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Mathematics
UTME / JAMB 2014
Fractions, Decimals, Percentages & Approximations
Solution
Express the product of 0.00043 and 2000 in standard form.
A
8.6 x 10-3
B
8.3 x 10-2
C
8.6 x 10-1
D
8.6 x 10
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
0.00043 x 2000
= 43 x 10-5 x 2 x 103
= 43 x 2 x 10-5+3
= 86 x 10-2
= 8.6 x 101 x 10-2
= 8.6 x 10-1
Source: Myschool Past Questions Archive (Record #26998)
Mathematics
UTME / JAMB 2014
Fractions, Decimals, Percentages & Approximations
Solution
A man donates 10% of his monthly net earnings to his church. If it amounts to N4,500, what is his net monthly income?
A
N40,500
B
N45,000
C
N52,500
D
N62,000
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Let;
M = Man monthly net earnings
Then;
\(\text{N4500} = \frac{\text{10%}}{\text{100%}} \times M \)
\(M = \frac{\text{N4500} \times \text{100%}}{\text{10%}} \)
M = N45,000
Source: Myschool Past Questions Archive (Record #26999)
Mathematics
UTME / JAMB 2014
Indices, Logarithms & Surds
Solution
If log7.5 = 0.8751, evaluate 2 log75 + log750
A
6.6252
B
6.6253
C
66.252
D
66.253
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
If log 7.5 = 0.8751
Then 2log75 + log750
= 2(1.8751) + 2.8751
= 3.7502 + 2.8751
= 6.6253
Source: Myschool Past Questions Archive (Record #27000)
Mathematics
UTME / JAMB 2014
Plane Geometry, Polygons & Circle Theorems
Solution
Solve for x in 8x-2 = 2/25
A
4
B
6
C
8
D
10
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
8x-2 = 2/25
x-2 = 2/25 x 1/8
x-2 = 2/200
x-2 = 1/100
1/x2 = 1/100
x2 = 100
x = 10
Source: Myschool Past Questions Archive (Record #27001)
Mathematics
UTME / JAMB 2014
Indices, Logarithms & Surds
Solution
Simplify \(\frac{2\sqrt{2} - \sqrt{3}}{\sqrt{2} + \sqrt{3}}\)
A
3\(\sqrt{6} - 7\)
B
3\(\sqrt{6} + 7\)
C
3\(\sqrt{6} - 1\)
D
3\(\sqrt{6} + 1\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(= \frac{2\sqrt{2} - \sqrt{3}}{\sqrt{2} + \sqrt{3}} \times \frac{\sqrt{2} - \sqrt{3}}{\sqrt{2} - \sqrt{3}}\)
\(= \frac{2\sqrt{2}(\sqrt{2}) + (2\sqrt{2})(-\sqrt{3})-\sqrt{3}(\sqrt{2})-\sqrt{3}(-\sqrt{3})}{(\sqrt{2})^2-(\sqrt{3})^2}\)
\(= \frac{2 \times 2 - 2\sqrt{6} - \sqrt{6} + 3}{2 - 3}\)
\(= \frac{4 - 3\sqrt{6} + 3}{-1}\)
\(= \frac{7 - 3\sqrt{6}}{-1}\)
\(= \frac{7}{-1} - \frac{3\sqrt{6}}{-1}\)
\(= -7 + 3\sqrt{6}\)
\(= 3\sqrt{6}-7\)
Source: Myschool Past Questions Archive (Record #27002)
Mathematics
UTME / JAMB 2014
Indices, Logarithms & Surds
Solution
Evaluate Log28 + Log216 - Log24
A
3
B
4
C
5
D
6
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\( = log_2 \frac{8 \times 16}{4}\)
\( = log_2 32\)
\( = log_2 2^5\)
\( = 5log_2 2\)
\( = 5 \times 1\)
\( = 5 \)
Source: Myschool Past Questions Archive (Record #27003)
Mathematics
UTME / JAMB 2014
Sets, Logic & Venn Diagrams
Solution
If P = {1,2,3,4,5} and P \(\cup\) Q = {1,2,3,4,5,6,7}, list the elements in Q
A
{6}
B
{7}
C
{6,7}
D
{5,6}
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Q = (P \(\cup\) Q) - P
{6,7}
Source: Myschool Past Questions Archive (Record #27004)
Mathematics
UTME / JAMB 2014
Algebraic Expressions, Polynomials & Factorisation
Solution
If gt2 - k - w = 0, make g the subject of the formula
A
\(\frac{k + w}{t^2}\)
B
\(\frac{k - w}{t^2}\)
C
\(\frac{k + w}{t}\)
D
\(\frac{k - w}{t}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
gt2 - k - w = 0
gt2 = k + w
\(g = \frac{k + w}{t^2}\)
Source: Myschool Past Questions Archive (Record #27005)
Mathematics
UTME / JAMB 2014
Algebraic Expressions, Polynomials & Factorisation
Solution
Factorize 2y2 - 15xy + 18x2
A
(2y - 3x) (y + 6x)
B
(2y - 3x) (y - 6x)
C
(2y + 3x) (y - 6x)
D
(3y + 2x) (y - 6x)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
2y2 - 15xy + 18x2
2y2 - 12xy - 3xy + 18x2
2y(y - 6x) - 3x(y - 6x)
(2y - 3x) (y - 6x)
Source: Myschool Past Questions Archive (Record #27006)
Mathematics
UTME / JAMB 2014
Algebraic Expressions, Polynomials & Factorisation
Solution
Find the value of k if y - 1 is a factor of y3 + 4y2 + ky - 6
A
-6
B
-4
C
O
D
1
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
if y - 1 is a factor of y3 + 4y2 + ky - 6, then
f(1) = (1)3 + 4(1)2 + k(1) - 6 = 0 (factor theorem)
1 + 4 + k - 6 = 0
5 - 6 + k = 0
-1 + k = 0
k = 1
Source: Myschool Past Questions Archive (Record #27007)
Mathematics
UTME / JAMB 2014
Variations
Solution
y varies directly as w2. When y = 8, w = 2. Find y when w = 3
A
18
B
12
C
9
D
6
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(y \propto w^2\)
y = kw2
8 = k(2)2
8 = k(4)
k = 8/4
k = 2
Thus y = 2w2
When w = 3, y = 2(3)2
y = 2 x 9 = 18
Source: Myschool Past Questions Archive (Record #27008)
Mathematics
UTME / JAMB 2014
Variations
Solution
P varies directly as Q and inversely as R. When Q = 36 and R = 16, P = 27. Find the relation between P, Q and R.
A
\(P = \frac{Q}{12R}\)
B
\(P = \frac{12Q}{R}\)
C
\(P = 12QR\)
D
\(P = \frac{12}{QR}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(P \propto \frac{Q}{R}\)
\(P = K \frac{Q}{R}\)
When Q = 36, R = 16, P = 27
Then substitute into the equation
\(27 = K \frac{36}{16}\)
\(K = \frac{27 \times 16}{36}\)
\(K = 12\)
So the equation connecting P, Q and R is
\(P = \frac{12Q}{R}\)
Source: Myschool Past Questions Archive (Record #27009)
Mathematics
UTME / JAMB 2014
Plane Geometry, Polygons & Circle Theorems
Solution
What is the solution of \(\frac{x - 5}{x + 3} < -1\)?
A
-3 < x < 1
B
x 1
C
-3 < x < 5
D
x 5
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Consider the range -3 < x < -1
= { -2, -1, 0}, for instance
When x = -2,
\(\frac{-2 - 5}{-2 + 3} < -1\)
\(\frac{-7}{1} < -1\)
When x = -1,
\(\frac{-1 - 5}{-1 + 3} < -1\)
\(\frac{-6}{2} < -1\)
= -3 < -1
When x = 0,
\(\frac{0 - 5}{0 + 3} < -1\)
\(\frac{- 5}{3} < -1\)
Hence -3 < x < 1
Source: Myschool Past Questions Archive (Record #27010)
Mathematics
UTME / JAMB 2014
Inequalities & Linear Programming
Solution
Evaluate the inequality \(\frac{x}{2} + \frac{3}{4} \leq \frac{5x}{6} - \frac{7}{12}\)
A
\(x \geq 4\)
B
\(x \leq 3\)
C
\(x \geq -3\)
D
\(x \leq -4\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\frac{x}{2} + \frac{3}{4} \leq \frac{5x}{6} - \frac{7}{12}\)
\(12\frac{x}{2} + 12\frac{3}{4} \leq 12\frac{5x}{6} - 12\frac{7}{12}\)
6x + 9 \(\leq\) 10x - 7
6x - 10x \(\leq\) - 7 - 9
-4x \(\leq\) -16
-4x/-4 \(\geq\) -16/-4
x \(\geq\) 4
Source: Myschool Past Questions Archive (Record #27011)
Mathematics
UTME / JAMB 2014
Sequences & Series (AP & GP)
Solution
The 4th term of an A.P. is 13 while the 10th term is 31. Find the 24th term.
A
89
B
75
C
73
D
69
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
a + 3d = 13 .......... (1)
a + 9d = 31 .......... (2)
(2) - (1): 6d = 18
d = 18/6 = 3
From (1), a + 3(3) = 13
a + 9 = 13
a = 13 - 9 = 4
Hence,
T24 = a + 23d
T24 = 4 + 23(3)
T24 = 4 + 69
T24 = 73
Source: Myschool Past Questions Archive (Record #27012)