QUEEN’S COLLEGE



QUEEN’S COLLEGE

Yearly Examination, 2010-2011

Mathematics

Question-Answer Book

Secondary 3 Date: 14th June, 2011

Time: 8:30 am – 10:00 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. Attempts 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 |10 | |

|2 |8 | |

|3 |12 | |

|4 |10 | |

|5 |12 | |

|6 |12 | |

|7 |8 | |

|8 |8 | |

|Sub-total | |

|Section B | | |

|9 |20 | |

|10 |20 | |

|Sub-total | |

|Total |120 | |

SECTION A Short Questions. (80 marks)

1. (a) Simplify [pic], and express the answer with positive indices (5 marks)

|(b) Find the value of p if[pic]. (5 marks) |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

2. A, B and C share a sum of money. Initially, A takes 50% and B takes 30% of the sum. After some discussion, they agree that A and B decrease their shares by 20% and 10% respectively. Find the percentage increase in C’s share. (8 marks)

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

3. Given a triangle (ABC with A = (-1, 8), B = (2, -1) and C = (6, 7).

P is the mid-point of BC and Q is a point on AP such that 3AQ = 2QP.

(a) What is the ratio of AQ : QP? (2 marks)

(b) Find the coordinates of P. (4 marks)

(c) Find the coordinates of Q. (6 marks)

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

4. A wooden ladder stands on level ground. It consists of two sections PQ and PR in which they are connected by a metal bar AB (being horizontal). The sections PQ and PR incline at 68(and 80( with the ground respectively. P is 2m above the ground and is 75cm from the bar AB.

(a) Find the length of sections PQ and PR. (4 marks)

(b) Find the length of the bar AB. (3 marks)

(c) How far apart are the feet on the ground level? (3 marks)

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

5. The figure shows a solid, whose upper part is a cone, and lower part is a hemisphere of same radius r cm. It is given that the height of the cone is h cm Its vertical angle is 60(.

(a) Find r : h and express your answer in surd form. (2 marks)

(b) Find the volume ratio of the cone to the hemisphere in surd form. (4 marks)

(c) If the total volume of the solid is [pic]cm3, find the volume of the

hemisphere in terms of [pic]. Hence, find the value of r. (6 marks)

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

6. The figure shows a square based solid right frustum, where AB =16 cm, PQ = 4 cm and VN=3cm

a) Find NY. (3 marks)

b) Find the volume of the frustum. (4 marks)

c) Total surface area of the frustum (5 marks)

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

7. In the figure, ABCD is a parallelogram. AME and FNC are straight lines. Given that BM = MN = ND, show that AECF is a parallelogram. (8 marks)

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

8. (a) Solve the inequality [pic] (2 marks)

(b) Solve the inequality[pic] (4 marks)

(c) Give all the integers satisfying both inequalities [pic] and [pic] (2 marks)

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

SECTION B Long Questions. (40 marks)

9. In the figure, the volume of the metal cube is six times the volume of metal right circular cone.

1 metal cube and 4 metal circular cones are melted and recast to form a sphere.

[pic]

a) Find the volume of the cube. (2 marks)

b) Find the volume of the metal right circular cone. (2 marks)

c) Find a. (5 marks)

d) Find the radius of the sphere. (7 marks)

e) Find the surface area of the sphere. (4 marks)

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

10. In the figure, ABCD is a parallelogram, AC and BD meet at O , E is the mid-point of BC, AE cuts BD at F.

a) Show that (FBE ( (FDA, (4 marks)

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

b) Show that AF = 2EF (4 marks)

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

c) Show that OF = [pic]BD (4 marks)

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

d) Show that BF =[pic]BD. (4 marks)

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

e) Show that area of (ABF : area of (ADF = 1:2 (4 marks)

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

| |

End of Paper

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

Page total

Page total

Page total

Page total

Page total

Page total

Page total

Page total

( Take ( = 3.14 and give all answers in 3 sig. Fig.)

Page total

Page total

Page total

Page total

Page total

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download