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 reply on the Question Paper. Extra Materials: Geometric instruments
4024/12
May/June 2013 2 hours
READ THESE INSTRUCTIONS FIRST Write your Centre figure. candidate figure and name on all the work you manus in. Write in dark blue or black pen. You may utilize a pencil for any diagrams or graphs. Do non utilize basics. paper cartridge holders. highlighters. gum or rectification fluid. DO NOT WRITE IN ANY BARCODES. Answer all inquiries. If working is needed for any inquiry it must be shown in the infinite below that inquiry. Omission of indispensable working will ensue in loss of Markss. ELECTRONIC CALCULATORS MUST NOT BE USED IN THIS PAPER. The figure of Markss is given in brackets [ ] at the terminal of each inquiry or portion inquiry. The sum of the Markss for this paper is 80.
This papers 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 ruddy counters and bluish counters? On each counter there is either an odd or an even number? The tabular array shows the figure 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 ]
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3 3 ( a ) Write these lengths in order of size. get downing with the shortest? 500 m 5 centimeter 50 kilometer 500 millimeter For Examiner’s Use
Answer ???????????????????????? shortest ( B ) Convert 41?6 cm2 to mm2?
????????????????????????
????????????????????????
????????????????????????
[ 1 ]
4 A line has equation 3y = 2 – ten ? ( 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 ]
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4 5 The diagram shows the parts A to I?
y 5 4 3 2 1 0 A B D F 1 G 2 3 E H 4 I 5 tens C
For Examiner’s Use
Give the missive of the part defined by each set of inequalities? ( a ) ten & gt ; 0. Y & gt ; 0. Y & lt ; 1 and y & lt ; 4 – 2x
( B ) Y & gt ; 1. Y & lt ; x – 2 and y & lt ; 5 – ten
Answer ???????????????????????????????????????????? [ 1 ]
Answer ???????????????????????????????????????????? [ 1 ]
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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 ten For Examiner’s Use
( a ) Reflect triangle A in the line x = 1? Label the image B? ( B ) Rotate
trigon A through 90° clockwise about the point ( –1. 3 ) ? Label the image C?
[ 1 ] [ 1 ]
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6 7 The diagram shows a graduated table used to mensurate the H2O degree 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 tabular array shows the reading. in meters. 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 H2O degree at the beginning of June? Complete the tabular array with the June reading? ( B ) Work out the difference between the highest and lowest degrees shown in the table? [ 1 ]
Answer ????????????????????????????????????????m [ 1 ] ( degree Celsius ) The August reading was 0?4 m higher than the July reading? Work out the reading in August?
Answer ????????????????????????????????????????m [ 1 ]
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7 8 ( a ) James thinks of a two-digit number? It is a regular hexahedron number? It is an
even number? What is his figure? For Examiner’s Use
( B ) Omar thinks of a two-digit number? It is a factor of 78? It is a premier number? What is his figure?
Answer ???????????????????????????????????????????? [ 1 ]
( degree Celsius ) Write down an irrational figure between 1 and 2?
Answer ???????????????????????????????????????????? [ 1 ]
9
Answer ???????????????????????????????????????????? [ 1 ] ( a ) Write 0?004 075 1 correct to two important figures?
( B ) 131 prevarications between two back-to-back integers? Complete the inequality below with these integers?
Answer ???????????????????????????????????????????? [ 1 ]
Answer ???????????? 1 131 1 ????????????? [ 1 ] ( degree Celsius ) Add brackets to the statement below to do it correct?
3 ? 2 + 1 2 = 49
[ 1 ]
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8 10 ? = { 1. 2. 3. 4. 5. 6. 7. 8. 9. 10 } A = { uneven Numberss } B = { multiples of
3 } ( a ) Complete the Venn diagram to exemplify this information? For Examiner’s Use
A
Bacillus
[ 1 ] ( B ) Find the value of N ( A B ) ?
( degree Celsius ) List the elements of the set A B9?
Answer ???????????????????????????????????????????? [ 1 ]
11
Answer ???????????????????????????????????????????? [ 1 ] A exposure is 10 centimeter long? It is enlarged so that all dimensions are increased by 20 % ? ( a ) Find the length of the hypertrophied photo?
Answer ?????????????????????????????????????? centimeter [ 1 ] ( B ) Find the ratio of the country of the hypertrophied exposure to the country of the original photo? Give your reply in the signifier K: 1?
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Answer ??????????????????????????????????? : 1 [ 2 ]
9 12 The diagram below shows triangle ABC? ( a ) Concept the perpendicular bisector of AB? ( B ) Shade the part inside the trigon incorporating points that are closer to A than to B and more than 6 centimeter from C? [ 1 ] [ 2 ] For Examiner’s Use
A
Bacillus
C
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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 ]
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11 14 ( a ) Sofia earns $ 7?60 for each hr she works? She starts work at 7?45 a?m? and coatings at 4?30 p?m? She stops work for half an hr for lunch? How much does she gain for the twenty-four hours? For Examiner’s Use
( B ) Marlon earns $ 1500 each month? He pays rent of $ 525 each month?
Answer $ ?????????????????????????????????????????? [ 2 ]
Find the sum he pays in rent as a per centum of his earnings?
Answer ???????????????????????????????????????? % [ 1 ]
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12 15 P is straight relative to the square of Q? When P = 9. Q = 6? ( a ) Find the expression for P in footings 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 ]
vitamin E
9xy o ? x3y2
6
1 2
Answer ???????????????????????????????????????????? [ 2 ]
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13 17
45° 45° 3 2
For Examiner’s Use
The diagram shows portion of an earring? It is in the form of a sector of a circle of radius 3 centimeter and angle 45° . from which a sector of radius 2 centimeter and angle 45° has been removed? ( a ) Calculate the shaded area? Give your reply in the signifier a? . where aand B are whole numbers and every bit little 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 ? to be 3. estimation the mass of the earring?
Answer ????????????????????????????????????????? g [ 1 ]
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14 18 The tabular array shows information about the one-year java production of some states in 2010? Country Brazil Vietnam Colombia Indonesia For Examiner’s Use
Number of bags per twelvemonth 1. 85 ? 107 9. 2 ? 106
8. 5 ? 106
( a ) In 2010. Brazil produced 48 million bags of coffee? Complete the tabular array with the java production for Brazil. utilizing standard form? ( B ) How many more bags of java were produced in Vietnam than in Colombia? [ 1 ]
( degree Celsius ) The mass of a bag of java is 60 kg?
Answer
???????????????????????????????????????????? [ 2 ]
Work out the figure of kgs of java produced in Indonesia? Give your reply in standard form?
Answer
??????????????????????????????????????? kilogram [ 1 ]
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15 19 ( a ) Keith records the figure of letters he receives each twenty-four hours for 20 days? His consequences are shown in the table? Number of letters 0 1 2 3 4 5 ( I ) Write down the mode? ( two ) Work out the mean? Answer ???????????????????????????????????????????? [ 1 ] Frequency 4 6 3 2 1 4 For Examiner’s Use
Answer ???????????????????????????????????????????? [ 2 ] ( B ) Over the same 20 yearss. Emma received a mean of 1?7 letters each day? How many letters did Emma have wholly?
Answer ???????????????????????????????????????????? [ 1 ]
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16 20 ( a ) Solve 3x 2x – 1 + = 3? 4 2
For Examiner’s Use
( B ) Write as a individual fraction in its simplest signifier 5 2. + x+4 x-1
Answer x = ?????????????????????????????????????? [ 2 ]
Answer ???????????????????????????????????????????? [ 2 ]
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17 21 A group of 80 pupils took a Physics test? This tabular array 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 frequence table? Mark ( m ) Cumulative frequence [ 1 ] ( B ) Draw a cumulative frequence curve for this information? 80 70 60 50 Accumulative frequence 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 ]
( degree Celsius ) The base on balls grade for the trial is 45? Use your cumulative frequence curve to gauge the figure of pupils who passed?
Answer ???????????????????????????????????????????? [ 2 ]
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18 22 Varun leaves place at 13 00 and rhythms 12 kilometers to college? The distance-time graph below shows Varun’s journey? His sister Kiran leaves college at 13 10 and rhythms place on the same route at a changeless velocity of 16 km/h? ( a ) On the same grid. pull the distance-time graph for Kiran’s journey? College 12 10 8 Distance from place ( kilometer ) 6 4 2 Home 0 13 00 13 10 13 20 13 30 Time of twenty-four hours 13 40 13 50 14 00 For Examiner’s Use
[ 2 ]
( B ) How far was Kiran from place when she passed Varun? Answer ( degree Celsius ) Find Varun’s velocity for the first 20 proceedingss of his journey? Give your reply in
kilometers per hour? ??????????????????????????????????????km [ 1 ]
Answer ???????????????????????????????????km/h [ 1 ] ( vitamin D ) On the grid below. pull the speed-time graph for Varun’s journey? 25 20 Speed 15 ( kilometers per hour ) 10 5 0 13 00 13 10 13 20 13 30 Time of twenty-four hours 13 40 13 50 14 00
[ 2 ]
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19 23
B 68° O
For Examiner’s Use
C
A
Calciferol
B. C and Dare points on the circle. center 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 particular four-sided is ABOD? ( degree Celsius ) Angle BCD = 68°? Find angle BAD? Answer ???????????????????????????????????????????? [ 1 ]
Answer Angle BAD = ????????????????????? [ 2 ]
Question 24 is printed on the undermentioned page.
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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 ]
( degree Celsius ) Factorise 6ab – 2a– 3a2 + 4b ?
Answer ???????????????????????????????????????????? [ 1 ]
( vitamin D ) ( I ) Write x2 – 6x + 3 in the signifier ( ten – a ) 2 + B ?
Answer ???????????????????????????????????????????? [ 2 ]
Answer ???????????????????????????????????????????? [ 1 ] ( two ) Hence solve x2 – 6x + 3 = 0 go forthing your reply in the signifier P! Q ?
Answer x = ??????????????????????????????????????? [ 1 ]
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