Page 20 - Ranger SPM 2022 - Additional Mathematics

Additional Mathematics SPM Chapter 2 Quadratic Functions

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1. Solve 16 – x = 2x(2x + 3). Give the New SOR:
answer correct to three decimal places. (α + 2) + (β + 2) = α + β + 4
5
= + 4
Solution 3
16 – x = 2x(2x + 3) = 17 Form 4
16 – x = 4x + 6x New POR: 3
2
4x + 7x – 16 = 0 (α + 2)(β + 2) = αβ + 2α + 2β + 4
2
7
2
x = –7 ± – 4(4)(–16) 5
2(4) = –4 + 2   + 4
3
x = –7 ±305 = 10
8 3
x = –3.058 or x = 1.308 The new quadratic equation is
x – (SOR)x + (POR) = 0
2
2. Find the range of values of x where the 17 10
quadratic function f(x) = 12 – 4x – x is x – 3 x + 3 = 0
2
2
negative. 3x – 17x + 10 = 0
2
Solution 4. The diagram below shows a graph of
2
f(x) = 12 – 4x – x  0 quadratic function f(x) = –(x – h) + k
2
2
–x – 4x + 12  0 where h and k are constants.
x + 4x – 12  0 f(x)
2
(x – 2)(x + 6)  0
+ +
x
–6 – 2 –3 0 11 x

Find
x  –6 or x  2 (a) the equation of axis of symmetry,
3. Given that α and β are the roots of the (b) the maximum point.
quadratic equation 3x – 5x – 12 = 0. Solution
2
Form a new quadratic equation with the
roots α + 2 and β + 2. (a) Equation of axis of symmetry:
x = –3 + 11
Solution 2
= 4
3x – 5x – 12 = 0 (b) f(x) = –(x – 4) + k
2
2
b (–5) 5
α + β = – = – = At (11, 0),
a 3 3
2
c –12 0 = –(11 – 4) + k
αβ = = = –4 0 = –49 + k
a 3
k = 49
The maximum point is (4, 49).
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02 Ranger Add Mathematics Tg4.indd 27 25/02/2022 9:10 AM