Questions - 2015 Past Year suitable for PT3 and SPM too

1. 𝑥 + 2𝑦 2 = 54
𝑥2 + 4𝑦2 + 4𝑥𝑦 = 54 −− − ①
𝑥 − 2𝑦 2 = 30
𝑥2 + 4𝑦2 − 4𝑥𝑦 = 30 −− − ②
𝑥2 + 4𝑦2 − 4𝑥𝑦 = 30 −− − ②
8𝑥𝑦 = 24 −− − ① − ②
𝑥𝑦 = 6

2. ?

3. 𝑎𝑛𝑔𝑙𝑒 𝑜𝑓 𝐴 = 80°
O
D
A
40° 90°
50°
𝑎𝑟𝑐ℎ 𝐷𝐹: 𝐷𝐸: 𝐸𝐹
= 100 : 140 : 120
= 5 : 7 : 6
𝑎𝑛𝑔𝑙𝑒 𝑜𝑓 𝐵 = 40°
𝑎𝑛𝑔𝑙𝑒 𝑜𝑓 𝐶 = 60°

4. 𝑆𝑛 =
𝑛
2
𝑎 + 𝑇𝑛
𝑆𝑛
𝑛
=
𝑛
2
𝑎 + 𝑇𝑛
𝑛
= 8
𝑥1 + 𝑥𝑛
2
= 8
𝑆𝑛
𝑛
=
𝑛
2
𝑥1 + 3 + 𝑥𝑛 + 3
𝑛
=
16 + 6
2
𝑥1 + 𝑥𝑛 = 16
=
𝑥1 + 𝑥𝑛 + 6
2
= 11

5. distance between start and end point
south east north
90
80
150
?
?
start start
end end
60
80

6. 𝑎𝑟𝑒𝑎 𝑜𝑓 𝐴𝐵𝐶𝐷 = 140 𝑐𝑚2
10
8
6
𝑎𝑟𝑒𝑎 𝑜𝑓 2 ∆ = 48 𝑐𝑚2
92 𝑐𝑚2
𝑎𝑟𝑒𝑎 𝑜𝑓 𝑂𝑃𝑄𝑅
100𝜋
=
1
4
𝑎𝑟𝑒𝑎 𝑜𝑓 𝑂𝑃𝑄𝑅 = 25𝜋 𝑐𝑚2
𝑎𝑛𝑔𝑙𝑒 𝐶𝑂𝑅 + 𝑎𝑛𝑔𝑙𝑒 𝐵𝑂𝑃 = 90°
∴ 𝑎𝑛𝑔𝑙𝑒 𝑃𝑄𝑅 = 90°

7. profit or loss
cost = RM25 x 40 = RM 1000
4 broken
selling = RM30 x 36 = RM 1080 x 0.90 = RM972
loss = selling – cost = RM972 – RM 1000 = - RM28

8. Quiz Q marks if
correct
correct Final
Marks
1 10 4 x 4x
2 15 7 y 7y
Total x + y 4x + 7y
x + y = 15
4x + 7y = 84

9. D
E
A
B
F
C
𝐴𝐷 = 𝐵𝐶
𝐴𝐸 = 𝐹𝐶
𝑎𝑛𝑔𝑙𝑒 𝐷𝐴𝐸 = 𝑎𝑛𝑔𝑙𝑒 𝐵𝐶𝐹
h
D
A
60°
sin 60° =
ℎ
8
8
3
2
=
ℎ
8
ℎ = 4 3
𝑎𝑟𝑒𝑎 𝑜𝑓 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑜𝑔𝑟𝑎𝑚 = 𝑏ℎ
= 𝐴𝐵 ℎ
= 12 (4 3)
= 48 3 𝑐𝑚2
∴ ∆𝐴𝐷𝐸 = ∆𝐶𝐵𝐹

10. 𝑘 =
𝑖𝑚𝑎𝑔𝑒
𝑜𝑏𝑗𝑒𝑐𝑡
=
𝐴𝐸
𝐴𝐵
6
4
3
?
=
4 + 6
4
=
5
2
𝑘 =
𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑖𝑚𝑎𝑔𝑒
𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑜𝑏𝑗𝑒𝑐𝑡
5
2
=
𝐸𝐹
3
𝐸𝐹 =
15
2
𝑐𝑚
𝑘2 =
𝑎𝑟𝑒𝑎 𝑜𝑓 𝑖𝑚𝑎𝑔𝑒
𝑎𝑟𝑒𝑎 𝑜𝑓 𝑜𝑏𝑗𝑒𝑐𝑡
25
4
=
𝑎𝑟𝑒𝑎 𝑜𝑓 ∆𝐴𝐸𝐹
𝑎𝑟𝑒𝑎 𝑜𝑓 ∆𝐴𝐵𝐶
25
4
=
𝑎𝑟𝑒𝑎 𝑜𝑓 ∆𝐴𝐸𝐹
4
𝑎𝑟𝑒𝑎 𝑜𝑓 ∆𝐴𝐸𝐹 = 25 𝑐𝑚2