Hon Lam 翰林書齋 F

Answer all questions

Section A Short Questions (34M)

1. Simplify the following expressions and express the answers

with positive indices.

i) 5q³ ·(-q²/5)² (4M)

ii) (a )²∙ (2a b)³ (4M)

2. Find the value of x if 0.02 = 1.342 (4M)

(correct the answer to 4 sig.fig.)

3. If x > y > 0, simplify following expression (4M)

log (x+y) + log (x-y) – log (x² -y²)

4. The size of an angle is 85°, measured to the nearest degree.

Calculate the absolute error and the percentage error.

(Correct the answer to 3 sig. Fig if necessary)

5. If the population of a town increases by 10% each year, what

is the total percentage inorease in population over a period?

of 3 years.

6. PQRS is a rhombus. Prove that PR² + QS² = 4PQ² (5M)

7. Given BAC = XAY , AB = AC and AX = AY (5M)

Section B Long Questions (36M)

8. A sphere and a right solid cylinder have equal volumes. The

radius of the sphere and the radius of base circle of the

cylinder are equal to 3 cm.

a) Find the ratio of the surface area of the sphere to the total

Surface area of the cylinder. (3M)

b) Find the ratio of the surface area of the sphere to the total

surface area of the cylinder. (6M)

9. In the figure QP = RP, and PS = PT

a) Prove SRQ TQR (6M)

b) Hence prove QV =VR (3M)

10. A right circular veassel with radius 10cm and height 14cm is

standing vertically and containing 40 cm³ of water. Two

solid lead spheres, each of radius 1 cm are now lowered

completely into the vessel.

a) What is the volume of a solid lead sphere? (2M)

(leave your answer in terms of )

b) What is the total volume of the water and the spheres? (2M)

(leave your answer in terms of )

c) What is the new depth of water in the vessel? (5M)

(Assume that two spheres are totally immersed in water.)

(correct your answer to 2 decimal places)

11. In the figure, ABCD is a parallelogram. If AX//CY,

prove that

a) DAX = BCY (5M)

b) AXCY is a parallelogram.