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 25036–25050 of 29821 verified questions
Sort by:
Mathematics
WAEC / WASSCE 1990
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram below, O is the center of the circle if ∠QOR = 290o, find the size ∠QPR
Attached Figure / Diagram
A
110o
B
70o
C
55o
D
35o
E
20o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
360º - 290º = 70º
\(\frac{70}{2}\) = 35º
Source: Myschool Past Questions Archive (Record #22685)
Mathematics
WAEC / WASSCE 1990
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram above, PQ is a tangent at T to the circle ABT. ABC is a straight line and TC bisects ∠BTO. Find x.
Attached Figure / Diagram
A
20o
B
30o
C
35o
D
40o
E
50o
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
From the figure < TAB = < BTQ = 40^\circ (alternate segment)
\(\therefore\)< ATB = 180^\circ - (70^\circ + 40^\circ) = 70^\circ (angle on a straight line)
< BTC = \(\frac{40^\circ}{2} = \frac{< BTQ}{2}\)
\(\therefore < BTQ = 40^\circ\)
x^\circ = 180^\circ - (40^\circ + 70^\circ + 20^\circ)
= 50^\circ
Source: Myschool Past Questions Archive (Record #22687)
Mathematics
WAEC / WASSCE 1990
Plane Geometry, Polygons & Circle Theorems
Diagram
Which of the sketches above gives a correct method for constructed an angle of 120o at the point P?
Attached Figure / Diagram
A
I only
B
II only
C
III only
D
I and II only
E
I, II and III
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option D.
Source: Myschool Past Questions Archive (Record #22690)
Mathematics
WAEC / WASSCE 1990
Trigonometry, Elevation & Bearings
Solution
Use mathematical table to evaluate (cos40^\circ - sin30^\circ)
A
-0.2660
B
-0.0266
C
0.0266
D
0.2660
E
1.5320
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
(cos 40^\circ - sin 30^\circ)
= 0.7660 - 0.5
= 0.2660
Source: Myschool Past Questions Archive (Record #22691)
Mathematics
WAEC / WASSCE 1990
Trigonometry, Elevation & Bearings
Solution
If the shadow of a pole 7m high is 1/2 its length what is the angle of elevation of the sun, correct to the nearest degree?
A
90o
B
63o
C
60o
D
26o
E
0o
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
tan θ - 7/3.5 = 2
tan θ= 2.0000
θ = 63o
Source: Myschool Past Questions Archive (Record #22692)
Mathematics
WAEC / WASSCE 1990
Trigonometry, Elevation & Bearings
Solution
From the top of a building 10m high, the angle of depression of a stone lying on the horizontal ground is 69o. Calculate ,correct to one decimal place, the distance of the stone from the foot of the building
A
3.6m
B
3.8m
C
6.0m
D
9.3m
E
26.1m
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
tan21o =x/10
x = 10 tan 21o
= 3.3839 = 3.8m
Source: Myschool Past Questions Archive (Record #22695)
Mathematics
WAEC / WASSCE 1990
Trigonometry, Elevation & Bearings
Solution
The bearing of a point X from a point Y is 074^\circ. What is the bearing of Y from X?
A
106o
B
146o
C
164o
D
254o
E
286o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
< YXS = 74^\circ (alternate angles, N\(_1\) S\(_1\) // N\(_2\) S\(_2\))
N\(_2\) E\(_2\) S\(_2\) = 180^\circ
\(\therefore\) Bearing of Y from X = 180^\circ + 74^\circ
= 254^\circ
Source: Myschool Past Questions Archive (Record #22696)
Mathematics
WAEC / WASSCE 1990
Statistics (Data Representation, Central Tendency & Dispersion)
Diagram
Solution
The annual salary of Mr. Johnson Mohammed for 1989 was N12,000.00. He spent this on agriculture projects, education of his children, food items, saving , maintenance and miscellaneous items as shown in the pie chart
How much money did he invest in agriculture?
Attached Figure / Diagram
A
N1,200.00
B
N1,440.00
C
N2,000.00
D
N2,910.00
E
N4,000.00
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
Agric project = \(\frac{120}{360} \times N12,000.00\)
= \(N4,000.00\)
Source: Myschool Past Questions Archive (Record #22698)
Mathematics
WAEC / WASSCE 1990
Fractions, Decimals, Percentages & Approximations
Diagram
Solution
The table shows that the amount of money (in naira)collected through voluntary donations in a secondary school. What is the mode?
Attached Figure / Diagram
A
N3
B
N6
C
N9
D
N12
E
N15
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Mode = 12
Source: Myschool Past Questions Archive (Record #22699)
Mathematics
WAEC / WASSCE 1990
Fractions, Decimals, Percentages & Approximations
Diagram
The table shows that the amount of money (in naira)collected through voluntary donations in a secondary school.
What is the median of distribution
Attached Figure / Diagram
A
N3.00
B
N9.00
C
N12.00
D
N15.00
E
N18.00
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option C.
Source: Myschool Past Questions Archive (Record #22700)
Mathematics
WAEC / WASSCE 1990
Permutations, Combinations & Probability
Solution
Two groups of male students cast their votes on a particular proposal. The result are as follows:
In favor
Against
Group A
128
32
Group B
96
48
If a student in favor of the proposal is selected for a post, what is the probability that he is from group A?
A
8/19
B
16/35
C
10/19
D
4/7
E
4/5
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Probability that a student in favor is group A
= \(\frac{128}{128 + 32 + 96 + 48}\)
= \(\frac{128}{304}\)
= \(\frac{8}{19}\)
Source: Myschool Past Questions Archive (Record #22701)
Mathematics
WAEC / WASSCE 1990
Permutations, Combinations & Probability
Solution
Two groups of male students cast their vote on a particular proposal. The results are as follows:
In favor
Against
Group A
128
32
Group B
96
48
If a student is chosen at random, what is probability that he is against the proposal?
A
3/19
B
4/19
C
5/19
D
9/19
E
10/19
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Probability that the student is against the proposal
= \(\frac{32 + 48}{128 + 32 + 96 + 48}\)
= \(\frac{80}{304}\)
= \(\frac{5}{19}\)
Source: Myschool Past Questions Archive (Record #22702)
Mathematics
UTME / JAMB 1990
Plane Geometry, Polygons & Circle Theorems
Solution
The H.C.F. of a2bx + ab2x and a2b - b2 is
A
b
B
a + b
C
b(a \(\div\) b)
D
abx(a2 - b2)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
a2bx + ab2x; a2b - b2
abx(a + b); b(a2 - b2)
b(a + b)(a + b)
∴ H.C.F. = (a + b)
Source: Myschool Past Questions Archive (Record #31430)
Mathematics
UTME / JAMB 1990
Plane Geometry, Polygons & Circle Theorems
Solution
Simplify \(\sqrt{160r^2 + \sqrt{71r^4 + \sqrt{100r^8}}}\)
A
9r2
B
12\(\sqrt{3r}\)
C
13r
D
\(\sqrt{13r}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\sqrt{160r^2 + \sqrt{71r^4 + \sqrt{100r^8}}}\)
Simplifying from the innermost radical and progressing outwards we have the given expression
\(\sqrt{160r^2 + \sqrt{71r^4 + \sqrt{100r^8}}}\) = \(\sqrt{160r^2 + \sqrt{71r^4 + 10r^4}}\)
= \(\sqrt{160r^2 + \sqrt{81r^4}}\)
\(\sqrt{160r^2 + 9r^2}\) = \(\sqrt{169r^2}\)
= 13r
Source: Myschool Past Questions Archive (Record #31436)
Mathematics
UTME / JAMB 1990
Indices, Logarithms & Surds
Solution
Simplify 3log\(_6\)9 + log\(_6\)12 + log\(_6\)64 - log\(_6\)72
A
5
B
7776
C
log631
D
(7776)6
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
3 log\(_6\)9 + log\(_6\)12 + log\(_6\)64 - log\(_6\)72
= log\(_6\)9\(^3\) + log\(_6\)12 + log\(_6\)64 - log\(_6\)72
log\(_6\)729 + log\(_6\)12 + log\(_6\)64 - log\(_6\)72
log\(_6\)[\(\frac{(729 \times 12 \times 64)}{72}\)] = log\(_6\)7776
= log\(_6\)6\(^5\) = 5log\(_6\)6 = 5
N.B: log\(_6\)6 = 1
Source: Myschool Past Questions Archive (Record #31441)