Page 12 - Focus SPM KSSM Tg 4.5 - Add Maths

Additional Mathematics SPM Chapter 2 Quadratic Functions

(c) 2x – 5x + 2 . 0 Example of HOTS
2
HOTS Question
Table method
2x – 5x + 2 = 0 6.6 m
2
(2x – 1)(x – 2) = 0 x m
Factorise the
quadratic x  1 x = 1 1  x  2 x = 2 x . 2 x m 4.8 m
equation 2 2 2
(2x – 1) – 0 + + +
(x – 2) – – – 0 + The diagram above shows a rectangular piece of
(2x – 1)(x – 2) + 0 – 0 + land with a length of 6.6 m and a width of 4.8 m.
Amin wants to lay square tiles with side x m around
From the table, it shows that (2x – 1)(x – 2) . 0 the land to build a walkway. If the area of the Form 4
2
1 region where the tiles are laid is 12.24 m , find the
when x  or x . 2. value of x.
2
Try Question 18 in ‘Try This! 2.1’ Solution
Area of the region where the tiles are laid
= 2 × 6.6 × x + 2 × (4.8 – 2x) × x
8 = 13.2x + 9.6x – 4x 2
= 22.8x – 4x 2
Find the range of values of x for (2x – 1)(x + 4) < 4 + x.
2
Hence, 22.8x – 4x = 12.24
Solution 4x – 22.8x + 12.24 = 0
2
(2x – 1)(x + 4) < 4 + x 400x – 2 280x + 1 224 = 0
2
2x + 8x – x – 4 < 4 + x 50x – 285x + 153 = 0
2
2
2
2x + 7x – 4 – 4 – x < 0 –(–285) ± 
2
2x + 6x – 8 < 0 x = (–285) – 4(50)(153)
2
x + 3x – 4 < 0 285 ± 225 2(50)
2
a = 1 . 0 ⇒ the shape of the graph is . = 100
When x + 3x – 4 = 0 x = 510 or x = 60
2
(x – 1)(x + 4) = 0 100 100
x – 1 = 0 or x + 4 = 0 x = 5.1 or x = 0.6
x = 1 or x = –4
The graph intersects the x-axis at x = 1 and x = –4 5.1 m is longer than the width of the land which is
4.8 m. So, x = 5.1 is unacceptable.
Therefore, x = 0.6
x
–4 1
Try this HOTS question
Therefore, the range of values of x is –4 < x < 1. The profit made by a factory that is producing
nuts in packets is given by
2
SPM Tips P(t) = 40t – 7t – 5 676, where t is the time, in
hours, the production process is running. Find
Eliminating the common expression of (x + 4) in the the time of production needed for the factory to
inequality will cause the range of values of x obtained get back its capital.
incomplete. Answer: The time of production must be at least
(2x – 1)(x + 4) < (4 + x) 12 hours.
2x – 1 < 1
2x < 1 + 1
x < 1
Try Questions 20 – 21 in ‘Try This! 2.1’
Try Question 19 in ‘Try This! 2.1’

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