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 1516–1530 of 4910 verified questions
Sort by:
Mathematics
WAEC / WASSCE 2013
Number and Numeration
Solution
If y varies directly as the square root of (x + 1) and y = 6 when x = 3, find x when y = 9
A
8
B
7
C
6
D
5
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
y \(\alpha\) \sqrt{x + 1}\), y = k\sqrt{x + 1}\)
6 = k\(\sqrt{3 + 1}\)
6 = k\(\sqrt{4}\)
6 = 2k
k = \(\frac{6}{2}\) = 3
y = \(\sqrt{(x + 1)}\)
9 = 3\(\sqrt{(x + 1)}\)(divide both side by 3)
\(\frac{9}{3}\) = \(\frac{3\sqrt{x + 1}}{3}\)
3 = \(\sqrt{x + 1}\)(square both sides)
9 = x + 1
x = 9 - 1
x = 8
Source: Myschool Past Questions Archive (Record #36885)
Mathematics
WAEC / WASSCE 2013
Number and Numeration
Solution
The graph of the relation y = x2 + 2x + k passes through the point (2, 0). Find the values of k
A
zero
B
-2
C
-4
D
-8
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
y = x2 + 2x + k at point(2,0) x = 2, y = 0
0 = (2)2 + 2(20 + k)
0 = 4 + 4 + k
0 = 8 + k
k = -8
Source: Myschool Past Questions Archive (Record #36886)
Mathematics
WAEC / WASSCE 2013
Number and Numeration
What is the locus of the point X which moves relative to two fixed points P and M on a plane such that o
A
thebisector of the straight line joining P and M
B
an arc of a circle with PM as a chord
C
the bisector of angle PXM
D
a circle centre X and radius PM
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option B.
Source: Myschool Past Questions Archive (Record #36887)
Mathematics
WAEC / WASSCE 2013
Number and Numeration
Solution
Express \(\frac{2}{x + 3} - \frac{1}{x - 2}\) as a simple fraction
A
\(\frac{x - 7}{x^2 + x - 6}\)
B
\(\frac{x - 1}{x^2 + x - 6}\)
C
\(\frac{x - 2}{x^2 + x - 6}\)
D
\(\frac{x - 27}{x^2 + x - 6}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\frac{2}{x + 3} - \frac{1}{x - 2}\) = \(\frac{2(x - 2) - (x - 3)}{(x + 3) (x - 2)}\)
= \(\frac{2x - 4 - x - 3}{x^2 - 2x + 3x - 6}\)
= \(\frac{x -7}{x^2 + x - 6}\)
= \(\frac{x - 7}{x^2 + x - 6}\)
Source: Myschool Past Questions Archive (Record #36896)
Mathematics
WAEC / WASSCE 2013
Geometry and Trigonometry
Solution
An interior angle of a regular polygon is 5 times each exterior angle. How many sides has the polygon?
A
15
B
12
C
9
D
6
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Let the interior angle = xo
interior angle = 5xo (sum of int. angle ann exterior)
(angles = angle or straight line)
6x = 180
x = \(\frac{180}{6}\)
x = 30o
no. of sides = \(\frac{\text{sum of exterior angles}}{\text{exterior angle}}\)
= \(\frac{360}{30}\) = 12
Source: Myschool Past Questions Archive (Record #36898)
Mathematics
WAEC / WASSCE 2013
Number and Numeration
Solution
Given that P = x2 + 4x - 2, Q = 2x - 1 and Q - p = 2, find x
A
-2
B
-1
C
1
D
2
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
P = x2 + 4x - 2, Q = 2x - 1
Q - p = 2, (2x - 1) - (x2 + 4x - 2) = 2
2x - 1 - x2 - 4x + 2 = 2
-2x - x2 + 1
-x2 - 2x - 1 = 0
x2 + 2x + 1 = 0
x2 + x + x + 1 = 0
x(x + 1) + 1(x + 1) = 0
(x + 1)(x + 1) = 0
x + 1 = 0 or x + 1 = 0
x = -1 or x = -1
x = -1
Source: Myschool Past Questions Archive (Record #36900)
Mathematics
WAEC / WASSCE 2013
Number and Numeration
Solution
A pyramid has a rectangular base with dimensions 12m by 8m. If its height is 14m, calculate the volume
A
322m3
B
448m3
C
632m2
D
840m2
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Volume of pyramid = \(\frac{1}{3}\) x base area x height
= \(\frac{1}{3} \times 124 \times 8 \times 14\)
= 4 x 8 x 14 = 448m\(^3\)
Source: Myschool Past Questions Archive (Record #36903)
Mathematics
WAEC / WASSCE 2013
Number and Numeration
Solution
The slant height of a cone is 5cm and the radius of its base is 3cm. Find, correct to the nearest whole number, the volume of the cone. ( Take \(\pi = \frac{22}{7}\))
A
48cm3
B
47cm3
C
38cm3
D
12cm3
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Volume of a cone = \(\frac{1}{3} \pi r^2h\)
h2 = 52 = 32
= 25 - 9 = 16
h = \(\sqrt{16}\)
h = 4cm
v = \(\frac{1}{3} \times \frac{22}{7} \times 3^2 \times 4\)
\(\frac{1}{3} \times \frac{22}{7} \times 9 \times 4\)
= \(\frac{22 \times 3 \times 4}{7}\)
= 37.7cm3
= 38cm3
Source: Myschool Past Questions Archive (Record #36904)
Mathematics
WAEC / WASSCE 2013
Geometry and Trigonometry
Solution
The distance between two towns is 50km. It is represented on a map by 5cm. Find the scale used
A
1: 1,000,000
B
1: 500,000
C
1: 100,000
D
1: 10,000
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
1km = 100,000cm
on the map 1 cm represent every 10 km which is equal to (10 x 100,000cm)
= 1,000,000cm
the scale is 1:1,000,000
Source: Myschool Past Questions Archive (Record #36905)
Mathematics
WAEC / WASSCE 2013
Number and Numeration
Solution
Given that (x + 2)(x2 - 3x + 2) + 2(x + 2)(x - 1) = (x + 2) M, find M
A
(x + 2)2
B
x(x + 2)
C
xv + 2
D
x2 - x
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
(x + 2)(x\(^2\) - 3x + 2) + 2(x + 2)(x - 1) = (x + 2)m
(x + 2)[(x\(^2\) - 3x + 2) + 2(x - 1)] = (x + 2)M
divide both side by (x + 2)
(x\(^2\) - 3x + 2) + 2(x - 1) = M
x\(^2\) - 3x + 2 + 2x - 2 = M
x\(^2\) - 3x + 2 + 2x - 2 = M
x\(^2\) - 3x + 2x = M
x\(^2\) - x = M
M = x\(^2\) - x
Source: Myschool Past Questions Archive (Record #36907)
Mathematics
WAEC / WASSCE 2013
Number and Numeration
Solution
An open cone with base radius 28cm and perpendicular height 96cm was stretched to form sector of a circle. calculate the arc of the sector (Take \(\pi = \frac{22}{7}\))
A
8800cm2
B
8448cm2
C
4400cm2
D
4224cm2
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
L2 = 962 + 282
= 9216 + 784
= 10000
L = \(\sqrt{10000}\)
= 100cm
curved surface area = \(\pi r l\)
= \(\frac{22}{7} \times 28 \times 100\)
= 8800cm2
area of cone = area of sector
area of sector = 8800cm2
Source: Myschool Past Questions Archive (Record #36908)
Mathematics
WAEC / WASSCE 2013
Geometry and Trigonometry
Diagram
Solution
In the diagram, PRST is a square. If |PQ| = 24cm. |QR| = 10cm and < PQR = 90o, find the perimeter of the polygon PQRST.
Attached Figure / Diagram
A
112cm
B
98cm
C
86cm
D
84cm
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
< PQR is a right-angled triangle
PR\(^2\) = 24\(^2\) + 10\(^2\) = 676
PR = \(\sqrt{676}\) = 26cm
PQRTS is a square and PR = 26cm. meaning the remaining sides of the square are 26cm each
Therefore, the perimeter of PQRST = 26 + 26 + 26 + 24 + 10 = 112cm
Source: Myschool Past Questions Archive (Record #36917)
Mathematics
WAEC / WASSCE 2013
Number and Numeration
Diagram
Solution
in the diagram, the height of a flagpole |TF| and the length of its shadow |FL| re in the ratio 6:8. Using k as a constant of proportionality, find the shortest distance between T and L
Attached Figure / Diagram
A
7K units
B
10K units
C
12K units
D
14k units
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
by Pythagoras x2 = 62 + 82
36 + 64 = 100
x = \(\sqrt{100}\)
x = 10
Source: Myschool Past Questions Archive (Record #36918)
Mathematics
WAEC / WASSCE 2013
Number and Numeration
Diagram
In the diagrams, |XZ| = |MN|, |ZY| = |MO| and |XY| = |NO|. Which of the following statements is true?
Attached Figure / Diagram
A
\(\bigtriangleup\) ZYX = \(\bigtriangleup\) OMN
B
\(\bigtriangleup\) YZX = \(\bigtriangleup\) NOM
C
\(\bigtriangleup\) ZXY= \(\bigtriangleup\) MON
D
\(\bigtriangleup\) XYZ= \(\bigtriangleup\) NOM
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 #36919)
Mathematics
WAEC / WASSCE 2013
Geometry and Trigonometry
Diagram
Solution
In the diagram, PQRS is a rhombus and < PSQ = 35º. Calculate the size of < PRQ
Attached Figure / Diagram
A
65o
B
55o
C
45o
D
35o
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
From the figure above, < PRQ = 55º
Source: Myschool Past Questions Archive (Record #36920)