Sacred Heart Canossian College

Sacred Heart Canossian College Mathematics Common Test 3 (2012-2013)

Time allowed: 1 hour S2 ___ No. ___ Group ___

Name______Total marks: 75 This paper consists of three sections, A, B and C. The diagrams in this paper are not necessarily drawn to scale. Section A (18 marks) Answer all six questions in this section. In the following table, put a ‘  ’ in the box corresponding to the right answer. Each question carries 3 marks.

1 2 3 4 5 6 A B C D

1. If the circumference of a circle is 4 m, find its area.

A.  2 m2 B. 2 m2 C. 4 m2 D. 16 m2

2. In the figure, ABD and ACEF are straight lines. Which of the following must be correct?

D A. p  q  r  s B B. p  r  q  s q s C. p  s  q  r D. p  q  r  s  360 p r F E C A 1 1 1 3. It is given that   . If u  24 and f  6 , find the value of v. u v f

A. 8 1 B. 18 24 C. 5 D. 8 S.2 __ Group ___ Name: ______( )

4. Which of the following is an identity / are identities?

(I) (2x 1)(x  3)  2x 2  5x  3 (II) 11x- 5(6 - 5 x ) = 36 x - 30 (III) (1-x )2 = 1 - x 2

A. (I) only B. (II) only C. (I) and (II) only D. (II) and (III) only

5. Expand and simplify (3m2 - 1)(2 m + 5) - 3(2 - m ) .

A. 5m3 + 15m2 + m – 11 B. 6m3 + 15m2 – 5m – 11 C. 6m3 + 15m2 + m – 1 D. 6m3 + 15m2 + m – 11

6. The arc length of the sector in the figure is 24 cm and its radius is 18 cm. Find the value of .

18 cm A. 120° B. 240° C. 267°  D. 333°

24 cm Section B (28 marks) Answer all six questions in this section. Show your working steps clearly in the space provided. 1. In the figure, ADC is a straight line.

(a) Show that BCD is a right-angled triangle. (3 marks) A

D 4.5 C 10 6 7.5

(b) Find ABD. (Give your answer correct to the nearest degree.) (2 marks)

P. 2 S.2 __ Group ___ Name: ______( )

2. In the figure, APRB, CQSD, FRS and EPQ are straight lines. It is given that AB // CD, BRS = 130, AQC = 65 and APE = 130. (a) Prove that PA = PQ. (3 marks) F E

B 130 R 130 P A D

65° S Q C

(b) Prove that EQ // FS. (2 marks)

3. (a) Prove that (5x  3)(5x  2)  5x(5x 1)  6 is an identity. (3 marks)

2 (b) If (x  7)(Ax  2)  3x  Bx  C , find the constants A, B and C. (3 marks)

P. 3 S.2 __ Group ___ Name: ______( ) 2 - x 4. (a) It is given that y =5 + . Express x in terms of y. (2 marks) 3

xy (b) It is given that z  . Express x in terms of y and z. (2 marks) x  y

5. In the figure, BAC is a quarter of a circle. D, E and F are points lying on arc AC, BA and BC respectively such that BEDF is a rectangle. It is given that BD = 17 and FD = 8. (a) Find the length of BF. (2 marks) A

E D

17 8

B F C

(b) Find the area of the shaded region. (Give your answer correct to 3 significant figures.) (2 marks)

P. 4 S.2 __ Group ___ Name: ______( ) 6. The height and the volume of the cylinder are 6 cm and 96 cm3 respectively. (a) Find the base radius of the cylinder. (2 marks)

6 cm

(b) Find the total surface area of the cylinder in terms of . (2 marks)

Section C (29 marks) Attempt both questions in this section. Show your working steps clearly in the space provided. 1. Factorize the following algebraic expressions. (a) (i) 3xy + 3y2 + 2x + 2y (2 marks)

(ii) 2 f 3  6 f 2  5 f 15 (2 marks)

P. 5 S.2 __ Group ___ Name: ______( ) 1. (b) (i) 9a2 - 12 a + 4 (1 mark)

(ii) (m  2)2  8(m  2) 16 (2 marks)

(ii) g 2  4h2  3g  6h (1 mark)

(d) (i) 16a2- 40 ab + 25 b 2 (1 mark)

(ii) 9c2- (16 a 2 - 40 ab + 25 b 2 ) (2 marks)

P. 6 S.2 __ Group ___ Name: ______( ) 2. Simplify the following algebraic expressions. 10c 2 15c d 2 (a)   (2 marks) d 5 d c

5m2 10mn 6m3n 12m2n2 (b)  (3 marks) 4n 12m2

12 3 1 (c)   (3 marks) 5x 2x 6x

7z 3z  6 (d)  (2 marks) 3  5z 5z  3

P. 7 S.2 __ Group ___ Name: ______( )

3. (a) In the figure, ABC is an equilateral triangle with sides of 28 cm each and AD  BC. Find the area of ABC. (Give your answer correct to 4 decimal places.) (3 marks)

28 cm

D C

(b) Using the triangle ABC from 3(a), an arc DE is drawn with C as the centre. Given that BD  DC, find the area of the shaded region. (Give your answer correct to 3 significant figures.) (2 marks)

28 cm

E B

D C

(c) In the figure, O is the centre of all sectors. Find the area of the shaded region. (Give your answer correct to 3 significant figures.) (2 marks)

2 cm O 100° 1 cm 1 cm

1 cm

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