QUEEN’S COLLEGEHalfYearly Examination, 2009

—2010

MATHEMATICS

PAPER I

Question-Answer Book

Secondary2 Date: 8—1—2010Time: 8:30 am

—9:45 am

I. Write your class, class number in the spacesprovided on this cover.

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

3. Attempts ALL questions in this paper. Write youranswer in the spaces provided in thisQuestion-Answer Book.

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4. Unless otherwise specified, all working must beclearly shown.

5. Unless otherwise specified, numerical answersshould either be exact or correct to 3 significantfigures.

6. The diagrams in this paper are not necessarilydrawn to scale.

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Section A: Short Questions. (80 marks)

(a) Write down the number of significant figures for 0.0003485. (1 mark)

(b) Write down the number of significant figures for —4.30, which is colTected to (1 mark)thenearest0.01.

(c) Round off 2.718 28 correct to 3 significant figures. (1 mark)

(d) Round off 3 I 415 926 correct to 4 significant figures. (1 mark)

(a) (b) (c) (d) 3i c o

2. Simplify the following expressions and express your answers in positive indices.

(a) (2 marks)

(b)(2a)

(3 marks)

(c)5(x — 2y) 4x2 — 9y2

(4 marks)4x—6y (2y—x)

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3. Expand and simplify x2(2.v_1)_ (5 marks)

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4. Intheexpansionof (3x2

(a) what is the coefficient of the term with the highest degree? (2 marks)

(b) what is the constant term? (2 marks)

5 105 candies are divided among Peter, Paul, and Mary. The ratio of Peter’s candies to

Paul’s candies is 1:4, and the ratio of Paul’s candies to Mary’s candies is 3:5.(a) Hnd the ratio of Peter’s candies to Mary’s candies. (3 marks)

() I low many candies does Paul have? (3 marks)

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6. Factorize the following polynomials:

(a) 3a2h2 + 27ah2 (2 marks)

(b) 12p+4q—31p—(q (3 marks)

(c) x2(x—y)+(4x—4)(y—x) (3 marks)

7. Simplify the following expressions:

1 k—i(a)

kk+1 (3 marks)

(b) 83-a (3 marks)

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rs+pq8. Itis given that p = 1 +r

(a) Make r the subject of the formula. (5 marks)

(b) lfp —2, q = 3, and s = 5, find the value of r. (3 marks)

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-L-9. Find the quotiéiit and remainder of (1 — 4x + 5x4) ± (—1 + x). (7 marks)

Arrange the answer in ascending powers of x.

L 5x

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10. (a) Show that (a — 2b)2 + (a + 2b)2 = 2(a — 2b)(a + 2b) + I 6b is an identity. (6 marks)

(b) Given that the equation (x + 3)(Ax — 2) = 2x2 + Bx — 6 can be satisfied by (4 marks)any values ofx. Find the values of A and B.

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a.

=14?( Z?r’-J”’

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11. Peter wanted to estimate the depth of’ a hole in the ground. The shape of the hole was a perfect

cylinder with a circular opening. lie filled the hole with water of volume 16 m3, correct to the

nearest m3. lie also measured the area of the opening to be 0.75 1112. with percentage error being 2%.

(a) Find the niaximum error of the volume of water Peter used. (1 marks)

(b) hnd the range of the actnal area of the hole open!ng. (5 marks)

(c) Let V m3 be the volume of the water Peter used, A m2 be the area of the

opening, and d m be the depth of the hole. Express din terms of 1’ and A. (I marks)

(d) If Peter used the formula in (c) to calculate the depth, find the lower and upperlimits of the actual depth. (6 marks)

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Section B: Long Questions. (40 marks)

I—x+y+8=012. (a) Solve the simultaneous equations by the method of (10 marks)

2x—5y+2=Osubstitution.

1—(2a+b)+(a—2b)+8=0 (lOmarks)(b) Hence solve c .

2(2a+b)—5(a—2b)+2——O

tc200

13. The following table shows the frequency distribution of the yearly average scores of 100 Secondary

2 students in School A with unknowns a, b, c and d.

The frequency distribution of the yearly average scores of all the Secondary 2 students in School A

(a) Find the values of a, b, c and d (4 marks)

(b) Complete the corresponding cumulative frequency table (Table 1). (4 marks)

(c) Complete the cumulative frequency polygon (Figure I). (5 marks)

(d) The students who score less than 46 will have to take a remedial course. Find (3 marks)

the number of students who will take the remedial course. Show workings on

your cumulative frequency polygon.(e) If the top 6 % of students are invited to join an overseas study tour, estimate the (4 marks)

minimum mark for getting an invitation. Show workings on your cumulativefrequency polygon.

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(Table I and Figure 1 are on the next page.)

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n inued)

Yearly average score

Figure 1

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