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 106–120 of 2096 verified questions
Sort by:
Mathematics
WAEC / WASSCE 2020
Number and Numeration
Solution
Given that \(\frac{\sqrt{3} + \sqrt{5}}{\sqrt{5}}\)
= x + y\(\sqrt{15}\), find the value of (x + y)
A
1\(\frac{3}{5}\)
B
1\(\frac{2}{5}\)
C
1\(\frac{1}{5}\)
D
\(\frac{1}{5}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{\sqrt{3} + \sqrt{5}}{\sqrt{5}}\) = x + y\(\sqrt{15}\)
cross multiply to have: \(\sqrt{3}\) + \(\sqrt{5}\) = x\(\sqrt{5}\) + 5y\(\sqrt{3}\)
Collect like roots : x\(\sqrt{5}\) = \(\sqrt{5}\) → x = 1
5y\(\sqrt{3}\) = \(\sqrt{3}\) → y = \(\frac{1}{5}\)
∴ ( x + y ) = 1 + \(\frac{1}{5}\)
= 1\(\frac{1}{5}\)
Source: Myschool Past Questions Archive (Record #58254)
Mathematics
WAEC / WASSCE 2020
Number and Numeration
Solution
If x = 3 and y = -1, evaluate 2(x\(^2\) - y\(^3\))
A
24
B
22
C
20
D
16
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
2(\(x^2 - y^3\))
= 2(\(3^2 - (-1)^3\))
= 2(9 - (-1))
= 2 x 10 = 20
Source: Myschool Past Questions Archive (Record #58265)
Mathematics
WAEC / WASSCE 2020
Number and Numeration
Solution
The first term of a geometric progression (G.P) is 3 and the 5th term is 48. Find the common ratio.
A
2
B
4
C
8
D
16
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
T\(_5\) = ar\(^4\)
\(\frac{48}{3} = \frac{3r^4}{3}\)
16 = r\(^4\)
r = \(4\sqrt{16}\)
= 2
Source: Myschool Past Questions Archive (Record #58292)
Mathematics
WAEC / WASSCE 2020
Number and Numeration
Solution
Make m the subject of the relation k = \(\sqrt{\frac{m - y}{m + 1}}\)
A
m = \(\frac{y + k^2}{k^2 + 1}\)
B
m = \(\frac{y + k^2}{1 - k^2}\)
C
m = \(\frac{y - k^2}{k^2 + 1}\)
D
m = \(\frac{y - k^2}{1 - k^2}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
k = \(\sqrt{\frac{m - y}{m + 1}}\)
k\(^2\) = \(\frac{m - y}{m + 1}\)
k\(^2\)m + k\(^2\) = m - y
k\(^2\) + y = m - k\(^2\)m
\(\frac{k^2 + y}{1 - k^2}\) = m\(\frac{(1 - k^2)}{1 - k^2}\)
m = \(\frac{y + k^2}{1 - k^2}\)
Source: Myschool Past Questions Archive (Record #58298)
Mathematics
WAEC / WASSCE 2020
Number and Numeration
Solution
Two buses start from the same station at 9.00am and travel in opposite directions along the same straight road. The first bus travel at a speed of 72 km/h and the second at 48 km/h. At what time will they be 240km apart?
A
1:00 pm
B
12:00 noon
C
11:00 am
D
10:00 am
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Let x be the time
Then 72x + 48x = 240
\(\frac{120}{120} \times \frac{240}{120}\)
x = 2hrs
9:00 + 2hrs = 11:00 am
Source: Myschool Past Questions Archive (Record #58303)
Mathematics
WAEC / WASSCE 2020
Number and Numeration
Solution
A solid cuboid has a length of 7 cm, a width of 5 cm, and a height of 4 cm. Calculate its total surface area.
A
280 cm\(^2\)
B
166 cm\(^2\)
C
140 cm\(^2\)
D
83 cm\(^2\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Total = 2(LB + BH + LH)
Surface area
= 2(7 x 5 + 5 x 4 + 7 x 4)
= 2(35 + 20 + 28)
= 2(83)
= 166cm\(^2\)
Source: Myschool Past Questions Archive (Record #58304)
Mathematics
WAEC / WASSCE 2020
Number and Numeration
Solution
In the diagram, PQ // SR. Find the value of x
A
34
B
46
C
57
D
68
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
x + 68\(^o\) + 246\(^o\) = 360\(^o\)
x + 314\(^o\) = 360\(^o\)
x = 360\(^o\) - 314\(^o\)
x = 46\(^o\)
Source: Myschool Past Questions Archive (Record #58305)
Mathematics
WAEC / WASSCE 2020
Number and Numeration
Solution
The expression \(\frac{5x + 3}{6x (x + 1)}\) will be undefined when x equals
A
{0, 1}
B
{0, -1}
C
{-3, -11}
D
{-3, 0}
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
6x(x + 1) = 0
When 6x = 0 and
x + 1 = 0
x = 0 and x = -1
(0, -1)
Source: Myschool Past Questions Archive (Record #58307)
Mathematics
WAEC / WASSCE 2020
Number and Numeration
Solution
A man is five times as old as his son. In four years' time, the product of their ages would be 340. If the son's age is y, express the product of their ages in terms of y.
A
5y\(^2 - 16y - 380 = 0\)
B
5y\(^2 - 24y - 380 = 0\)
C
5y\(^2 - 16y - 330 = 0\)
D
5y\(^2 + 24y - 324 = 0\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Man = x, Son = y
x = 5y
(x + 4)(y + 4) = 350
(5y + 4)(y + 4) = 340
5y\(^2\) + 20y + 4y + 16 - 240 = 0
5y\(^2\) + 24y - 324 = 0
Source: Myschool Past Questions Archive (Record #58308)
Mathematics
WAEC / WASSCE 2020
Number and Numeration
Solution
Simplify; \(\frac{a}{b} - \frac{b}{a} - \frac{c}{b}\)
A
\(\frac{a - b + c}{ab}\)
B
\(\frac{ab - bc - ac}{ab}\)
C
\(\frac{a^2 - b^2 + ac}{ab}\)
D
\(\frac{a^2 - b^2 - ac}{ab}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{a}{b} - \frac{b}{a} - \frac{c}{b}\)
\(\frac{a^2 - b^2- ac}{ab}\)
Source: Myschool Past Questions Archive (Record #58309)
Mathematics
WAEC / WASSCE 2020
Number and Numeration
Solution
Fati buys milk at ₦x per tin sells each at a profit of ₦y. If she sells 10 tins of milk, how much does she receives from the sales?
A
₦(xy + 10)
B
₦(x + 10y)
C
₦(10x + y)
D
₦10(x + y)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Selling Price for each = ₦x + ₦y
= 10(₦x + ₦y)
Source: Myschool Past Questions Archive (Record #58314)
Mathematics
WAEC / WASSCE 2020
Number and Numeration
Solution
The dimension of a rectangular base of a right pyramid is 9 cm by 5cm. If the volume of the pyramid is 105 cm\(^3\), how high is the pyramid?
A
10cm
B
6cm
C
8cm
D
7cm
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Volume = \(\frac{1}{3}\) x 9 x 5 x h
105 = \(\frac{1}{3}\) x 9 x 5 x h
\(\frac{105}{15} = \frac{15h}{15}\)
h = 7cm
Source: Myschool Past Questions Archive (Record #58316)
Mathematics
WAEC / WASSCE 2020
Number and Numeration
Diagram
Solution
In the diagram, \(\overline{PU}\)/\(\overline{SR}\), \(\overline{PS}\)/\(\overline{TR}\), \(\overline{QS}\)/\(\overline{UR}\), \(\overline{UR}\) = 15cm, \(\overline{SR}\) = 8 cm, \(\overline{PS}\) = 10 cm and area of △SUR = 24 cm\(^2\). Calculate the area of PTRS.
Attached Figure / Diagram
A
40 cm\(^2\)
B
48 cm\(^2\)
C
80 cm\(^2\)
D
120 cm\(^2\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Area PTRS = 10cm x 8cm
= 80cm
Source: Myschool Past Questions Archive (Record #58331)
Mathematics
WAEC / WASSCE 2020
Number and Numeration
Solution
The diameter of a sphere is 12 cm. Calculate, correct of the nearest cm\(^3\), the volume of the sphere, [Take \(\pi = \frac{22}{7}\)]
A
903 cm\(^3\)
B
904 cm\(^3\)
C
905 cm\(^3\)
D
906 cm\(^3\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Volume of sphere = \(\frac{4}{3}\)\(\pi\)r\(^3\)
diameter = 12cm ⇒ r = 6cm
V. of sphere = \(\frac{4}{3}\) x \(\frac{22}{7}\) x 6\(^3\) \(\approxeq\) 905cm\(^3\)
Source: Myschool Past Questions Archive (Record #58347)
Mathematics
WAEC / WASSCE 2020
Number and Numeration
Solution
The interquartile range of distribution is 7. If the 25th percentile is 16, find the upper quartile.
A
35
B
30
C
23
D
9
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Q\(_3\) - Q\(_1\) = 7
Q\(_3\) - 16 = 7
Q\(_3\) - 7 + 16
= 23
Source: Myschool Past Questions Archive (Record #58406)