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Mathematics
WAEC / WASSCE 1989
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram above, what is the size of angle ACB?
Attached Figure / Diagram
A
40o
B
50o
C
60o
D
80o
E
100o
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
< ABC = 80^\circ (alternate angles)
< ACB = 180^\circ - (80^\circ + 40^\circ) = 60^\circ
Source: Myschool Past Questions Archive (Record #22404)
Mathematics
WAEC / WASSCE 1989
Inequalities & Linear Programming
Diagram
Solution
With reference to the graph above, which of the following solution sets is represented by \DeltaOPQ?
Attached Figure / Diagram
A
y ≥ x, y ≤ 0, y + x ≥ 7
B
y ≤ x, y ≥ 0, y + x ≤ 7
C
y ≥ x, y ≥ 0, y + x ≤ 7
D
y ≤ x, y ≤ 0, y + x ≤ 7
E
y ≤ x, y ≥ 0, y + x ≥ 7
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
from the graph, the solution sets represented by OPQ is the shaded region where y \le x, y \ge 0, and y + x \le 7
Source: Myschool Past Questions Archive (Record #22405)
Mathematics
WAEC / WASSCE 1989
Mensuration (Areas, Perimeters & Volumes)
Solution
Find the volume of a cone of radius 3.5cm and vertical height 12cm [Take \pi = 22/7]
A
3.4cm3
B
15.5cm3
C
21.0cm3
D
42.0cm3
E
154.0cm3
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
The volume of a cone = \(\frac{1}{3}\) x \(\pi\) x r\(^2\) x h
= \(\frac{1}{3}\) x \(\frac{22}{7}\) x \(\frac{7}{2}\) x \(\frac{7}{2}\) x 12 = 154cm\(^3\)
Source: Myschool Past Questions Archive (Record #22406)
Mathematics
WAEC / WASSCE 1989
Permutations, Combinations & Probability
Diagram
Solution
The table above gives the scores of a group of students in an English Language test
If a student is chosen at random from the group, what is the probability that the scored at least 6 marks?
Attached Figure / Diagram
A
3/20
B
1/5
C
1/4
D
3/10
E
3/4
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Probability = 5/20 = 1/4
Source: Myschool Past Questions Archive (Record #22407)
Mathematics
WAEC / WASSCE 1989
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram above, O is the center of the circle QRT and PT is a tangent to the circle at T. Calculate the angle x
Attached Figure / Diagram
A
55o
B
40o
C
35o
D
25o
E
20o
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
< PTQ =
Source: Myschool Past Questions Archive (Record #22409)
Mathematics
WAEC / WASSCE 1989
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
Which of the following gives the point of intersection of the graph y = x2 and y = x + 6 shown above?
Attached Figure / Diagram
A
(0,6), (3,9)
B
(-3, 0)(2,4)
C
(-2,4)(3,9)
D
(-2,3)(-3,2)
E
(-2,2)(3,6)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
From the graph; when x = -2, y = 4
(-2, 4)
x = 3.0, y = 9; (3,9)
(-2, 4)(3,9)
Source: Myschool Past Questions Archive (Record #22410)
Mathematics
WAEC / WASSCE 1989
Mensuration (Areas, Perimeters & Volumes)
Solution
A sector is cut off from a circle radius 8.2cm to form a cone, if the radius of the resulting cone is 3.5cm, calculate the curved surface area of the cone. [take \pi = 22/7]
A
11.25cm2
B
12.83cm2
C
22.0cm2
D
67.2cm2
E
90.2cm2
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
r = 3.5 cm; l = 8.2 cm.
Curved surface area = \(\pi rl\)
= \(\frac{22}{7} \times \frac{7}{2} \times \frac{41}{5}\)
= 90.2 cm\(^2\)
Source: Myschool Past Questions Archive (Record #22411)
Mathematics
WAEC / WASSCE 1989
Indices, Logarithms & Surds
Solution
If logax = p, express x in terms of a and p
A
x = u + p
B
x = a/p
C
x = p
D
x = ap
E
x = ap
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
\(\log_{a} x = p\)
\(x = a^p\)
Source: Myschool Past Questions Archive (Record #22412)
Mathematics
WAEC / WASSCE 1989
Mensuration (Areas, Perimeters & Volumes)
Solution
Calculate and correct to three significant figures, the length of an arc subtends an angle of 70o at the center of the circle radius 4cm. [Take π = 22/7]
A
2.44cm
B
4.89cm
C
9.78cm
D
25.1cm
E
50.3cm
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Circumference of circle = 2πr = 2 x 3.14 x 4
= 25.1cm 360o = 25.1cm
70o = 25.1/360 x 70 = 4.89
Source: Myschool Past Questions Archive (Record #22413)
Mathematics
WAEC / WASSCE 1989
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram above, O is the center of the circle. If ∠POR = 114o, calculate ∠PQR
Attached Figure / Diagram
A
123o
B
118.5o
C
117o
D
114o
E
54o
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Reflex POR = 2PQR
Reflex PQR = 360o - 114o = 246o
PQR = 246/2 = 123o
Source: Myschool Past Questions Archive (Record #22414)
Mathematics
WAEC / WASSCE 1989
Trigonometry, Elevation & Bearings
Solution
The angle of depression of a point on the ground from the top of a building is 20.3o. If the foot of the building is 40m, calculate the height of the building, correct to one decimal place
A
37.5m
B
28.1m
C
27.8m
D
14.8m
E
13.9m
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Tan 69.7 = 40/h
h = 40/tan 69.7 = 40/2.703 h = 14.79 = 14.8
Source: Myschool Past Questions Archive (Record #22415)
Mathematics
WAEC / WASSCE 1989
Linear, Simultaneous & Quadratic Equations
Solution
Solve for x: (x\(^2\) + 2x + 1) = 25
A
-6, -4
B
6, -4
C
6, 4
D
-6, 4
E
5, 5
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
x\(^2\) + 2x + 1 = 25
x\(^2\) + 6x - 4x -24= 0
x(x + 6) - 4(x + 6) = 0
(x - 4)(x + 6) = 0
x = 4 or -6
Source: Myschool Past Questions Archive (Record #22416)
Mathematics
WAEC / WASSCE 1989
Indices, Logarithms & Surds
Solution
Given that logp = 2 logx + 3logq, which of the following expresses p in terms of x and q?
A
p = 5xq
B
p = 6xq
C
p = x2 + q3
D
p = 2x + 3q
E
p = x2q3
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
log p = 2log x + 3log q
log p = logx 2 + logq 3
logp = log x 2q 3
p = x 2q 3
Source: Myschool Past Questions Archive (Record #22417)
Mathematics
WAEC / WASSCE 1989
Trigonometry, Elevation & Bearings
Solution
sin\theta = \(\frac{1}{2}\) and cos\theta = -\(\frac{\sqrt{3}}{2}\), what is the value of \theta?
A
30 0
B
60 0
C
90 o
D
120 o
E
150 o
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
In the 2nd Quadrant, SINE is the only Positive.
Where \theta is 30 for the first quadrant and
150 in the 2nd quadrant, which makes COSINE negative
Sin \theta = \(\frac{1}{2}\)
\theta = Sin\(^{-1}(\frac{1}{2}\)) = 30º which is positive in the first quadrant
Sin 30 = Sin 150, i.e, (180 - 30), which is also positive in the second quadrant.
BUT Cos \theta = -\(\frac{\sqrt{3}}{2}\)
\theta = Cos\(^{-1}\)(-\(\frac{\sqrt{3}}{2}\)) = 150º which is in the second quadrant but negative
Hence, \theta = 150º
Source: Myschool Past Questions Archive (Record #22418)
Mathematics
WAEC / WASSCE 1989
Sequences & Series (AP & GP)
Solution
What is the probability that 3 customers waiting in a bank will be served in the sequence of their arrival at the bank
A
1/6
B
1/3
C
1/2
D
2/3
E
5/6
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Probability that 3 customers are attended to in the sequence they arrive
= prob of attending to the 1st arrival x prob of attending to the second last x prob of attending to the last
= \(\frac{1}{3} \times \frac{1}{2} \times \frac{1}{1}\)
= \(\frac{1}{6}\)
Source: Myschool Past Questions Archive (Record #22419)