Page 67 - PRE-U STPM MATHEMATICS (T) TERM 1

Mathematics Term 1 STPM Answers

(c) (i) 5 , (±4 5 , 0) 2. (a) (x – 9) 2 + (y + 12) 2 = 1 ; ellipse
2
2
2 a b
16 5 1 (b) The conic is a circle with centre (9, –12) and radius 15.
(ii) x = ± , y = ± x
5 2 y
(d) (i) 6 , (±3 6 , 0) 0
2 18 x
2
(ii) x = ±2 6 , y = ± x
2 (9, –12)
13
(e) (i) 3 , (1 ± 13, 0) –24
2
(ii) x = 1 ± 9 , y = ± (x – 1)
13 3 4. m x´ – my´ + a = 0
2
(f) (i) 14 , (1 ± 70 , 2) 5. (a) (p + q)y = 2x + 8pq ; py = x + 4p 2
3 2
5
(ii) x = 1 ± 3 70 , (y – 2) = ± (x – 1) (b) M(–4p , 0)
14 7 (c) A(4, 0)
6.
3. (a) xy = 9 (b) 4xy = 25 y
(c) xy + 4 = 0 (d) 9xy + 4 = 0
(e) xy = y + 1 (f) xy – x + 16 = 0 2 x + 4y = 2x
2
2
5
5
4. (a) x = 4t, y = 4 t (b) x = t, y = 3t ( )
1
1, –
3
2
1
(c) x = t, y = – 1 (d) x = 8t, y = 8 x
4 4t t – 4 0 2 4
2
1
(e) x = 1 + 2t, y = (f) x = 2 + t, y = 1 ( )
–
1, –
t t 2
2
2
4
5. (a) t y + x = 6t ; ty – t x = 3(1 – t ) –2 x + 4y = 16
3
2
(b) 9y + 4x = 24 ; 12y – 27x + 65 = 0
(c) t y + x = 3t ; 2ty – 2t x = 3(1 – t )
2
4
3
(d) 6y + x = 9 ; 4y – 24x + 105 = 0 7. (2, 1), (–1, 3)
6. (a) 4y + 3x + 8 3 = 0, 4y + 3x – 8 3 = 0 8. (a) (x – 1) 2 + (y – 4) 2 = 1
(b) y + 4x = 8 9 16
(b) C = (1, 4) ; F = (1, 4 – 7 ) ; F = (1, 4 + 7 )
2
1
3
7. 1 – , – 242 , 51 17 (c) Vertices = (1, 0) and (1, 8)
8 8 y
8. QR = 10 ; Q´R´ = 35 (1, 8)
12
9. x + 3y = 9 8 7
1 16 8 F (1, 4 + 7)
10. , –4 ; 1 , – 2 6 2
2 7 7 5
4
11. 1 , 4k2 (–2, 4) 4 C(1, 4) (4, 4)
k
–1 35
12. tan 1 2 or 69°37´ 3
13 2 F (1, 4 – 7)
14. p = 1 1 1
3 –3 –2 –1 0 1 2 3 4 5 x
b
2
15. ± b + c 2 , y = ± x. 2
a a 12. (b) q y + x = 2cq
3
3
STPM PRACTICE 5 13. (a) (–5, 0), (5, 0) (b) y = – x, y = x
4
4
1. (a) (x + 2) 2 + (y – 3) 2 = 1; ellipse 17. (a) (y – 3) 2 – x 2 = 1 ; centre = (0, 3) ; vertices = (0, 0), (0, 6)
16 12 9 9
(b) Centre, C = (–2, 3); Foci, F = (–4, 3) and F = (0, 3) (b) y = x + 3, y = –x + 3
1 2
(c) y (c) y
y = –x + 3 y = x + 3
6 (0, 6)
F (–4, 3) C(–2, 3) F (0, 3) (0, 3)
2
1
x
x –3 0 3
–6 –5 –4 –3 –2 –1 0 1 2
286
Answers STPM Math T S1.indd 286 3/28/18 4:25 PM