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Mathematics
UTME / JAMB 2015
Linear, Simultaneous & Quadratic Equations
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
Permutations, Combinations & Probability
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
Sets, Logic & Venn Diagrams
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
Linear, Simultaneous & Quadratic Equations
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
Fractions, Decimals, Percentages & Approximations
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
Indices, Logarithms & Surds
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
Plane Geometry, Polygons & Circle Theorems
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
Mensuration (Areas, Perimeters & Volumes)
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
Permutations, Combinations & 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)
Mathematics
UTME / JAMB 2015
Number Bases & Modular Arithmetic
Solution
If (159.75)10 = (x)6. Find x
A
x6 = 123.346
B
x6 = 424.56
C
x6 = 122.436
D
x6 = 124.456
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
(159.75)10 = (y)6
\( \begin{array}{c|c}
6 & 159 \\
\hline
6 & 26 \text{ rem 3} \\
6 & 4 \text{ rem 2} \\
& 0 \text{ rem 4} \\
\end{array}\uparrow \)
15910 = 4236
Then Convert 0.75 to base 6
0.75 x 6 =4.5 i.e 4.5 - 3.00 = 1.5
0.5 x 6 = 3.00 423 + 1.5 =424.5
159.75 = (424.5)6
(159)10 = (424.5)6
Source: Myschool Past Questions Archive (Record #40725)
Mathematics
UTME / JAMB 2015
Fractions, Decimals, Percentages & Approximations
Solution
A man bought a car for N800 and sold it for N520. Find his loss per cent
A
15%
B
25%
C
35%
D
10%
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Percentage Loss = (actual loss ) ÷ (Cost price) × 100
Actual loss = Cost Price − Selling Price (sold price)
= N800 − N520 = N280
Percentage loss = (280 ÷ 800) × 100 = 35%
∴ His loss percent = 35%
Source: Myschool Past Questions Archive (Record #40726)
Mathematics
UTME / JAMB 2015
Plane Geometry, Polygons & Circle Theorems
Solution
Simplify \(6\frac{1}{12} − 2 ¾ + 1 ½ \)
A
\( 3 \frac{5}{6}\)
B
\( 4 \frac{5}{6}\)
C
\( 2 \frac{1}{6}\)
D
\( \frac{1}{3} \)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
6½ − 2¾ + 1½
73/12 − 11/4 + 3/2
[(73 − 33 + 18) ÷ (12)]
58/12
29/6
\( 4\frac{5}{6}\)
Source: Myschool Past Questions Archive (Record #40728)
Mathematics
UTME / JAMB 2015
Coordinate Geometry
Find the distance between the points (-2,-3) and (-2,4)
A
3m
B
2.4m
C
3.2m
D
7.0m
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 #40729)
Mathematics
UTME / JAMB 2015
Sequences & Series (AP & GP)
Solution
Determine the third term of a geometrical progression whose first and second term are 2 and 54 respectively
A
1458
B
1485
C
1345
D
1258
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
1st G.P. = a =2
2nd G.P. = ar\(^{2 −1}\) = 54
2(r) = 54
r = 54/2 = 27
r = 27
3rd term = ar\(^2\) = (2) (27)\(^2\)
2 \times 27 \times 27
= 1458
Source: Myschool Past Questions Archive (Record #40730)
Mathematics
UTME / JAMB 2015
Inequalities & Linear Programming
Solution
Given that S and T are sets of real numbers such that S = {x : 0 \(\leq\) x \(\leq\) 5} and T = {x : − 2 < x < 3} Find S \(\cup\) T
A
−3 < x < \(\leq\)3
B
−2< x < \(\leq\)5
C
2< x < \(\geq\) −5
D
−1< x \(\geq\) \(\leq\)2
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
S = {0, 1, 2, 3, 4, 5}
T = {− 1, 0, 1, 2}
S \(\cup\) T = {− 1, 0, 1, 2, 3, 4, 5 }
⇒ − 2 < x ≤ 5
Source: Myschool Past Questions Archive (Record #40732)