QUEEN’S COLLEGE

Half-yearly Examination, 2011– 2012

MATHEMATICS PAPER 1

Question-Answer Book

Secondary 5Date:9-1-2011

Time:3:00 – 4:30 p.m.

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 carry80and 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 / 6
2 / 6
3 / 8
4 / 8
5 / 8
6 / 10
7 / 12
8 / 10
9 / 12
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

2011-12 S5 HALF-YEARLY MATH PAPER 1 - 1 -

SECTION A (80 marks)

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

1.Solve for .

(6 marks)

2.Solve.

(6 marks)

3.The straight line touches the quadratic curve at only one point P.

(a)Find the possible values of k.

(b)Find the coordinates of P for the larger value of k.

(8 marks)

4.A wire of length 100cm is cut into two parts. Each part is then bent to form a square.

Let x cm be the side of one of the squares.

(a)Express the sum of areas of the two squares in terms of x.

(b)If the sum of areas of the two squares is greater than 425cm2,

find the range of values of x.

(8 marks)

5.Given that  and  are the two distinct real root of the quadratic equation

, where k is a constant.

(a)Express in terms of k.

(b)If < 2 <, using the result of (a), find the range of values of k.

(8 marks)

6.A brewery has a backup motor for its bottling machine. The backup motor will be automatically turned on if the original motor breaks down during operating hours. The probability that the original motor breaks down during operating hours is 0.15 and when the backup motor is turned on, it has a probability of 0.24 of breaking down. Only when both the original and backup motors break down is the machine not able to work.

(a)What is the probability that the machine is not working during operating hours?

(b)If the machine is working, what is the probability that it is operated by the original motor?

(c) The machine is working today. Find the probability that the first break down of the machine occurs on the 10th day after today.

(10 marks)

7.Let.

In the figure, the graph of y = g(x) is obtained by translating the graph ofy = f(x) in the direction of the x-axis.

The graphs of y = f(x) and y = g(x) intersect at P(0, p).

The graph of y = f(x) cuts the x-axis at Q(q, 0) and R(r, 0). The graph of y = g(x) cuts the x-axis at S(s, 0) and T(t, 0). It is given that A(a, 6) lies on the graph of y = f(x).

(a)Find the values of a, p, q and r.

(b)(i)Find the symbolic relation between f(x) and g(x).

(ii)Hence, find the values of s and t.

(c)Find the area of ΔPQT.

(12 marks)

  1. A pocket contains 15 coins and a boy takes 4 of them at random.

(a)In how many different ways can he take those 4 coins.

(b)If 3 out of 15 coins are gold coins, find the probability that the boy will get

(i)3 gold coins,

(ii)at least one gold coin.

(10 marks)

  1. In a quiz, there are two sections.

Section A consists of three true-or-false questions, each with two options. 10 marks are awarded for each correct answer.

Section B consists of four multiple-choice questions, each with four options. 5marks are awarded for each correct answer.

0 marks are given for an incorrect answer or an unanswered question in each section.

For each question in the quiz, the probability that Raymond knows the answer is 80%. If he knows the answer, he will make a mistake by giving a wrong answer with a probability of 5%. If he does not know the answer, he guesses an answer randomly.

(a)Find the probability that Raymond gets exactly 1 correct answer in Section A.

(b)Find the probability that Raymond gets exactly 3 correct answers in Section B.

(c)Find the probability that Raymond gets 10 marks more in Section B than that inSection A.

(12 marks)

SECTION B (40 marks)

10.In the figure, A, B and C are points on the graph of

(a) Write down the coordinates of A, B and C.

(3 marks)

(b) It is given that the horizontal line y = k passes through A.

(i)Find the value of k.

(ii) Solve graphically.

(4 marks)

(c) Solve graphically.

(3 marks)

(d) Let .

If the graph ofis first translated upwards by 5 units, and then translated

rightwards by 2 units to the graph of ,

(i)Find the new coordinates of A, B and C.

(ii)By using the result of (c), solve .

(10 marks)

11.(a)6 boys and 6 girls are arranged to sit in a row.

How many possible arrangements are there if

(i)there is no restriction?

(ii)a particular boy must sit in the left most?

(iii)6 boys are on one side and 6 girls are on another side?

(iv)the boys and girls must alternate?

(v)the girls must be separated and they are not allowed to sit together?

(14 marks)

(b)A teacher wants to divide them into 3 groups to do 3 different statistical probjects.

(i) In how many ways can the students be grouped?

(ii)Find the probability that there aretwo girls in each group.(6 marks)

End of Paper

2011-12 S5 HALF-YEARLY MATH PAPER 1 - 1 -