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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