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Mathematics
WAEC / WASSCE 2018
Coordinate Geometry
Solution
The equation of the line through the points (4,2) and (-8, -2) is 3y = px + q, where p and q are constants. Find the value of p.
A
1
B
2
C
3
D
9
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Using the two - point from
\(\frac{y - y_1}{y_2 - y_1} = \frac{x - x_1}{x_2 - x_1}\)
\(\frac{y - 2}{-2 - 2} = \frac{x - 4}{-8 - 4}\)
\(\frac{y - 2}{-4} = \frac{x - 4}{-12}\)
\(\frac{-12(y -2)}{-4}\) = x - 4
3(y -2) = x -4
3y - 6 = x - 4
3y = x - 4 + 6
3y = x + 2...
By comparing the equations;
3y = px + , p = 1
Source: Myschool Past Questions Archive (Record #49349)
Mathematics
WAEC / WASSCE 2018
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
The mean of 1, 3, 5, 7 and x is 4. Find the value of x
A
2
B
4
C
6
D
8
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Mean = \(\frac{\sum x}{n}\)
4 = \(\frac{1 + 3 + 5 + 7 + x}{5}\)
4 x 5 = 16 + x
20 - 16 = x
4 = x
x = 4
Source: Myschool Past Questions Archive (Record #49352)
Mathematics
WAEC / WASSCE 2018
Permutations, Combinations & Probability
Diagram
Solution
The table shows the distribution of goals scored by 25 teams in a football competition. Calculate the probability that a team selected at randon scored either 4 or 7 goals.
Attached Figure / Diagram
A
\(\frac{9}{25}\)
B
\(\frac{1}{5}\)
C
\(\frac{6}{25}\)
D
\(\frac{2}{5}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Prob. (team scored 4 goals) = Prob. (team scored 7 goals) = \(\frac{3}{25}\)
Hence, probability that a team selected at random scored either 4 or 7 goals;
= \(\frac{6}{25} + \frac{3}{25}\)
= \(\frac{9}{25}\)
Source: Myschool Past Questions Archive (Record #49355)
Mathematics
WAEC / WASSCE 2018
Permutations, Combinations & Probability
Diagram
Solution
The table shows the distribution of goals scored by 25 teams in a football competition. Calculate the probability that a team selected at random scored at most 3 goals.
Attached Figure / Diagram
A
\(\frac{3}{25}\)
B
\(\frac{1}{5}\)
C
\(\frac{6}{25}\)
D
\(\frac{2}{5}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
No. of teams that scored at most 3 goals = 3 + 1 + 6 = 10
Hence, probability that a team selected at random scored at most 3 goals
= \(\frac{10}{25}\) = \(\frac{2}{5}\)
Source: Myschool Past Questions Archive (Record #49357)
Mathematics
WAEC / WASSCE 2018
Mensuration (Areas, Perimeters & Volumes)
Solution
The total surface area of a hemispher is 75\(\pi cm^2\). Find the radius.
A
5.0 cm
B
7.0 cm
C
8.5 cm
D
12.0 cm
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Total surface area of hemisphere is
3\(\pi r^2\) = 75\(\pi cm^2\)
\(r^2\) = \(\frac{75 \pi}{3 \pi}\)
\(r^2\) = 25
r = \(\sqrt{25}\)
r = 5cm
Source: Myschool Past Questions Archive (Record #49360)
Mathematics
WAEC / WASSCE 2018
Algebraic Expressions, Polynomials & Factorisation
Solution
Find the value of x for which \(\frac{x - 5}{x(x - 1)}\) is undefined.
A
0 or 5
B
-5 or 5
C
-11 or 5
D
0 or 1
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
The expression \(\frac{x - 5}{x(x - 1)}\) is undefined when
x(x - 1) = 0
either x = 0 or x - 1 = 0
Hence, x = 0 or x = 1
Source: Myschool Past Questions Archive (Record #49364)
Mathematics
WAEC / WASSCE 2018
Linear, Simultaneous & Quadratic Equations
Solution
Solved the equation \(2x^2 - x - 6\) = 0
A
x = \(\frac{-3}{2}\) or 2
B
x = -2 or \(\frac{3}{2}\)
C
x = -3 or 2
D
x = 3 or -2
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(2x^2 - x - 6\) = 0
\(2x^2 - 4x + 3x - 6\) = 0
2x(x - 2) + 3(x - 2) = 0
(2x + 3) (x - 2) = 0
Either; 2x + 3 = 0 or x - 2 = 0
x = \(\frac{-3}{2}\) or x = 2
Source: Myschool Past Questions Archive (Record #49371)
Mathematics
WAEC / WASSCE 2018
Algebraic Expressions, Polynomials & Factorisation
Solution
Factorise completely the expression
\((x + 2)^2\) - \((2x + 1)^2\)
A
(3x + 2)(1 - x)
B
(3x + 2)(2x + 1)
C
3\((x + 2)^2\)
D
3(x + 1)(1 - x)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\((x + 2)^2\) - \((2x + 1)^2\)
= \((x^2 + 4x + 4) - (4x^2 + 4x + 1)\)
= \(x^2 \) + 4x + 4 - 4 \(x^2 \) - 4x - 1
= -3 \(x^2 \) + 3
= 3 - 3 \(x^2 \)
= 3(1 - \(x^2 \))
= 3(1 + x)(1 - x)
Source: Myschool Past Questions Archive (Record #49387)
Mathematics
WAEC / WASSCE 2018
Indices, Logarithms & Surds
Solution
Find the \(n^{th}\) term of the sequence 2 x 3, 4 x 6, 8 x 9, 16 x 12...
A
2\(^n\) x 3(n + 1)
B
2\(^n\) x 3n
C
2\(^n\) x 3\(^n\)
D
2\(^n\) x 3\(^n - 1\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
2 x 3, 4 x 6, 8 x 9, 16 x 12,...
2\(^1\) x 3 x 1, 2\(^2\) x 3 x 2, 2\(^3\) x 3 x 3, 2\(^4\) x 3 x 4,.... 2\(^n\) x 3n
Source: Myschool Past Questions Archive (Record #49398)
Mathematics
WAEC / WASSCE 2018
Number Bases & Modular Arithmetic
Solution
If 3x\(^o\) 4(mod 5), find the least value of x
A
1
B
2
C
3
D
4
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
3x \(\equiv\) 4(mod 5)
In modulo 5, multiples of 5 that give solution to the given equation are 5, 20, 35, 50,... but 5 will yield the leaast value of x.
Thus; 3x = 4 + 5 = 9
x = \(\frac{9}{3}\)
x = 3
Source: Myschool Past Questions Archive (Record #49402)
Mathematics
WAEC / WASSCE 2018
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
Find the inter-quartile range of 1, 3, 4, 5, 8, 9, 10, 11, 12, 14, 16
A
6
B
7
C
8
D
9
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(Q_1 = \frac{1}{4}\) (N + 1)th
\(\frac{1}{4} \times 12^{th}\) no.
= 3rd no (\(\cong\) 4)
\(Q_3 = \frac{3}{4}\) (N + 1)th
= \(\frac{3}{4}\) x 12th no.
= 9th no. (\(\cong\) 12)
Hence, interquartile range
= \(Q_3 - Q_1\)
= 12 - 4
= 8
Source: Myschool Past Questions Archive (Record #49403)
Mathematics
WAEC / WASSCE 2018
Plane Geometry, Polygons & Circle Theorems
Solution
If x : y = \(\frac{1}{4} : \frac{3}{8}\) and y : z = \(\frac{1}{3} : \frac{4}{9}\), find x : z
A
2:3
B
3:4
C
3:8
D
1:2
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{x}{y}\) = \(\frac{1}{4} \div \frac{3}{8}\) = \(\frac{1}{4} \times \frac{8}{3}\) = \(\frac{2}{3}\)
\(\frac{y}{z}\) = \(\frac{1}{3} \div \frac{4}{9}\) = \(\frac{1}{3} \times \frac{9}{4}\) = \(\frac{3}{4}\)
But,
x = \(\frac{2}{5}T_1\), y = \(\frac{3}{5}T_1\)
y = \(\frac{3}{7}T_2\), z = \(\frac{4}{7}T_2\)
Using y = y
\(\frac{3}{5}T_1\) = x = \(\frac{3}{7}T_2\)
\(\frac{T_1}{T_2}\) = \(\frac{3}{7}\) x \(\frac{5}{3}\) = \(\frac{15}{21}\)
\(T_1 = 15\) and \(T_2 = 21\)
Thus , x = \(\frac{2}{5}\) x 15 = 6
y = \(\frac{3}{5}\) x 15 = 9
y = \(\frac{3}{7}\) x 21 = 9
z = \(\frac{4}{7}\) x 21 = 12
Hence; x : z = 6 : 12
= 1 : 2
Source: Myschool Past Questions Archive (Record #49414)
Mathematics
WAEC / WASSCE 2018
Plane Geometry, Polygons & Circle Theorems
Solution
Expression 0.612 in the form \(\frac{x}{y}\), where x and y are integers and y \(\neq\) 0
A
\(\frac{153}{250}\)
B
\(\frac{68}{111}\)
C
\(\frac{61}{100}\)
D
\(\frac{21}{33}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
0.612 = \(\frac{0.612}{1}\) x \(\frac{1000}{1000}\)
= \(\frac{612}{1000}\)
= \(\frac{153}{250}\)
Source: Myschool Past Questions Archive (Record #49425)
Mathematics
WAEC / WASSCE 2018
Trigonometry, Elevation & Bearings
Solution
The angle of elevation of the top of a tree from a point 27m away and on the same horizontal ground as the foot of the tree is 30\(^o\). Find the height of the tree.
A
27m
B
13.5 \(\sqrt{3m}\)
C
13.5 \(\sqrt{2m}\)
D
9\(\sqrt{3m}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
From the diagram,
tan 30\(^o\) = \(\frac{h}{27}\)
h = 27 tan 30\(^o\)
= 27 x \(\frac{1}{\sqrt{3}}\)
= \(\frac{27}{\sqrt{3}}\) x \(\frac{\sqrt{3}}{\sqrt{3}}\)
= \(\frac{27 \sqrt{3}}{3}\)
= 9\(\sqrt{3m}\)
Source: Myschool Past Questions Archive (Record #49443)
Mathematics
WAEC / WASSCE 2018
Fractions, Decimals, Percentages & Approximations
Diagram
Solution
In the diagram, which of the following ratios is equal to \(\frac{|PN|}{|PQ|}\)?
Attached Figure / Diagram
A
\(\frac{|PN|}{|PR|}\)
B
\(\frac{|PM|}{|PQ|}\)
C
\(\frac{|PM|}{|PR|}\)
D
\(\frac{|PR|}{|PQ|}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{|PN|}{|PQ|}\) = \(\frac{|PM|}{|PR|}\)
Source: Myschool Past Questions Archive (Record #49448)