Page 3 - 1202 Question Bank Additional Mathematics Form 4

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KNOW Common Mistakes

Solving Quadratic Equations Functions
Use the method of completing the squares to solve 2x + 5x + 1 = 0 . The diagram shows the f g
2
Correct Wrong function f maps set A to
2x + 5x + 1 = 0 2x + 5x + 1 = 0 set B and g maps set B x x + 2 5x + 4
2
2
to set C. Find g(x).
5
2
2
1
2
2
2 x + x + 1 = 0 1 2x + 5 + 1 = 0
2
2
31
2 x + 5 4 2 2 – 25 4 + 1 = 0 Correct A B Wrong C
16
1
2 x + 5 4 2 2 – 25 + 1 = 0 Note: 1 5 is g(x + 2) = 5x + 4 g(x + 2) = 5x + 4
2
2
When 2x +
8
2
1
2 x + 5 4 2 2 = 17 expended, it becomes Let y = x + 2 g(y) = 5y + 4
Then, x = y − 2
8
1 x + 5 4 2 2 = 17 4x + 10x + 25 . g(y) = 5(y – 2) + 4
2
4
16
= 5y – 10 + 4

x = – ± ABBB = 5y – 6
17
5
4 16 ∴ g(x) = 5x – 6
= –0.219, –2.281
Common Mistakes (Chapter 2) 8 @ Pan Asia Publications Sdn. Bhd. Common Mistakes (Chapter 1) 2 @ Pan Asia Publications Sdn. Bhd.
Vertex Form of Quadratic Equations Composite Function
Complete the square for f (x) = 2x + 4x – 3. Hence, find the If f (x) = 2x + 1 and g(x) = x – 5, find fg(x).
2
coordinates of the minimum point. Correct Wrong
Correct Wrong fg(x) = f (x – 5) fg(x) = g(2x + 1)

= 2x + 1 – 5
= 2(x – 5) + 1
f (x) = 2x + 4x – 3 6 ©PAN ASIA PUBLICATIONS
f (x) = 2x + 4x – 3
2
2

= 2x – 10 + 1
= 2x – 4
1
2
= 2 x + 2x – 3 2 = (2x + 2) – 4 – 3 = 2x – 9
2
2
= (2x + 2) – 7
2
1
= 2 (x + 1) – 1 – 3 2 Note: Substitute g(x) first followed Do not substitute f (x) first.
2
2
2
2
= 2(x + 1) – 5 (2x + 2) ≠ 2x + 4x + 4 by f (x).
2
The coordinates of the The coordinates of the
minimum point is (–1, –5). minimum point is (1, –5).
Note:
The vertex for
f (x) = a(x – h) + k is (h, k).
2
Common Mistakes (Chapter 2) 10 @ Pan Asia Publications Sdn. Bhd. Common Mistakes (Chapter 1) 4 @ Pan Asia Publications Sdn. Bhd.
Roots for Quadratic Equations Inverse Function
Determine the sum of roots and product of roots for the quadratic If f (x) = x – 1 , g (x) = x + 5 and fg(x) = 2x – 9, find (fg) (x).
–1
–1
–1
equation 2x + x – 6 = 0. 2
2
Correct Wrong
Correct Wrong fg(x) = 2x – 9 (fg) (x) = f g (x)
–1
–1
–1
1 Sum of roots = 1 or –1 Let y = 2x – 9 = f (x + 5)
–1
Sum of roots = –
2 Product of roots = –6 then x = y + 9 (x + 5) – 1
Product of roots = – 2 = 2
2 Note: –1 y + 9 x + 4
= –3 For ax + bx + c = 0. (fg) (y) = 2 = 2
2
Then, (fg) (x) = x + 9
–1
2
Sum of roots = – b Note:
a
Product of roots = c a (fg) (x) ≠ f g (x)
–1
–1
–1
(fg) (x) = g f (x)
–1
–1
–1
fg(x) ≠ gf(x)
Common Mistakes (Chapter 2) 12 @ Pan Asia Publications Sdn. Bhd. Common Mistakes (Chapter 1) 6 @ Pan Asia Publications Sdn. Bhd.
00B_1202 QB AMath F4.indd 4 09/05/2022 11:30 AM