2012 Chij Sjc 4 Exp Emath Prelim

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Index Number Class Name

CHIJ ST JOSEPHS CONPRELIMINARY EXAMIN

OMATHEMATICSPaper 1

Secondary 4 Express / 5 Normal Academic

T

Candidates answer on the Question Paper.No additional materials are required.

READ THESE INSTRUCTIONS FIRST

Write your index number, class and name on the cover page in the spaces provided.

Answer all questions.

Write in dark blue or black pen.Do not use staples, paper clips, highlighters, glue or correction fluid.All working must be shown clearly.Omission of essential working or units may result in loss of marks.Working in pencil will not be marked.

You may use a soft pencil for any diagrams or graphs.

You are expected to use an electronic calculatorto evaluate explicit numerical expIf the degree of accuracy is not specified in the question, and if the answer is not three significant figures. Give answers in degrees to one decimal place.For , use either your calculator value or 3.142, unless the question requires the ans

The number of marks is given in brackets [ ] at the end of each question or part que


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2

Mathematical Formulae

Compound interest

Total amount = Pnr )

1001( +

Mensuration

Curved surface area of a cone = rl

Surface area of a sphere =24 r

Volume of a cone = hr2

3

1

Volume of a sphere =3

3

4r

Area of triangle ABC = Abcsin2

1

Arc length = r , where is in radians

Sector area = 221 r , where is in radians

Trigonometry

C

c

B

b

A

a

sinsinsin==

Abccba cos2

222+=

Statistics

Mean =f

fx


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1. (a) Express1

11as a recurring decimal.

Answer (a)

(b) Express 3.94 as an improper fraction in its lowest terms.

Answer (b)

2. Calculate( )

2

3.21

1.23 2.34 3.12.

Give your answer correct to 2 significant figures.

Answer..

3. (a) Given that17

49 1

7k

= , findk.


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4. The numbers 42 and 90, expressed as product of their prime factors

42 2 3 7= and 290 2 3 5= .

Find

(a)the largest integer which is a factor of 42 and 90.

Answer (a)

(b)the smallest integerk, such as 90kis a perfect square.

Answer (b)

(c)the smallest positive integer value ofp for which 42p is a multip

Answer (c)

5. (a) Given that 3 5x y= , find the ratio of :x y .

Answer (a)


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6. Given that 2 8x < and 6 5y , for whichx andy are integers.

(a) Find the largest possible value of 3 2x y .

Answer (a)

(b) Find the smallest possible value of3

2

y

x.

Answer (b)

7. Solve the inequality2

3 7 143

x < .

Illustrate your solution on the number line.


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8. Factorise each of the following completely.

(a) ( )2

2 4 2 2x x y xy+ + .

Answer (a) .

(b)( ) 21a b a b .

Answer (b)

9. Given thaty is inversely proportional tox2 and thaty = 3 whenx = Find

(a) the equation connectingy andx,

Answer (a)


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10.The cumulative frequency curve below illustrates the marks of 400

Mathematics and English Examinations.

(a) Use the graph for the Mathematics examination to estimate the percenwho scored more than 64 marks.

Answer (a)

(b) State with a reason, which you think is the more difficult examination.

Answer (b) .

...

Mathematics

English

1806040200

50

100

250

300

350

400

200

150

Cumulative Frequency

Marks(x)


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11.Given { }is an integer :1 12x x = < , and

A = {x :x is a prime number}B = {x :x is an even number}

(a) Draw the Venn diagram to represent sets ,A andB.

(b) List the elements in the set A B .

Answer (b) {A B =

(c) Find ( )'n A B .

Answer (c)

12.Solve the equations3 4

7a b

= ,

1 5

11a b+ = .


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13.In the diagram, PQR and PSTare straight lines, PQ = 5 cm , QS=

PRT = 24 cm2

.

(a) Explain why PRT and PSQ are similar.

Answer (a) .

..

(b) Find the area of PSQ .

Answer (b)

( ) C l l ST

R S

T

Q

P


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14. Sketch the graph of 29 ( 3)y x= , indicating the turning point,x-

y-intercept clearly.

Answer

15.A road of length 43.5 10 m is represented by a length of 7 cm on a

(a)Find the scale of the map. Give your answer in the form of 1 : n

Answer (a) n =

(b) The area of the city of 20 cm2 on the map. Find the actual area

square kilometres. Express your answer in standard form.

y

O


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16.The pointsA,B andChave coordinates ( )5,0A , ( )0, 4B and ( C

(a) Find the length of lineAB.

Answer (a)

(b) Find the equation ofAB.

Answer (b)

(c) A point ( ), 0.5E b lies on the lineAC. Find the value ofb.

Answer (c) b =

(d) Given thatABCD is a parallelogram, find the coordinates of po


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17.The number of goals scored during 30 soccer matches in an inter-sc

is shown in the table below.

Number of goals 1 2 3 4

Number of matches 2 4 8 5

Find

(a) the modal number of goals,

Answer (a)

(b) the interquartile range,

Answer (b)

(c) the mean,

Answer (c)

(d) the standard deviation of the number of goals per match.


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18.Three pointsA,B andCare shown below.

Answer (a), (b) and (d)

(a)Construct the perpendicular bisector ofAB. (b)Construct the angle bisector ofCAB.

(c)These two bisectors meet at point P .

Complete the statement below.

A B

C


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19.In the figure below,ABCandADEare tangents to the circle with ce

84

Given theDFis parallel toABCand 84DAB = , stating your rea

(a) ADB ,

Answer (a)

(b) BOF ,

Answer (b) .

(c) FBC ,

AB

D

C

E

F

O


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20.The diagram below shows the speed-time graphs of a bus and a car.

The bus was uniformly retarded from a speed of 15 m/s to a speed o

seconds. It then continued to travel at this constant speed for the res

(a) Calculate the speed of the bus after it travelled for 7 seconds.

Answer (a) .

(b) Calculate the distance travelled by the bus in 30 seconds.

Answer (b)

(c) The car started travelling from the same place as the bus 10 sec

the bus. It accelerated uniformly until it overtook the bus at 30

the speed of the car when it overtook the bus.

Time (s)

Speed (m/s)

8

10 20 300

15

bus

car


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Marking Scheme of Sec 4Exp / 5NA Prelim P1 201

1(a)

(b)

0.09& &

394 197

100 50=

2 3.21

1.232.34 3.12

267500

62361

4.2895399368195 M1= 4.3 (2sf) A1

3(a)

(b)

7

7 49 1

7 7 M1

1 2

1 A1

3

3

33

1 5

51

1or

5 5

x

x

xx

=

=

4(a)

(b)

(c)

6

2 3 5 90 M1

10 A1

42 2 3 5 7

15

5 (a)

(b)

3 5

5

3

12x8 --------- 500

96 500 M1


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7 23 7 or 3 7 14

3

2 9 21 3 21

12 7 M1

9 12 7 A1

9

x x

x x

x x

x

.

(e) On the same axes, draw the graph of 5 2y x= for 3 3x .

(i) Write down thex-coordinates of the points where the two grap

(ii) These values ofx are solutions of the equation 3 2x Ax Bx+ + +

the value ofA, ofB and ofC.


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2012 Chij Sjc 4 Exp Emath Prelim