Page 69 - PRE-U STPM MATHEMATICS (T) TERM 1

Mathematics Term 1 STPM Answers
Exercise 6.7 21. (b) 3 26 unit 2 (c) 5 i + j – 13 k
1
1. (1, –2, 5) 4 8 4
2. (4, 5, 9) (d) 35 16 201
16 201
3. (a) (–3, 1, 5) (b) (3, –5, 4) 1 9
4. (a) l = 2, l = 1 (b) c = –5 22. 1 2 1 2
–1 + t 14 where t ∈ R
1
2
(c) (2, –3, –3) 0 1
5. (5, –3, 7) 23. (1, 2, 3)
6. (1, –5, 1) 24. 47°7´
7. (2, 14, 6) 25. 8i + 4j – 4k, –8i + 12j + 16k
5
y + z – 13
8. x = 2y + 5 = 2z – 13 or x = 2 = 2 , 26. 2i – 3j + 4k
7
–17
7 – 17 27. (a) 22 units (b) 12i – 15j – 9k
2 2
5
7
r = – j + 13 k + l(i + j – 17 k) 28. (a) 7 390 (b) 1 329 unit 2
2 2 2 2 390 2
.
(c) r (–10i – 15j + 2k) = –30
4
y + z + 8 29. (a) 13x – 2y + 5z = –4 (b) (–1, –22, –7)
9. x 1 = 3 = 3 (c) 14.9°
5 1
3 3
STPM Model Paper (954/1)
10. x – 11 = y + 8 = z
4 –3 1. (a) f : x ↦ x – 6x = (x – 3) – 9
2
2
STPM PRACTICE 6 y
y = f(x)
1. (a) 474 units (b) 46 units y = k
2. (a) –i – 4j – 2k (b) –5i – 7j + 11k x
3. (a) 1 (5i – j – k) (b) 1 (–i – j + 3k) 0 3
27 11
4. (a) 2 (i + j – k) (b) 5 (–3i – j – k) (3, –9)
3 11
Any horizontal line y = k is drawn horizontally with
5. (a) –8 (b) 4 x-axis, will cut the graph at only one point.
–1
6. (a) 83°44´ (b) 127°25´ Therefore f is a one-to-one function and f exists.
7. (a) 78.7° (b) 36.8° (shown)
–1
Let f (x) = y
–1
7
8. (a) p = 1 ; q = –1 (b) 1 2 x = f(y) 2
x = (y – 3) – 9
9. 35° –2 ± x + 9 = y – 3
→
10. (a) PQ = –6i + 6j + 12k (b) 61.9° y = 3 – x + 9 as y < 3
–1
→ f (x) = 3 – x + 9
PR = 6i + 6j + 12k
–1
f : x ↦ 3 – x + 9

11. (b) 58.7° D –1 = [–9, ∞)
1
(c) 152 unit , 25 unit 3 f
2
3 R –1 = (–∞, 3]
f
12. (a) –2i + j + 4k (b) –4i + 4j – 8k (b) y
1
13. ± (–2i + j + 4k)
21 4 g(x) = 4 – e –x
14. 41 unit 2 3
15. (a) 11i – 29j + 5k (b) 1 987 unit 2
2 x
16. (a) 5 (b) 3 0
18 10 R = (–∞, 4)

1 g
17. (a) (3i – 4j + 6k) (b) 8i + (4 + l)j + 8k R = (–∞, 4) ⊄ D = (–∞, 3]
f
g
61
(c) l = –9 Therefore fg does not exist. (shown)
18. (a) a = 10, b = 2 (b) 64.4° We need R = (–∞, 3]
g
–x
19. (b) x + y – 3z = 7 4 – e < 3
x < 0
20. Yes Therefore the maximum domain of g for which fg exists
= (–∞, 0]
288
Answers STPM Math T S1.indd 288 3/28/18 4:25 PM