Page 302 - Matematik Tambahan Tingkatan 4 KSSM
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Latihan Intensif 2.3 LATIHAN PENGUKUHAN
7 1. 3.066
1. (a) k = −1 atau k = 4 (b) k > –
2
3 2. (a) x – 8x + 13 = 0 (b) 8, 13
2. 5 (c) Dua punca nyata dan berbeza
3. (a) (x + 3) – 9 + n (b) 4 3. (a) k = −8, 4 (b) k < −8, k > 4
2
(c) y (c) k –8, k 4
4. (a) p = 2 (b) p = −1
5. h : k = 7 : 6 ; x = 1
6. x < 2 atau x > 5, 0 x 7; 0 x < 2 atau 5 < x 7
7. (a) 3, 7 (b) p = −5, q = −12
4
2
f ( x ) = (x + 3) − 5 (c) x = 5 (d) 3 < x < 7
− 3
x
0 8. (a) b = −8, c = 12 (b) (4, −4)
(c) 2 < x < 6 (d) 4
− 5
9. 9 km/j
4. r < −2, r = –6 atau r = –2 10. 67.229 unit
5. (a) Kelebaran graf berkurang. Paksi simetri graf dan 11. (a) 20 unit (b) 20 unit
nilai minimumnya tidak berubah. 1
2
(b) Graf dengan bentuk yang sama bergerak secara 12. (a) y = – (x – 3) + 2.5
18
mengufuk 3 unit ke kanan. Persamaan paksi (b) 9.708 m
simetrinya menjadi x = 4 dan nilai minimumnya
tidak berubah, iaitu 2.
(c) Graf dengan bentuk yang sama bergerak secara BAB 3 SISTEM PERSAMAAN
menegak 3 unit ke atas. Nilai minimumnya Latih Diri 3.1
menjadi 5 dan paksi simetrinya tidak berubah,
iaitu x = 1. 1. 3x + 2y + z = 750
6. (a) h ( t ) 2. (a) Ya, kerana ketiga-tiga persamaan mempunyai
tiga pemboleh ubah, m, n dan p dengan
t = 3
18 kuasa pemboleh ubah bernilai 1. Persamaan
mempunyai nilai n sifar.
(b) Bukan, kerana terdapat persamaan yang
mempunyai kuasa pemboleh ubah bernilai 2.
(c) Ya, kerana ketiga-tiga persamaan mempunyai
tiga pemboleh ubah, a, b dan c, dengan kuasa
t
0 3 pemboleh ubah bernilai 1.
(b) r ( t )
Latih Diri 3.2
36
1. (a) x = 1, y = 3, z = 2 (b) x = −1, y = 2, z = 3
t = 3
2. (a) x = −1, y = 3, z = −1
28 16
(b) x = – , y = 8, z =
3 3
t Latih Diri 3.3
0 3
(c) Graf fungsi h(t) dengan nilai a = 2 lebih lebar 1. P = RM8 000, Q = RM2 000, R = RM14 500
daripada graf r(t) dengan nilai a = 4. Maka, 2. Teluki = 80, mawar = 50, daisi = 70
burung yang diwakili oleh fungsi r(t) bergerak 3. Pen = 3, pensel = 5, buku nota = 8
pada kedudukan tertinggi, iaitu 36 m dari paras
air berbanding burung yang diwakili oleh fungsi Latihan Intensif 3.1
h(t) dengan 18 m. 1. (a) x + y + z = 180, x – 20 = y + z, x – 10 = 3z;
7. p = 3, q = 7
100°, 50°, 30°
8. (a) b = −1 (b) c > 2 (b) x + y + z = 19, 2x + y + z = 22
(c) c = 4 x + 2y + z = 25; 3, 6, 10
9. (a) 4 saat (b) 64 m 2. (a) x = 2, y = 1, z = 0 (b) x = 3, y = 2, z = 1
10. (a) (i) α (ii) β (c) x = 5, y = −3, z = 1 (d) x = , y = – , z = –6
8
44
α + β 5 5
(iii) −αβ (iv)
2 (e) x = −1, y = 3, z = 1 (f) Tiada penyelesaian
α + β 3. Mentega = 500, coklat = 750, kelapa = 900
(b) ialah koordinat-x bagi titik maksimum
2 4. Kecil = 9, sederhana = 6, besar = 3
graf dan – αβ ialah pintasan-y bagi graf tersebut. 5. Ayam = 20, arnab = 10, itik = 20
294
