b) Simplify

Answer �������������������������������������������� [1]

e

9xy o � x3y2
6

1 2

Answer �������������������������������������������� [2]

© UCLES 2013

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13 17
45° 45° 3 2
For Examiner’s Use

The diagram shows part of an earring� It is in the shape of a sector of a circle of radius 3 cm and angle 45°, from which a sector of radius 2 cm and angle 45° has been removed� (a) Calculate the shaded area� Give your answer in the form aπ , where aand b are integers and as small as possible� b

(b) The earring is cut from a sheet of silver� The mass of 1 cm2 of the silver sheet is 1�6 g�

Answer �������������������������������������cm2 [2]

By taking the value of π to be 3, estimate the mass of the earring�

Answer ����������������������������������������� g [1]

© UCLES 2013

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14 18 The table shows information about the annual coffee production of some countries in 2010� Country Brazil Vietnam Colombia Indonesia For Examiner’s Use

Number of bags per year 1.85 × 107 9.2 × 106
8.5 × 106

(a) In 2010, Brazil produced 48 million bags of coffee� Complete the table with the coffee production for Brazil, using standard form� (b) How many more bags of coffee were produced in Vietnam than in Colombia? [1]

(c) The mass of a bag of coffee is 60 kg�

Answer

�������������������������������������������� [2]

Work out the number of kilograms of coffee produced in Indonesia� Give your answer in standard form�

Answer

��������������������������������������� kg [1]

© UCLES 2013

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15 19 (a) Keith records the number of letters he receives each day for 20 days� His results are shown in the table� Number of letters 0 1 2 3 4 5 (i) Write down the mode� (ii) Work out the mean� Answer �������������������������������������������� [1] Frequency 4 6 3 2 1 4 For Examiner’s Use

Answer �������������������������������������������� [2] (b) Over the same 20 days, Emma received a mean of 1�7 letters each day� How many letters did Emma receive altogether?

Answer �������������������������������������������� [1]

© UCLES 2013

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16 20 (a) Solve 3x 2x – 1 + = 3� 4 2
For Examiner’s Use

(b) Write as a single fraction in its simplest form 5 2 . + x+4 x-1

Answer x = �������������������������������������� [2]

Answer �������������������������������������������� [2]

© UCLES 2013

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17 21 A group of 80 students took a Physics test� This table shows the distribution of their marks� Mark (m) Frequency 0 1 m G 10 10 1 m G 20 20 1 m G 30 30 1 m G 40 40 1 m G 50 50 1 m G 60 4 12 14 22 18 10 For Examiner’s Use

(a) Complete the cumulative frequency table� Mark (m) Cumulative frequency [1] (b) Draw a cumulative frequency curve for this information� 80 70 60 50 Cumulative frequency 40 30 20 10 0 0 10 20 30 Mark 40 50 60

m G 10

m G 20

m G 30

m G 40

m G 50

m G 60

[2]

(c) The pass mark for the test is 45� Use your cumulative frequency curve to estimate the number of students who passed�

Answer �������������������������������������������� [2]

© UCLES 2013

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18 22 Varun leaves home at 13 00 and cycles 12 km to college� The distance-time graph below shows Varun’s journey� His sister Kiran leaves college at 13 10 and cycles home on the same road at a constant speed of 16 km/h� (a) On the same grid, draw the distance-time graph for Kiran’s journey� College 12 10 8 Distance from home (km) 6 4 2 Home 0 13 00 13 10 13 20 13 30 Time of day 13 40 13 50 14 00 For Examiner’s Use

[2]

(b) How far was Kiran from home when she passed Varun? Answer (c) Find Varun’s speed for the first 20 minutes of his journey� Give your answer in
kilometres per hour� ��������������������������������������km [1]

Answer �����������������������������������km/h [1] (d) On the grid below, draw the speed-time graph for Varun’s journey� 25 20 Speed 15 (km/h) 10 5 0 13 00 13 10 13 20 13 30 Time of day 13 40 13 50 14 00

[2]

© UCLES 2013

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19 23
B 68° O
For Examiner’s Use

C

A

D

B, C and Dare points on the circle, centre O� BA and DA are tangents to the circle at B and D� (a) Show that triangles ABO and ADO are congruent�

��������������������������������������������������������������������������������������������������������������������������������������������������� ��������������������������������������������������������������������������������������������������������������������������������������������������� ��������������������������������������������������������������������������������������������������������������������������������������������������� ��������������������������������������������������������������������������������������������������������������������������������������������������� ���������������������������������������������������������������������������������������������������������������������������������������������������
���������������������������������������������������������������������������������������������������������������������������������������������� [3] (b) What type of special quadrilateral is ABOD? (c) Angle BCD = 68°� Find angle BAD� Answer �������������������������������������������� [1]

Answer Angle BAD = ��������������������� [2]

Question 24 is printed on the following page.

© UCLES 2013

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20 24 (a) Expand and simplify (t – 5)(t + 3)�
For Examiner’s Use

(b) Factorise 64×2 – 9y2 �

Answer �������������������������������������������� [1]

(c) Factorise 6ab – 2a– 3a2 + 4b �

Answer �������������������������������������������� [1]

(d) (i) Write x2 – 6x + 3 in the form (x – a)2 + b �

Answer �������������������������������������������� [2]

Answer �������������������������������������������� [1] (ii) Hence solve x2 – 6x + 3 = 0 leaving your answer in the form p ! q �

Answer x = ��������������������������������������� [1]

Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

© UCLES 2013

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