Page 17 - Modul A+1 Matematik Tambahan Tingkatan 5

2. Rajah menunjukkan sebuah sektor AOB berpusat O. 3. Rajah menunjukkan dua sektor, POQ dan SOR,
The diagram shows a sector AOB with centre O. berpusat O.
KBAT Menilai The diagram shows two sectors, POQ and SOR, with centre O.
KBAT Menganalisis
S
A
BAB 1 130° 7.5 cm B O θ P
O
Cari
Find Q
(a) ∠AOB, dalam radian, R
∠AOB, in radians, [2 markah/marks] Diberi bahawa OP = 6 cm, OP : OS = 2 : 3 dan luas
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(b) perimeter, dalam cm, sektor AOB. kawasan berlorek ialah 33.75 cm , cari
2
the perimeter, in cm, of the sector AOB. Given that OP = 6 cm, OP : OS = 2 : 3 and the area of the
[3 markah/marks] shaded region is 33.75 cm , find
2
(a) panjang OS,
(a) 130° × π = 2.27 rad the length of OS, [2 markah/marks]
180° (b) nilai q, dalam radian.
(b) Perimeter = 7.5 + 7.5 + 7.5(2.27) the value of q, in radians. [3 markah/marks]
= 32.03 cm
2
(a) OP = = 6 = OS = 9 cm
OS 3 OS
1
(b) 1 (9) q – (6) q = 33.75
2
2
2 2
22.5q = 33.75
q = 1.5 rad
Bahagian B/Section B
4. Rajah menunjukkan dua bulatan sepusat berpusat O. 5. Rajah menunjukkan sebuah segi tiga sama sisi OPQ dan
KLON Sudut yang dicangkum pada pusat O oleh lengkok titik S yang terletak di dalam segi tiga itu dengan keadaan
SPM M major PQ ialah 8p rad dan perimeter bagi seluruh rajah OS = SP = SQ.
SP
ialah 48 cm. The diagram shows an equilateral triangle OPQ and the
The diagram shows two concentric circles with centre O. point S lies inside the triangle such that OS = SP = SQ.
The angle subtended at the centre O by the major arc PQ is KBAT Menganalisis
8p rad and the perimeter for the whole diagram is 48 cm. O
KBAT Menganalisis
P
12 cm
A S
P Q
O
B Q
X

Diberi OP = 3 OA, OA = j cm dan ∠AOB = 4p rad, Diberi bahawa S ialah pusat bagi sektor SPXQ dan
2 panjang lengkok PXQ ialah 12 cm. Cari perimeter
ungkapkan j dalam sebutan p. kawasan berlorek, dalam sebutan π dan ! 3.
3
Given OP = OA, OA = j cm and ∠AOB = 4p rad, express Given that S is the centre of the sector SPXQ and the length of
2
j in terms of p. [8 markah/marks] arc PXQ is 12 cm. Find the perimeter of the shaded region, in
3
OP = OA terms of π and ! 3 . [8 markah/marks]
2 kos ∠OQS = 6
3
= j SQ
2 kos 30° = 6
3
Panjang lengkok major PQ = j(8p) SQ
2
6
6
12
= 12jp SQ = kos 30° = ! 3 = ! 3 = 4! 3 cm
Panjang lengkok AB = j(4p) 2
= 4jp Perimeter kawasan berlorek O
Jumlah perimeter: ( π )
3
12jp + 4jp + 2( j – j) = 48 = 4! 3 + 4! 3 + (4! 3) 120° × 180°
2 S
16jp + j = 48 = 8! 3 + 8! 3 π 30° 120° 6
j(16p + 1) = 48 3 P 12 Q
(
j = 48 = 8! 3 1 + π ) cm
16p + 1 3
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