Lesson notes for students for students preparing for WASSCE, NECO & JAMB Exams

1. PIE CHART
Pie chart
𝑄1
𝑇𝑜𝑡𝑎𝑙
× 360°
𝑇𝑜𝑡𝑎𝑙 = 𝑄1 + 𝑄2 + 𝑄3
𝑄2
𝑇𝑜𝑡𝑎𝑙
× 360°
𝑄3
𝑇𝑜𝑡𝑎𝑙
× 360°
To represent information of quantities, 𝑄1, 𝑄2 𝑎𝑛𝑑 𝑄3 on a pie chart. We find th
total quantity and the sectoral angle each corresponds to. We then use our
Protractor to measure the angles in a circle drawn with a reasonable radius.
Angle of each sector

2. The pie chart below
show Ghana’s exports in
a particular year. The
total value of exports
amounted to
ℂ301,500.00
Solution
Q31. 𝐴𝑛𝑔𝑙𝑒 𝑜𝑓 𝑠𝑒𝑐𝑡𝑜𝑟 𝑜𝑓 𝑐𝑜𝑐𝑜𝑎
= 3600
− 600
+ 400
+ 200
= 2400
⇒ 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑐𝑜𝑎𝑐𝑜 𝑒𝑥𝑝𝑜𝑟𝑡𝑒𝑑 =
2400
3600
× 301,500
= ℂ201,000.00
Q32. 𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑜𝑓 𝑡𝑖𝑚𝑏𝑒𝑟 𝑒𝑥𝑝𝑜𝑟𝑡𝑒𝑑
=
200
3600
× 100%
= 5.56% correct to 2 d. p

3. WASSCE
2004
Solution
Q31. 𝐴𝑛𝑔𝑙𝑒 𝑜𝑓 𝑠𝑒𝑐𝑡𝑜𝑟 𝑜𝑓 𝑐𝑜𝑐𝑜𝑎
= 3600
− 600
+ 400
+ 200
= 2400
⇒ 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑐𝑜𝑎𝑐𝑜 𝑒𝑥𝑝𝑜𝑟𝑡𝑒𝑑 =
2400
3600
× 301,500
= ℂ201,000.00
Q32. 𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑜𝑓 𝑡𝑖𝑚𝑏𝑒𝑟 𝑒𝑥𝑝𝑜𝑟𝑡𝑒𝑑
=
200
3600
× 100%
= 5.56% correct to 2 d. p

4. JAMB 2004 Solution
𝑇ℎ𝑒 𝑠𝑒𝑐𝑡𝑜𝑟 𝑜𝑓𝑚𝑖𝑙𝑙𝑒𝑡 = 1500
𝑇ℎ𝑒 𝑠𝑒𝑐𝑡𝑜𝑟 𝑜𝑓 𝑏𝑒𝑎𝑛𝑠 = 3600 − 150 + 90 + 60 0
= 600
𝐵𝑦 𝑢𝑠𝑖𝑛𝑔 𝑟𝑎𝑡𝑖𝑜 𝑎𝑛𝑑 𝑝𝑟𝑜𝑝𝑜𝑟𝑡𝑖𝑜𝑛,
⇒ 𝑇ℎ𝑒 𝑎𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑏𝑒𝑎𝑛𝑠 =
600
1500 × 3000
= 1200 𝑡𝑜𝑛𝑛𝑒𝑠

5. 1. The pie chart represents the minerals of a certain mining company.
What is the value of 𝑥°.
A. 45°
B. 46°
C. 55°
D. 40°
E. 20°
The correct answer is 40°
Gold
𝑥°
Diamon
d
𝑥°
Bauxite
2𝑥°
Manganes
e
5𝑥°

6. 1. The pie chart represents the minerals of a certain mining company.
What is the value of 𝑥°.
A. 45°
B. 46°
C. 55°
D. 40°
E. 20°
The correct answer is 40°
Gold
𝑥°
Diamon
d
𝑥°
Bauxite
2𝑥°
Manganes
e
5𝑥°
Solution
5𝑥 + 𝑥 + 𝑥 + 2𝑥 = 360
9𝑥 = 360
𝑥 =
360
9
𝑥 = 40°

7. 2. The pie chart represents the minerals of a certain mining company.
What is the percentage of the sector occupied by manganese?
A. 45.55%
B. 46.66%
C. 55.55%
D. 55.56%
E. 20.56%
The correct answer is 55.56%
Gold
𝑥°
Diamon
d
𝑥°
Bauxite
2𝑥°
Manganes
e
5𝑥°

8. 2. The pie chart represents the minerals of a certain mining company.
What is the percentage of the sector occupied by manganese?
A. 45.55%
B. 46.66%
C. 55.55%
D. 55.56%
E. 20.56%
The correct answer is 55.56%
Gold
𝑥°
Diamon
d
𝑥°
Bauxite
2𝑥°
Manganes
e
5𝑥°
Solution
𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑜𝑓 𝑀𝑎𝑛𝑔𝑎𝑛𝑒𝑠𝑒
=
5𝑥
9𝑥
× 100%
= 55.56%

9. 3. The following data represents the prices of gasoline in the United States from
2001 to 2006. Calculate the sectoral angle that correspond to gasoline price in 2001.
A. 46.64°
B. 47.64°
C. 48.64°
D. 49.64°
E. 50.64°
The correct answer is 46.64°
𝑌𝑒𝑎𝑟 𝑮𝒂𝒔 𝑷𝒓𝒊𝒄𝒆
2001 $1.46
2002 $1.39
2003 $1.60
2004 $1.90
2005 $2.31
2006 $2.61

10. 3. The following data represents the prices of gasoline in the United States from
2001 to 2006. Calculate the sectoral angle that correspond to gasoline price in 2001.
A. 46.64°
B. 47.64°
C. 48.64°
D. 49.64°
E. 50.64°
The correct answer is 46.64°
𝑌𝑒𝑎𝑟 𝑮𝒂𝒔 𝑷𝒓𝒊𝒄𝒆
2001 $1.46
2002 $1.39
2003 $1.60
2004 $1.90
2005 $2.31
2006 $2.61
Solution
𝑆𝑒𝑐𝑡𝑜𝑟𝑎𝑙 𝑎𝑛𝑔𝑙𝑒 𝑜𝑓 𝑔𝑎𝑠 𝑝𝑟𝑖𝑐𝑒 𝑖𝑛 2001
=
$1.46
$11.27
× 360°
= 46.64°

11. 4. The following data represents the prices of gasoline in the United States from
2001 to 2006. Calculate the largest sectoral angle of gasoline price.
A. 83.37°
B. 84.37°
C. 85.37°
D. 86.37°
E. 87.37°
The correct answer is 83.37°
𝑌𝑒𝑎𝑟 𝑮𝒂𝒔 𝑷𝒓𝒊𝒄𝒆
2001 $1.46
2002 $1.39
2003 $1.60
2004 $1.90
2005 $2.31
2006 $2.61

12. 4. The following data represents the prices of gasoline in the United States from
2001 to 2006. Calculate the largest sectoral angle of gasoline price.
A. 83.37°
B. 84.37°
C. 85.37°
D. 86.37°
E. 87.37°
The correct answer is 83.37°
𝑌𝑒𝑎𝑟 𝑮𝒂𝒔 𝑷𝒓𝒊𝒄𝒆
2001 $1.46
2002 $1.39
2003 $1.60
2004 $1.90
2005 $2.31
2006 $2.61
Solution
𝐿𝑎𝑟𝑔𝑒𝑠𝑡 𝑎𝑛𝑔𝑙𝑒 =
$2.61
$11.27
× 360°
= 83.37°

13. 5. The following data represents the population of students in class 6 of some 6
different schools. What is the population of school C?
A. 15
B. 25
C. 5
D. 35
E. 20
The correct answer is 15
𝑺𝒄𝒉𝒐𝒐𝒍 𝑷𝒐𝒑𝒖𝒍𝒂𝒕𝒊𝒐𝒏 Sectoral
angle
𝐴 40 120°
𝐵 10 𝑥°
𝐶 𝑢 45°
𝐷 20 𝑦°
𝐸 𝑣 75°
𝐹 10 𝑥°

14. 5. The following data represents the population of students in class 6 of some 6
different schools. What is the population of school C?
A. 15
B. 25
C. 5
D. 35
E. 20
The correct answer is 15
𝑺𝒄𝒉𝒐𝒐𝒍 𝑷𝒐𝒑𝒖𝒍𝒂𝒕𝒊𝒐𝒏 Sectoral
angle
𝐴 40 120°
𝐵 10 𝑥°
𝐶 𝑢 45°
𝐷 20 𝑦°
𝐸 𝑣 75°
𝐹 10 𝑥°
Solution
120°: 40
45°: 𝑢
If less more divides,
𝑢 =
45 × 40
120
= 15

15. 6. The following data represents the population of students in class 6 of some 6
different schools. What is the population of the 6 schools?
A. 130
B. 150
C. 120
D. 100
E. 240
The correct answer is 120
𝑺𝒄𝒉𝒐𝒐𝒍 𝑷𝒐𝒑𝒖𝒍𝒂𝒕𝒊𝒐𝒏 Sectoral
angle
𝐴 40 120°
𝐵 10 𝑥°
𝐶 𝑢 45°
𝐷 20 𝑦°
𝐸 𝑣 75°
𝐹 10 𝑥°

16. 6. The following data represents the population of students in class 6 of some 6
different schools. What is the population of the 6 schools?
A. 130
B. 150
C. 120
D. 100
E. 240
The correct answer is 120
𝑺𝒄𝒉𝒐𝒐𝒍 𝑷𝒐𝒑𝒖𝒍𝒂𝒕𝒊𝒐𝒏 Sectoral
angle
𝐴 40 120°
𝐵 10 𝑥°
𝐶 𝑢 45°
𝐷 20 𝑦°
𝐸 𝑣 75°
𝐹 10 𝑥°
Solution
Let total population be p
120°: 40
360°: 𝑝
If more less divides,
𝑢 =
360 × 40
120
= 120

17. 7. The following data represents the population of students in class 6 of some 6
different schools. What is the value of 𝑥?
A. 30°
B. 50°
C. 20°
D. 10°
E. 40°
The correct answer is 30°
𝑺𝒄𝒉𝒐𝒐𝒍 𝑷𝒐𝒑𝒖𝒍𝒂𝒕𝒊𝒐𝒏 Sectoral
angle
𝐴 40 120°
𝐵 10 𝑥°
𝐶 𝑢 45°
𝐷 20 𝑦°
𝐸 𝑣 75°
𝐹 10 𝑥°

18. 7. The following data represents the population of students in class 6 of some 6
different schools. What is the value of 𝑥?
A. 30°
B. 50°
C. 20°
D. 10°
E. 40°
The correct answer is 30°
𝑺𝒄𝒉𝒐𝒐𝒍 𝑷𝒐𝒑𝒖𝒍𝒂𝒕𝒊𝒐𝒏 Sectoral
angle
𝐴 40 120°
𝐵 10 𝑥°
𝐶 𝑢 45°
𝐷 20 𝑦°
𝐸 𝑣 75°
𝐹 10 𝑥°
Solution
120°: 40
𝑥°: 10
If less more divides,
𝑢 =
120 × 10
40
= 30°

19. 8. The following data represents the population of students in class 6 of some 6
different schools. What is the value of y?
A. 30°
B. 50°
C. 60°
D. 80°
E. 40°
The correct answer is 60°
𝑺𝒄𝒉𝒐𝒐𝒍 𝑷𝒐𝒑𝒖𝒍𝒂𝒕𝒊𝒐𝒏 Sectoral
angle
𝐴 40 120°
𝐵 10 𝑥°
𝐶 𝑢 45°
𝐷 20 𝑦°
𝐸 𝑣 75°
𝐹 10 𝑥°

20. 8. The following data represents the population of students in class 6 of some 6
different schools. What is the value of y?
A. 30°
B. 50°
C. 60°
D. 80°
E. 40°
The correct answer is 60°
𝑺𝒄𝒉𝒐𝒐𝒍 𝑷𝒐𝒑𝒖𝒍𝒂𝒕𝒊𝒐𝒏 Sectoral
angle
𝐴 40 120°
𝐵 10 𝑥°
𝐶 𝑢 45°
𝐷 20 𝑦°
𝐸 𝑣 75°
𝐹 10 𝑥°
Solution
120°: 40
𝑦°: 20
If less more divides,
𝑢 =
120 × 20
40
= 60°

21. 9. The pie chart represents the minerals of a certain mining company.
What is the value of 𝑥°.
A. 45°
B. 46°
C. 50°
D. 70°
E. 20°
The correct answer is 50°
Gold
𝑥°
Diamon
d
𝑥°
Bauxite
2𝑥°
Manganes
e
160°

22. 9. The pie chart represents the minerals of a certain mining company.
What is the value of 𝑥°.
A. 45°
B. 46°
C. 50°
D. 70°
E. 20°
The correct answer is 50°
Gold
𝑥°
Diamon
d
𝑥°
Bauxite
2𝑥°
Manganes
e
160°
Solution
𝑥 + 𝑥 + 2𝑥 + 160 = 360
4𝑥 = 200
𝑥 = 50°

23. 10 The pie chart represents the minerals of a certain mining company.
What is the angle of bauxite?
A. 45°
B. 46°
C. 75°
D. 170°
E. 100°
The correct answer is 100°
Gold
𝑥°
Diamon
d
𝑥°
Bauxite
2𝑥°
Manganes
e
160°

24. 10 The pie chart represents the minerals of a certain mining company.
What is the angle of bauxite?
A. 45°
B. 46°
C. 75°
D. 170°
E. 100°
The correct answer is 100°
Gold
𝑥°
Diamon
d
𝑥°
Bauxite
2𝑥°
Manganes
e
160°
Solution
𝑥 + 𝑥 + 2𝑥 + 160 = 360
4𝑥 = 200
𝑥 = 50°
Bauxite = 2(50) = 100°

25. PIE CHART
Pie chart is used to represent information pictorially in a circle
Apply your knowledge of ratio and proportion to find the missing angl
𝑆𝑢𝑚 𝑜𝑓 𝑎𝑙𝑙 𝑡ℎ𝑒 𝑎𝑛𝑔𝑙𝑒𝑠 𝑜𝑓 𝑒𝑎𝑐ℎ 𝑠𝑒𝑐𝑡𝑜𝑟 𝑖𝑛 𝑎 𝑝𝑖𝑒 𝑐ℎ𝑎𝑟𝑡 𝑖𝑠 360°