Page 49 - Spotlight A+ SPM Additional Mathematics Form 4 & 5

Additional Mathematics SPM Model Paper
Paper 2

Time: 2 hours and 30 minutes
Section A
(50 marks)
Instruction: Answer all the questions
1. A married couple has three sons. At one time, the eldest child is 4 years older than the total age of his younger
1
brothers. Two years ago, the age of the youngest child was of the age difference between his older brothers.
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Next seven years later, age of three of them is 51 years old. 4
Determine the age of each son of the couple. [6 marks]

2. Diagram 2 shows the mapping x to y which drerived by the function of f : x ˜ 9x – a and mapping of y to z
is derived by the function of g : y ˜ b , y ≠ 12.
12 – y

x y z

3
3
4
SPM MODEL PAPER (a) Find the values of a and of b. Diagram 2

(b) Express the function that maps the element x to the element z in a similar form.
[6 marks]
(c) Determine the element x that does not change when mapped to the z.
2
2
3. (a) The roots of equation 3x – 2kx + k + 4 = 0 are a and b. If a + b = 16 , find the possible value of k.
2
9 [3 marks]
2
(b) Diagram 3 shows a part of graph function f(x) = (x – 3) – 2 with minimum point A(h, 2k) and intersect
the f(x)-axis at 7. This graph is moved by 3 units to the right and 4 units upwards with new minimum
point, B as shown in the Diagram 3.
f(x)

7

f(x) = (x – 3) – 2
2
B
0
A (h, 2k)
Diagram 3
Determine
(i) the value of h and of k,
(ii) the coordinate of minimum point, B,
(iii) the new equation of f(x) in the vertex form. [4 marks]

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