Yearly Examination, 2007 2008

QUEEN’S COLLEGE

Yearly Examination, 2007 – 2008

MATHEMATICS PAPER I

Question-Answer Book

Secondary 4 Date: 17– 6– 2008

Time: 10:30 – 12:00

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 and B carry 80 and 40 marks respectively.

3. Attempt ALL questions in this paper. Write your answer in the spaces provided in this Question-Answer Book. Supplementary answer sheets will be supplied on request. Write your class and class number on each sheet and put them inside this book.

4. Unless otherwise specified, all working must be clearly shown.

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

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

Class
Class Number
Teacher’s Use Only
Section A
Question No. / Max Marks / Marks
1 / 12
2 / 6
3 / 8
4 / 8
5 / 8
6 / 9
7 / 10
8 / 9
9 / 10
Section A
Total / 80
Section B
Question No. / Max Marks / Marks
10 / 20
11 / 20
Section B
Total / 40
Teacher’s
Use Only /

Paper I Total

2008-S4 yearly exam -Math 1 - 8 - 8 -

SECTION A (80 marks)

Answer ALL questions in this section and write your answers in the spaces provided.

1. Solve the following equations.

(a) (2 marks)

(b) (5 marks)

2. The figure shows the graph of for one period.

Give the coordinates of the points P, Q and R. (There is no need to show working steps.)

(6 marks)

3. In , AB= 10 cm , and .

(a) find the length of BC; (4 marks)

(b) find the area of the triangle. (4 marks)

4. ABCDHGFE is a rectangular box with AB = 3, BC = 4 and BF = 2.

Find the angles between

(a) line AG and the plane ABFE and

(b) Find the angle between the planes AHG and EFGH.

. (8 marks)

5. The weight (w) of a cylindrical metal varies jointly as its height (h) and

the square of its radius (r). When h = 10 and r = 1, w = 20.

(a)` Find the weight of the metal in terms of h and r. (4 marks)

(b) Two cylindrical metals with heights and ; radii and respectively. If and . Find the ratio of their weights. (4 marks)

6.(a) If , find the values of A, B and C. (6 marks)

(b) Hence, or otherwise, solve . (3 marks)

7. The parabola touches the x-axis at point A.

(a) Find the y-intercept, value of k and the coordinates of point A. (8 marks)

(b) Use the above information to sketch the graph of . (2 marks)

8. ABCD is a quadrilateral with ÐA : ÐB : ÐC : ÐD = 6 : 5 : 3 : 4.

(a) Find ÐB and ÐD.

(b) Is ABCD is a cyclic quadrilateral? Explain your answer. (9 marks)

9. In the figure, BN is a tangent to the circle passing points A, B, C and with centre at O.

OCN and ACM are straight lines.

(a) If , find . (8 marks)

(b) From , find a pair of angles which are equal. (2 marks)

SECTION B (40 marks)

Answer both questions in this section and write your answers in the spaces provided.

10. y varies partly as and partly as the square of .

When , ; when , .

(a) Find the relationship between y and. (6 marks)

(b) If y = 3, find the values of where . (6 marks)

(ii) By using (i) or otherwise, find the maximum value of y.

(iii) Does y has a minimum value? If no, explain your answer; if yes, find it. (8 marks)

11 A kite V held by Peter with a string at A. V is vertically above B and the angle of elevation of V from A is. Paul stands at a point C on the circle ABC observes the kite with an angle of elevation. C is due south of point B and AC is the diameter of the circle.

VA = 100 m.

(a) Find AB, VB, BC, VC and AC. (give the answers in surd form if necessary.) (6 marks)

(b) Find the compass bearing of C from A. (3 marks)

(d) Mary, after walking along the circle ABC for a complete revolution, says that from a point P on the circumference, she can see point V with the smallest angle of elevation. Where is point P? Find also, correct to the nearest degree, this smallest angle of elevation. (5 marks)

(e) Mary further claims that , is she correct? Explain your answer. (3 marks)

END OF PAPER

2008-S4 yearly exam -Math 1 - 8 - 8 -