Matematik Tingkatan 3

Matematik Tingkatan 3 Jawapan

Bahagian B / Section B (c) Apabila saiz sudut bertambah, nilai tangen bertambah
When the size of the angle increases, the value of tangent
10 (a) (i) 24 cm (ii) 1.2 m increases
(b)
4 (a) (i) 0.4067 (ii) 0.9135 (iii) 0.4452

(b) (i) 0.6218 (ii) 0.7832 (iii) 0.7940

(c) (i) 0.7216 (ii) 0.6924 (iii) 1.0422

(d) (i) 0.8572 (ii) 0.5150 (iii) 1.6643

(e) (i) 0.9260 (ii) 0.3776 (iii) 2.4525

(f) (i) 0.9665 (ii) 0.2566 (iii) 3.7671
1 1 (a) Pentagon D/ Pentagon D
(b) (i) C (ii) A (g) (i) 0.9867 (ii) 0.1628 (iii) 6.0624

Bahagian C / Section C (iii) B (h) (i) 0.9974 (ii) 0.0718 (iii) 13.8940

1 2 (a) 1 : 15 5 (a) 3 (b) 8 (c) 24
(b) (i) 1 : 200 (ii) 391 m2 4 15 7
(c) (i) 1 : 500 (ii) 6.6 km
1 3 (a) 10 cm2 (d) 8 (e) 5 (f) 19
(b) (i) 12 cm 7 18 9
(ii)
6 (a) (i) 1 (ii) 23 (iii) 1
2 3

(b) (i) 1 (ii) 1 (iii) 1
22

(c) (i) 3 (ii) 12 (iii) 3
2
(c) 80° 45′
7 (a) 47° 38′ (b) 64° 27′ (f) 80° 55′
(d) 29° 27′ (e) 49° 21′ (i) 81° 39′
(g) 31° 56′ (h) 42° 41′ (c) 15° 4′
8 (a) 39° 10′ (b) 61° 56′ (f) 73° 30′
(d) 65° 6′ (e) 66° 49′ (i) 70° 1′
(g) 27° 34′ (h) 62° 35′ (c) 21
(f) 7.5
9 (a) 12.5 (b) 16.8 (i) 24

(d) 19.8 (e) 33

(g) 12 (h) 22.4

10 (a) (i) 3 (ii) 153
5
(c) (i) 1 : 2 (ii) 18 cm2
(b) (i) 36.94 cm (ii) 17° 7′

Cabaran TIMSS/PISA (c) (i) 53° 8′ (ii) 275
1 156 cm
2 24 cm2 1 1 (a) 82.71 m (b) 19° 6′ (c) 8
3
Zon KBAT
(b) 624 cm2 Praktis ke Arah P T 3
1 (a) 24 cm (b) 2 464 cm2
2 (a) 28 cm Bahagian A / Section A
3 1 : 500 4 D 5 C
1 B 2 C 3 A 9 A
6 D 7 B 8 D

Bab 5 Bahagian B / Section B

Sinus, Kosinus dan Tangen bagi Sudut Tirus dalam 1 0 (a) sin x = 12 , kos/ cos x = 5 , tan y = 5
5.1 Segi Tiga Bersudut Tegak 13 13 12

Sine, Cosine and Tangent of Acute Angles in Right-angled (b) 1
Triangles
1 1 (a) c
1 (a) (i) EF (ii) DE (iii) DF a b
(b) sin x → c , kos/ cos x→ c , tan x → a
(b) (i) XZ (ii) YZ (iii) XY b

2 (a) (i) AC (ii) ABBC (iii) AC Bahagian C / Section C
AB BC
3
(b) (i) a (ii) bc (iii) ab 12 (a) (i) 8 cm (ii) 5
c

(c) (i) 15 (ii) 187 (iii) 185 (b) (i) 2.936 m (ii) 4.073 m
17
(c) 244.64 m
3 x 20° 45° 80° 13 (a) (i) 4.578 m (ii) 39° 1′
0.9848 (b) 25° 4′
sin x 0.342 0.7071 (c) 1.775 m

kos/ cos x 0.9397 0.7071 0.1736
5.6728
tan x 0.3639 1 Cabaran TIMSS/PISA

(a) Apabila saiz sudut bertambah, nilai sinus bertambah 1 (a) 12 cm (b) 28° 27′
When the size of the angle increases, the value of sine (b) 8.354 m
increases
(b) Apabila saiz sudut bertambah, nilai kosinus berkurangan Zon KBAT
When the size of the angle increases, the value of consine
decreases 1 43° 14′
2 (a) 43° 46′

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Matematik Tingkatan 3 Jawapan

Sudut HEBAT Matematik Praktis ke Arah PT3

Bahagian A / Section A

1 B 2 A 3 C 1 B 2 A 3 C 4 D 5 B
6 C 7 A 8 D 9 B
4 (a) 3 (b) 15 cm
4

5 Kedua-dua segi tiga itu adalah serupa. Semua sisi itu Bahagian B / Section B

adalah berkadaran. 1 0 (a) 65°
(b) (i) PALSU/ FALSE
Both the triangles are similar. All the sides are in proportion. (ii) BENAR/ TRUE
(iii) PALSU/ FALSE
tan ∠ABC = tan ∠PQR 1 1 (a)
6 100° 36′

Bab 6
2 tangen sepunya
Sudut pada Lilitan dan Sudut Pusat yang Dicangkum
6.1 oleh Suatu Lengkok 2 common tangents

Angle at the Circumference and Central Angle Subtended by
an Arc

1 (a) 40° (b) 81° (c) 80° (b) x = 30°, y = 55°

2 (a) 250° (b) 43° (c) 55° Bahagian C / Section C

3 (a) 25° (b) 22.5° (c) 55° 12 (a) (i) 30° (ii) 105°
(b) (i) 26.124 cm (ii) 27.046 cm
4 (a) 39° (b) 42° (c) (i) 76° (ii) 34°
1 3 (a) (i) 10° (ii) 30°
(c) 51° (d) 166° (b) (i) 55° (ii) 30°
(c) (i) 75° (ii) 125°
5 (a) x = y = 53° (b) x = 100°, y = 40° (iii) 17°
(iii) 40°
(c) x = 18°, y = 72° (d) x = 38°, y = 30° (iii) 47°

(e) x = 70°, y = 55°

6.2 Sisi Empat Kitaran

Cyclic Quadrilaterals

1 (a) Ya/ Yes (b) Bukan/ No (c) Ya/ Yes Cabaran TIMSS/PISA (b) 42°
2 (a) r = 85°, s = 105° (b) r = 120°, s = 25° (b) 18°
(c) r = 130°, s = 70° (d) r = 60°, s = 20° 1 (a) x = 42°, y = 84°
(e) r = 65°, s = 102°
3 (a) m = 75°, n = 65° (b) m = 80°, n = 50°
(c) m = 75°, n = 25° (d) m = 106°, n = 26° Zon KBAT
(e) m = 105°, n = 110°
4 (a) 105° (b) x = 75°, y = 27° 1 102°
(c) 85° (d) 200° 2 (a) 3x
3 x = 106°, y = 53°, z = 63°

6.3 Tangen kepada Bulatan Sudut HEBAT Matematik

Tangents to Circles

1 (a) Ya/ Yes (b) Bukan/ No (c) Bukan/ No 1 125° (b) 111°
2 (a) (i) 90° (ii) 20° (iii) 21.98 cm 2 x = 34°, y = 62°
(b) (i) 22° (ii) 90° (iii) 29.70 cm 3 (a) 122°
(c) (i) 90° (ii) 58° (iii) 24.01 cm
(d) (i) 28° (ii) 62° (iii) 16.93 cm Bab 7
(e) (i) 32° (ii) 29° (iii) 20.80 cm
3 (a) x = 54°, y = 27°, z = 63° 7.1 Unjuran Ortogon
(b) x = 50°, y = 130°, z = 25°
4 (a) x = 64°, y = 52° (b) x = 45°, y = 95° Orthogonal Projections
(c) x = 40°, y = 77° (d) x = 40°, y = 36°
(e) x = 20°, y = 110° 1 (a) Bukan/ No (b) Ya/ Yes
5 (a) 2 tangen sepunya/ 2 common tangents 2 (a) (b)
(b) 1 tangen sepunya/ 1 common tangent
(c) 4 tangen sepunya/ 4 common tangents (c)
6 (a) (i) KQ (ii) QL
(b) (i) MT (ii) LT (iii) ML 3 (a) (b)
(c) (i) ∠KTQ
(ii) ∠LQP
(iii) ∠JPT = ∠LQT = ∠MPT
7 (a) 21 cm (b) 20.78 cm (c) 218.19 cm2

6.4 Sudut dan Tangen bagi Bulatan

Angles and Tangents of Circles

1 (a) 20 cm (b) 19.60 cm (c)
(c) 11° 32′ (d) 40 cm

2 (a) 55° (b) 24.41 cm

(c) 14.28 cm (d) 41.84 cm

J5

Matematik Tingkatan 3 Jawapan

4 (a) Ya/ Yes (b) Ya/ Yes (c) Ya/ Yes (b) (i)
5 (a) Tidak/ No (b) Ya/ Yes E/D

P/N L/C
5 cm
7.2 Pelan dan Dongakan
K/B
Plans and Elevations
K/L
1 (a) (i) 2 cm
B/C
E/D F/C

3 cm G F/A 2 cm G/H 4 cm
K

3 cm 7 cm (ii) J/M
J/A G/K 4 cm
H/B F/E 2 cm G/P
(ii)
3 cm

H/J 5 cm
F/E H/N

4 cm A/D 6 cm

B/A (iii) P/E
6 cm C/D 1 cm
(iii) M
G/F
2 cm
K J
J/E G K/H L/N

1 cm
H/F

4 cm B/A 5 cm 2 cm
C/D

A/D 7 cm B/C

J6