UNIVERSITY OF CAMBRIDGE INTERNATIONAL ... width of the rug is given as 0.6 m, correct to the nearest...
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This document consists of 24 printed pages. DC (LEO/SW) 49518/3 UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level READ THESE INSTRUCTIONS FIRST © UCLES 2012 [Turn over 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. Section A Answer all questions. Section B Answer any four 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. You are expected to use an electronic calculator to evaluate explicit numerical expressions. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For π , use either your calculator value or 3.142, unless the question requires the answer in terms of π . 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 100. *1444910844* MATHEMATICS (SYLLABUS D) 4024/21 Paper 2 May/June 2012 2 hours 30 minutes Candidates answer on the Question Paper. Additional Materials: Geometrical instruments Electronic calculator For Examiner’s Use www.XtremePapers.com www.theMATHelp.com
Transcript of UNIVERSITY OF CAMBRIDGE INTERNATIONAL ... width of the rug is given as 0.6 m, correct to the nearest...
This document consists of 24 printed pages.
DC (LEO/SW) 49518/3
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONSGeneral Certificate of Education Ordinary Level
READ THESE INSTRUCTIONS FIRST
© UCLES 2012 [Turn over
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.
Section AAnswer all questions.
Section BAnswer any four 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.You are expected to use an electronic calculator to evaluate explicit numerical expressions. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place.For π, use either your calculator value or 3.142, unless the question requires the answer in terms of π.
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 100.
*1
44
49
10
84
4*
MATHEMATICS (SYLLABUS D) 4024/21
Paper 2 May/June 2012
2 hours 30 minutes
Candidates answer on the Question Paper.
Additional Materials: Geometrical instruments Electronic calculator
For Examiner’s Use
www.Xtrem
ePapers.com
www.theM
ATHelp.com
2
4024/12/M/J/12© UCLES 2012
ForExaminer’s
Use
ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER.
1 (a) Express 72% as a fraction in its lowest terms.
Answer ..................................... [1]
(b) Write down two fractions that are equivalent to 0.4 .
Answer ............... and ............... [1]
2 The temperature in a freezer is –18 °C. The outside temperature is 24 °C.
(a) Find the difference between the outside temperature and the freezer temperature.
Answer ................................°C [1]
(b) The temperature in a fridge is 22 °C warmer than the freezer temperature.
Find the temperature in the fridge.
Answer ................................°C [1]
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3 (a) On the grid below, draw a quadrilateral with
no rotational symmetryand just 1 line of symmetry.
[1]
(b) Complete this description.
A parallelogram has rotational symmetry of order ...........................
and ........................... lines of symmetry. [1]
4 (a) A bag contains red and blue counters in the ratio 3 : 8. There are 24 blue counters in the bag.
How many red counters are there?
Answer ..................................... [1]
(b) Amy and Ben share $360 in the ratio 3 : 2.
How much is Ben’s share?
Answer $ ................................... [1]
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5 y is inversely proportional to the square of x.
Given that y = 2 when x = 6, find the value of y when x = 2.
Answer y = ............................... [2]
6 A circle of diameter 6 cm is cut from a square of side 8 cm.
Find an expression, in the form a – bπ , for the shaded area.86
Answer ..............................cm2 [2]
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Use7 (a) Solve x + 2
3 � 2.
Answer ..................................... [1]
(b) Write down all the integers that satisfy this inequality.
–1 � 4y + 3 � 11
Answer ..................................... [1]
8 The length of a rectangular rug is given as 0.9 m, correct to the nearest ten centimetres. The width of the rug is given as 0.6 m, correct to the nearest ten centimetres.
(a) Write down the upper bound, in metres, of the length of the rug.
Answer .................................m [1]
(b) Find the lower bound, in metres, of the perimeter of the rug.
Answer .................................m [1]
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9 (a) Evaluate 25 + 38 .
Answer ..................................... [1]
(b) Evaluate 123 × 21
4 , giving your answer as a mixed number in its lowest terms.
Answer ..................................... [2]
10 (a) Evaluate 6 × 3 + 8 ÷ 2 .
Answer ..................................... [1]
(b) By writing each number correct to 1 significant figure, estimate the value of
19.2 × 9.090.583 .
Answer ..................................... [2]
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11 c = b(a – b)a
(a) Find c when a = 4 and b = –2.
Answer c = ............................... [1]
(b) Rearrange the formula to make a the subject.
Answer a = .............................. [2]
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12 m = � 3–2� n = � –1
4� (a) Calculate m – 2n .
Answer � � [1]
(b) Given that sm + 3n = � 12t� , calculate s and t .
Answer s = ...............................
t = ............................... [2]
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13 The diagram shows two triangles, A and B.
–7
–1
–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 x
A
B
y
1
2
3
4
5
6
7
–2
–3
–4
–5
–6
–7
(a) Write down the vector that represents the translation that maps triangle A onto triangle B.
Answer [1]
(b) Triangle C is an enlargement of triangle A with centre (5, 3) and scale factor 3.
Draw and label triangle C. [2]
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14 A is the point (0, 4) and B is the point (–6, 1).
(a) M is the midpoint of the line AB.
Find the coordinates of M.
Answer (............, ............) [1]
(b) Find the equation of the line AB.
Answer ..................................... [2]
15A B
D
4 65
C
ABCD is a rectangle with AC = 65 cm and AD = 4 cm.
Calculate the area of ABCD.
Answer ..............................cm2 [3]
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16
A B
D
C
The diagram shows parts of two identical regular 12-sided polygons.
(a) Calculate angle ABC.
Answer ..................................... [2]
(b) A different regular shape will fit exactly into the space at B.
Name this shape.
Answer ........................................................ [1]
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17 (a) A carton contains 2.5 litres of juice. Carlos drinks 650 ml of the juice.
How much juice is left in the carton? Give your answer in litres.
Answer ........................... litres [1]
(b) The time in Chennai is 412 hours ahead of the time in London.
(i) What time is it in London when it is 14 45 in Chennai?
Answer ..................................... [1]
(ii) A flight leaves London at 13 25 local time. It arrives in Chennai at 04 00 local time the next day.
Work out, in hours and minutes, the length of the flight.
Answer ............... hours ............... minutes [2]
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18 (a) Find the value of
(i) 121,
Answer ..................................... [1]
(ii) –273 .
Answer ..................................... [1]
(b) Write the following numbers in order of size, starting with the smallest.
23 32 40 5–1
Answer ................ ................ ................ ................ [1] smallest
(c) Evaluate 16 32.
Answer ..................................... [1]
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19 (a) f(x) = x3 – 4
Find
(i) f(–2),
Answer f(–2) = ......................... [1]
(ii) f –1(x).
Answer f –1(x) = ................................. [1]
(b) g(y) = y2 – 3y + 1
Write down and simplify an expression for g(a – 2).
Answer g(a – 2) = ........................................ [2]
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20 The table below shows the populations of some countries in 2010.
Country Population
Indonesia 2.4 × 108
Mexico
Russia 1.4 × 108
Senegal 1.4 × 107
South Korea 4.8 × 107
(a) The population of Mexico was 111 210 000.
In the table above, complete the row for Mexico. Give your answer in standard form, correct to two significant figures. [1]
(b) Complete the following sentences.
The population of Russia is ten times the population of .....................................
The population of ..................................... is one fifth of the population of Indonesia. [2]
(c) Calculate the difference in population between South Korea and Senegal. Give your answer in standard form.
Answer ..................................... [1]
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21 In class A there are 10 boys and 15 girls. In class B there are 20 boys and 10 girls. One student is picked from each class at random.
(a) Complete the tree diagram to show the probabilities of the possible outcomes.
[2]
(b) Find the probability that one student is a boy and one is a girl. Express your answer as a fraction in its lowest terms.
Answer ..................................... [2]
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22 The diagrams below show the first three patterns in a sequence.
Pattern 1 Pattern 2 Pattern 3
(a) Complete the table.
Pattern number 1 2 3 4 5
Number of dots 5 8
[1]
(b) Find an expression, in terms of n, for the number of dots in Pattern n.
Answer ..................................... [1]
(c) In this sequence, Pattern p has 83 dots.
Find the value of p.
Answer p = .............................. [2]
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23 The table summarises the times, in minutes, taken by a group of people to complete a puzzle.
Time (t minutes) 0 < t � 4 4 < t � 8 8 < t � 12 12 < t � 16 16 < t � 20
Frequency 4 8 7 4 2
(a) On the grid draw a frequency polygon to represent this information.
0
Frequency
Time (t minutes)2 4 6 8 10 12 14 16 18 20
[2]
(b) Write down the modal class.
Answer ..................................... [1]
(c) How many people took more than 8 minutes to complete the puzzle?
Answer ..................................... [1]
(d) Imran says:
‘The longest time to complete the puzzle was 20 minutes.’
Explain why he may not be correct.
...................................................................................................................................................
.............................................................................................................................................. [1]
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24 (a) The price of a television is $350. In a sale, its price is reduced by 30%.
Calculate the sale price of the television.
Answer $ ................................... [1]
(b) The exchange rate between dollars and euros is $1 = €0.80 . Ben changes $275 into euros.
Calculate the number of euros Ben receives.
Answer € ................................... [1]
(c) Aisha buys a new car.
Cash price
$4500
Credit terms
Deposit: 25% of cash price
+12 monthly payments of $320
She buys the car using the credit terms.
How much more than the cash price will she pay overall for the car?
Answer $ ................................... [3]
Question 25 is printed on the following page.
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25 (a) Factorise
(i) x2 + x – 12 ,
Answer ............................................... [1]
(ii) 25x2 – 4y2 .
Answer ............................................... [1]
(b) Write as a single fraction 43p + 1
6p .
Answer ..................................... [1]
(c) Solve the simultaneous equations.
3x + 5y = 2 2x – 3y = 14
Answer x = ...............................
y = ............................... [3]
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.
Page 2 Mark Scheme: Teachers’ version Syllabus Paper
GCE O LEVEL – May/June 2012 4024 12
© University of Cambridge International Examinations 2012
Abbreviations
cao correct answer only
cso correct solution only
dep dependent
ft follow through after error
isw ignore subsequent working
oe or equivalent
SC Special Case
www without wrong working
soi seen or implied
Qu Answers Mark Part marks
1 (a) 25
18 cao 1
(b) 1
1
5
2
k
k and
2
2
5
2
k
k 1
2 (a)
(b)
42
4
1
1
3 (a)
(b)
Drawing of kite or isosceles
trapezium
2
0
1
1
4 (a)
(b)
9
144
1
1
5 18 2 B1 for x2y = k soi or
for 2 × 62 = y × 22 soi
6 64 – 9π cao isw 2 B1 for π × 32 or for 64 – πr 2
7 (a)
(b)
(x) Y 4
–1, 0, 1
1
1
8 (a)
(b)
0.95
2.8(0)
1
1
SC1 for both 95 and 280
9 (a) 40
31 oe 1
(b) 4
33 cao 2 B1 for
4
9
3
5× oe
Page 3 Mark Scheme: Teachers’ version Syllabus Paper
GCE O LEVEL – May/June 2012 4024 12
© University of Cambridge International Examinations 2012
10 (a)
(b)
22
300
1
2
B1 for two of 20, 9, 0.6 seen
11 (a) –3 cao 1
(b) cb
ba
−
=
2
2 B1 for ac = b(a – b) or a
bbc
2
−=
12 (a)
−10
5 oe 1
(b) (s =) 5
(t =) 2
2 C1 for one correct or
M1 for
− s
s
2
3 +
−
12
3 =
t
12 oe
13 (a)
− 4
2 oe 1
(b) Correct triangle 2 B1 for two vertices correct or
triangle correct size and orientation
14 (a) (–3, 2.5) oe 1
(b) 42
1+= xy isw 2 B1 for
2
1=m or c = 4 soi
15
28
3 M1 for CD2 = their 2)65( – 42 oe and
A1 for CD = 7 or
B1 for theirCD × 4
After 0 SC1 for ( 65 )2 = 65
16 (a) 150° 2 B1 for 12
360 soi or (12 – 2) × 180 soi
(b) Equilateral triangle 1
17 (a)
(b) (i)
(ii)
1.85
10 15 oe
10 hours 5 minutes
1
1
2
B1 for 17 55 or 23 30 seen or
M1 for 24 00 – (13 25 + 4 30) + 4 oe
18 (a) (i)
(ii)
(b)
(c)
11
–3
5–1, 40, 23, 32 oe
64
1
1
1
1
Page 4 Mark Scheme: Teachers’ version Syllabus Paper
GCE O LEVEL – May/June 2012 4024 12
© University of Cambridge International Examinations 2012
19 (a) (i) –12 1
(ii) 34+x oe 1
(b) a2 – 7a + 11 2 B1 for (a – 2)2 – 3(a – 2) + 1
20 (a)
(b)
(c)
1.1 × 108
Senegal
South Korea
3.4 × 107
1
2
1
C1 for one correct in the correct place
21 (a)
Tree diagram correct
2 B1 for both 25
10, 25
15 oe correct or
both 30
20, 30
10 oe correct
(b) 15
8 cao 2 M1 for
30
20
25
15
30
10
25
10×+× oe
22 (a)
(b)
(c)
11, 14, 17
3n + 2
27 cao
1
1
2
M1 for 3p + 2 = 83 ft
23 (a) Correct frequency polygon 2 Frequency axis scaled to show 4, 8, 7, 4, 2
Plots at midpoints 2, 6, 10, 14, 18
and joined by straight lines
B1 for 1 mis plot , everything else correct or
if plots not joined, everything else correct or
if there is no vertical scale, everything else
correct or
for 5 correct frequencies not at midpoints but
correctly spaced, everything else correct. or
SC1 for a completely accurate frequency polygon
seen alongside other graphs on the same diagram.
(b) 4 < t Y 8 1
(c) 13 1
(d) Convincing explanation 1 e.g. longest time is in the group 16 < t Y 20, but
may not be 20
Page 5 Mark Scheme: Teachers’ version Syllabus Paper
GCE O LEVEL – May/June 2012 4024 12
© University of Cambridge International Examinations 2012
24 (a)
(b)
(c)
245
220
465
1
1
3
B2 for 4965 or
M2 for 100
25 × 4500 + 320 × 12 – 4500 or
B1 for 1125 or 3840 seen
25 (a) (i) (x + 4)(x – 3) 1
(ii) (5x + 2y)(5x – 2y) 1
(b)
p2
3 oe
1
(c) x = 4 y = –2 3 C2 for one correct or
M1 for correct method to eliminate one variable
