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Mathematics
WAEC / WASSCE 1991
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram above, ATR is a tangent at the point T to the circle center O, if ∠TOB = 145^\circ, find ∠TAO
Attached Figure / Diagram
A
20o
B
35o
C
45o
D
55o
E
65o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
From the figure, < ATO = 90^\circ
< AOT = 180^\circ - 145^\circ = 35^\circ
\(\therefore\) < TAO = 180^\circ - (90^\circ + 35^\circ)
= 55^\circ (sum of angle in a triangle)
Source: Myschool Past Questions Archive (Record #22925)
Mathematics
WAEC / WASSCE 1991
Sets, Logic & Venn Diagrams
Solution
P={2, 1,3, 9, 1/2}; Q = {1,21/2,3, 7} and R = {5, 4, 21/2}. Find P∪Q∪R
A
(21/2)
B
(1, 9)
C
(1, 2, 3, 4, 5, 6, 7)
D
(5, 4, 21/2)
E
(1/2, 1, 2, 21/2, 3, 4, 5, 7, 9)
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
P = {2,1,3,9,1/2}; Q = {1,21/2,3,7}
R = {5,4,212}
P∪Q∪R = {1/2,1,2,21/2,3,4,5,7,9}
= {1/2,1,2,21/2,3,4,5,7,9}
Source: Myschool Past Questions Archive (Record #22926)
Mathematics
WAEC / WASSCE 1991
Sets, Logic & Venn Diagrams
P = {2, 1,3, 9, 1/2}; Q = {1,21/2,3, 7} and R = {5, 4, 21/2}. Find P∩Q∩R
A
(21/2)
B
∅
C
(1, 3, 7)
D
(4)
E
(5,7,9)
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 #22927)
Mathematics
WAEC / WASSCE 1991
Sets, Logic & Venn Diagrams
Solution
In a class of 80 students, every student had to study Economics or Geography or both Economics and Geography. lf 65 students studied Economics and 50 studied Geography, how many studied both subjects?
A
15
B
30
C
35
D
45
E
50
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Applying the formula
80 = 65 - x + x + 50 - x
x = 35
Source: Myschool Past Questions Archive (Record #22928)
Mathematics
WAEC / WASSCE 1991
Statistics (Data Representation, Central Tendency & Dispersion)
Which of the following is not a measure of dispersion?
A
Mode
B
Mean deviation
C
Range
D
interquartile range
E
Standard deviation
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 #22929)
Mathematics
WAEC / WASSCE 1991
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
The mean of 30 observations recorded in an experiment is 5. lf the observed largest value of 34 is deleted, find the mean of the remaining observations
A
5
B
4
C
3.9
D
3.4
E
3.0
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
x = 5, \(\frac{\sum {fx}}{\sum {f}}\) =
5= \(\frac{\sum {fx}}{30}\)
\(\sum {fx}\) = 5 x 30 = 150; 150 - 34 = 116
\(\sum {f}\) = 29
\(\sum {fx}\) = 116
= \(\frac{116}{29}\) = 4
Source: Myschool Past Questions Archive (Record #22930)
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)