QUEEN’S COLLEGE



QUEEN’S COLLEGE

Yearly Examination, 2010-2011

Mathematics

Question-Answer Book

Secondary 2 Date: 16 Jun 2011

Time: 8:30 am – 9:45 am

[pic]

1. Write your class, class number in the spaces provided on this cover.

2. This paper consists of TWO sections, A and B. Section A carries 80 marks. Section B carries 40 marks.

3. Attempt ALL questions in this paper. Write your answers in the spaces provided in this Question-Answer Book.

4. Unless otherwise specified, numerical answers should either be exact or correct to 3 significant figures.

5. All the working steps should be shown clearly.

6. The diagrams in this paper are not necessarily drawn to scale.

7. Total marks in this paper is 120.

|Class | | |

|Class Number | | |

| |Teacher’s Use Only |

|Question No. |Max. marks |Marks |

|Section A | | |

|1 |4 | |

|2 |5 | |

|3 |5 | |

|4 |6 | |

|5 |10 | |

|6 |13 | |

|7 |7 | |

|8 |7 | |

|9 |10 | |

|10 |5 | |

|11 |8 | |

|Sub-total | |

|Section B | | |

|12 |20 | |

|13 |20 | |

|Sub-total | |

|Total |120 | |

SECTION A: Short Questions (80 marks)

1. Simplify [pic]. (4 marks)

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2. An amount of $500 was divided among Alan, Brian and Calvin such that Alan’s share : Brian’s share = 2 : 3 and Brian’s share : Calvin’s share = 2 : x. Given that Alan got $80.

(a) Find the amount that Brian got.

(b) Find the amount that Calvin got.

(c) Find the value of x. (5 marks)

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3. The length of the three sides of a triangle are [pic], [pic] and [pic], respectively, where c is a positive irrational number. Is the triangle right-angled? Explain your answer. (5 marks)

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4. (a) Prove that x3 – y3 = (x – y) (x2 + xy + y2) is an identity. (3 marks)

(b) Hence, factorize 2x3 – 128. (3 marks)

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5. The histogram below shows the marks of Mathematics examination in F.2S class.

a) Find the total number of students in F.2S. (1 mark)

b) The data above are used to construct a cumulative frequency polygon.

(i) Complete the following cumulative frequency table. (3 marks)

|Marks less than |Cumulative frequency |

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|50.5 | |

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| |33 |

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(ii) Draw a cumulative frequency polygon to present the data in (b)(i) in the graph below. (3 marks)

(c) The top 20% students will be given grade ‘A’. Refer to the cumulative frequency polygon, find the minimum mark that a student should obtain in order to get an ‘A’. Show your working on the graph. (3 marks)

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6. In the figure below, ABCDE is a regular pentagon. EA and BA are produced to J and G respectively so that ∠AJG = 25°. DA is produced to cut JG at H. F

[pic]

(a) Find ∠AED, an interior angle of regular pentagon ABCDE. (2 marks)

(b) Find a. (4 marks)

(c) Find b. (7 marks)

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7. In the figure below, ABC is a triangle. Prove that DE // BC. (7 marks)

[pic]

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8. In the figure, ABCG is a square of side 15 cm, HCDE is another square and DFE is an isosceles triangle with DF = 6[pic]cm. Find the length of GF. (7 marks)

[pic]

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9. In the figure, AE = EB, CB ( AB and ED ( CA. Given that AD = 3 and AC = 9. Let AE = x. Find BC. Leave your answer in simplest surd form. (10 marks)

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10. Without using calculator, find the value of [pic]. Rationalize your answer and leave it in surd form. (5 marks)

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11. Simplify [pic]. (8 marks)

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End of Section A

SECTION B: Long Questions (40 marks)

12.

In Figure A, XY is a diameter of a semi-circle. O is the centre of the semi-circle and Z is a point on the semi-circle. OY = 6 cm and (XYZ = (.

(a) Prove that (XOZ = 2(. (3 marks)

(b) Show that the area of ∆OYZ is 18 sin 2(. (4 marks)

(c) In Figure B, region XYZ is shaded. If ( = 15°, find, in terms of (, the area of the shaded region. (4 marks)

(d) A prism is formed with height 10 cm and the shaded region in Figure B as cross-section (Figure C). Find the total surface area of the prism, correct to 3 significant figures. (9 marks)

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13. In Figure A, ABCD is the cross-section of a rectangular box which leans against a vertical wall. There is a door on the box with an unknown width. Its hinge is at point D. Originally, the door is tightly closed.

Figure A Figure B

(a) Find ∠ADH. (4 marks)

(b) Using (a) or otherwise, find the height of the vertex A from the ground, correct to the nearest cm. (6 marks)

(c) For some reasons, the door suddenly becomes open (Figure B). It hits the ground, CG, at point X. According to measurements, CX : XG = 1 : 3. Find ∠CDX , the angle by which the door is open. (10 marks)

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END OF PAPER

-----------------------

Page total

Marks of Mathematics examination in F.2S

20.5

Marks

Number of students

40

10 cm

Y’

X’

Z’

Figure C

Z

Y

X

Page total

9

3

D

C

B

A

E

45

30

35

25

20

15

10

5

100.5

90.5

80.5

70.5

60.5

50.5

40.5

30.5

0

(

Figure A

O

Z

Y

X

Figure B

Z

Y

X

Door slightly open

X G

H

H

G

Door

Page total

Page total

Page total

Page total

Page total

Page total

Page total

Page total

Page total

Page total

x

20.5

Marks of Mathematics examination in F.2S

Marks

Cumulative frequency

40

45

30

35

25

20

15

10

5

100.5

90.5

80.5

70.5

60.5

50.5

40.5

30.5

0

Q.5 continues on the next page.

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