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Mathematics
WAEC / WASSCE 2002
Variations
Solution
If (x + 3) varies directly as y and x = 3 when y = 12, what is the value of x when y = 8?
A
1
B
\(\frac{1}{2}\)
C
\(-\frac{1}{2}\)
D
-1
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\((x+3) \propto y\\
∴x + 3 = ky\hspace{1mm}when\hspace{1mm}x = 3, y = 12\\
3+3 = 12k\\
∴ k = \frac{1}{2}\\
\Longrightarrow x + 3 = \frac{1}{2}y\) to find x when y = 8
\(x + 3 = \frac{1}{2}\times 8\\
x=4-3\\
x = 1\)
Source: Myschool Past Questions Archive (Record #26535)
Mathematics
WAEC / WASSCE 2002
Trigonometry, Elevation & Bearings
Diagram
From the diagram, find the bearing of Q from P.
Attached Figure / Diagram
A
236o
B
214o
C
146o
D
124o
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 #26536)
Mathematics
WAEC / WASSCE 2002
Sequences & Series (AP & GP)
Solution
Find the nth term of the sequence 4, 10, 16 ,...
A
2(3n- 1)
B
2(2 + 3 n-1)
C
2 n + 2
D
2(3n+2)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(T_{1} = 4; T_2 = 10; T_3 = 16\)
\(T_{2} - T_1 = T_3 - T_1 = 6\)
\(T_n = a + (n - 1) d\)
= \(4 + (n - 1) \times 6\)
= \(4 + 6n - 6\)
= \(6n - 2\)
= 2(3n - 1)
Source: Myschool Past Questions Archive (Record #26537)
Mathematics
WAEC / WASSCE 2002
Plane Geometry, Polygons & Circle Theorems
Solution
If (-3, -4) is a point on the line y = mx + 2 find the value of m.
A
-2
B
\(\frac{7}{4}\)
C
2
D
\(\frac{8}{3}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
If (-3, -4) is a point on the line then
-4 = -3m + 2
-4 - 2 = -3m
-6 = -3m
m = 2
Source: Myschool Past Questions Archive (Record #26538)
Mathematics
WAEC / WASSCE 2002
Linear, Simultaneous & Quadratic Equations
Diagram
Solution
Which of the following is represented by the above sketch?
Attached Figure / Diagram
A
y = x2 + x - 6
B
y = x2 - x - 6
C
y = x2 - x + 6
D
y = x2 + x + 6
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
From the graph, the zeros of the equation exist at x = -2 and x = 3
\(\therefore\) (x + 2) = 0 and (x - 3) = 0
\(\implies (x + 2)(x - 3) = 0\)
\(x^2 - 3x + 2x - 6 = 0\)
\(x^2 - x - 6 = 0\) is the equation represented on the graph.
Source: Myschool Past Questions Archive (Record #26539)
Mathematics
WAEC / WASSCE 2002
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram, SQ is a tangent to the circle at P, XP||YQ, ∠XPY = 56 o and ∠PXY = 80 o.Find angle PQY
Attached Figure / Diagram
A
34o
B
13.36o
C
44o
D
46o
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
< XYQ = 180^\circ - (80^\circ + 56^\circ)
= 44^\circ
< PYQ = 56^\circ (alternate angles, XP||YQ)
< QPY = 90^\circ
< PQY = 180^\circ - (90^\circ + 56^\circ)
= 34^\circ
Source: Myschool Past Questions Archive (Record #26540)
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)