Mathematics

Michaelmas Term 2010

Form 4

Paper 2(2 hrs 15 mins)

Instructions to Candidates

1. Answer all questions. 2. Full marks may not be awarded unless full working is shown.3. Mathematical instruments and silent electronic calculators may be used for

this paper.

DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO

1. The Venn diagram below shows the number of students doing Mathematics (M), Accounts (A) and French (F) in a class of 50.

(i) Write down the expression, in terms of x , for the number of students who do Accounts. (2 marks)

(ii) Write down an equation, in terms of x , which shows all the information in the Venn diagram. (3 marks)

(iii) Determine the number of students who do Mathematics only. (2 marks)

(iv) Determine the number of students who do French. (2 marks)

2.

In the Venn diagram above,

U = {whole numbers less than 10}, and

A and B are subsets of U.

(i) Describe A and B in words. (2 marks)(ii) List the members of A B and describe the set, in words, in relation to A and B. (2 marks)(iii) Determine n [( A∩B )' ] (2 marks)

3. (a) Given a=2, b=−3, and c=0, evaluate

(i) 4 a –2b+3 c (2 marks)(ii) √ (a2+b2) (3 marks)(iii) b+ac – a(iv) ab

(v) bc (2 marks)

(b) Evaluate the following: -

(i) 4 (5 x+3 y)+3 (4 x+5 y ) (3 marks)

(ii) 8(5x –3 y )– (4 x+7 y) (3 marks)

(iii) 3 x+2(4 x+3) – 4(1 –5 x ) (3 marks)

4. Study the number pattern in the table below and complete lines (i), (ii) and (iii) in your answer booklet.

331× (32−1 )+(2×32)+1 27

432× (42−1 )+(2×42)+2 64

533× (52−1 )+(2×52)+3 125

634× (62−1 )+(2×62)+4 216

73

103

n3 (n−2 )×()+(2×n2 )+n n3

5. Expand and Simplify:-(i) (x+ y )(x−3 y) (3 marks)(ii) (x+5)(x – 5) (3 marks)(iii) (3a – 7)(3a –7) (3 marks)(iv) (9 x+2 y)(5 x+3 y) (3 marks)(v) ( y+4)( y+4 ) (3 marks)(vi) (xy –8a)(xy – 8a) (3 marks)(vii) (7 x – 3)(2 x –5) –3(4 x –1) (4 marks)

6. Transpose(i) k=l+b ( for l) (2 marks)(ii) 4 t−3 j=2h ( for h) (3

marks)

(iii)2k−pm

=3 f ( for f ) (3 marks)

(iv) 2m ( x+ y )=2 f ( for x) (4 marks)

(v) A=π r2 ( for r ) (3 marks)

(vi)x

(2 x−7)=6 ( for x) (4 marks)

(vii)a x2+b y2=c z2 ( for y ) (4 marks)

7. Evaluate the following.

(i) 73×7−2×7 (2 marks)

(ii) (62 )−1 (2 marks)

(iii) ( 23 )−2

(2 marks)

(iv) 6−7×362×63 (3 marks)

(v)33×4−2

37×4−4 (3

marks)

(vi) 64−23 (3 marks)

8. Solve for x(a) 32 x=81 (3 marks)

(b) 62x×36=6x×62 (3 marks)

(c) ( 23 )2 x−1

=( 32 )−1

(2 marks)

(d) 23 x−1=42 x−7×2 (3 marks)9. Simplify the following.

(a) t35×t

−85 (2 marks)

(b) 2 xy×8 x6 y7÷16 x3 y2 (3 marks)

(c) 6 pqr2

18 pq2×9 p7qr30 pqr

(3

marks)

(d) 15 pqr×3√ p6q9 (3 marks)