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Mathematics
WAEC / WASSCE 1991
Number and Numeration
Solution
Mrs. Kofi sold an article for C7.50 instead of C12.75. Calculate her percentage of error, correct to one decimal place.
A
41.2%
B
18.3%
C
5.3%
D
1.7%
E
1.4%
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Error =12.75 - 7.50 = 5.25
Error % = \(\frac{5.25}{12.75}\) x 100% = 41.2%
Source: Myschool Past Questions Archive (Record #22880)
Mathematics
WAEC / WASSCE 1991
Number and Numeration
Diagram
Solution
Find the coordinates of point B
Attached Figure / Diagram
A
(0,11/2)
B
(O,2)
C
(2,0)
D
(11/2, 2)
E
(11/2, 0)
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
B occurs at the point y = 0.
When y = 0, we have
4x + 3(0) = 6
4x = 6
x = 1\(\frac{1}{2}\)
B = \((1\frac{1}{2}, 0)\)
Source: Myschool Past Questions Archive (Record #22915)
Mathematics
WAEC / WASSCE 1991
Number and Numeration
Solution
The common ratio of a G.P. is 2. If the 5th term is
greater than the 1st term by 45, find the 5th term,
A
3
B
6
C
45
D
48
E
90
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
a = 1st term ; ar\(^4\) = 5th term
∴ ar\(^4\) = a(2)\(^4\) = 16a; 16a = 45 + a, a = 3;
3(2)\(^4\) = 48
Source: Myschool Past Questions Archive (Record #22917)
Mathematics
WAEC / WASSCE 1991
Number and Numeration
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
Number and Numeration
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
Number and Numeration
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
Number and Numeration
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
Number and Numeration
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
Number and Numeration
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
Number and Numeration
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
Number and Numeration
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
Number and Numeration
Diagram
In the diagram above , |AD| = 10cm, |DC| = 8cm and |CF| = 15cm. Which of the following is correct?
Attached Figure / Diagram
A
Area BCF = Area DCF
B
Area ADE = Area ADF
C
Area ADE = Area DCFE
D
Area CBF = Area DABC
E
Area DABO = Area CFEO
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option E.
Source: Myschool Past Questions Archive (Record #23119)
Mathematics
UTME / JAMB 1991
Number and Numeration
Solution
Simplify 3\(\frac{1}{3}\) - 1\(\frac{1}{4}\) x \(\frac{2}{3}\) + 1\(\frac{2}{5}\)
A
2
B
3
C
4
D
5
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
3 - \(\frac{1}{3}\) - (\(\frac{5}{4}\) x \(\frac{2}{3}\)) + 1\(\frac{2}{5}\)
= \(\frac{10}{3}\) - \(\frac{5}{6}\) + \(\frac{7}{5}\)
= \(\frac{100 - 25 + 42}{30}\)
= \(\frac{117}{30}\)
= 3.9
\(\approx\) 4
Source: Myschool Past Questions Archive (Record #31367)
Mathematics
UTME / JAMB 1991
Number and Numeration
Solution
If 2257 is the result of subtracting 4577 from 7056 in base n, find n
A
8
B
9
C
10
D
11
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\begin{array}{c|c} 7056 \\ \text{- 4577} \\\hline 2257 \end{array}\)
By trial and error method
Let the base to 8
i.e. Let n = 8 and it is easily verified that the subtraction holds.
The subtraction does not hold when other values of n are tried
n = 8
Source: Myschool Past Questions Archive (Record #31370)
Mathematics
UTME / JAMB 1991
Number and Numeration
Solution
Find correct to 3 decimal places (\(\frac{1}{0.05} \div\frac{1}{5.005}\)) - (0.05 x 2.05)
A
99.998
B
98.999
C
89.899
D
9.998
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
(\(\frac{1}{0.05} \div \frac{1}{5.005}\)) - (0.05 x 2.05)
(\(\frac{1}{0.05}\) x 5.005) - (0.05 x 2.05)
\(\frac{5.005}{0.05}\) - 0.1025
100.1 - 0.1025
= 99.9975
99.998 to 3 decimal place.
Source: Myschool Past Questions Archive (Record #31371)