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Mathematics
WAEC / WASSCE 1993
Number and Numeration
Solution
Factorize 2x\(^2\) - 21x + 45
A
(2x - 9)(x - 5)
B
(2x-15)(x + 3)
C
(2x +15)(x - 3)
D
(2x -15(x - 3)
E
(2x - 9)(x + 5)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
2x\(^2\) - 21x + 45
= 2x\(^2\) - 15x - 6x + 45
= x(2x - 15) - 3(2x - 15)
= (x - 3)(2x - 15)
Source: Myschool Past Questions Archive (Record #23198)
Mathematics
WAEC / WASSCE 1993
Number and Numeration
Solution
Calculate the total surface area of a cone of height 12cm and base radius 5cm. [Take \pi = 22/7]
A
180\(\frac{5}{7}\)cm\(^2\)
B
240\(\frac{2}{7}\)cm\(^2\)
C
235\(\frac{5}{7}\)cm\(^2\)
D
282\(\frac{6}{7}\)cm\(^2\)
E
361\(\frac{3}{7}\)cm\(^2\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\pirl + \pir2 = \pir(l + r)
\(\frac{22}{7}\) x 5(13 + 5)
282\(\frac{6}{7}\)cm\(^2\)
Source: Myschool Past Questions Archive (Record #23201)
Mathematics
WAEC / WASSCE 1993
Number and Numeration
Solution
A cone is 14cm deep and the base radius is 4\(\frac{1}{2}\)cm. Calculate the volume of water that is exactly half the volume of the cone.[Take \pi = \(\frac{22}{7}\)]
A
49.5cm3
B
99cm3
C
148.5cm3
D
297cm3
E
445.5cm3
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Volume of a cone = \(\frac{1}{3} \pi r^2 h\)
r = 4\(\frac{1}{2}\) cm; h = 14 cm
Volume of cone = \(\frac{1}{3} \times \frac{22}{7} \times \frac{9}{2} \times \frac{9}{2} \times 14\)
= 297 cm\(^3\)
When half- filled, the volume of the water = \(\frac{297}{2} = 148.5 cm^3\)
Source: Myschool Past Questions Archive (Record #23202)
Mathematics
WAEC / WASSCE 1993
Number and Numeration
Diagram
Solution
In the diagram above, |PQ| = |QR|, |PS| = |RS|, ∠PSR = 30o and ∠PQR = 80o. Find ∠SPQ.
Attached Figure / Diagram
A
15o
B
25o
C
40o
D
50o
E
55o
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Join PR
QRP = QPR
= 180 - 80 = \(\frac{100}{20}\) = 50º
SRP = SPR
= 180 - 30 = \(\frac{150}{2}\) = 75º
∴ SPQ = SPR - QPR
= 75 - 50 = 25º
Source: Myschool Past Questions Archive (Record #23208)
Mathematics
WAEC / WASSCE 1993
Number and Numeration
Solution
At a point 500m from the base of a water tank the angle of elevation of the top of the tank is 45o. Find the height of the tank,
A
250m
B
353m
C
354m
D
433m
E
500m
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
\(\tan 45 = \frac{x}{500}\)
\(x = 500 \tan 45\)
= \(500 m\)
Source: Myschool Past Questions Archive (Record #23221)
Mathematics
WAEC / WASSCE 1993
Number and Numeration
Diagram
What is A∩B in the diagram above?
Attached Figure / Diagram
A
(2,3)
B
(2,3,4)
C
(1,2,3)
D
(2,3,8)
E
(6,4,7)
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 #23223)
Mathematics
WAEC / WASSCE 1993
Number and Numeration
Diagram
Solution
How many student took the examination
Attached Figure / Diagram
A
18
B
20
C
21
D
23
E
24
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
= 2 + 4 + 3 + 6 + 6 + 2 + 1
= 24 students
Source: Myschool Past Questions Archive (Record #23228)
Mathematics
WAEC / WASSCE 1993
Number and Numeration
Diagram
Solution
How many students scored less than 7 marks?
Attached Figure / Diagram
A
9
B
15
C
18
D
21
E
25
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
= 2 + 4 + 3 + 6
= 15 students scored less than 7 marks.
Source: Myschool Past Questions Archive (Record #23229)
Mathematics
WAEC / WASSCE 1993
Number and Numeration
Solution
What is the probability that an integer selected from the set of integers (20, 21, ...., 30) is a prime number?
A
2/11
B
5/11
C
6/11
D
9/11
E
2/3
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
S = {20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30}
n(S) = 11
P = {23, 29}
n(P) = 2
Prob(P) = \(\frac{2}{11}\)
Source: Myschool Past Questions Archive (Record #23230)
Mathematics
UTME / JAMB 1993
Number and Numeration
Solution
change 7110 to base 8
A
1078
B
1068
C
718
D
178
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\begin{array}{c|c} 8 & 71 \\ 8 & 8 \text{rem} 7\\ 8 & 1 \text{rem} 0\end{array}\)
= 1078
Source: Myschool Past Questions Archive (Record #31127)
Mathematics
UTME / JAMB 1993
Number and Numeration
Solution
Evaluate \(\frac{3524}{0.05}\) correct to 3 significant figures
A
705
B
70,000
C
70, 480
D
70, 500
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{3524}{0.05}\) = 70480
\(\approx\) 70500(3 s.g)
Source: Myschool Past Questions Archive (Record #31128)
Mathematics
UTME / JAMB 1993
Number and Numeration
Solution
If 9\(^{(x - \frac{1}{2})} = 3^{x^2}\) Find the value of x
A
\(\frac{1}{2}\)
B
1
C
2
D
3
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
9(x - \(\frac{1}{2}\)) 3x2 = 3\(^{2(x - \frac{1}{2})}\) = 3\(^x{^2}\)
∴ 2(x - \(\frac{1}{2}\)) = x2
2x - 1 = x\(^2\)
hence x\(^2\) - 2x + 1 = 0
(x - 1)(x - 1) = 0
x = 1
Source: Myschool Past Questions Archive (Record #31130)
Mathematics
UTME / JAMB 1993
Number and Numeration
Solution
Solve for y in the equation 10\(^y\) x 5\(^{(2y - 2)}\) x 4\(^{(y - 1)}\) = 1
A
\(\frac{3}{4}\)
B
\(\frac{5}{4}\)
C
\(\frac{2}{3}\)
D
5
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
10\(^y\) x 5\(^{(2y - 2)}\) x 4\(^{(y - 1)}\) = 1
but 10\(^y\) = (5 x 2)\(^y\) = 5\(^y\) x 2\(^y\)
= (Law of indices)
5\(^y\) x 2\(^y\) x 5\(^{(2y - 2)}\) x 4\(^{(y - 1)}\) = 1
but 4\(^{(y - 1)}\) = 2\(^{2(y - 1)}\)
= 2\(^{2y - 2}\) (Law of indices)
5\(^y\) x 5\(^{(2y -2)}\) x 2\(^{(2y- 2)}\) x 2\(^y\) = 1
5\(^{(3y -2)}\) x 2\(^y\) x 2\(^{(2y -2)}\) = 1
= 5\(^{(3y -2)}\) x 2\(^{(3y -2)}\) = 1
But a\(^o\) = 1
10\(^{(3y -2)}\) = 10\(^o\)
3y - 2 = 0
∴ y = \(\frac{2}{3}\)
Source: Myschool Past Questions Archive (Record #31135)
Mathematics
UTME / JAMB 1993
Number and Numeration
Solution
simplify \(\frac{1}{√3 - 2}\) - \(\frac{1}{√3 + 2}\)
A
3
B
\(\frac{2}{3}\)
C
7
D
-4
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{1}{√3 - 2}\) - \(\frac{1}{√3 + 2}\)
L.C.M = (3- 2) (3 + 2)
∴ \(\frac{1}{\sqrt{3 - 2}}\) - \(\frac{1}{\sqrt{3 - 2}}\) = \(\frac{\sqrt{3 + 2} - \sqrt{3 - 2}}{\sqrt{3 - 2} + \sqrt{3 - 2}}\)
\(\frac{√3 + 2 - √3 + 2}{3 - 2√3 + 2√3 - 4}\) = \(\frac{4}{3 - 2}\)
= \(\frac{4}{-1}\)
= -4
Source: Myschool Past Questions Archive (Record #31138)
Mathematics
UTME / JAMB 1993
Number and Numeration
Solution
If 2log3 y + log3 x2 = 4, then y is
A
4 - log3
B
\(\frac{4}{log_3 x}\)
C
\(\frac{4}{x}\)
D
\(\pm\) \(\frac{9}{x}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
2log3y + log3x2 = 4
log3y2 + log3x2 = 4
∴ log3 (x2y2) = log381(correct all to base 4)
x2y2 = 81
∴ xy = \(\pm\)9
∴ y = \(\pm\)\(\frac{9}{x}\)
Source: Myschool Past Questions Archive (Record #31142)