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Mathematics
WAEC / WASSCE 2015
Number and Numeration
Solution
Given that logx 64 = 3, evaluate x log\(_2\)8
A
6
B
9
C
12
D
24
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
If logx 64 = 3, then \(64 = x^3\)
\(4^3 = x^3\)
Since the indices are equal,
x = 4
Hence, x log\(_2\)8
= 4(3.log\(_2\)2)
= where log\(_2\)2 = 1(1)
= 12 X 1
= 12
Source: WAEC / JAMB / NECO Classroom Archive (Record #45704)
Mathematics
WAEC / WASSCE 2015
Number and Numeration
Solution
If m = 4, n = 9 and r = 16., evaluate \(\frac{m}{n}\) - 1\(\frac{7}{9}\) + \(\frac{n}{r}\)
A
1\(\frac{5}{16}\)
B
1\(\frac{1}{16}\)
C
\(\frac{5}{16}\)
D
- \(\frac{37}{48}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
If m = 4, n = 9, r = 16,
then \(\frac{m}{n}\) - 1\(\frac{7}{9}\) + \(\frac{n}{r}\)
= \(\frac{4}{9}\) - \(\frac{16}{9}\) + \(\frac{9}{16}\)
= \(\frac{64 - 256 + 81}{144}\)
= \(\frac{-111}{144}\)
= - \(\frac{37}{48}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #45708)
Mathematics
UTME / JAMB 2015
Number and Numeration
Solution
In a town of 6250 inhabitants, there were 62 births during 1984. Find the percentage birth rate
A
3%
B
1.0%
C
2.5%
D
5.40%
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Percentage birthrate = \(\frac{62}{6250} \times 100%\)
= \(\frac{6200}{6250}\)
= 0.992% \(\approx\) 1.0%.
Source: Myschool Past Questions Archive (Record #40493)
Mathematics
UTME / JAMB 2015
Number and Numeration
Solution
Simplify 1¼ ÷ (2 ÷ ¼ of 28)
A
1 \( \frac{3}{8}\)
B
2 \( \frac{3}{4}\)
C
4 \( \frac{3}{8}\)
D
3 \( \frac{1}{5}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
1¼ ÷ [ 2 ÷ ¼] of 28
Apply BODMAS rules
\( \frac{5}{4}\) ÷ [ 2 ÷ ¼ × 28 ]
\( \frac{5}{4} ÷ \frac{2}{7} \)
\( \frac{5}{4} × \frac{7}{2} \)
\( \frac{35}{8}\)
= \(4 \frac{3}{8}\)
Source: Myschool Past Questions Archive (Record #40505)
Mathematics
UTME / JAMB 2015
Number and Numeration
Solution
Factorize x2 + 9x + 20
A
(x − 5) 2
B
(x + 5)(x + 4)
C
(x – 5)(x + 3)
D
(x + 3) 2
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\( x^2 + 9x + 20 \)
Find the two numbers whose product is 20 and its sum is 9}
\( 5x \times 4x = 20x^2\)
\(5x + 4x = 9x\)
\((x^2 + 5x) + (4x + 20)\)
\(
x(x + 5)+ 4(x + 5)
= (x + 5)(x + 4)\)
Source: Myschool Past Questions Archive (Record #40546)
Mathematics
UTME / JAMB 2015
Number and Numeration
Solution
If three staff of Myschool Limited agreed to share their salary arrears in the ration of their ages, which are 18 years, 20 years, 22 years respectively. If the sum of the money collected is N120,000.00K, How much does the second staff received?
A
N36,000
B
N44,000
C
N40,000
D
N15,000
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Total of their ages: 18 + 20 + 22 = 60
The second staff will get \(\frac{20}{60} \times 120,000\)
= N40,000.00K
Source: Myschool Past Questions Archive (Record #40615)
Mathematics
UTME / JAMB 2015
Number and Numeration
Solution
X and Y are two sets such that n(X) = 15, n(Y) = 12 and n{X ∩ Y} = 7. Find ∩{X ∪ Y}
A
21
B
225
C
15
D
20
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
n(X ∪ Y) = n(X) + n(Y) − n(X ∩ Y)
= 15 + 12 − 7
∴ n(X ∪ Y) = 20
Source: Myschool Past Questions Archive (Record #40616)
Mathematics
UTME / JAMB 2015
Number and Numeration
Solution
Simplify log101.5 + 3 log102 − log100.3
A
log104
B
log1040
C
log10-40
D
log104-
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
log101.5 + 3 log102 − log100.3
log101.5 + log1023 − log100.3
[log10(1.5 × 23) ÷ log100.3]
[log10(15/10 × 8 ) ÷ log10( 3/10)]
log10(15/10 × 8 × 10/3 )
log1040
Source: Myschool Past Questions Archive (Record #40621)
Mathematics
UTME / JAMB 2015
Number and Numeration
Solution
Find the total surface area of a cylinder of base radius 5cm and length 7cm ( \pi = 3.14)
A
17.8cm2
B
15.8cm2
C
75.4cm2
D
54.7cm2
E
\(377.0cm^{2}\)
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
The total surface area of a cylinder = 2\pirl + 2\pir2
= 2\pir(l + r)
= 2 \times 3.14 x 5(7+5)
2 \times 3.14 \times 12 x 5
= 377.1cm (1DP)
Source: Myschool Past Questions Archive (Record #40622)
Mathematics
UTME / JAMB 2015
Number and Numeration
Solution
A man with an annual salary of N2000, has allowances of N600. If Income Tax is 5%. How much income tax expenses does he pay each year?
A
15
B
50
C
70
D
25
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
His annual salary = N2000
His allowances = N600
So his taxable income = Annual salary − allowance
= N2000 − N600
= N1400
He pay at 5%
Then, his allowance income tax 5/100 \times 1400 = N70
Source: Myschool Past Questions Archive (Record #40628)
Mathematics
UTME / JAMB 2015
Number and Numeration
Solution
If log520 = x, find x
A
1.761
B
1.354
C
1.861
D
2.549
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
log520 = x
5x = 20(Take log10 of both sides)
log5x = log20
xlog5 = log20
x= [log20 ÷ log5]
[1.30103 ÷ 0.69897]
x = 1.861
Source: Myschool Past Questions Archive (Record #40647)
Mathematics
UTME / JAMB 2015
Number and Numeration
Solution
Find at which rate per annum simple interest N525 will amount to N588 in 3 years.
A
3%
B
2%
C
5%
D
4%
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
I = A − P
= N588 − N525
∴I = N63
I = PRT ÷ 100
R = [100I ÷PT]
R = [(100 × 63 ) ÷ (525 × 3)]
= (6300 ÷ 1575) = 4
∴ The rate = 4 %
Source: Myschool Past Questions Archive (Record #40649)
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)