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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
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
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
Number and Numeration
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
Number and Numeration
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
Number and Numeration
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
Number and Numeration
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)
Mathematics
UTME / JAMB 2015
Number and Numeration
Solution
If an investor invest N450,000 in a certain organization in order to yield X as a return of N25,000. Find the return on an investment of N700,000 by Y in the same organization.
A
N14,950.50K
B
N25,150.30K
C
N15,000.00K
D
N38,888.90K
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
[Return ÷ Investment] as a ratio ;
i.e The Ratio is Return : Investmen
[(Return1÷ Investment1 ) = (Return2÷ Investment2)]
R1 = N 25000
R2 =?
I1 = N450,000,
I1 = N 700000
(25000 ÷ 450000) = (R2 ÷ 700000)
R2 = [(25000 × 700000 ) ÷ 450000]
= N38,888.90K
∴ The return on a investment of Y = N38888.90K
Source: Myschool Past Questions Archive (Record #40735)
Mathematics
UTME / JAMB 2015
Number and Numeration
Solution
Evaluate log717
A
1.35
B
1.353
C
1.455
D
0.455
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
log717
= [log 17 ÷ log7]
= [1.2304 ÷ 0.8451]
[100.0899 ÷ 101.9270]
= 1.455(antilog)
Source: Myschool Past Questions Archive (Record #40738)
Mathematics
UTME / JAMB 2015
Number and Numeration
Solution
100112 + *****2 + 111002 + 1012 = 10011112
A
11112
B
110112
C
101112
D
110012
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Convert the binary to base 10 and they convert back to base two
100112 + xxxxx2 + 111002 + 1012 = 10011112
(1 × 24 + 0 × 23 + 1 × 22 + 1 × 21 + 1 × 20) + xxxxx2 +(1 × 24 + 1 × 23 + 1 × 22 + 0 × 21 + 0 × 20) + (1 × 22 + 0 × 21 + 1 × 20)
= (16 + 0 + 0 + 2 + 1) + xxxxx2 + (16 + 8 + 4 + 0 + 0 ) + (4 + 0 + 1)
=(64 + 0 + 0 + 8 + 4 + 2 + 1)
19 + xxxxx2 + 33 = 79
xxxxx2 + 52 = 79
xxxxx2 = 79 − 52
xxxxx2 = 2710
\( \begin{array}{c|c}
2 & 27 \\
\hline
2 & 13 \text{ rem 1}\\
2 & 6 \text{ rem 1}\\
2 & 3 \text{ rem 0}\\
2 & 1 \text{ rem 1}\\
& 0 \text{ rem 1}\\
\end{array}\uparrow \)
2710 = 110112
Therefore xxxxx2 = 2710 = 110112
Source: Myschool Past Questions Archive (Record #40740)