Other School 3 EM P1

7/29/2019 Other School 3 EM P1

1/21

Class Registration No.Name:

PAPER 1

MATHEMATICS

O LEVEL PRELIMINARY EXAMINATION

SECONDARY 4 EXPRESS /

Duration: 2 hours

Candidates answer on the Question Paper.

READ THESE INSTRUCTIONS FIRST

Write your name, class and registration number in the spaces at the top of this page and on all thework 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.

Answerall questions.

If working is needed for any question it must be shown with the answer. Omission of essentialworking will result in loss of marks. You are expected to use a scientific calculator to evaluate explicitnumerical expressions.If the degree of accuracy is not specified in the question, and if the answer is not exact, give theanswer to 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 answer in terms

of .

At the end of the examination, fasten all your work securely together.The number of marks is given in brackets [ ] at the end of each question or part question.

The total number of marks for this paper is 80.

FOR EXAMINER'S USE

TOTAL MARK S / 80

This question paper consists of16printed pages (including this cover page).[Turn over


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Mathematical Formulae

Compound interest

Total amount =

nr

P

+

100

1

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= Csinab2

1

Arc length = r , where is in radians

Sector area = 2

2

1r , where is in radians

Trigonometry

Asin

a=

Bsin

b=

Csin

c

Acosbccba 2222 +=

Statistics

Mean =f

fx

Standard deviation =

22

f

fx

f

fx


3/21

1 (a) Factorise .822 + xx(b) Simplify .)x(x 233 +

Answer (a) ___________________ [1]

(b) ___________________ [1]

2 Given that1

2123+

= x

xy , express in terms of .

Answer ________________________ [3]

3 (a) Calculate97856641

7323

..

.

, showing all the figures on your calculator display.

(b) Give your answer in (a) correct to 1 decimal place.

Answer (a) ___________________ [1]

(b) ___________________ [1]

3[Turn over


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4

4 (a) An art dealer bought a painting for $9000 and sold it for $12800. Find the profit as apercentage of the cost price of the painting.

(b) During a sale, the art dealer reduced the price of his paintings by 28 %. Calculate thenormal selling price of a painting which was priced at $14184.

Answer (a) __________________% [1]

(b) $__________________ [1]

5 Two different mobile plans are available for Kevin. He makes 10000 minutes of call monthly.Determine which plan gives the better value and give a reason for your answer.You must showall your working clearly.

Freebies Monthly subscription Charge per minute

Plan A - $39.89 $0.11

Plan B First 500 minutes free $50.52 $0.10

Answer Plan _______ gives the better value. [2]

Reason: _____________________________________________________________________. [1]


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6 (a) Solve the equation .( ) 1553 2 = xx(b) If is a perfect square, find the value ofa.49282 ++ xax

Answer (a) x = ________________ [2]

(b) a = ________________ [2]

7 The diagram shows part of the graph of .qpxxy ++= 2

(a) Find the value ofp and ofq.

5[Turn over

- 3

(b) Hence, state the coordinates of the minimum point.

.

- 5

Answer (a) p =______, q = ______ [2]

(b) ( , ) [1]

_-4


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8 (a) Use set notation to describe the set shaded in the following Venn diagram.

6

BA

(b) Given that = { x : x is an integer and 30 x 80},P= {x :x is a perfect square} and

Q = {x : x is a multiple of 12}, find

(i) PQ,(i) n(PQ).

Answer (a) __________________ [1]

(b) (i) ________________ [1]

(ii) ________________ [1]

9 A Singaporean obtained US$5500 at a rate of S$1.72 to US$1. He spent US$3150 andexchanged the remaining US dollars for Singapore dollars at a rate of S$1.70 to US$1. Calculatethe equivalent Singapore dollars he had spent.

Answer S$______________________ [3]


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10 The pointsP, Q andR on the sides of triangleABCare such thatRQ is parallel toBC, RPisparallel toACandBQ meets RPatX.(a) Name two triangles similar to triangleBQC.

5 7

Q

6

C

R

B P

(b) Given thatBP= 5 cm,PC= 7 cm and QC= 6 cm, calculate thelength of(i) XP,

(ii) AQ.

Answer (a) ________and________ [2]

(b)(i) _________________cm [1]

(ii)_________________cm [1]

7[Turn over

Q

11 In the diagram,PRSis a straight line,PQ = 7 cm,PR = 4 cm and sin QRS=

8

3. Calculate the

value of sin PQR, giving your answer as a fraction in its lowest term.

7

R SP 4

Answer _______________________ [3]


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8

12 (a) In a student-initiated CIP activity, three students helped out at a senior citizens homeregularly. Judy went every three days, Sandy went every six days and Denise went everyfour days. If the girls first visit to the home was on the 1

stof January, which dates in

January would all the three girls go to the home together again?

(b) The living room of a 5-room HDB flat measures 620 cm by 540 cm. Find(i) the area of the largest square tile that can be used to completely cover the

floor without cutting the tile,(ii) the total number of such tiles required to cover the floor of the living room.

Answer (a) __________________ [3]

(b) (i) ____________ cm2

[2]

(ii) ____________ tiles [2]


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13 ABCis an equilateral triangle with sides which are tangents to the smaller (inscribed) circleand vertices on the circumference of the larger circle (circumcircle). O is the common centre ofthe two circles. Find the ratio of the area of the circumcircle to the area of the inscribed circle.

B

O

C

Answer ___________:____________ [3]

9[Turn over


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14 O is the centre of a circle of radius 6 cm and OQR is a triangle. Calculate

(a) the length of arc QSR,(b) the area of the shaded segment.

O

R120

SQ

Answer (a) ________________________ cm [2]

(b) ________________________ cm2

[3]

15 Given thatAB = ,

6

8

(a) calculate

AB .

(b) find the coordinates of the pointB ifA is the point (7, 3).

It is also given that CD is parallel toAB and that it is half as long asAB.

(c) Express as a column vector.CD

Answer (a) _______________units [1]

(b) ( , ) [2]

(c) ___________________ [1]

10


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16 The dot diagram shows the number of children living in the houses in a certain village.(a) Construct a pie chart in the answer space to represent the data.(b) Find the percentage of houses that have at least 3 children living in them.

1 2 3 54Number of children

Answer (a)

[2]

Answer (b) ___________________ [1]

17 The table below shows the distribution of the mass of a number of eggs.

11[Turn over


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Mass (m) in grams Frequency

40 < m 5050 < m 6060 < m 70

15205

Calculate an estimate of(a) the mean mass of the eggs,(b) the standard deviation of the mass of the eggs.

Answer (a) ________________ g [2]

(b) ________________ g [2]

18 (a) Find the matrix M such that 3M + = 2 .

38

79

43

16

(b) Given that = , find the value of p and ofq.

10

21

1

13

q

41

7p

Answer (a) ___________________ [2]

(b) p = ______, q = ______ [3]

12


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13[Turn over

19 A box contains 5 red marbles and 4 blue marbles. A game is played by 2 playersA andB. Eachplayer takes turn to draw a marble from the box, without replacement. The game is over if 2marbles of the same colour have been drawn (not necessarily successively). A wins if 2 redmarbles are drawn andB wins if 2 blue marbles are drawn. Find the probability that(a) the game is over in 3 draws,(b) B wins the game in exactly 2 draws,

(c) A wins given that the first draw is blue.

Answer (a) __________________ [2]

(b) __________________ [2]

(c) __________________ [2]


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20 The quadrilateral below represents a lake. A treasure chest is buried at the bottom of the lake

below a point,X.(a) On the quadrilateral, construct

(i) the bisector ofBCD,(ii) the perpendicular bisector of the lineAB.

(b) Xis the point of intersection of these two lines. Mark and label the pointX.

[3]

D

B

C

14


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21 Consider the following sequence,

.

.

.

4843211593

27331593

122393

2

2

2

==+++

==++

==+

(a) Find the sum of 3 + 9 + 15 + 21 + 27 + 33.(b) A given line of the sequence is as follows:

3 5073...2721159 2 ==++++++ yx

Find the value ofx and ofy.

Answer (a) ___________________ [1]

(b) x = _____,y =_______ [3]

15[Turn over


16/21

22 RQ is the diameter of a circle. TPA and TQ are tangents to the circle. Given that

, calculate022=RQP

(a) ,PQTR

Q

TP

22

(b) ,PTQ

(c)

.APR

Answer (a) __________________ [2]

(b) __________________ [1]

(c) __________________ [1]

End-of-paper

16


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Qn. No. Solutions

1(a) (x 2) (x + 4)

1(b) 3x 3x 6 = -6

2

( )( )89

323y2or

89

94

9489

8499

1

2149

22

2

22

22

2

+

+

+

=

=+

=+

+

=

y

y

y

yx

yxxy

xyxy

x

)x(y

3(a) 0.090380867

3(b) 0.1

4(a)%.242100

9000

900012800=

4(b)1970014184

72

100$$ =

5 Plan A: Mthly amt = 891139893901110000 .$. =+ Plan B: Mthly amt = ( ) 521000525010050010000 .$.. =+

Plan B gives the better value.Reason: Monthly bill for Plan B is lower by $139.37.

6(a)

( ) ( )( )( )8or3

05330353

2

=

=

=

x

xxxx

6(b) ( )

4

2

2814

49284914

49287

22

22

=

=

=

++=++

++=+

a

a

a

xaxxaax

xaxxa

7(a) ( )( )158

15835 2

==

++=++

q,p

xxxx

Qn Solutions

17[Turn over


18/21

7(b)

x-coordinate of minimum point = 42

35=

+ )(

y-coordinate of minimum point = ( ) ( ) 115484 2 =++

Minimum point = ( -4, -1)

8(a) !AB U

8(bi)

}{QP

},,,{Q

},,{P

36

72604836

644936

=

=

=

I

8(bii)

45651

5113080

6

726460494836

==

=+=

=

=

!)QP(n

)(n

)QP(n

},,,,,{QP

U

U

U

9 US$ 5500 = 5500 x 1.72 = S$ 9460US$ 5500 3150 = US$ 2350US$ 2350 = 2350 x 1.7 = S$ 3995

Expenditure in S$ = S$ 9460 3995 = S$ 5465

10(a) Triangles BXP and QXR

10(bi)

cm.XP

XP

52or2

12

12

5

6

=

=

10(bii)

cm.AQ

AQ

AQ

48or5

28

12

7

6

=

=+

11

14

3

7

4

8

374

8

3

==

=

=

xPQRsin

QRPsinPQRsin

QRPsin

Qn Solutions

18


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19[Turn over

12(a) 2 3, 6, 4

2 3, 3, 2

3 3, 3, 1

1, 1, 1

LCM = 2x2x3=12

irls next meet on : 13th and 25th of Januaryg

12(bi) 2 620, 540

10 310, 270

31 , 27

HCF = 2 x 10 = 20

00 sq. cmArea of largest square tile required = 20 x 20 = 4

12(bii)

= 27otal no. of tiles required = 31 x 27 = 837

No. of tiles needed along length = 620 / 20 = 31

No. of tile needed along breadth = 540 / 20T

13perpendicular bisector of AC.D is on AC such that OD is the

00 601202

==AOD 1

Radius of inscribed circle = OD

= OA cos 60

=2

1OA

Area of big circle : Area of small circle

OA2

: (2

1OA)

2

1 :4

1

4 : 1

B

C

O

D

14(a)

Arc QSR =

180

120

6 =12.6 cm14(b)

Area of shaded region = 022 12062

1

186

2

0

1201sin

= 22.1 sq. cm

Qn Solutions


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15(a)

( ) 1068 22 =+=>

AB units

15(b) >OB - =

>

OA

6

8

>

OB - =

3

7

6

8

>

OB = + =

6

8

3

7

9

1

B = (-1, 9)

15(c) >CD =

>

AB2

1or

>

AB2

1

= or

3

4

3

4

16(a)

16(b)% of house with at least 3 children = 444100

18

8.= %

17(a)Mean mass of eggs =

40

65555204515 ++=52.5 kg

17(b)Standard deviation = 2

222

55240

65555204515.

++

= 6.61 kg

18(a)

=

=

51493

3879

862123M

=

3

21

3

24

31M

Qn Solutions

6040

60

80

3

4

5

1

2120

20


21/21

18(b)

=

+ 41

7

21

73 p

q

p = 3

-2 + q = 4 q = 6

19(a) P(A wins in 3 draws) + P(B wins in 3 draws)= P(RBR) + P(BRR) + P(BRB) + P(RBB)

=42

5

42

5

63

10

63

10+++

=9

5

19(b)P(B wins in 2 draws) = P(BB) =

8

3

9

4 =

6

1

19(c)P(A wins given that first draw is blue) =

7

4

8

5 =

14

5

20 All construction lines must be shown.

21(a) 10863 2 = 21(b) 135073 2 == yy

x is the 13th term, therefore, =+= 6123x 75

22(a) 090=RQT (rad tan)000 682290 ==PQT

22(b) TP = TQ (tangents from the same external point)0000 446868180 ==PTQ

22(c) 090=RPQ (rt in a semi-circle)0000 229068180 ==APR

21

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