Questions - 2013 Past Year suitable for PT3 and SPM too

1. a =
3+𝑏
5+2𝑏
a (5+2b) = 3+b
5a+2ab = 3+b
3+b-2ab = 5a
b(1-2a) = 5a-3
b =
5𝑎−3
1−2𝑎

2. log10 3 = 0.4771 → 100.4771 = 3
log10 𝑥 = 3.4771 → 103.4771
= 𝑥
𝑥 = 103
× 100.4771
= 1000 × 3
= 3000

3. 𝑎2 + 𝑏2 = 𝑐2
∆𝐶𝐷𝐹: 𝐷𝐹2
= 52
+ (5 3)2
𝐷𝐹 = 10
DE = 10
tan 𝜃 =
𝐶𝐹
𝐶𝐷
=
5
5 3
𝑎𝑛𝑔𝑙𝑒 𝐶𝐷𝐹 = 𝑎𝑛𝑔𝑙𝑒 𝐶𝐷𝐹 = 𝜃
𝜃 = 30 °
𝜃 = 30°
∆𝐷𝐸𝐹
𝑎𝑛𝑔𝑙𝑒 𝐶𝐷𝐹 =
180 ° − 30 °
2
= 75 °

4. mean =
3 4 +6 10 +9 4 +12(2)
20

5. 4,5,6

6. V = 144 𝜋
V hemisphere =
2
3
𝜋𝑟3
144 𝜋 =
2
3
𝜋𝑟3
r = 6

7. 𝑥 = original price
𝑦 = selling price
𝑦 − 𝑥
𝑥
× 100 % = 20 %
𝑦 - 𝑥 = 0.2 𝑥
𝑦 = 1.2 𝑥−−−−①
0.9 𝑦 - 𝑥 = 24 −−②

8. ?
?
CD = 𝐵𝐷 = 15 cm
angle ABC = 75°
angle ABE = 30°
angle EBD = 30°
angle CBD = 15°
∆𝐴𝐵𝐷
sin 30° =
𝐴𝐵
𝐵𝐷
1
2
=
𝐴𝐵
15
𝐴𝐵 = 7.5 cm
∆𝐴𝐵𝐸
sin 60° =
𝐴𝐵
𝐵𝐸
3
2
=
7.5
𝐵𝐸
𝐵𝐸 =
15
3
=
15 3
3
= 5 3 cm

9. = 9 − 1 2 + 2 − 8 2
= 8 2 + −6 2
AB = 10 AC = 𝐵𝐶 = 50
= 5 2
𝑎2 + 𝑏2 = 𝑐2
1
4
=
𝐴𝐷𝐵
2𝜋𝑟