Page 14 - PRE-U STPM MATHEMATICS (T) TERM 2

Mathematics Term 2 STPM Answers

7. (b) right 2 Differentiation
f(x )
Exercise 2.1
2 1. 3x 2 2. 4x 3
x 3. 10x 4. – 2
–3 0 5 x 3
–2
5. 2x + 5 6. 2x – 1
7. 12x 2 8. – 3
x
4
not continuous 9. 4x 10. 4x – 3
8. k = – 3 ; Continuous
4
9. c = 1 Exercise 2.2
1. 0 2. 3
10. (a) 2 3. –4 4. 5x 4
(b) 5. –4x 6. 1 – — 2
–5
x
3
f(x ) 3
7. – 1 8. 3 x
x 2 2
1 – —
x
9. – x 2 3 10. 2 – — 1
3
2 3
x 11. –15x –4 12. 70x 9
0 2 4 5
13. – 5 14. 21 2
x
continuous x 5 8
15. 16
STPM Practice 1 x 9
1. (a) 1 (b) 3 Exercise 2.3
2 1 x 1
1. 2 ln 2 2. 1 2 ln
x
lim
lim
2. (a) (i) x → c f(x) ≠ x → c f(x) 5 3 5 2
+
–
lim
lim
(ii) x → c f(x) = x → c f(x) ≠ f(c) 3. 10x + 3 4. 4x – 18x
4
–
+
lim
lim
(iii) x → c f(x) = x → c f(x) but f(c) is not defined 5. 6x – 5 1 6. 2x – x 2
–
+
2
x
3
(b) {k: –∞ < k < 0 or 0 < k < 3 or < k < ∞} 7. – x 3 – x 2 8. e + cos x
2 2
3. a = –32, b = 3 9. 2 10. 8x + x 2 2 + x 9 4
x
4. (a) 1, 0, 2, 1 (b) Yes, No 2 1
11. – – 2x 12. –
5. (a) 8 (b) –2√ 7 3x 2x
27 13. 10x – 3 + 8 14. 1 + 4
6. (a) b = 3 (b) a = ±√ 6 x 2 x 3 x 2 x 3
lim lim lim 15. – 3 16. 2 cos x – 3 sin x
7. (a) x → 0 f(x) = x → 0 + f(x) = 1, x → 0 f(x) exists. 2x
–
3
lim
(b) x → 0 f(x) = 1 ≠ f(0) = 2 17. 13 18. 13
4
f(x) is discontinuous at x = 0
f(x) is continuous in the interval (–∞, 0) < (0, ∞) Exercise 2.4
1. 2x(2x + 1) 2. 24x – 5

2
8. a = 1, b = –1 12 1
2
3. 8x – 30x + 1 4. – – 2x
3
lim lim x 4 x 2
–
9. x → 3 f(x) = –6 ≠ x → 3 + f(x) = 6 2
f(x) is discontinuous at x = 3 5. 3x – 4x – 1 6. 5(cos x – x sin x)
sin x
8. (cos x) ln x +
10. (a) 2 (b) – 1 7. 2x(2 sin x + x cos x) 10. e (x + 2x – 1) x
2
9. 1 + ln x
x
2
13. (a) 3 (b) 2 11. e (tan x – cos x + sec x + sin x)
2
x
8
2
14. No, not continuous at 1 12. sin x (1 + sec x)
13. x(2 cos x – x sin x)
lim lim
–
15. (a) x → 0 f(x) = 8, x → 0 + f(x) = 2 + c, c = 6 14. 2x (sin x + cos x) + x (cos x – sin x)
2
(b) (i) f(x) continuous at x = 0 only when c = 6
(ii) f(x) continuous at x , 0. (quadratic) 15. cos 2x
(iii) f(x) continuous at x . 0. (exponential function) Exercise 2.5
1. –6x 2. 2
(2x – 3) 2 (x + 1) 2
2
196
Ans STPM Math T Term2.indd 196 02/11/2018 12:47 PM