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Mathematics
WAEC / WASSCE 2018
Sets, Logic & Venn Diagrams
Solution
If P and Q are two statements, under what condition would p|q be false?
A
If p is true and q is true
B
If p is true and q is false
C
If p is false and q is false
D
If p is false and q is true
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
From the truth table above, p \(\to\) q would be false if p is true and q is false
Source: Myschool Past Questions Archive (Record #49455)
Mathematics
WAEC / WASSCE 2018
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
Find the median of 2, 1, 0, 3, 1, 1, 4, 0, 1 and 2
A
0.0
B
0.5
C
1.0
D
1.5
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
First arrange the numbers in ascending order of magnitude; 0, 0, 1, 1, 1, 1, 2, 2, 3, 4
Counting from the right, the fifth number is 1
Counting from the left, the fifth number is 1
Hence, median = \(frac{1 + 1}{2}\)
= \(\frac{2}{2}\)
= 1
Source: Myschool Past Questions Archive (Record #49459)
Mathematics
WAEC / WASSCE 2018
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
Find the mean deviation of 20, 30, 25, 40, 35, 50, 45, 40, 20 and 45
A
8
B
9
C
10
D
12
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Mean = \(\frac{\sum f x}{\sum f}\)
= \(\frac{350}{10}\)
= 35
= \(\frac{\sum f |d|}{\sum f}\)
= \(\frac{90}{10}\)
= 9
Source: Myschool Past Questions Archive (Record #49462)
Mathematics
WAEC / WASSCE 2018
Linear, Simultaneous & Quadratic Equations
Diagram
Solution
Find the value of t in the diagram
Attached Figure / Diagram
A
63\(^o\)
B
117\(^o\)
C
126\(^o\)
D
234\(^o\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
In the diagram,
\(\alpha\) = 180\(^o\) - 177\(^o\) (angles on a straight line)
\(\alpha\) = 63\(^o\)
t = 2 x 63\(^o\) (angle at centre = 2 x angle at circum)
= 126\(^o\)
Source: Myschool Past Questions Archive (Record #49478)
Mathematics
WAEC / WASSCE 2018
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram, PR is a tangent to the circle at Q, QT//RS, < SQR = 35º and < RSQ = 50º. Find the value of
Attached Figure / Diagram
A
40\(^o\)
B
65\(^o\)
C
85\(^o\)
D
95\(^o\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
In the diagram,
a = 50\(^o\) (alternate angles)
b\(_1\) + a + 35\(^o\) = 180\(^o\) (sum of angles on a straight line)
i.e; b\(_1\) + 50\(^o\) + 35\(^o\)
= 180º
b\(_1\) + 180\(^o\) - 85\(^o\) = 90\(^o\)
But b\(_2\) = \(b_1\) = 95\(^o\) (angles in alternate segment)
Source: Myschool Past Questions Archive (Record #49487)
Mathematics
WAEC / WASSCE 2018
Plane Geometry, Polygons & Circle Theorems
Diagram
In the diagram, WXYZ is a rectangle with dimension 8cm by 6cm. P, Q, R and S are the midpoints of the sides of the rectangle as shown. Using this information, what type of quadrilateral is the shaded region?
Attached Figure / Diagram
A
Trapezium
B
Prism
C
Rectangle
D
Rhombus
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 #49491)
Mathematics
WAEC / WASSCE 2018
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram, WXYZ is a rectangle with diamension 8cm by 6cm. P, Q, R and S are the midpoints of the rectangle as shown. Using this information calculate the area of the part of the rectangle that is not shaded
Attached Figure / Diagram
A
25cm\(^2\)
B
24cm\(^2\)
C
16cm\(^2\)
D
12cm\(^2\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Area of shaded part = 2 x area of \(\bigtriangleup\)SPQ
= 2 x \(\frac{1}{2}\) 8 x 3 =24cm
Hence, area of the unshaded part of the rectangle = area of rectangle - area of shaded part
= 8 x 6 - 24
= 48 - 24
= 24 cm\(^2\)
Source: Myschool Past Questions Archive (Record #49520)
Mathematics
WAEC / WASSCE 2018
Inequalities & Linear Programming
Diagram
Solution
The solution of x + 2 \(\geq\) 2x + 1 is illustrated
Attached Figure / Diagram
A
i
B
ii
C
iii
D
iv
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
x + 2 \(\geq\) 2x + 1
x - 2x \(\geq\) 1 - 2
-x \(\geq\) -1
\(\frac{-x}{-1}\) \(\geq\) \(\frac{-1}{-1}\)
x \(\leq\) 1
Source: Myschool Past Questions Archive (Record #49535)
Mathematics
WAEC / WASSCE 2018
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
The diagram shows a trapezium inscribed in a semi-circle. If O is the mid-point of WZ and |WX| = |XY| = |YZ|, calculate the value of m
Attached Figure / Diagram
A
90\(^o\)
B
60\(^o\)
C
45\(^o\)
D
30\(^o\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
In the diagram, < WOZ = 180\(^o\) (angle on a straight line)
< WOX = < XOY = < YOZ
(|WX| = |XY| = |YZ|)
\(\frac{180^o}{3}\) = 60\(^o\)
= 60\(^o\)
M + m =2m (base angles of isosceles \(\bigtriangleup\), |OY| and |OZ| are radii)
< YOZ + 2m (base angles of a \(\bigtriangleup\))
60\(^o\) + 2m = 180\(^o\) (sum of a \(\bigtriangleup\))
60\(^o\) + 2m = 180\(^o\)
2m = 180\(^o\) - 60\(^o\)
2m = 120\(^o\)
m = \(\frac{120^o}{2}\)
= 60\(^o\)
Source: Myschool Past Questions Archive (Record #49549)
Mathematics
WAEC / WASSCE 2018
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram, PQ//RS. Find x in terms of y and z
Attached Figure / Diagram
A
x = 240\(^o\) - y - z
B
x = 180\(^o\) - y - z
C
x = 360\(^o\) + y -z
D
x = 360\(^o\) - y - z
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
In the diagram,
a = z (alternate angles)
b = 180\(^o\) - a (angles on a straight line)
b = 180\(^o\) - z
c = 180\(^o\) - x (angles on a straight line)
y = b + c (sum of oposite interior angles)
y = 180\(^o\) - z + 180\(^o\) - x
y = 360\(^o\) - z - x
x = 360\(^o\) - y - z
Source: Myschool Past Questions Archive (Record #49564)
Mathematics
WAEC / WASSCE 2018
Fractions, Decimals, Percentages & Approximations
Diagram
Solution
In the diagram, PQ is a straight line, (m + n) = 110\(^o\) and (n + r) = 130\(^o\) and (m + r) = 120\(^o\). Find the ratio of m : n : r
Attached Figure / Diagram
A
2 : 3 : 4
B
3 : 4 : 5
C
4 : 5 : 6
D
5 : 6 : 7
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
m + n = 110\(^o\), (n + r) = 130\(^o\)
(m + n) = 120\(^o\)
then, r = 130\(^o\) - n
and;
m + (130^o - n) = 120\(^o\)
m - n = -10\(^o\)
2m + (n + r) = 110 + 120 = 230
2m + 130 = 230
2m = 230 - 130
m = \(\frac{100}{2}\) = 50\(^o\)
n = 110\(^o\) - 50\(^o\)
= 60\(^o\)
r = 130\(^o\) - 60\(^o\) = 70\(^o\)
Hence, the ratio m : n : r
= 50 : 60 : 70
= 5 : 6 : 7
Source: Myschool Past Questions Archive (Record #49580)
Mathematics
WAEC / WASSCE 2018
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
Donations during the launching of a church project were sent in sealed envolopes. The table shows the distribution of the amount of money in the envelope. How much was the donation?
Attached Figure / Diagram
A
N26,792.00
B
N26,972.00
C
N62.792.00
D
N62,972.00
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Total donation = 4 x 500 + 7 x 2000 + 20 x 1000 + 9 x 700 + 4 x 500 + 5 x 100 + 3 x 50 + 1 x 2 + 2 x 10
= 20000 + 14000 + 20000 + 6300 + 2000 + 500 + 150 + 2 + 20
= N62,972
Source: Myschool Past Questions Archive (Record #49584)
Mathematics
WAEC / WASSCE 2018
Mensuration (Areas, Perimeters & Volumes)
Solution
A piece of thread of length 21.4cm is used to form a sector of a circle of radius 4.2cm on a piece of cloth. Calculate, correct to the nearest degree, the angle of the sector. [Take \(\pi = \frac{22}{7}\)]
A
170\(^o\)
B
177\(^o\)
C
182\(^o\)
D
192\(^o\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Length of arc, L = 21.4 - 2 x 4.2cm
= 21.4 - 8.4
= 13cm
But L = \(\frac{\theta}{360^o}\) x 2\(\pi r\)
i.e 13 = \(\frac{\theta}{360^o}\) x 2 x \(\frac{22}{7}\) x 4.2
= 13 x 360\(^o\) x 7
= \(\theta\) x 2 x 22 x 4.2
\(\theta\) = \(\frac{13 \times 360^o \times 7}{44 \times 4.2}\)
= \(\approx\) 177.27\(^o\)
\(\approx\) 177\(^o\) (to the nearest degree)
Source: Myschool Past Questions Archive (Record #49598)
Mathematics
WAEC / WASSCE 2018
Indices, Logarithms & Surds
Solution
If tan x = \(\frac{4}{3}\), 0\(^o\) < x < 90\(^o\), find the value of sin x - cos x
A
\(\frac{1}{10}\)
B
\(\frac{1}{5}\)
C
\(\frac{5}{12}\)
D
1\(\frac{2}{5}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
From the diagram,
h\(^2\) = 4\(^2\) + 3\(^2\) (pythagoras')
h\(^2\) = 16 + 9 = 25
h = \(\sqrt{25}\) = 5
Hence, sin x - cos x
= \(\frac{4}{5} - \frac{3}{5}\)
= \(\frac{1}{5}\)
Source: Myschool Past Questions Archive (Record #49606)
Mathematics
WAEC / WASSCE 2018
Trigonometry, Elevation & Bearings
Solution
Given that Y is 20cm on a bearing of 300\(^o\) from x, how far south of y is x?
A
10cm
B
15cm
C
25cm
D
30cm
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
In \(\bigtriangleup\)YSC, sin 30\(^o\) = \(\frac{YS}{20}\)
|YS| = 20 sin 30\(^o\)
= 20 x 0.5
10m
Source: Myschool Past Questions Archive (Record #49615)