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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
Geometry and Trigonometry
Solution
Solve 3x - 2y = 10 and x + 3y = 7 simultaneously
A
x = -4 and y = 1
B
x = -1 and y = -4
C
x = 1 and y = 4
D
x = 4 and y = 1
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
3x - 2y = 10 - - x 3
x + 3y = 7 ---x 2
------------------------
9x - 6y = 30
2x + 6y = 14
-------------------------
\(\frac{11x}{11} \frac{44}{11}\)
x = 4
From x + 3y = 7
3y = 7 - 4
\(\frac{3y}{3}\) = \(\frac{3}{3}\)
y = 1
Source: Myschool Past Questions Archive (Record #58273)
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
Algebra
Solution
Find the quadratic equation whose roots are \(\frac{1}{2}\) and -\(\frac{1}{3}\)
A
3x\(^2\) + x + 1 = 0
B
6x\(^2\) + x - 1 = 0
C
3x\(^2\) + x - 1 = 0
D
6x\(^2\) - x - 1 = 0
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
x = \(\frac{1}{2}\) and x = \(\frac{-1}{3}\)
(2x - 1) = 0 and (3x + 1) = 0
(2x - 1) (3x + 1) = 0
6x\(^2\) - x - 1 = 0
Source: Myschool Past Questions Archive (Record #58300)
Mathematics
WAEC / WASSCE 2020
Algebra
Solution
Given that x is directly proportional to y and inversely proportional to Z, x = 15 when y = 10 and Z = 4, find the equation connecting x, y and z
A
x = \(\frac{6y}{z}\)
B
x = \(\frac{12y}{z}\)
C
x = \(\frac{3y}{z}\)
D
x = \(\frac{3y}{2z}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(x\) x \(\frac{y}{z}\)
x = \(\frac{ky}{z}\)
15 = \(\frac{10k}{4}\)
\(\frac{60}{10}\) = k = 6
Therefore; x = \(\frac{6y}{z}\)
Source: Myschool Past Questions Archive (Record #58302)
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
Algebra
Solution
Find the equation of the line parallel to 2y = 3(x - 2) and passes through the point (2, 3)
A
y = \(\frac{2}{3} x - 3\)
B
y = \(\frac{2}{3} x - 2\)
C
y = \(\frac{3}{2} x\)
D
y = \(\frac{-2}{3} x\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
2y = 3(x - 2)
\(\frac{2y}{2} = \frac{3x}{2} - \frac{6}{2}\)
y = \(\frac{3}{2}x - 3\)
m = \(\frac{3}{2}\)
\(\frac{y - y_1}{x - x_1}\) = m
\(\frac{y - 3}{x - 2} = \frac{3}{2}\)
2y - 6 = 3x - 6
\(\frac{2y}{2} = \frac{3x}{2}\)
y = \(\frac{3}{2}\)x
Source: Myschool Past Questions Archive (Record #58306)
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
Geometry and Trigonometry
Solution
In the diagram, XYZ is an equilateral triangle of side 6cm and Y is the midpoint of \(\overline{XY}\). Find tan (< XZT)
A
\(\frac{1}{\sqrt{3}}\)
B
\(\frac{\sqrt{3}}{2}\)
C
\(\sqrt{3}\)
D
\(\frac{1}{2}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
ZT = \(\sqrt{6^2 - 3^2}\)
ZT = \(\sqrt{27}\) = \(3\sqrt{3}\)
tan (< XZT) = \(\frac{3}{3\sqrt{3}}\)
= - \(\frac{1}{\sqrt{3}}\)
Source: Myschool Past Questions Archive (Record #58311)
Mathematics
WAEC / WASSCE 2020
Geometry and Trigonometry
Solution
A fence 2.4 m tall, is 10m away from a tree of height 16m. Calculate the angle of elevation of the top of the tree from the top of the fence.
A
76.11\(^o\)
B
53.67\(^o\)
C
52.40\(^o\)
D
51.32\(^o\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Tan \(\theta\) = \(\frac{13.6}{10}\)
= tan\(^{-1}\)(1.36)
\(\theta\) = 53.67\(^o\)
Source: Myschool Past Questions Archive (Record #58312)