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Mathematics
WAEC / WASSCE 1992
Permutations, Combinations & Probability
Solution
Three balls are drawn one after the other with replacement, from a bag containing 5 red, 9white and 4 blue identical balls, What is the probability that they are one red, one white and one blue?
A
5/102
B
5/136
C
5/162
D
5/204
E
5/243
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Total number of balls = 18
P(1R, 1W, 1B) = 5/18 x 9/18 x 4/18 = 5/162
Source: Myschool Past Questions Archive (Record #23184)
Mathematics
WAEC / WASSCE 1992
Permutations, Combinations & Probability
The data below shows the number of worker?
employed in the various sections of a construction
company in Lagos.
Carpenters 24 Labourers 27
Plumbers 12 Plasterers 15
Painters 9 Messengers 3
Bricklayers 18
If one of the workers is absent on a certain day,
what is the probability that he is a bricklayer?
A
1/12
B
1/9
C
2/9
D
1/6
E
1/4
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 #23185)
Mathematics
WAEC / WASSCE 1992
Permutations, Combinations & Probability
The data below shows the number of worker?
employed in the various sections of a construction
company in Lagos.
Carpenters 24 Labourers 27
Plumbers 12 Plasterers 15
Painters 9 Messengers 3
Bricklayers 18
If a worker is retrenched, what is the probability that he is a plumber or plasterer.
A
1/27
B
1/9
C
5/36
D
1/4
E
3/4
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 #23186)
Mathematics
UTME / JAMB 1992
Number Bases & Modular Arithmetic
Solution
Find n if 34n = 100112
A
5
B
6
C
7
D
8
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
To find n if 34n = 100112, convert both sides to base 10
= 3n + 4 = (1 x 24) + (0 x23) + (0 x 22) + (1 x 21) + 1 x 2o
= 3n + 4 = 16 + 0 + 0 + 2 + 1
3n + 4 = 19
3n = 15
n = 5
Source: Myschool Past Questions Archive (Record #31291)
Mathematics
UTME / JAMB 1992
Fractions, Decimals, Percentages & Approximations
Solution
The radius of a circle is given as 5cm subject to an error of 0.1cm. What is the percentage error in the area of the circle?
A
\(\frac{1}{25}\)
B
\(\frac{1}{4}\)
C
4
D
25
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
% error in Area = \(\frac{\pi(5.1)^2 - \pi(5)^2 \times 100%}{\pi(5)^2}\)
= \(\frac{\pi 26.01 - 25 \times 100%}{\pi(25)}\)
= \(\frac{1.01}{25}\) x 100%
= 4.04%
Source: Myschool Past Questions Archive (Record #31292)
Mathematics
UTME / JAMB 1992
Indices, Logarithms & Surds
Solution
Evaluate \(\log_{b} a^{n}\) if \(b = a^{\frac{1}{n}}\).
A
n2
B
n
C
\(\frac{1}{n}\)
D
\(\frac{1}{n^2}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Let \(\log_{b} a^{n} = x\)
\(\therefore a^{n} = b^{x}\)
\(a^{n} = (a^{\frac{1}{n}})^{x}\)
\(a^{n} = a^{\frac{x}{n}} \implies n = \frac{x}{n}\)
\(x = n^{2}\)
Source: Myschool Past Questions Archive (Record #31293)
Mathematics
UTME / JAMB 1992
Indices, Logarithms & Surds
Solution
What is the value of x satisfying the equation \(\frac{4^{2x}}{4^{3x}}\) = 2?
A
-2
B
-\(\frac{1}{2}\)
C
\(\frac{1}{2}\)
D
2
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\frac{4^{2x}}{4^{3x}}\) = 2
42x - 3x = 2
4-x = 2
(22)-x
= 21
Equating coefficients: -2x = 1
x = -\(\frac{1}{2}\)
Source: Myschool Past Questions Archive (Record #31294)
Mathematics
UTME / JAMB 1992
Indices, Logarithms & Surds
Solution
Simplify \(\frac{(1.25 \times 10^{-4}) \times (2.0 \times 10^{-1})}{(6.25 \times 10^5)}\)
A
4.0 x 10-11
B
5.0 x 10-2
C
2.0 x 10-1
D
5.0 x 10-3
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\frac{(1.25 \times 10^{-4}) \times (2.0 \times 10^{-1})}{(6.25 \times 10^5)}\) = \(\frac{1.25 \times 2}{6.25}\) x 10\(^{-4 - 1 - 5}\)
\(\frac{2.50}{6.25}\) x 10\(^{-10}\) = \(\frac{250}{625}\) x 10\(^{-10}\)
0.4 x 10\(^{-10}\) = 4.0 x 10\(^{-11}\)
Source: Myschool Past Questions Archive (Record #31295)
Mathematics
UTME / JAMB 1992
Indices, Logarithms & Surds
Solution
Simplify 5\(\sqrt{18}\) - 3\(\sqrt{72}\) + 4\(\sqrt{50}\)
A
17\(\sqrt{4}\)
B
4\(\sqrt{17}\)
C
17\(\sqrt{2}\)
D
12\(\sqrt{4}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
5\(\sqrt{18}\) - 3\(\sqrt{72}\) + 4\(\sqrt{50}\) = 5(3\(\sqrt{2}\)) - 3(6\(\sqrt{2}\)) + 4(5\(\sqrt{2}\))
15\(\sqrt{2}\) - 18\(\sqrt{2}\) + 20\(\sqrt{2}\) = 35\(\sqrt{2}\) - 18\(\sqrt{2}\)
= 17\(\sqrt{2}\)
Source: Myschool Past Questions Archive (Record #31296)
Mathematics
UTME / JAMB 1992
Indices, Logarithms & Surds
Solution
If x = 3 - \(\sqrt{3}\), find x2 + \(\frac{36}{x^2}\)
A
9
B
18
C
24
D
27
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
x = 3 - \(\sqrt{3}\)
x2 = (3 - \(\sqrt{3}\))2
= 9 + 3 - 6\(\sqrt{34}\)
= 12 - 6\(\sqrt{3}\)
= 6(2 - \(\sqrt{3}\))
∴ x2 + \(\frac{36}{x^2}\) = 6(2 - \(\sqrt{3}\)) + \(\frac{36}{6(2 - \sqrt{3})}\)
6(2 - \(\sqrt{3}\)) + \(\frac{6}{2 - \sqrt{3}}\) = 6(- \(\sqrt{3}\)) + \(\frac{6(2 + \sqrt{3})}{(2 - \sqrt{3})(2 + \sqrt{3})}\)
= 6(2 - \(\sqrt{3}\)) + \(\frac{6(2 + \sqrt{3})}{4 - 3}\)
6(2 - \(\sqrt{3}\)) + 6(2 + \(\sqrt{3}\)) = 12 + 12
= 24
Source: Myschool Past Questions Archive (Record #31297)
Mathematics
UTME / JAMB 1992
Sets, Logic & Venn Diagrams
Solution
If x = (all prime factors of 44) and y = (all prime factors of 60), the elements of X ∪ Y and X ∩ Y respectively are
A
(2, 4, 3, 5, 11) and (4)
B
(4, 3, 5, 11) and (3, 4)
C
(2, 5, 11) and (2)
D
(2, 3, 5, 11) and (2)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
x = (all prime factors of 44) and y = (all prime factors of 60)
∴ x = (2, 11), y = (2, 3, 5)
X ∪ Y = (2, 3, 5, 11),
X ∩ Y = (2)
Source: Myschool Past Questions Archive (Record #31304)
Mathematics
UTME / JAMB 1992
Sets, Logic & Venn Diagrams
Solution
If U = (1, 2, 3, 6, 7, 8, 9, 10) is the universal set. E = (10, 4, 6, 8, 10) and F = {x: 1x\(^2\) = 2\(^6\), x is odd}. Find (E ∩ F)', where ' means the complement of a set.
A
(0)
B
U
C
(8)
D
\(\phi\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
U = (1, 2, 3, 6, 7, 8, 9, 10)
E = (10, 4, 6, 8, 10)
F = (x : x\(^2\) = 2\(^6\), x is odd)
∴ F = \(\phi\) Since x\(^2\) = 2\(^6\) = 64
x = \(\pm 8\) which is even
∴ E ∩ F = \(\phi\) Since there are no common elements
Since E ∩ F = \(\phi\), then ( E ∩ F)' = U = (1, 2, 3, 6, 7, 8, 9, 10)
Source: Myschool Past Questions Archive (Record #31306)
Mathematics
UTME / JAMB 1992
Algebraic Expressions, Polynomials & Factorisation
Solution
Factorize \(9p^2 - q^2 + 6qr - 9r^2\)
A
(3p - 3q + r)(3p - q - 3r)
B
(6p - 3q - 3r)(3p - q - 4r)
C
(3p - q + 3r)(3p + q - 3r)
D
(3q - p + 3r)(3q - p + 3r)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(9p^{2} - q^{2} + 6qr - 9r^{2}\)
= \(9p^{2} - (q^{2} - 6qr + 9r^{2})\)
= \(9p^{2} - (q^{2} - 3qr - 3qr + 9r^{2})\)
= \(9p^{2} - (q(q - 3r) - 3r(q - 3r))\)
= \(9p^{2} - (q - 3r)^{2}\)
= \((3p + (q - 3r))(3p - (q - 3r))\)
= \((3p + q - 3r)(3p - q + 3r)\)
Source: Myschool Past Questions Archive (Record #31307)
Mathematics
UTME / JAMB 1992
Linear, Simultaneous & Quadratic Equations
Solution
Solve the equation: \(y - 11\sqrt{y} + 24 = 0\)
A
8, 3
B
64, 9
C
6, 4
D
9, -8
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(y - 11\sqrt{y} + 24 = 0 \implies y + 24 = 11\sqrt{y}\)
Squaring both sides,
\(y^{2} + 48y + 576 = 121y\)
\(y^{2} + 48y - 121y + 576 = 0 \implies y^{2} - 73y + 576 = 0\)
\(y^{2} - 64y - 9y + 576 = 0\)
\(y(y - 64) - 9(y - 64) = 0\)
\((y - 9)(y - 64) = 0\)
\(\therefore \text{y = 64 or y = 9}\)
Source: Myschool Past Questions Archive (Record #31308)
Mathematics
UTME / JAMB 1992
Plane Geometry, Polygons & Circle Theorems
Solution
Make t the subject of formula S = ut + \(\frac{1}{2} at^2\)
A
\(\frac{1}{a}\) (-u + \(\sqrt{U^2 - 2as}\))
B
\(\frac{1}{a}\) {u \(\pm\) (U2 - 2as)}
C
\(\frac{1}{a}\) {u \(\pm\) \(\sqrt{2as}\)}
D
\(\frac{1}{a}\) {-u + \(\sqrt{( 2as)}\)}
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Given S = ut + \(\frac{1}{2} at^2\)
S = ut + \(\frac{1}{2} at^2\)
∴ 2S = 2ut + at2
= at2 + 2ut - 2s = 0
t = \(\frac{-2u \pm 4u^2 + 2as}{2a}\)
= -2u \(\pi\) \(\frac{\sqrt{u^2 4u^2 + 2as}}{2a}\)
= \(\frac{1}{a}\) (-u + \(\sqrt{U^2 - 2as}\))
Source: Myschool Past Questions Archive (Record #31311)