Question Library
Browse, filter, and study verified past examination questions with step-by-step mathematical reasoning.
Searching 18,000+ Questions...
Sifting topics, KaTeX formulas & verified solutions
Showing 601–615 of 4910 verified questions
Sort by:
Mathematics
WAEC / WASSCE 2020
Geometry and Trigonometry
Diagram
Solution
In the diagram, PQR is a circle with center O. If ∠OPQ = 48°, find the value of M.
Attached Figure / Diagram
A
96\(^o\)
B
90\(^o\)
C
68\(^o\)
D
42\(^o\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
< O\(Q\)P = 48\(^o\) (base angles of isoceles \(\triangle\))
m = 48\(^o\) + 48\(^o\) = 96\(^o\) (exterior angle of a \(\triangle\))
Source: WAEC / JAMB / NECO Classroom Archive (Record #58333)
Mathematics
WAEC / WASSCE 2020
Geometry and Trigonometry
Diagram
Solution
In the diagram, PQ is a straight line. If m = \(\frac{1}{2}\) (x + y + z), find value of m.
Attached Figure / Diagram
A
45\(^o\)
B
60\(^o\)
C
90\(^o\)
D
100\(^o\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
x + y + m + z = 180º
but m = \(\frac{1}{2}\)(x + y + z)
2m = ( x + y + z )
Thus ( x + y + z) + m = 180º
(2m) + m = 180º
3m = 180º
m = \(\frac{180º}{3}\) = 60º
Source: WAEC / JAMB / NECO Classroom Archive (Record #58361)
Mathematics
WAEC / WASSCE 2020
Geometry and Trigonometry
Diagram
Solution
In the diagram, O is the center of the circle. \(\overline{PQ}\) and \(\overline{RS}\) are tangents to the circle. Find the value of (M + N).
Attached Figure / Diagram
A
120\(^o\)
B
90\(^o\)
C
75\(^o\)
D
60\(^o\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
m + n + 90\(^o\) + 180\(^o\) (sum of angle in a \(\triangle\))
m + n = 180\(^o\) - 90\(^o\)
m + n =90\(^o\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #58373)
Mathematics
UTME / JAMB 2020
Number Bases
Solution
Evaluate (212)\(_3\) - (121)\(_3\) + (222)\(_3\)
A
(313)\(_3\)
B
(1000)\(_3\)
C
(1020)\(_3\)
D
(1222)\(_3\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Evaluate (212)\(_3\) - (121)\(_3\) + (222)\(_3\)
(212)\(_3\) + (222)\(_3\) = 1211\(_3\)
→ 1211\(_3\) - 121\(_3\)
= 1020\(_3\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #56726)
Mathematics
WAEC / WASSCE 2020
Fractions, Decimals, Percentages & Approximation
Solution
Evaluate and correct to two decimal places, 75.0785 - 34.624 + 9.83
A
30.60
B
50.29
C
50.28
D
30.63
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
75.0785
-35.624
--------------
40.4545
+9.83
-------------
50.28 to 2d.p
Source: WAEC / JAMB / NECO Classroom Archive (Record #58214)
Mathematics
WAEC / WASSCE 2020
Fractions, Decimals, Percentages & Approximation
Solution
Solve \(\frac{1}{3}\)(5 - 3x) < \(\frac{2}{5}\)(3 - 7x)
A
x > \(\frac{7}{22}\)
B
x < \(\frac{7}{22}\)
C
x > \(\frac{-7}{27}\)
D
x < \(\frac{-7}{27}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{1}{3}\)(5 - 3x) < \(\frac{2}{5}\)(3 - 7x)
5(5 - 3x) < 6(3 - 7x)
25 - 15x < 18 - 42x
- 15x + 42x < 18 - 25
\(\frac{27x}{27}\) < \(\frac{-7}{27}\)
x < \(\frac{-7}{27}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #58296)
Mathematics
WAEC / WASSCE 2020
Graphs of Linear & Quadratic Functions
Diagram
Solution
The graph of the equations y = 2x + 5 and y = 2x\(^2\) + x - 1 are shown. Use the information above to answer this question.
Find the point of intersection of the two graphs.
Attached Figure / Diagram
A
(2.0, 9.0) and (-1.5, 2.0)
B
(2.0, 8.5) and (-1.5, 2.0)
C
(2.0, 8.0) and (-1.5, 2.5)
D
(2.0, 7.5) and (-1.5, 2.5)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
The point of intersection are (2.0, 9.0) and (-1.5, 2.0)
Source: WAEC / JAMB / NECO Classroom Archive (Record #58411)
Mathematics
WAEC / WASSCE 2020
Graphs of Linear & Quadratic Functions
Diagram
Solution
The graph of the equations y = 2x + 5 and y = 2x\(^2\) + x - 1 are shown. Use the information above to answer this question.
If x = -2.5, what is the value of u on the curve?
Attached Figure / Diagram
A
y = 8.0
B
y = 8.5
C
y = 9.0
D
y = 9.5
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
If x = -2.5
y = 8.5
Source: WAEC / JAMB / NECO Classroom Archive (Record #58413)
Mathematics
UTME / JAMB 2020
Functions and Relations
Solution
Find the gradient of the line passing through the points (-2, 0) and (0, -4)
A
2
B
-4
C
-2
D
4
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Given (-2, 0) ans (0, -4).
Gradient = \(\frac{y_2 - y_1}{x_2 - x_1}\)
= \(\frac{-4 - 0}{0 - (-2)}\)
= \(\frac{-4}{2}\)
= -2
Source: WAEC / JAMB / NECO Classroom Archive (Record #56801)
Mathematics
WAEC / WASSCE 2020
Functions and Relations
Solution
The implication x \(\to\) y is equivalent to?
A
~ y \(\to\) ~ x
B
y \(\to\) ~ x
C
~ x \(\to\) ~ y
D
y \(\to\) x
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
x→y means "if x is true, then y is true."
The contrapositive of x→y is \simy → \simx, which is logically equivalent to the original implication.
Source: WAEC / JAMB / NECO Classroom Archive (Record #58289)
Mathematics
UTME / JAMB 2020
Number and Numeration
Solution
Factorise (4a + 3) \(^2\) - (3a - 2)\(^2\)
A
(a + 1)(a + 5)
B
(a - 5)(7a - 1)
C
(a + 5)(7a + 1)
D
a(7a + 1)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
[(4a + 3) \(^2\) - (3a - 2)\(^2\) = a\(^2\) - b\(^2\) = (a + b) (a - b)
= [(4a + 3) + (3a - 2)] [(4a + 3) - (3a - 2)]
= [4a + 3 + 3a - 2] [4a + 3 - 3a + 2]
= (7a + 1)(a + 5)
(a + 5) (7a + 1)
Source: Myschool Past Questions Archive (Record #56743)
Mathematics
UTME / JAMB 2020
Statistics and Probability
Solution
Find the median of the numbers 89, 141, 130, 161, 120, 131, 131, 100, 108 and 119
A
131
B
125
C
123
D
120
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Arrange in ascending order
89, 100, 108, 119, 120,130, 131, 131, 141, 161
Median = \(\frac{120 + 130}{2}\) = 125
Source: Myschool Past Questions Archive (Record #56745)
Mathematics
UTME / JAMB 2020
Algebra
Solution
Find all real number x which satisfy the inequality \(\frac{1}{3}\) (x + 1) - 1 > \(\frac{1}{5}\)(x + 4)
A
x < 11
B
x < -1
C
x > 6
D
x > 11
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{1}{3}\) (x + 1) - 1 > \(\frac{1}{5}\)(x + 4) = \(\frac{x + 1}{3} - 1\) > \(\frac{x + 4}{5}\)
\(\frac{x + 1}{3} - \frac{x + 4}{5} -1\) > 0
= \(\frac{5x + 5 - 3x - 12}{15}\)
2x - 7 > 15
2x > 22 = x > 11
Source: Myschool Past Questions Archive (Record #56746)
Mathematics
UTME / JAMB 2020
Number and Numeration
Solution
Reach each number to two significant figures and then evaluate \(\frac{0.02174 \times 1.2047}{0.023789}\)
A
0
B
0.9
C
1.1
D
1.2
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{0.021741 \times 1.2047}{0.023789}\) = \(\frac{0.022 \times 1.2}{0.024}\) (to 2 s.f)
= \(\frac{0.0264}{0.024}\) = 1.1
Source: Myschool Past Questions Archive (Record #56747)
Mathematics
UTME / JAMB 2020
Number and Numeration
Solution
Four boys and ten girls can cut a field first in 5 hours. If the boys work at \(\frac{5}{4}\) the rate at which the girls work, how many boys will be needed to cut the field in 3 hours?
A
180
B
60
C
25
D
20
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Let x rep. numbers of boys that can work at \(\frac{5}{4}\) the rate at
which the 10 girls work
For 1 hrs, x boys will work for \(\frac{\frac{1}{5} \times 10}{4}\)
x = \(\frac{5}{4}\) x 10
= 8 boys
8 boys will do the work of ten girls at the same rate
4 + 8 = 12 bous cut the field in 5 hrs for 3 hrs,
\(\frac{12 \times 5}{3}\) boys will be needed = 20 boys.
Source: Myschool Past Questions Archive (Record #56749)