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Mathematics Term 1 STPM Answers
11. U = 6r – 1; 9n + 2n 2. (a) 1 – x + 3 x – 5 x ; |x| , 2
1
2
3
2
r
128
4
12. 1 + 2r 2 , n(n + 2) 4 2 32 40 1
r (r + 1) (n + 1) 2 (b) 1 – x – x – 81 x ; |x| , 2
2
3
2
9
3
13. A = 1, B = –3, C = 2 1 1 1 1
3
(c) 2 – x + x – 16 x ; |x| , 2
2
4
8
Exercise 2.6 (d) 1 – x + x – 5 x ; |x| , 1
3
1
3
2
1. (a) 120 (b) 40 320 (c) 3 628 800 2 1 8 5 16
3
3
2
(d) 336 (e) 720 (f) 4896 (e) 1 – x – x + 16 x ; |x| , 1
2
8
(g) 285 (h) 8008 (i) 1260 (f) –1 + 2x – 2x + 2x ; |x| , 1
3
2
(j) 252 33 2 81 3 1
2. (a) 10! (b) 12! (c) 22! (g) 2 + 4x + 4 x + 4 x ; |x| , 3
7! 10! 19! (h) – + x – 13 x + 51 x ; |x| , 1
3
1
2
3
(d) 18! 2! (e) 21! 5! (f) n! 2 4 8 16 2
15! 5! 18! 8! (n – 3)! (i) 1 – x + x ; – (1 + 5 ) , x , ( 5 – 1)
1
1
3
(g) (n + 2)! (h) (2n + 5)! (i) n! 2 2
(n – 2)! (2n + 2)! (n – 1)! 3! 3. 1.1255
(j) (n – 5)! 2! 4. 30.43168
(n – 9)! 5! 5. 1 + 30x + 420x + 3 640x ; 1.03042
2
3
3. (a) 11(9!) (b) 15(7!) 2 3 4 5 6
(c) 291(7!) (d) (n + 2)n! 6. 1 – x + x – x
2
2
1
(e) (n + n – 1)(n – 1)! (f) n(n + n + 2)n! 7. 1 – x – x – 1 x ; 0.9487
2
1
2
3
2
(g) (n + 1) (n – 1)! (h) 31(7!) 2 8 16
2
30(3! 2!) 8. 1.732
(i) 263(7!) (j) (n – 1)! (nr + n + 1) 9. 3.1623 (5 sig.fig.)
210(3! 2!) (r + 1)! 1 1 3 1 5
3
4
2
4. (a) 70 (b) 120 (c) 1140 (d) 1 10. 4 + x + 16 x + x + 64 x ; 0.309
8
4
1
1
(e) 200 (f) 560 (g) 15 (h) 26 11. 1 + x – x + x ; 2.236
3
2
2
45
4
2
(i) 6188 (j) 84 12. 1 – 7x + 28x – 112x ; |x| , 1
2
3
4
4
3
Exercise 2.7 13. 1 – 5x + 30x – 15x ; 0.950 030
3
3
4
2 2
1. (a) p + 4p q + 6p q + 4pq + q 4 STPM PRACTICE 2
2
5
4
6
3
7
3
4
(b) m – 7m n + 21m n – 35m n + 35m n – 21m n + th
5
2
7mn – n 7 1. n(n – 1); 15
6
1
1
(c) 64 + 192k + 240k + 160k + 60k + 12k + k 12 2. (a) 3, 4 , 4 , 4 + 1 , n . 1
2
6
10
4
8
6
2
n(n – 1)
(d) 32a – 80a b + 80a b – 40a b + 10ab – b 5 (b) 2, 4, 18, n(n!), n . 1
5
4
3 2
2 3
4
3
(e) x + 3x + + 1
3
x x 3 3. (a) 250 (b) 510
(f) y – 4y + 7y – 7y + 35 – 7 2 + 7 4 – 1 6 + 1 (c) n(n + 1) (d) (n + 1)! – 1
8
6
4
2
8 4y 16y 16y 256y 8 n(n + 2)
6.
2. (a) 210x 4 (b) 16 128x 2 3(2n + 1)(2n + 3)
4
3 9
(c) 1760 a b (d) –945p q 6 7. b 2
(e) –20 (f) 36 8. 11, 20
x 3 9. Explicit formula: u = 4n – 1
n
5
3. 64x + 160 + 20 7 Recursive formula: u = u n – 1 + 4 for n = 2, 3, 4, … and u = 3
n
1
x
x
4. 14 or u n + 1 = u + 4 for n = 1, 2, 3, 4, … and u = 3
n
1
5. 15 10. (a) w = 8n + 4
n
6. 2 (b) First term = 12; Common difference = 8
7. n = 8, a = – 1 (c) S = u + w – 3
2 11. 11 n n n
2
8. (a) 1 + 7x + 21x + 35x 3 3 3
3 2
(b) 1 + 7x + 14x – 7x 3 12. (a) U = 23 1 + 1 24 , U = 23 1 + 1 2 + 1 2 4 ,
2
5
5
5
3
2
2
9. 1 + 16x + 136x + 784x 3 3 3 2 3 3
10. 1 + 9x + 24x 2 U = 23 1 + 1 2 + 1 2 + 1 2 4
5
5
4
5
11. (a) –16 464 (b) –151 164 (b) lim U = 5
(c) –1760 (d) 26 r → ∞ r
Exercise 2.8 14. (a) (n + 1)(2n + 1) (b) –975
1. (a) 1 – 2x + 3x – 4x 3 (b) 1 + x + x + x 3 15. (a) mn 1
2
2
1
1
3
2
2
n
(c) 1 – 6x + 24x – 80x 3 (d) 1 4 – x + 16 x – x 3 (b) mn – m + 1; S = m(2mn – m + 1)
2
5
8
4
2
(e) 1 – x + 4 x – 8 x 3 16. (a) u = 2 4r + 1
2
r
3 9 27 81
279
Answers STPM Math T S1.indd 279 3/28/18 4:25 PM
