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Mathematics
UTME / JAMB 2015
Number and Numeration
Solution
Given that A = {1, 5, 7}
B = {3, 9, 12, 15}
C = {2, 4, 6, 8}
Find (A ∪ B) ∪ C
A
{1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 15}
B
{1, 2, 3, 5, 6, 8, 12, 15}
C
{2, 4, 5, 9, 12, 15}
D
{1, 5, 6, 7, 8, 9, 12, 15}
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
{A ∪ B ∪ C}
{A ∪ B} = {1, 3, 5, 7, 9, 12, 15}
∪ C={2,4,6,8}
{A ∪ B} ∪ C = {1, 3, 5, 7, 9, 12, 15} ∪ {2, 4, 6, 8}
= {1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 15}
{A ∪ B} ∪ C = {1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 15}
Source: Myschool Past Questions Archive (Record #40654)
Mathematics
UTME / JAMB 2015
Number and Numeration
Solution
The extension of a stretched string is directly proportional to its tension. If the extension produced by a tension of 8 Newton’s is 2cm, find the extension produced by a tension of 12 newton’s.
A
2
B
1
C
0
D
3
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Let the extension be E and the tension be T.
Then \(E \propto T\)
\(E = kT\)
when T = 8N, E = 2cm
\(2 = k \times 8\)
\(k = \frac{2}{8} = 0.25\)
\(\therefore E = 0.25T\)
when T = 12N, \(E = 0.25 \times 12 = 3cm\)
Source: Myschool Past Questions Archive (Record #40657)
Mathematics
UTME / JAMB 2015
Number and Numeration
Solution
Factorize \( x^2 − 2x − 15 \)
A
(x + 3)2
B
(x + 5)(x − 3)
C
(x − 5)2
D
(x − 5)(x + 3)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
x2 − 2x − 15
(x2 − 5x) + (3x − 15)
x(x − 5)+ 3(x − 5)
(x − 5)(x + 3)
Source: Myschool Past Questions Archive (Record #40664)
Mathematics
UTME / JAMB 2015
Number and Numeration
Solution
If A = (−3,5) and B = (4,−1) find the co-ordinate of the mid point
A
2, ½
B
½ , 2
C
1, ½
D
0, 2
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
The coordinate of the midpoint is \((\frac{-3 + 4}{2}, \frac{5 + (-1)}{2})\)
= \((\frac{1}{2}, 2)\)
Source: Myschool Past Questions Archive (Record #40667)
Mathematics
UTME / JAMB 2015
Number and Numeration
Solution
Find the simple interest on N325 in 5years at 3% per annum.
A
N48.75K
B
N50.10K
C
N75.50K
D
N15.75K
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
I =[ PRT ÷ 100]
[(325 × 5 × 3) ÷ (100)]
N(195 ÷ 4)
N48.75K
Source: Myschool Past Questions Archive (Record #40669)
Mathematics
UTME / JAMB 2015
Number and Numeration
Solution
Simplify (0.09)2 and give your answer correct to 4 significant figures
A
0.81
B
0.081
C
0.0081
D
8.0001
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
(0.09)2 = 0.09 × 0.09
= 0.0081
= 0.008100 to 4 significant figures
Please, start counting first from the non-zero digits i.e. 8
Source: Myschool Past Questions Archive (Record #40676)
Mathematics
UTME / JAMB 2015
Geometry and Trigonometry
Solution
Simplify \( [1 ÷ (x^2 + 3x + 2)] + [1 ÷ (x^2 + 5x + 6)] \)
A
\( \frac{2}{(x + 1)^2} \)
B
\( \frac{2}{(x + 1)(x + 2} \)
C
\( \frac{2}{(x + 1)(x + 2} \)
D
\( \frac{2}{(x + 1)(x + 3} \)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\( [1 ÷ (x^2 + 3x + 2)] + [1 ÷ (x^2 + 5x + 6)] \)
= \( 1 ÷ (x^2 + 3x + 2) + [1 ÷ (x^2 +5x + 6)]\)
= \( [1 ÷ ((x^2 + x) + (2x + 2) )] + [1 ÷ ((x^2 + 3x) + (2x + 6) )] \)
= [1 ÷ (x(x + 2) + 2(x +1))] + [1 ÷ (x(x + 3) +2(x + 3) )]
= [1 ÷ (x + 1)(x + 2)] + [1 ÷ ((x + 3) + (x + 2))]
=((x + 3) + (x + 1)) ÷ (x + 1)(x + 2)(x + 3)
Using the L.C.M
=((x + x + 3 + 1)) ÷ (x + 1)(x + 2)(x + 3)
=(2x+4)/(x+1)(x+2)(x+3) =2(x+2)/(x+1)(x+2)(x+3)
= \( \frac{2 }{(x + 1)(x + 3)} \)
Source: Myschool Past Questions Archive (Record #40682)
Mathematics
UTME / JAMB 2015
Geometry and Trigonometry
Solution
One bag contain 3 blue and 5 red balls, another bag contain 2 blue and 4 red balls respectively. One ball is drawn for each bag. What is the probability both balls are blue
A
\( \frac{2}{15} \)
B
\( \frac{3}{24} \)
C
\( \frac{3}{21} \)
D
\( \frac{3}{28} \)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
The probability of drawing a blue ball from the first bag is \( \frac{3}{8} \), since there are 3 blue balls out of 8 total balls.
The probability of drawing a blue ball from the second bag is \( \frac{2}{6} = \frac{1}{3} \), since there are 2 blue balls out of 6 total balls.
Since the draws from each bag are independent, the probability that both balls are blue is the product of the individual probabilities:
\( \frac{3}{8} \times \frac{2}{6} = \frac{3 \times 2}{8 \times 6} = \frac{6}{48} = \frac{1}{8}. \)
Source: Myschool Past Questions Archive (Record #40685)
Mathematics
UTME / JAMB 2015
Number and Numeration
Solution
Given that A = {3, 4, 1, 10, ⅓ }
B = {4, 3,⅓, ⅓, 7}.
Find A∩B
A
{}
B
{⅓, 1, 2}
C
{3, 4, ⅓}
D
{1, 3, ⅓}
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
A ∩ B = {3, 4, ⅓}
Source: Myschool Past Questions Archive (Record #40686)
Mathematics
UTME / JAMB 2015
Number and Numeration
Solution
Find x if 132x = 70 eight.
A
5
B
3
C
6
D
1
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
132x = 708
\( 1 × x^2 + 3 × x^1 + 2 × x^0 \)
\( 7 × 8^1 + 0 × 8^0 \)
\( x^2 + 3x + 2 − 56 = 0 \)
\( x^2 + 3x − 54 = 0 \)
x(x + 9)−6(x + 9) = 0
(x + 9)(x − 6) = 0
Either (x + 9) = 0 or (x − 6) = 0
x = − 9 or +6
The positive values for x = 6
The base number for 132x = 1326
Source: Myschool Past Questions Archive (Record #40687)
Mathematics
UTME / JAMB 2015
Geometry and Trigonometry
Solution
A man sells his new brand car for N420,000 at a gain of 15%. What did it cost him?
A
N410,000
B
N365, 217
C
N157, 250
D
N257,000
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Cost Price:
Selling price = 100 : (100 + 15)
= 100 : 115
Cost Price
= 100 \div 115 of selling price (i.e N420,000)
= 100 \div 115 \times N420,000
= N365,217.4
∴ Cost Price = N365, 217
Source: Myschool Past Questions Archive (Record #40688)
Mathematics
UTME / JAMB 2015
Number and Numeration
Solution
Find the value of x if \( [ 1 ÷ 64^{(x + 2)}]= [4^{(x − 3)} ÷ 16^x ] \)
A
\( \frac{3}{2} \)
B
\( \frac{2}{3} \)
C
\( \frac{1}{3} \)
D
\( -\frac{3}{2} \)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\( [ 1 ÷ 64^{(x + 2)}]= [4^{(x − 3)} ÷ 16^x ] \)
\( 64^{−(x + 2)} = [4^{(x − 3)}] ÷[16^x] \)
breakdown 4,16,64 into a small index no
\( 2^{−6(x + 2)} = 2^{2(x − 3)} ÷ 2^{4(x)} \)
\( 2^{−6x− 12} = 2^{2x − 4x − 6} \)
\( 2^{−6x −12} = 2^{−2x − 6} \)
− 6x − 12 = − 2x − 6
Collect the like term
−6x + 2x = −6 + 12
−4x =6
x = \( \frac{6}{4} \)
x = \( \frac{−3}{2} \)
Source: Myschool Past Questions Archive (Record #40694)
Mathematics
UTME / JAMB 2015
Number and Numeration
Solution
Solve x2 − 2x − 3 = 0
A
x = 2 or 1
B
x = 3 or -1
C
x = 1 or 0
D
x = 1 or 2
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
x2 − 2x − 3 = 0
−3x + x = − 2x
− 3x × x = − 3x2
(x2 − 3x)(x − 3) = 0
(x − 3)(x + 1) = 0
Either (x − 3) = 0 or (x + 1) = 0
x = 3 or − 1
Source: Myschool Past Questions Archive (Record #40702)
Mathematics
UTME / JAMB 2015
Number and Numeration
Solution
The volume of a cylinder whose height is 4cm and whose radius 5cm is equal to (π = 3.14)
A
3.13cm2
B
145cm2
C
314cm2
D
214cm2
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
“Explanation
V = πr2h
V = ?, h = 4cm, r = 5cm
V = 3.14(5)2 (4)
V = 3.14(25)(4)
V = 3.14 × 1200
= 314cm2
Source: Myschool Past Questions Archive (Record #40706)
Mathematics
UTME / JAMB 2015
Statistics and Probability
Solution
The probability of an event A is 1/5. The probability of B is 1/3 . The probability both A and B is 1/15. What is the probability of either event A or B or both
A
\( \frac{2}{15} \)
B
\( \frac{3}{4} \)
C
\( \frac{9}{15} \)
D
\( \frac{1}{15} \)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
In probability, or = +
Prob( A or B or Both ) = \(\frac{1}{3} + \frac{1}{5} + \frac{1}{15}\) = \(\frac{5+ 3 + 1}{15}\) = \(\frac{9}{15}\) = \(\frac{3}{5}\)
Source: Myschool Past Questions Archive (Record #40716)