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Mathematics
WAEC / WASSCE 2022
Mensuration
Solution
The lengths of the parallel sides of a trapezium are 9cm and 12cm. If the area of the trapezium is 105cm\(^2\), find the perpendicular distance between the parallel sides.
A
5cm
B
7cm
C
10cm
D
15cm
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Area of a trapezium = \(\frac{[a+b]h}{2}\)
105 = \(\frac{[9+12]h}{2}\) → 105 x 2 =21h
h = \(\frac{210}{21}\) → 10cm
Source: WAEC / JAMB / NECO Classroom Archive (Record #65389)
Mathematics
WAEC / WASSCE 2022
Mensuration
Solution
Find the volume of a cone of radius 3.5cm and vertical height 12cm. [Take π = 22/7]
A
15.5cm\(^3\)
B
21.0cm\(^3\)
C
142cm\(^3\)
D
154cm\(^3\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
volume of a cone = ⅓ \pi r2h → \(\frac{1*22*3.5*3.5*12}{3*7}\)
= 154cm\(^3\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #65391)
Mathematics
WAEC / WASSCE 2022
Lengths and Perimeters
Diagram
Solution
In the diagram, ∠POQ = 150 and the radius of the circle PSQR is 4.2cm. [take π = 22/7]
What is the length of the minor arc?
Attached Figure / Diagram
A
11cm
B
15.4cm
C
17.64cm
D
23.10cm
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\frac{\theta}{360}\) * 2 * \pi * r → \(\frac{150 * 2 * 22 * 4.2}{360 x 7}\)
= 11cm
Source: WAEC / JAMB / NECO Classroom Archive (Record #64823)
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
UTME / JAMB 2022
Circles & Circle Theorems
Solution
The locus of points equidistant from a fixed point.
A
circle
B
perpendicular lines
C
straight line
D
bisector
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Definition of a circle
Source: WAEC / JAMB / NECO Classroom Archive (Record #64277)
Mathematics
UTME / JAMB 2022
Coordinate Geometry
Solution
Find the equation of a straight line parallel to the line 2x - y = 5 and having intercept of 5
A
2x + y = 5
B
2x + y = -5
C
2x - y = -5
D
2x - y = 5
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Condition for Parallelism means that their gradient value is same
line 2x - y = 5 is rearranged
As y = 2x - 5 from y = mx + c
: line 2x - y = 5 has the gradient of 2
A parallel line with gradient of 2 and intercept of 5
→ 2x - y = -5
Rearranged as y = 2x + 5
Source: WAEC / JAMB / NECO Classroom Archive (Record #64351)
Mathematics
UTME / JAMB 2022
Coordinate Geometry
Solution
The coordinates of the mid-point of the line joining the points (-3,5) and (2,10) is given by?
A
( \(\frac{1}{2}\), \(\frac{15}{2}\) )
B
( \(\frac{1}{2}\), \(\frac{-15}{2}\) )
C
( \(\frac{-1}{2}\), \(\frac{-15}{2}\) )
D
( \(\frac{-1}{2}\), \(\frac{15}{2}\) )
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Given Data: x\(_1\) = -3, x\(_2\) = 2, y\(_1\) = 5, y\(_2\) = 10
coordinates of the mid-point of the line = (\(\frac{x_1 + x_2}{2}\) , \(\frac{y_1 + y_2}{2}\))
(\(\frac{-3 +2}{2}\) , \(\frac{5 + 10}{2}\))
= \(\frac{-1}{2}\)) , \(\frac{15}{2}\))
Source: WAEC / JAMB / NECO Classroom Archive (Record #64368)
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)