Form 4 Set 001 Paper I

7/30/2019 Form 4 Set 001 Paper I

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F.4 QUIZ 01MATHCOMPULSORYPARTPAPER 1

F.4 MATHS

QUIZ 01

(Full mark: 81)

MATHEMATICS Compulsory Part

PAPER 1

QuestionAnswer Book

Time allowed: 1 hours 45 minutes (3 lessons)

This paper must be answered in English.

INSTRUCTIONS

1. Write your Name, Class and Class Number in thespaces provided on Page 1.

2. This paper consists of THREE sections, A(1), A(2)and B. Each section carries 27 marks.

3. Attempt ALL questions in this paper. Write youranswers in the spaces provided in this QuestionAnswer Book. Do not write in the margins.Answers written in the margins will not bemarked.

4. Graph paper and supplementary answer sheets willbe supplied on request. Write your Name andmark the question number box on each sheet, andfasten them with string INSIDE this book.

5. Unless otherwise specified, all working must beclearly shown.

6. Unless otherwise specified, numerical answersshould be either exact or correct to 3 significantfigures.

7. The diagrams in this paper are not necessarilydrawn to scale.

Name

Class ( )

MarkersUse Only

ExaminersUse Only

Marker

No.

Examiner

No.

Question

No.

Marks Marks

12

34

56

78

9

10

11

12

13

14

15

16

Total

MATH COMPULSORY PART PAPER 1 1


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Answerswritteninthemarginswillnotbemarked.

11(I) 2


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Page totalGo on to the next page

Answers written in the margins will not be marked.



SECTION A(1) (27 marks)

1. Simplify( )3

12

4

2

ab

ba

and express your answer with positive indices. (3

marks)

2. Make y the subject of the formulayx

yxa

+= . (3

marks)



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3. Factorize x2 4y2 and hence x2 4y2 + 10x 20y. (3

marks)

4. The cost of 5 apples and 2 oranges are $20 and the cost of 4 apples and 6 oranges are $38.Find the cost of an apple. (3

marks)



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5. A merchant sold an article at $100, which is 20% discount of the marked price.

(a) Find the marked price of the article.

(b) Find the cost price of the article if the merchant gained 150%.

(3 marks)

6. (a) Find EDC.

(b) Prove that AEparallel to CD.

(3 marks)


A

B

C D

E

109o

129o

122o

110o


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7. A (5 , 38o) and B (12, xo) are two points on the polar coordinate plane, where AB = 13 units.

(a) Show that AOB is a right-angled triangle, where O is a pole.

(b) If 0o < xo < 180o , write down the value ofx.

(3 marks)

8. In ABC, AB = 6cm, AC= 9cm. D is a point on ACsuch that AD = 4cm.

Write down a pair of similar triangles and prove it.

(3 marks)

9. Referring to the figure,

(a) find the distance between A and B,

(b) find the reduced bearing ofB from A.


N

A

B

9 km

40 km


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SECTION A(2) (27 marks)

10. Let A (9 , 12) and B (25 , 0) are two points on the coordinate plane.

(a) Is OA perpendicular to AB? Explain your answer. (3

marks)

(b) Cis a point between the line segment AB such that AC: CB = 1 : 3,

find the coordinates ofC. (3marks)

(c) Is OCan angle bisector of AOB? Explain your answer. (3

marks)



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11. Simplify( ) ( )( ) 23

2

23

1

1

1

22+

+ xxxxx

. (6

marks)



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12. A sealed ( ) sphere ( ) with radius 6 cm is recast to be a cylinderX( X)

with the base radius 6 cm.

(a) Find the height of the cylinderX. (2

marks)

(b) Find the curve surface area of cylinderXin terms of . (2

marks)(c) Another cylinderYwith base radius 12 cm and volume 576 cm3.

Is cylinderXsimilar to cylinderY? Explain your answer. (3

marks)

(Hint: The volume of sphere with radius ris given by3

3

4r .

The volume of cylinder with radius rand height h is given by hr2 .)

The curve surface area of cylinder with radius rand height h is given by rh2 .)



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13.

V

A B C

In the figure, the angle of elevation ( ) from A to Vand from Cto Vis given by 44o

and 21o respectively. It is known that the distance between A and Cis 50m.

Find the distance VB, where B is the foot of perpendicular from Vto AC. (5

marks)

(Hint Let x m and h m be the distances ofAB and VB respectively.)


44o 21o


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SECTION B (27 marks)

14. (a) For the set of date 10, 10, 11, 12, 13, 16, find

(i) the mode,

(ii) the median,

(iii) the mean.

(4 marks)(b) Four unknown data are combined with the six data in (a) to form a set of ten data.

(i) Find the least and the greatest possible values of the median of the

combined set of ten data.

(ii) If the mean of the four unknown data is 11, find the mean of the

combined set of ten data.

(5 marks)



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15. (a) (i) Expand 2(r+ 1)(r+ 2)(3r 2).

(ii) Using (a)(i) or otherwise, solve 6r3 + 14r2 8 = 0 forr.

(5 marks)

(b)

A figure consists of a hemisphere with radius rcm and a cone with the base radius r

cm and height3

14cm respectively.

(i) Show that volume of the figure is given by ( )23 1439

2rr + .

(ii) If the volume of the figure is9

8 cm3, using the result of (a) and (b)(i),

or otherwise, find the value(s) ofr.

(4 marks)


rcm

3

14cm


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16. Cis a point lying on DE. AEand BCintersect at F. It is given that AC= AD, BC= DE

and CADBCE = .

(a) Prove that AEDABC . (3

marks)(b) If AD // BC,

(i) prove that DEAABF ~ ;

(ii) write down two other triangles which are similar to ABF .

(6 marks)



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END OF PAPER

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