Page 7 - Grab A+ Kertas Model SPM Matematik

(iii) Purata laju/ Average speed ∴ Potongan bulanan PCB adalah mencukupi untuk
20 + 30 + 50
= —––————– membayar cukai pendapatan.
120/60 Monthly deduction of MTD is enough to pay the income
= 50 km j / km h –1
–1
tax.
5. (a) Luas kawasan berlorek 9. (a) 2x – 10 = 0
Area of the shaded region 2x = 10
42° 22 28° 22 10
= —––– × —– × 21 – —––– × —– × 7 2 x = —–
2
360° 7 360° 7 2
13 x = 5
= 149—– cm 2
18 ∴ Jarak di antara rumah Lisa dan rumah Melissa ialah
(b) Perimeter kawasan berlorek 5 km.
Perimeter of the shaded region The distance between Lisa’s house and Melissa’s house
= OA + AB + BP + PR + RQ + QO is 5 km.
42° 22 28° 22
= 21 + —––– × 2 × —– × 21 + 7 + 7 + —––– × 2 × —– × 7 (b) y = 2x – 10 .........................1
360° 7 360° 7
©PAN ASIA PUBLICATIONS
+ 7 y + 2x = 20 .........................2
Gantikan 1 ke dalam 2,
37
= 60—– cm
45 Substitute 1 into 2,
6. (a) Katakan/ Let A = Mukah, B = Sibu, C = Sarikei, D = Kapit, 2x – 10 + 2x = 20
E = Bintulu, F = Miri dan/ and G = Limbang 4x = 20 + 10
30
x = —–
G 4
15
x = —–
E 2
F 15
A Gantikan x = —– ke dalam 1,
2
15
Substitute x = —– into 1,
B 2
15
1 2
y = 2 —– – 10
2
C D y = 5
15
1
2
(b) V = {A, B, C, D, E, F, G} Koordinat bagi perpustakaan ialah —–, 5 .
E = { (A, B), (A, C), (A, E), (B, C), (B, D), (B, E), (C, D), 2
15
1
2
(D, E), (D, F), (E, F), (F, G)} The coordinates of the library is —–, 5 .
2
n(V) = 7 Persamaan garis lurus bagi laluan di antara rumah Lisa dan
n (E) = 11
sekolah ialah y = 2x.
7. Menggunakan teorem Pythagoras, The equation of the straight line of the path between Lisa’s
Using Pythagoras theorem, house and school is y = 2x.
x 2 + (3x – 3) = (2x + 3) 2 y = 2x .................................3
2
x 2 + 9x – 18x + 9 = 4x + 12x + 9 Gantikan 3 ke dalam 2,
2
2
10x – 4x – 18x – 12x = 0 Substitute 3 into 2,
2
2
6x – 30x = 0 2x + 2x = 20
2
20
6x(x – 5) = 0 x = —–
x = 0 atau/ or x = 5 4
Perimeter bagi segi tiga PQR x = 5
Perimeter of triangle PQR Gantikan x = 5 ke dalam 3,
= 5 + [3(5) – 3] + [2(5) + 3] Substitute x = 5 into 3,
= 5 + 12 + 13 y = 2(5)
= 30 cm y = 10
8. (a) Pendapatan bercukai/ Chargeable income Koordinat bagi sekolah ialah (5, 10).
= RM93 600 – (RM9 000 + RM7 000 + RM2 400 The coordinates of the school is (5, 10).
+ RM2 400 + RM2 200) Jarak di antara sekolah dan perpustakaan
= RM70 600 Distance between the school and the library
15
2
1
2
Cukai pendapatan/ Income tax = ABBBBBBBBBBBBB 2
—– – 5 + (5 – 10)
= RM4 600 + (RM70 600 – RM70 000) × 21% 2
= RM4 600 + RM126 = 5.590 km 3
x
= RM4 726 10. (a) —–—— = —
7
16 + x
(b) Jumlah PCB yang dibayar oleh Puan Wendy 7x = 3(16 + x)
Total MTD paid by Madam Wendy 7x = 48 + 3x
= RM450 × 12 7x – 3x = 48
= RM5 400 4x = 48
Lebihan cukai pendapatan yang dibayar x = —–
48
Excess income tax paid 4
= RM5 400 – RM4 726 x = 12
= RM674
© Pan Asia Publications Sdn. Bhd. J – 2