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Mathematics
WAEC / WASSCE 1991
Statistics (Data Representation, Central Tendency & Dispersion)
Diagram
Solution
Find the mean of the distribution
Attached Figure / Diagram
A
3.5
B
4.0
C
4.4
D
5.0
E
5
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\bar{x}\) = \(\frac{2 + 14 + 15 + 16 + 45 + 42 + 42}{40}\) = \(\frac{176}{40}\) = 4.4
Source: Myschool Past Questions Archive (Record #22931)
Mathematics
WAEC / WASSCE 1991
Statistics (Data Representation, Central Tendency & Dispersion)
Diagram
Find the mode of the distribution
Attached Figure / Diagram
A
40
B
9
C
7
D
5
E
2
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 #22932)
Mathematics
WAEC / WASSCE 1991
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
No. of chairs
1
2
3
4
5
6
7
Frequency
2
7
5
4
9
7
6
Find the median of the distribution
A
9
B
6.5
C
5
D
4.5
E
4
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Median = 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5,| 5, 5, |5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7,
Median = \(\frac{5 + 5}{2}\) = 5
Source: Myschool Past Questions Archive (Record #22933)
Mathematics
WAEC / WASSCE 1991
Permutations, Combinations & Probability
Solution
If two events are mutually exclusive, their intersection is empty. This means that there are no outcomes that are common to both events. In probability terms, if X and Y are mutually exclusive events, then:
Pr(X ∩ Y) = 0
A
0
B
2/15
C
11/15
D
4/15
E
1
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Since X and Y are mutually exclusive, Pr(X ∩ Y) = 0
Source: Myschool Past Questions Archive (Record #22934)
Mathematics
WAEC / WASSCE 1991
Sets, Logic & Venn Diagrams
Solution
If events X and Y are mutually exclusive, P(X) = 1/3 and P(Y) = 2/5, P(X∪Y) is
A
o
B
2/15
C
4/14
D
11/15
E
1
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
P(X \(\cup\) Y) = \(\frac{1}{3} + \frac{2}{5}\)
= \(\frac{11}{15}\)
Source: Myschool Past Questions Archive (Record #22935)
Mathematics
WAEC / WASSCE 1991
Permutations, Combinations & Probability
Solution
A box contains 2 white and 3 blue identical marbles. If two marbles are picked at random, one after the other without replacement, what is the probability of picking two marbles of different colors?
A
2/3
B
3/5
C
2/5
D
7/20
E
3/10
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Total number of marbles = 5; 1st pick = 2/5 2nd pick = 3/4; 3rd pick = 3/5; 4th pick = 2/4
∴ Probability of picking two marbles of different colors = (2/5 x 3/4) + (3/5 + 2/4) = 12/20 = 3/5
Source: Myschool Past Questions Archive (Record #22936)
Mathematics
WAEC / WASSCE 1991
Permutations, Combinations & Probability
Solution
Mrs. Jones is expecting a baby. The probability that it will be a boy is 1/2 and probability that the baby will have blue eyes is 1/4. What is the probability that she will have a blue-eyed boy?
A
1/8
B
1/4
C
3/8
D
1/2
E
3/4
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
(1/2)(1/4) = 1/8
Source: Myschool Past Questions Archive (Record #23107)
Mathematics
WAEC / WASSCE 1991
Plane Geometry, Polygons & Circle Theorems
Which of the following about a rhombus may not be true?
A
The diagonals are equal
B
The diagonals bisect the angles through which they pass
C
the diagonals bisect each other
D
The adjacent sides are equal
E
Opposite angles are equal
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 #23108)
Mathematics
WAEC / WASSCE 1991
Plane Geometry, Polygons & Circle Theorems
Solution
The angles of a pentagon are x^\circ, 2x^\circ, (x + 60)^\circ, (x + 10)^\circ, (x -10)^\circ. Find the value of x.
A
40
B
60
C
75
D
80
E
90
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Sum of ∠s in a pentagon = (n - 2)180 = 540^\circ
x^\circ + 2x^\circ + x^\circ + 60^\circ + x^\circ + 10^\circ + x^\circ - 10^\circ = 540^\circ
6x^\circ + 60^\circ = 540^\circ; x = 80^\circ
Source: Myschool Past Questions Archive (Record #23109)
Mathematics
WAEC / WASSCE 1991
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram above, ∠PTQ = ∠URP = 25^\circ and XPU = 4URP. Calculate ∠USQ.
Attached Figure / Diagram
A
100o
B
120o
C
125o
D
130o
E
150o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Since < URP = 25^\circ, then < XPU = 4 x 25^\circ = 100^\circ
\(\therefore\) < TPQ = 180^\circ - 100^\circ = 80^\circ
\(\therefore\) < PQT = 180^\circ - (80^\circ + 25^\circ) = 75^\circ
< SQR = 75^\circ - 25^\circ = 50^\circ (exterior angle = 2 opp interior angles)
\(\therefore\) < USQ = 180^\circ - 50^\circ = 130^\circ
Source: Myschool Past Questions Archive (Record #23110)
Mathematics
WAEC / WASSCE 1991
Plane Geometry, Polygons & Circle Theorems
Solution
In a given regular polygon, the ratio of the exterior angle to the interior angles is 1:3. How many side has the polygon?
A
40
B
5
C
6
D
8
E
12
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Let x be the exterior angle; interior = 3x; but x + 3x = 180o
4x = 180o; x = 45
= \(\frac{360}{45}\) = 8
Source: Myschool Past Questions Archive (Record #23112)
Mathematics
WAEC / WASSCE 1991
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram above, O is the center of the circle, |SQ| = |QR| and ∠PQR = 68^\circ. Calculate ∠PRS
Attached Figure / Diagram
A
34o
B
45o
C
56o
D
62o
E
68o
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
From the figure, < PQR = 68^\circ
\(\therefore\) < QRS = < QSR = \(\frac{180 - 68}{2}\) (base angles of an isos. triangle)
= 56^\circ
\(\therefore\) < PRS = 90^\circ - 56^\circ = 34^\circ (angles in a semi-circle)
Source: Myschool Past Questions Archive (Record #23113)
Mathematics
WAEC / WASSCE 1991
Trigonometry, Elevation & Bearings
Solution
Find the area of an equivalent triangle of side 16cm
A
64√3cm2
B
72√3cm2
C
96cm2
D
128√3cm2
E
128cm2
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Area = 1/2 x 16 x 16sin60o = 64√3cm2
Source: Myschool Past Questions Archive (Record #23115)
Mathematics
WAEC / WASSCE 1991
Fractions, Decimals, Percentages & Approximations
Diagram
Solution
In the diagram above, PQ and XY are two concentric arc; center O, the ratio of the length of the two arc is 1:3, find the ratio of the areas of the two sectors OPQ and OXY
Attached Figure / Diagram
A
1:3
B
1:6
C
1:9
D
2:3
E
4:9
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Let the radius of the arc PQ = r and the radius of the arc XY = R.
Length of arc PQ = \(\frac{\theta}{360} \times 2\pi r = 1\)
Length of arc XY = \(\frac{\theta}{360} \times 2\pi R = 3\)
Ratio of the arc = \(\frac{r}{R} = \frac{360 \times 2\pi \theta}{2\pi \theta \times 360 \times 3}\)
= \(\frac{1}{3}\)
Ratio of their area = \((\frac{1}{3})^2 = \frac{1}{9}\)
= 1 : 9
Source: Myschool Past Questions Archive (Record #23116)
Mathematics
WAEC / WASSCE 1991
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram above , |AD| = 10cm, |DC| = 8cm and |CF| = 15cmIf the area of triangle DCF = 24cm2, find the area of the quadrilateral ABCD.
Attached Figure / Diagram
A
24cm2
B
48cm2
C
80cm2
D
96cm2
E
120cm2
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Area of \(\Delta\)DCF = 24cm2
Area of Quad= 2 x 24 = 48cm2
Source: Myschool Past Questions Archive (Record #23117)