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Mathematics
WAEC / WASSCE 2002
Linear, Simultaneous & Quadratic Equations
Solution
For what values of x is the expression \(\frac{3x-2}{4x^2+9x-9}\) undefined?
A
\(\frac{-3}{4} \hspace{1mm}or \hspace{1mm}3\)
B
\(\frac{-2}{3} \hspace{1mm}or \hspace{1mm}-3\)
C
\(\frac{2}{3} \hspace{1mm}or \hspace{1mm}3\)
D
\(\frac{3}{4} \hspace{1mm}or \hspace{1mm}-3\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
The equation \(\frac{3x - 2}{4x^2 + 9x - 9}\) is undefined when the denominator = 0.
\(4x^2 + 9x - 9 = 0\)
\(4x^2 + 12x - 3x - 9 = 0\)
\(4x(x + 3) - 3(x + 3) = 0\)
\((4x - 3)(x + 3) = 0\)
x = \(\frac{3}{4}\) or x = -3.
Source: Myschool Past Questions Archive (Record #26541)
Mathematics
WAEC / WASSCE 2002
Plane Geometry, Polygons & Circle Theorems
Solution
Simplify \(\frac{1}{1-x} + \frac{2}{1+x}\)
A
\(\frac{x+3}{1-x^2}\)
B
\(\frac{x-3}{1+x^2}\)
C
\(\frac{3-x}{1-x^2}\)
D
\(\frac{3-x}{1+x^2}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{1}{1-x} + \frac{2}{1+x}\\
\frac{1+x+2-2x}{(1-x)(1+x)} = \(\frac{3-x}{1-x^2}\)\)
Source: Myschool Past Questions Archive (Record #26542)
Mathematics
WAEC / WASSCE 2002
Plane Geometry, Polygons & Circle Theorems
Solution
The lengths of the parallel sides of a trapezium are 9 cm and 12 cm. lf the area of the trapezium is 105 cm\(^2\), find the perpendicular distance between the parallel sides.
A
5cm
B
7cm
C
10cm
D
15cm
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{1}{2}(a+b)\times h = 105cm^2\)
\(\frac{1}{2}(9+12)\times h = 105\)
h = \(\frac{105 \times 2}{21} = 10cm\)
Source: Myschool Past Questions Archive (Record #26543)
Mathematics
WAEC / WASSCE 2002
Mensuration (Areas, Perimeters & Volumes)
Solution
The base diameter of a cone is 14cm, and its volume is 462 cm3. Find its height. [Taken \(\pi = \frac{22}{7}\)]
A
3.5cm
B
5cm
C
7cm
D
9cm
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
From \(V = \frac{1}{3}\pi r^2 h. \hspace{1mm} r =\frac{14}{2}\\
462 = \frac{1}{3} \times \frac{22}{7} \times 7^2 \times h \\
h = \frac{3 \times 462}{22 \times 7}\\ h = 9\)
Source: Myschool Past Questions Archive (Record #26544)
Mathematics
WAEC / WASSCE 2002
Permutations, Combinations & Probability
Solution
A number is selected at random from the set Y = {18, 19, 20, . . . 28, 29}. Find the probability that the number is prime.
A
\(\frac{1}{4}\)
B
\(\frac{3}{11}\)
C
\(\frac{1}{2}\)
D
\(\frac{3}{4}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Y = {18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29}
Number of prime numbers = 3
Prob(picking a prime number) = \(\frac{3}{12}\)
= \(\frac{1}{4}\)
Source: Myschool Past Questions Archive (Record #26545)
Mathematics
WAEC / WASSCE 2002
Statistics (Data Representation, Central Tendency & Dispersion)
Diagram
The median of the distribution is
Attached Figure / Diagram
A
25
B
17.5
C
15
D
12.5
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option C.
Source: Myschool Past Questions Archive (Record #26546)
Mathematics
WAEC / WASSCE 2002
Plane Geometry, Polygons & Circle Theorems
Diagram
The range of the distribution is
Attached Figure / Diagram
A
50
B
30
C
25
D
15
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option C.
Source: Myschool Past Questions Archive (Record #26547)
Mathematics
WAEC / WASSCE 2002
Statistics (Data Representation, Central Tendency & Dispersion)
Diagram
The upper quartile of the distribution is
Attached Figure / Diagram
A
30
B
27.5
C
25
D
17.75
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 #26548)
Mathematics
WAEC / WASSCE 2002
Trigonometry, Elevation & Bearings
Diagram
Solution
In the diagram O and O' are the centres of the circles radii 15cm and 8cm respectively. If PQ = 12cm, find |OO'|.
Attached Figure / Diagram
A
8.46cm
B
19.04cm
C
20.81cm
D
26.16cm
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
In \(\Delta\) POQ,
\(12^2 = 15^2 + 15^2 - 2(15)(15) \cos < POQ\)
\(144 = 450 - 450\cos < POQ\)
\(450 \cos < POQ = 450 - 144 = 306\)
\(\cos
Source: Myschool Past Questions Archive (Record #26549)
Mathematics
WAEC / WASSCE 2002
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram O is the centre of the circle. Which of the following is/are not true? I. a = b II. b + c = 180o III. a + b = c
Attached Figure / Diagram
A
I and II only
B
II and III only
C
II only
D
III only
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
i.a and b are 90( angles in same segment are equal)
ii. angle b+c=180 (opposite angles in a cyclic quadrilateral)
iii. a=90 and b=90 .:a+b=180 which is not equal to c
Source: Myschool Past Questions Archive (Record #26550)
Mathematics
WAEC / WASSCE 2002
Indices, Logarithms & Surds
Solution
Simplify \(\frac{2^{\frac{1}{2}}\times 8^{\frac{1}{2}}}{4}\)
A
1
B
2
C
4
D
16
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\frac{2^{\frac{1}{2}}\times 8^{\frac{1}{2}}}{4}\\=\frac{2^{\frac{1}{2}}\times 2^{\frac{3}{2}}}{2^2}\\=2^{\frac{1}{2}}+2^{\frac{3}{2}}-2=2^0 = 1\)
Source: Myschool Past Questions Archive (Record #26551)
Mathematics
WAEC / WASSCE 2002
Plane Geometry, Polygons & Circle Theorems
Diagram
In the diagram, |SR| = |RQ| and ∠PRQ = 58o ∠VQT = 19o, PQT, SQV and PSR are straight lines. Find ∠QPS
Attached Figure / Diagram
A
42o
B
39o
C
38o
D
30o
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option A.
Source: Myschool Past Questions Archive (Record #26552)
Mathematics
WAEC / WASSCE 2002
Trigonometry, Elevation & Bearings
Solution
The angle of depression of a point Q from a vertical tower PR, 30m high, is 40^\circ. If the foot P of the tower is on the same horizontal level as Q, find, correct to 2 decimal places, |PQ|.
A
35.75m
B
25.00m
C
22.98m
D
19.28
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\tan 40^\circ = \frac{30}{|PQ|}\)
\(|PQ| = \frac{30}{\tan 40^\circ} = \frac{30}{0.839}\)
= 35.75m
Source: Myschool Past Questions Archive (Record #26553)
Mathematics
WAEC / WASSCE 2002
Mensuration (Areas, Perimeters & Volumes)
Solution
The volume of a cylinder of radius 14cm is 210cm3. What is the curved surface area of the cylinder?
A
15cm2
B
30cm2
C
616cm2
D
1262cm2
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(V = \pi r^2 h\)
210 = \(\frac{22}{7} \times 14^2 \times\) h
h = \(\frac{210}{22 \times 28}\)
Curved surface area = 2\(\pi\) rh
= 2 \(\times \frac{22}{7} \times 14 \times \frac{210}{22 \times 26} = 30cm^2\)
Source: Myschool Past Questions Archive (Record #26554)
Mathematics
WAEC / WASSCE 2002
Indices, Logarithms & Surds
Solution
Simplify \(3\sqrt{12} + 10\sqrt{3} - \frac{6}{\sqrt{3}}\)
A
\(7\sqrt{3}\)
B
\(10\sqrt{3}\)
C
\(14\sqrt{3}\)
D
\(18\sqrt{3}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(3\sqrt{12} + 10\sqrt{3} - \frac{6}{\sqrt{3}}\)
= \(3(\sqrt{4 \times 3}) + 10\sqrt{3} - (\frac{6}{\sqrt{3}})(\frac{\sqrt{3}}{\sqrt{3}})\)
= \(6\sqrt{3} + 10\sqrt{3} - 2\sqrt{3}\)
= \(14\sqrt{3}\)
Source: Myschool Past Questions Archive (Record #26555)