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MOCK 11-12MATH

PAPER 1

QUEENS COLLEGEMOCK Examination, 2011 2012

MATHEMATICS PAPER 1Question-Answer Book

Secondary 6 Date : 7/2/2012

Time: 8:30 am 10:45 am

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 35 marks.

3. Attempt ALL questions in Sections A(1), A(2) andSection B. Write your answers in the spaces

provided in this Question-Answer Book. Do notwrite in the margins.

4. Graph paper and supplementary answer sheets willbe supplied on request. Write your Name on eachsheet, and fasten 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.

Class

Class Number

ExaminersUse Only

Examiner

No.

Section AQuestion No.

Total

Marks

Marks

1 , 2 3 + 5

3 , 4, 5 4 + 3 + 3

6, 7 4 + 4

8, 9 5 + 4

10 6

11 6

12 7

13 9

14 7

Section ATotal

70

Section BQuestion no.

Total Marks Marks

15 10

16 7

17 8

18 10

Section BTotal

35

CheckersUse Only

Total

Checker No.

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FORMULAS FOR REFERENCE

SPHERE Surface area = 24r

Volume = 33

4r

CYLINDER Area of curved surface = rh2

Volume = hr2

CONE Area of curved surface = rl

Volume =hr2

3

1

PRISM Volume = base area height

PYRAMID Volume =

3

1 base area

height

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SECTION A(1) (35 marks)Answer ALL questions in this section and write your answers in the spaces provided.

1. MakeHthe subject of the formulac

b

H

aH=

(3 marks)

2. (a) Simplifyyx

yx3

23

and express your answer with positive indices.

(b) Simplify16log

4log8log +

(5 marks)

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3. Factorize (4 marks)

(a) 92x ,

(b) bdadbcac + .

4. Find x and y in the Figure . (3 marks)

S.6 Mathematics PAPER 1 (2011-12) 4

6

y

x 80

35

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5. The length of a rectangle is increased by 5% and its width is decreased by 5% . Find the percentage

change in the area of the rectangle. (3 marks)

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6. Find the value(s) of k if the quadratic equation 014 2 =++ kxx has equal real roots. (4 marks)

7. InFigure 1,AD and BCare two parallel chords of the circle. ACandBD intersect atE.

Findx andy. (4 marks)

S.6 Mathematics PAPER 1 (2011-12) 6

y25

56x

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8. Let .652)( 23 += xxxxf (5 marks)

(a) Show that 2x is a factor of ).(xf

(b) Factorize ).(xf

9. In the Figure,A ,B and Care three points on the same horizontal ground.B is due west ofCandA is due

north ofC.AC= 9 km andBC= 12 km. Find the distance between A andB and the compass bearing ofA

fromB . (4 marks)

S.6 Mathematics PAPER 1 (2011-12) 7

Figfiur

e 2

A

9 km

B 12 km C

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SECTION A(2) (35 marks)Answer ALL questions in this section and write your answers in the spaces provided.

10 The roots of the equation 0472 2 =+ xx are and . (6 marks)

(a) Write down the values of + and .

(b) Find the equation whose roots are 2+ and 2+ .

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11. A circle passes throughA(2, 0) andB(5, 3), and the centre G of the circle lies on thex-axis.

(a) Find the equation of the circle. (4 marks)

(b) Find the area of the sectorAGB. (2 marks)

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12. Suppose y is partly constant and partly varies directly as the square of x .

When x = 1 ,y = 8 ; when x = 5 ,y = 40 .

(a) Express y in terms ofx . (5 marks)

(b) Hence find the value ofy when x = 9 . (2 marks)

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13. In Figure 2 ,A (0, 6),B (-10, 0) and C(2, 0) are the vertices ofABC.

Figure 2

(a) Find the equation of AC. (2

marks)

(b) D is a point onACsuch thatBD is perpendicular toAC. Find the equation ofBD . (3 marks)

(c) BD cuts the y-axis at a pointP. Find the coordinates ofP . Hence find the area ofABP. (4

marks)

S.6 Mathematics PAPER 1 (2011-12) 11

O

y

A(0, 6)

xC(2, 0)B(-10, 0)

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14. The scores (in marks) obtained by a class of 20 students in a Putonghua test are shown below,

where a

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15. Figure 3 shows the graph kxxyC += 4:2

1. It cuts they-axis atPand cuts thex-axis atA

andB. The vertex of the graph isD.

(a) (i) find the value of k.

(1 mark)

(ii) find the area of ABP . (2 marks)

(iii) find the coordinates of the vertexD. (1 marks)

(b) If )(:2 xgyC = is the image obtained by translating 1C two units to

the right and reflected along the x-axis, findg(x). (3 marks)

(c) If )(:3 xhyC = is the image of 1C after a certain transformation such that itsy- intercept remains

unchanged and the area of ABP is four times of the original one. Describe the way of thetransformation and find h(x). (3 marks)

16.

S.6 Mathematics PAPER 1 (2011-12) 14

P

A B

D

kxxyC += 4: 21

Figure 3

4 cm

10 cm

2 cm

V

K A

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(a) Figure 4(a) shows a right circular cylindrical water tank of base radius 4 cm and height 10 cm .

The tank is filled with water to a depth of 6 cm . Express the volume of water in the tank in terms

of . (1

mark)

(b) Figure 4(b) shows a solid metal right circular cone. V is the vertex and VH is the height of the

cone.Kis a point on VHandA is a point on the curved surface of the cone such that VKA = 90

, KA = 2 cm and KH= 4 cm . If the radius of the base is x cm , show that the volume of the

cone is )2(3

4 3

x

x

cm

3

.

(3 marks)

(c) The cone is put into the tank and is just submerged in water [see the longitudinal section as

shown in Figure 4(c)] . Show that 0144243 =+ xx . (3marks)

S.6 Mathematics PAPER 1 (2011-12) 15

6 cm

x cm

4 cm

BH

Figure 4(a) Figure 4(b) Figure 4(c)

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17. A group of students visited the English Activity Room (EAR).

The following table shows the distribution of their number of visits made last week.

Number of visits 0 1 2 3 4

Number of boys 8 10 6 2 2

Number of girls 4 8 8 6 0

(a) Two students are selected at random from the group.

(i) Find the probability that both students visited the E.A.R. once last week. (2 marks)

(ii) Find the probability that one boy and one girl are selected. (2

marks)

(b) Five students are selected at random from the group.

(i) Find the probability that exactly three students selected visited the E.A.R. at least twice

last week. (2 marks)

(ii) Given that five people selected visited the E.A.R. at least twice last week, find the

probability that three boys and two girls are selected. (2 marks)

18.

S.6 Mathematics PAPER 1 (2011-12) 17

A

B C

B1

C1

C2

B2

Figure 5(b)

D

D1

A

B C

B1

C1

Figure 5(a)

D

A

B C

B1

C1

C2

B2

B3

C3

B4 C4

C5

B5

D

D1

D2

D3

D4

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In Figure 5(a),B1C1CD is a square inscribed in the right-angled triangle ABC. C= 90 ,BC= a ,AC= 2a ,

B1C1 = b .

(a) Express b in terms of a . (2

marks)

(b) B2C2C1D1 is a square inscribed in AB1C1 as shown in Figure 5(b).

(i) ExpressB2C2 in terms of b .

(ii) Hence expressB2C2 in terms of a . (2

marks)

(c) If squaresB3C3C2D2 , B4C4C3D3 , B5C5C4D4 , are drawn successively as indicated in Figure5(c),

(i) write down the length ofB5C5 in terms of a ,

(ii) find, in terms of a , the sum of the areas of the infinitely many squares drawn in this way.

(6

marks)

S.6 Mathematics PAPER 1 (2011-12) 18

Figure 5(c)

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END OF PAPER