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Mathematics
WAEC / WASSCE 2020
Plane Geometry, Polygons & Circle Theorems
Solution
Find the sum of the interior angle of a pentagon.
A
340\(^o\)
B
350\(^o\)
C
540\(^o\)
D
550\(^o\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Sum = (5 - ) 180\(^o\)
= (5 - 2) 180\(^o\) = 3 x 180\(^o\)
= 540\(^o\)
Source: Myschool Past Questions Archive (Record #58344)
Mathematics
WAEC / WASSCE 2020
Mensuration (Areas, Perimeters & Volumes)
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
Permutations, Combinations & Probability
Solution
A box contains 12 identical balls of which 5 are red, 4 blue, and the rest are green. If a ball is selected at random from the box, what is the probability that it is green?
A
\(\frac{3}{4}\)
B
\(\frac{1}{2}\)
C
\(\frac{1}{3}\)
D
\(\frac{1}{4}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
No. of red = 5
No. of blue = 4
No. of green = 3
Total = 12
Pr(Green) = \(\frac{3}{12} = \frac{1}{4}\)
Source: Myschool Past Questions Archive (Record #58349)
Mathematics
WAEC / WASSCE 2020
Permutations, Combinations & Probability
Solution
A box contains 12 identical balls of which 5 are red, 4 blue, and the rest are green. If two balls are selected at random one after the other with replacement, what is the probability that both are red?
A
\(\frac{25}{144}\)
B
\(\frac{5}{33}\)
C
\(\frac{5}{6}\)
D
\(\frac{103}{132}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Pr(RR) = \(\frac{5}{12}\) = \(\frac{5}{12} \times \frac{5}{12} = \frac{25}{144}\)
Source: Myschool Past Questions Archive (Record #58355)
Mathematics
WAEC / WASSCE 2020
Plane Geometry, Polygons & Circle Theorems
Solution
x
6.20
6.85
7.50
y
3.90
5.20
6.50
The points on a linear graph are as shown in the table. Find the gradient (slope) of the line.
A
2\(\frac{1}{2}\)
B
2
C
1
D
\(\frac{1}{2}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Gradient = \(\frac{y_2 - y_ 1}{x_2 - x_1}\)
= \(\frac{5.20 - 3.90}{6.85 - 6.20}\)
= \(\frac{1.3}{0.5}\)
= 2
Source: Myschool Past Questions Archive (Record #58365)
Mathematics
WAEC / WASSCE 2020
Plane Geometry, Polygons & Circle Theorems
Which of the following is not a sufficient condition for two triangles to be congruent?
A
AAS
B
SSS
C
SAS
D
SSA
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 #58381)
Mathematics
WAEC / WASSCE 2020
Fractions, Decimals, Percentages & Approximations
Solution
A woman received a discount of 20% on a piece of cloth she purchased from a shop. If she paid $525.00, what was the original price?
A
$675.25
B
$660.25
C
$656.25
D
$616.25
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{20}{100}\) x \(x\) = \(x - 525\)
\(\frac{x}{5} = x\) - 535
x = 5x - 2625
\(\frac{4x}{4} = \frac{2625}{4}\)
x = $656.25
OR
To find the original price of the cloth after a 20\% discount, we can set up the equation:
\(\text{Final Price} = \text{Original Price} - \text{Discount}\)
Let \( P \) be the original price. Since the woman received a 20\% discount, she paid 80\% of the original price:
\(525 = 0.8P\)
To find \( P \), divide both sides by 0.8:
\(P = \frac{525}{0.8}\)
Calculating this gives:
\(P = 656.25\)
Thus, the original price of the cloth was \(\$656.25\).
Source: Myschool Past Questions Archive (Record #58402)
Mathematics
WAEC / WASSCE 2020
Statistics (Data Representation, Central Tendency & Dispersion)
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)
Mathematics
WAEC / WASSCE 2020
Linear, Simultaneous & Quadratic Equations
Solution
If (x + 2) is a factor of x\(^2\) +px - 10, find the value of P.
A
3
B
-3
C
7
D
-7
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
x + 2 = 0
x -2
x\(^2\) = px - 10 = 0
(-2)\(^2\) - 2p - 10 = 0
4 - 2p - 10 = 0
\(\frac{-2p}{-2} = \frac{6}{-2}\) \(\to\) p = -3
Source: Myschool Past Questions Archive (Record #58417)
Mathematics
WAEC / WASSCE 2020
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram, O is the centre of the circle. If < NLM = 74\(^o\), < LMN = 39\(^o\) and < LOM = x, find the value of x.
Attached Figure / Diagram
A
134\(^o\)
B
126\(^o\)
C
113\(^o\)
D
106\(^o\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
L\(N\)M = 180\(^o\) - (74\(^o\) + 39\(^o\))
180\(^o\) - 113\(^o\)
= 67\(^o\)
L\(^O\)
M = x = 2 x 67\(^o\)
= 134\(^o\)
Source: Myschool Past Questions Archive (Record #58465)
Mathematics
WAEC / WASSCE 2020
Number Bases & Modular Arithmetic
Solution
Find the least value of x which satisfies the equation 4x = 7(mod 9)
A
7
B
6
C
5
D
4
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
4x = 7 (mod 9)
4x = 7 + 9 (mod 9)
\(\frac{4x}{4} = \frac{16}{4}\) (mod 9)
x = 4
Source: Myschool Past Questions Archive (Record #58619)
Mathematics
WAEC / WASSCE 2020
Sets, Logic & Venn Diagrams
Solution
(a) If A = {multiples of 2}, B = {multiples of 3} and C = {factors of 6} are subsets of \(\mu\) = {x:1 \(\leq\) x \(\leq\) 10} find A ′ \(\cap\) B ′ \(\cap\) C′
(b) Tickets for a movie premiere cost $18.50 each while the bulk purchase price for 5 tickets is $80.00. If 4 gentlemen decide to get a fifth person to join them so that they can share the bulk purchase price equally, how much would each person save?
medium Difficulty
Verified Correct Answer: Option
Step-by-Step Mathematical Solution
\(\mu\) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {2, 4, 6, 8, 10}
B = {3,6,9}
C = {1, 2, 3, 6}
A` ={1, 3, 5, 7, 9}
B` = {1, 2, 4, 5, 7, 8, 10}
C` = {4, 5, 7, 8, 9, 10}
a` \(\cap\) B` C` = { 5 and 7 }
(b) bulk cost $80
1 will cost \(\frac{$80}{5}\) = $16
for 5 gentlemen each cost $18.50
total cost = 18.50 x 5
= $92.50
5 cost for $16 each = 5 x $16
= $(92.50 - 80.00)
each will save \(\frac{$12.50}{5}\)
= $2.50
Source: Myschool Past Questions Archive (Record #58706)
Mathematics
WAEC / WASSCE 2020
Fractions, Decimals, Percentages & Approximations
Solution
(a) Given that P = (\(\frac{rk}{Q} - ms\))\(^{\frac{2}{3}}\)
(i) Make Q the subject of the relation;
(ii) find, correct to two decimal places, the value of Q when P = 3, m = 15, s = 0.2, k = 4 and r = 10.
(b) Given that \(\frac{x + 2y}{5}\) = x - 2y, find x : y
medium Difficulty
Verified Correct Answer: Option
Step-by-Step Mathematical Solution
P = (\(\frac{rk}{Q} - ms\))\(^{\frac{2}{3}}\)
P\(^{\frac{3}{2}}\) = \(\frac{rk}{Q}\) - ms
P\(^{\frac{3}{2}}\) + ms = \(\frac{rk}{Q}\)
Q = \(\frac{rk}{p^{\frac{3}{2}}ms}\)
(a)(ii)
Q = \(\frac{10 \times 4}{3\frac{3}{2} + 15 (0.2)}\)
Q = \(\frac{40}{5.1958 + 3}\)
Q = \(\frac{40}{8.1958}\)
= 4.88 to 2 d.p
(b) \(\frac{x + 2y}{5} = x - 2y\)
x + 2y = 5(x - 2y)
x + 2y = 5x - 10y
x - 5x = -10y - 2y
-4x = -12y
\(\frac{x}{y} = \frac{12}{4}\)
x : y = 3 : 1
Source: Myschool Past Questions Archive (Record #58707)
Mathematics
WAEC / WASSCE 2020
Indices, Logarithms & Surds
Diagram
Solution
(a} In the diagram, O is the centre of the circle ABCDE, = I\(\overline{BC}\)I = |\(\overline{CD}\)| and < BCD = 108^\circ. Find < CDE.
(b) Given that tan x = \(\sqrt{3}\), 0\(^o\) \(\geq\) x \(\geq\) 90\(^o\), evaluate
\(\frac{(cos x)^2 - sin x}{(sin x)^2 + cos x}\)
Attached Figure / Diagram
medium Difficulty
Verified Correct Answer: Option
Step-by-Step Mathematical Solution
(a)
C\(B\)D = C\(D\)B = \(\frac{180^o - 108^o}{2}\)
= \(\frac{72^o}{2}\) = 36\(^o\)
< CDE = < BDE + 36\(^o\)
< CDE = 90\(^o\) + 36 = 126\(^o\)
(b) tan x = \(\sqrt{3}\)
y\(^2\) (\(\sqrt{3}\))\(^2\) - (l)\(^2\)
y\(^2\) 3 + 1, Cos x = \(\frac{1}{2}\)
y = \(\sqrt{4}\) = 2
sin x = \(\frac{\sqrt{3}}{2}\)
\(\frac{(cos x)^2 - sin x}{(sin x)^2 + cos x}\)
= \(\frac{(\frac{1}{2})^2 - \frac{\sqrt{3}}{2}} {(\frac{\sqrt{3}}{2})^2 + \frac{1}{2}}\)
= \(\frac{\frac{1}{4} - \frac{\sqrt{3}}{2}}{\frac{3}{4} + \frac{1}{2}}\)
= \(\frac{1 - 2\sqrt{3}}{4}\) \(\div\) \(\frac{5}{4}\)
= \(\frac{1 - 2 \sqrt{3}}{4}\) x \(\frac{4}{5}\)
= \(\frac{1 - 2\sqrt{3}}{5}\)
Source: Myschool Past Questions Archive (Record #58708)
Mathematics
WAEC / WASSCE 2020
Mensuration (Areas, Perimeters & Volumes)
Solution
The total surface area of a cone of slant height l cm and base radius r cm is 224\(\pi\) cm\(^2\). If r : l = 2:5, find:
(a) correct to one decimal place, the value of r
(b) correct to the nearest whole number, the volume of the cone [Take \(\pi\) = \(\frac{22}{7}\)]
medium Difficulty
Verified Correct Answer: Option
Step-by-Step Mathematical Solution
TSA = 224\(\pi\) cm\(^2\)
r : l = 2: 5
\(\frac{r}{l} = \frac{2}{5}\)
r = \(\frac{2l}{5}\)
\(\frac{3r}{2}\) = l
TSA \(\pi\)rl + \(\pi ^2\)
TSA = \(\pi\)(rl + r\(^2\))
224\(\pi\) = \(\pi\)r(l + r)
224 = r (\(\frac{5r}{2} + \frac{r}{1}\))
224 = r(\(\frac{5r + 2r}{2}\))
224 = \(\frac{7r^2}{2}\)
r\(^2\) = \(\frac{448}{7}\)
r = \(\sqrt{448}{7}\)
r = \(\sqrt{64cm}\)
l = \(\frac{5 \times 8}{2}\)
r = 8cm
l = 20cm
(b) Volume of cone = \(\frac{1}{3}\)\(\pi ^2\)h
h\(^2\) = l\(^2\) - r\(^2\)
h\(^2\) = (20)\(^2\) - (8)\(^2\)
h\(^2\) = 400 - 64
h = \(\sqrt{336}\)
= 18.33cm
Volume = \(\frac{1}{3} \times \frac{22}{7}\) x 8\(^2\) x 18.33
= \(\frac{25,809.06}{21}\)
= 1229 cm\(^3\)
Source: Myschool Past Questions Archive (Record #58709)