Revision P2 06

REVISION EXERCISES p2/2006

4037/2 ADDITIONAL MATHEMATICS PAPER 2 FORM 5 ‘O’ – Level 1.

2.

A curve x 2 + y 2 = 10 and a line 2 x + y = 5 intersect at two points A and B. Find the coordinates of A and B. Given that

a+b 3 =

13 4+ 3

[4]

, where a and b are integers, find, without using a

calculator, the value of a and of b

[4]

3.

Solve the equation 2 x 3 − 7 x 2 − 7 x + 30 = 0 .

[4]

4.

A curve is such that

5.

6.

7.

8.

dy = dx

6 3x + 1

. Given that the curve passes through the points (5,13)

and (k,17), find the value of k.

[5]

The line 2 x − y = 5 intersects the curve x 2 − xy + y 2 = 7 at the points A and B. Find (i) the coordinates of A and B (ii) the equation of the perpendicular bisector of AB.

[7]

Find the nature of the roots of the following quadratic equations: a. 5x2 + 1 = 7x b. 4x2 = a (4x – a)

[2] [3]

Given a. b. c.

y = 6 − x − x 2 , find the range of values of x for which y is positive, the maximum value of y Sketch the graph y = 6 − x − x 2

A rectangular box, with a lid, is made of thin metal. Its length is 2x cm and it width is x cm. If the box must have a volume of 72 cubic metres. a. show that the area A sq. metres of the metal used is given by

[2] [2] [3]

[4]

216 A = 4x 2 + x b. find the value of x so that A is minimum. 9.

The function f is defined as f : x a

[4]

20 . ax + b

-1 a. Find f ( x ) in term of a and b,

[2]

-1 b. Given that f (1) = 4 and f ( −4 ) = − 4 , find the value of a and of b,

[4]

c. From (ii) what will be the value of x for which f(x) = x.

[4]

2 Write down and simplify the first three terms in the expansion, in descending powers

10.

6

3⎞ ⎛ of x of ⎜ x − ⎟ . Given that the coefficients of x 5 and x 4 in the expansion of x⎠ ⎝

(

)

⎛ 1 + ax + bx ⎜ x − ⎝

11.

2

6

3⎞ ⎟ are 3 and 12 respectively, find the value of a and of b. x⎠

[6]

A spherical balloon is expanded so that its surface area is increasing at the rate of 2 m2/min. a. At what rate is its radius increasing when the radius is 4 m? b. At what rate is its volume increasing at the same instant?

[4] [4]

4 [ Surface areas, s = 4π r 2 ; volume, v = π r 3 ] 3

12. Answer only ONE of the following two alternatives.

[12 marks]

[ EITHER ] A particle moves in a straight line so that, t s after leaving a fixed points O, its velocity, v ms-1 , is given by v = 8 + 2t − t 2 . Find (i) Find the retardation of the particle when v = 8. (ii) Calculate, to the nearest metre, the displacement of the particle from O when t = 6. (iii) Sketch the velocity-time graph for the motion of the particle. [OR]

The diagram shows the shaded region PAQ bounded by the curve y = 9 – x2 , the line 3x + 2y = 9 and the x-axis. Find (i) (ii)

the coordinates of A, P and Q. area of the shaded region PAQ.

… The end.

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