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Mathematics
WAEC / WASSCE 2022
Lengths and Perimeters
Diagram
Solution
In the diagram, ∠ZWZY and WYX are right angles. Find the perimeter of WXYZ.
Attached Figure / Diagram
A
30cm
B
32cm
C
35cm
D
37cm
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
In \DeltaWYZ:
hyp\(^2\) = adj\(^2\) + opp\(^2\)
hyp\(^2\) =3\(^2\) + 4\(^2\) → 9 + 16
hyp\(^2\) = 25
hyp = 5
In \DeltaWXY:
hyp\(^2\) = adj\(^2\) + opp\(^2\)
hyp\(^2\) = 12\(^2\) + 5\(^2\) = 144 +25
hyp\(^2\) = 169
hyp = 13
the perimeter of WXYZ. = 3+4+12+13 → 32cm
Source: WAEC / JAMB / NECO Classroom Archive (Record #64828)
Mathematics
WAEC / WASSCE 2022
Lengths and Perimeters
Solution
A rectangle with width \(\frac{3}{4}\)cm and area 3 \(\frac{3}{8}\)cm\(^2\). Find the length
A
6cm
B
4\(\frac{1}{2}\)cm
C
2 \(\frac{5}{8}\)cm
D
12cm
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
The area of a rectangle = length ✕ width
: Length = area \div width → 3 \(\frac{3}{8}\) \div \(\frac{3}{4}\)
= \(\frac{27}{8}\) * \(\frac{4}{3}\)
= 4\(\frac{1}{2}\)cm
Source: WAEC / JAMB / NECO Classroom Archive (Record #65393)
Mathematics
WAEC / WASSCE 2022
Lengths and Perimeters
Solution
A chord subtends an angle of 72º at the centre of a circle of radius 24.5m. Calculate the perimeter of the minor segment. [Take π = \(\frac{22}{7}\)
medium Difficulty
Verified Correct Answer: Option
Step-by-Step Mathematical Solution
From \DeltaOKB
sin 36^\circ = \(\frac{|KB|}{24.5}\)
|KB| = 0.5878 x 24.5
=14.4011m
Or
Length of arc = \(\frac{72}{360} * 2 *{\frac{22}{7}} * 24.7\)
=30.8m
Perimeter = 2(14.4011) + 30.8
= 59.6022
= 59.6m
Source: WAEC / JAMB / NECO Classroom Archive (Record #65856)
Mathematics
WAEC / WASSCE 2022
Areas of Plane Figures
Solution
A cylinder, opened at one end, has a radius of 3.5cm and height 8cm. calculate the total surface area
A
126.5cm\(^2\)
B
165.0cm\(^2\)
C
212.0cm\(^2\)
D
214.5cm\(^2\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
The surface area of an open-top cylinder = \pir(r + 2h),
where 'r' is the radius and 'h' is the height of the cylinder.
= \(\frac{22}{7}\) * 3.5 (3.5 + 2 * 8)
= 11 (3.5 + 16) → 11 (19.5)
= 214.5cm\(^2\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #64827)
Mathematics
WAEC / WASSCE 2022
Areas of Plane Figures
Diagram
Solution
The length of a rectangle is 10 cm. If its perimeter is 28 cm, find the area
Attached Figure / Diagram
A
30cm\(^2\)
B
40cm\(^2\)
C
60cm\(^2\)
D
80cm\(^2\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
perimeter = 2( length + breadth)
→ 28 = 2 (10+ b)
14 - 10 = b
b = 4
Area = length x breadth
10 x 4 → 40cm\(^2\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #64829)
Mathematics
WAEC / WASSCE 2022
Volumes of Solids
Solution
Find the correct to two decimal places, the volume of a sphere whose radius is 3cm. [Take π = \(\frac{22}{7}\)]
A
72.57cm\(^3\)
B
88.12cm\(^3\)
C
10529cm\(^3\)
D
113.14cm\(^3\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Volume of sphere = \(\frac{4\pir^3}{3}\) → \(\frac{4 x 22 x 3^3}{3}\)
= \(\frac{792}{7}\)
= 113.14cm\(^3\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #64863)
Mathematics
WAEC / WASSCE 2022
Triangles and Polygons
Solution
An exterior angle of a regular polygon is 22.5°. Find the number of sides.
A
13
B
14
C
15
D
16
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
The sum of exterior angles of a polygon is 360^\circ
\(\frac{360}{22.5}\) = 16 sides
Source: WAEC / JAMB / NECO Classroom Archive (Record #64822)
Mathematics
WAEC / WASSCE 2022
Triangles and Polygons
Diagram
Solution
Find the area of the sector OPSQ
Attached Figure / Diagram
A
15.40cm\(^2\)
B
17.64cm\(^2\)
C
23.10cm\(^2\)
D
32.34cm\(^2\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{\theta}{360}\) *\pi * r\(^2\) → \(\frac{210 * 22 * 4.2 * 4.2}{360 * 7}\)
\(\frac{1617}{50}\) = 32.34cm\(^2\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #64825)
Mathematics
WAEC / WASSCE 2022
Angles of Elevation & Depression
Solution
A ladder 6m long leans against a vertical wall at an angle 53º to the horizontal. How high up the wall does the ladder reach?
A
3.611m
B
4.521m
C
4.792m
D
3.962m
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Sin \theta = \(\frac{opp}{hyp}\) → \(\frac{x}{6}\)
cross multiply:
sin53º * 6 = x
0.7986 * 6
4.792m
Source: WAEC / JAMB / NECO Classroom Archive (Record #64826)
Mathematics
WAEC / WASSCE 2022
Angles of Elevation & Depression
Solution
A boy 1.4 m tall, stood 10m away from a tree of height 12 m. Calculate, correct to the nearest degree, the angle of elevation of the top of the tree from the boy's eyes.
A
70º
B
47º
C
19º
D
8º
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
The angle of elevation
= Tan \theta = \(\frac{opp}{adj}\)
Tan \theta = \(\frac{12- 1.4}{10}\)
Tan \theta = \(\frac{10.6}{10}\)
\theta = Tan\(^{-1}\)(1.06)
\theta ≈ 47º
Source: WAEC / JAMB / NECO Classroom Archive (Record #64834)
Mathematics
WAEC / WASSCE 2022
Measures of Location (Mean, Median, Mode)
Solution
The mean of a set of 10 numbers is 56. If the mean of the first nine numbers is 55, find the 10th number.
A
75
B
65
C
55
D
45
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
10th number must be over 56 (as it increases the average)
55 x 9 = 495 = sum of first 9 numbers
56 x 10 = 560 = sum of all 10 numbers
560 - 495 = 65 = 10th number
Source: WAEC / JAMB / NECO Classroom Archive (Record #64844)
Mathematics
WAEC / WASSCE 2022
Measures of Location (Mean, Median, Mode)
Solution
The age (years) of some members in a singing group are: 12, 47, 49, 15, 43, 41, 13, 39, 43, 41 and 36.
Find the lower quartile
A
12
B
13
C
15
D
20
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Rearranged: 12,13,15, 36, 39, 41, 41, 43, 43, 47 and 49
Lower quartile or First quartile = \(\frac{total number of items}{4}\)
If odd: items numbers + 1 → \(\frac{11 items + 1}{4}\)
= \(\frac{12}{4}\)
Lower quartile = 3rd iems →15
Source: WAEC / JAMB / NECO Classroom Archive (Record #64857)
Mathematics
WAEC / WASSCE 2022
Measures of Location (Mean, Median, Mode)
Solution
The age (years) of some members in a singing group are: 12, 47, 49, 15, 43, 41, 13, 39, 43, 41 and 36.
Find the mean
A
33.35
B
35.54
C
34.45
D
36.44
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{12 + 47 + 49 + 15 + 43 + 41 + 13 + 39 + 43 + 41 + 36}{11}\)
= \(\frac{379}{11}\)
= 34.45
Source: WAEC / JAMB / NECO Classroom Archive (Record #64858)
Mathematics
WAEC / WASSCE 2022
Probability
Solution
Mrs Gabriel is pregnant. The probability that she will give birth to a girl is 1/2 and with blue eyes is 1/4. What is the probability that she will give birth to a girl with blue eyes?
A
1
B
\(\frac{3}{4}\)
C
\(\frac{1}{8}\)
D
\(\frac{1}{4}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Girl = \(\frac{1}{2}\)
Blue eyes = \(\frac{1}{4}\)
probability that she will give birth to a girl with blue eyes: \(\frac{1}{2}\) x \(\frac{1}{4}\)
= \(\frac{1}{8}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #64842)
Physics
WAEC / WASSCE 2022
Heat Energy & Temperature
Solution
The distance between the fixed points of a mercury-in-glass thermometer is 30 cm. Determine the temperature when the mercury level is 10.5 cm above the lower fixed point
A
28.6ºC
B
30.0 ºC
C
35.0 ºC
D
40.5 ºC
medium Difficulty
Verified Correct Answer: Option C
Physical Principles & Numerical Solution
\(\frac{10.5-0}{30-0}\) = \(\frac{c-0}{100-0}\)
\(\frac{10.5}{30}\) = \(\frac{c}{100}\)
cross multiply:
10.5 * 100 = 30c
35.0 ºC = c
Source: WAEC / JAMB / NECO Classroom Archive (Record #63391)