Page 61 - PRE-U STPM MATHEMATICS (T) TERM 1

Mathematics Term 1 STPM Answers

1
(b) S = 3 1 – 1 1 2 4 ; lim S = S = 1 6 –11 1 –17 –5
n
n 6 16 n → ∞ n ∞ 6 DA = 1 4 2 2 , DB = 1 2 –2 6 2
17. (a) 138 –7 0 –3 7 –7
(b) 1 (10 – 1); 1 (10 n + 1 – 9n – 10) 4. (a) –4 2 (b) –7 –4
n
9 81 1 10 9 2 1 7 12 2
18. (a) 676 (b) 493 (c) 1168
2475 825 1665 (c) 1 9 1 –1 4 2 2 (d) 1 –8 –2 –4 2
8
15
10
6
1
19. (b) u n + 1 = u n (c) S = lim S = 3 2 5. x = 2, y = 4, z = 1, w = 3
2
∞
n
n → ∞
2
20. 5 x + 15 x + 65 x 3
2 4 8 7. a = 1, b = –3
21. (a) 752 50 –50 100 0 –15 –30
0
0
0
1
1
22. 1 + apx + a p(p – 1)x + a p(p – 1)(p – 2)x ; 3 8. (a) 1 10 –10 20 2 (b) 1 0 0 –15 –30 2
2
2
3
2
30
60
6
8
4
3
– , – ; |x| , .

4 3 3 (c) (57) (d) (5)
2 1249
1
1
23. n = 4; 1 – x – x ; 12 –6 36
2 8 200 (e) 1 2 –1 6 2 (f) (17)
24. p = 3, q = 2, n = 8 –2 1 –6
1
6
8
25. 1 + x + x 2 9. (a) 1 38 27 2 (b) 1 11 16 16 2
2
24
26. 1 1 4 –16 –4 1 –1 12
1 2 , 0.98952
6 n
2

27. (a) 1 n(28n – 1) (b) 1 , 4 10. (a) –1 0 31 (b) 1 –1 –4 –12 2
2
24
8
3 999 37 1 –10 –4 104 2 –3 –12 –36
6
6
28. (a) 167 167; 111 445 (b) A = 13 , B = 1; 13 2 2
1
2
4
29. (a) 1 + x – 3 x 2 (b) 20x + 160x + 64; 1364 (c) 1 –11 –11 2 (d) 1 –5 –5 2
4 32 –18 –18 –32 –32
30. – 1 – 2 + 3 2 ; 0, 5, 6; 3r + 1 + (–1) r + 1 11 4 –135 2 8 24
1 + x 1 – x (1 – x)
(e) 1 –22 –8 270 2 (f) 1 –5 –20 –60 2
2 (1 – x
31. (a) S = 2x 3 n – 1 ) 4 33 12 –405 –32 –128 –384
n – 1 1 – x
15 Exercise 3.2
(b) ∑ (2r – 1)3 = 602 654 097 2 2
r
r = 1 1. (a) 9 (b) 2 (c) x + y – 2
14 2. (a) 0 (b) 0 (c) –14
∑ (2r + 1)3 r + 2 = 1 807 962 291
r = 1 3. (a) x(x – 1) (b) 8a(1 – 2a) (c) axy(2 – ay)
4. (a) –3 (b) 3 (c) 3
Chapter 3 Matrices 5
5. (a) –96 (b) 192 (c) 75
Exercise 3.1 6. (a) 18 (b) 2 (c) – 1
3
5
0
3
1
2
1. (a) 1 –6 12 0 6 2 (b) 1 –3 –5 –1 2 7. (a) 0, –9 (b) 0, –2 (c) –3, 0, 2
0
5
1
(c) 1 1 1 3 5 –3 2 (d) 1 –5 –5 3 1 2 Exercise 3.3
3
5
2
11
1
(e) 1 –13 –15 9 1 2 1. (a) 1 0 –1 2 (b) 1 –3 –3 2
2
1
7
(c) 1 –4 –5 2 (d) 1 3 –2 2
7 –5
3
16
24
24
24
16
16
2. (a) 1 33 –6 –39 2 (b) 1 18 5 –31 2 –2 –1
30 18 9 9 –2 28 (e) None (f) 1 3 2 2
1
3
2
2
3. A = 1 –5 8 5 2 , AB = 1 –1 13 8 3 2 (g) None (h) 1 — 0 2
2
3
1
2
2
BC = 1 3 4 –3 –2 2 , BD = 1 –10 –1 2 0 –1 3 1 0 – — 3 –2
2
2
16
1 5 1 3 2 1 5 10 2 2. (a) 1 1 4 2 (b) 1 2 1 2 (c) 1 0 2 2
C = –2 16 –5 , CD = 11 –1
2
–1
–1
–4 2 –3 –1 –7 3. (a) A B (b) BA
(c) B (d) A BA
–1
280
Answers STPM Math T S1.indd 280 3/28/18 4:25 PM