SPM Additional Mathematics (Model Test Paper)

SPM Additional Mathematics (Model Test Paper)

Section A
[40 marks]
 Answer all questions.

Question 1
Solve the simultaneous equations:
2(xy) = x + y – 1 = 2x2 – 11y2                                                                                                              [5 marks]

Question 2
Given that f:x 5x mx3 ,x 3 2 and g:x34x. Find
(a)    the value of m,                                                                                                        [2 marks]
(b)   gf-1(–2),                                                                                                                 [3 marks]
(c)    function h if hg (x) = 12x + 5                                                                                 [3 marks]

Question 3
Diagram 1 shows four rectangles. The largest rectangle has a length of L cm and a width of W cm. The measurement of the length and width of each subsequent rectangle are half of the measurements of its previous one. The areas of the rectangles form a geometric progression. The terms of the progression are in descending.

(a)    State the common ratio, hence find the area of the first rectangle given the sum of four rectangles is 510 cm2.                                                                                                 [4 marks]
(b)   Determine which rectangle has an area of 96 cm2.                                                  [2 marks]

Question 4
(a) A worker is pumping air into a spherical shape balloon at the rate of  25 cm3 s-1.
[ Volume of a sphere, V= 4 3 π r 3 ]
Leaving answer in terms of π, find,
       (i)     rate of change of radius of the balloon when its radius is 10 cm.                  [3 marks]
       (ii)   approximate change of volume when radius of the balloon decrease from 10cm to  9.95cm.  
             [2 marks]
(b) A curve y=h x 3 3 x  has turning point x = 1, find value of h.                              [3 marks]

Question 5
Diagram 2 shows a triangle EFG.

It is given ER:RF=1:2, FG:TG=3:1, ER =4 x ˜ and EG =6 y ˜ .
(a) Express in terms of x ˜ and y ˜ : (i) GR (ii) GT
[3 marks]

(b) If line GR is extended to point K such that GK =h GR and EK =6 x ˜ 3 y ˜ , find the value of h.   
[3 marks]

Question 6
Solution by scale drawing is not accepted.

Diagram 3 shows three points, A, B and D in a Cartesian plane. The straight line AB is perpendicular to straight line BD which intersect the y-axis at D. The equation of the line BDis y = 2x – 5.
(a)    Find the equation of the straight line AB.                                                             [2 Marks]
(b)   The straight line AB is extended to a point C such that AB : BC= 2 : 3. Find the coordinates of C.                                                                                                                           [3 Marks]

(c)    Point P moves such that its distance from A is equal to its distance from B. Find the equation of the locus P.                                                                                                       [2 Marks]

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