Question Library
Browse, filter, and study verified past examination questions with step-by-step mathematical reasoning.
Searching 18,000+ Questions...
Sifting topics, KaTeX formulas & verified solutions
Showing 46–60 of 543 verified questions
Sort by:
Mathematics
UTME / JAMB 2021
Indices, Logarithms & Surds
Solution
Find the mean deviation of 1, 2, 3 and 4
A
1.0
B
1.5
C
2.0
D
2.5
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
_
Mean deviation = Σ|x - x|
n
_
x = 2.5
= |1 - 2.5| + |2 - 2.5| + |3 - 2.5| + |4 - 2.5|
4
= 4/4 = 1
Source: WAEC / JAMB / NECO Classroom Archive (Record #60671)
Mathematics
UTME / JAMB 2021
Indices, Logarithms & Surds
Solution
Simplify and express in standard form \(\frac{0.00275 \times 0.00640}{0.025 \times 0.08}\)
A
8.8 x 10-1
B
8.8 x 10-2
C
8.8 x 10-3
D
8.8 x 103
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{0.00275 \times 0.0064}{0.025 \times 0.08}\)
Removing the decimals = \(\frac{275 \times 64}{2500 \times 800}\)
= \(\frac{88}{10^4}\)
88 x 10-4 = 88 x 10-1 x 10-4
= 8.8 x 10-3
Source: WAEC / JAMB / NECO Classroom Archive (Record #60677)
Mathematics
WAEC / WASSCE 2021
Indices, Logarithms & Surds
Solution
Solve: 2\(^{\sqrt{2x + 1}}\) = 32
A
13
B
24
C
12
D
11
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
2\(^{\sqrt{2x + 1}}\) = 32
2\(^{\sqrt{2x + 1}}\) = 2\(^5\)
\(\sqrt{2x + 1}\) = 5
square both sides
2x + 1 = 5\(^2\)
2x + 1 = 25
2x = 25 - 1
2x = 24
x = \(\frac{24}{2}\)
x = 12
Source: WAEC / JAMB / NECO Classroom Archive (Record #61139)
Mathematics
WAEC / WASSCE 2021
Indices, Logarithms & Surds
Solution
If 16 * 2\(^{(x + 1)}\) = 4\(^x\) * 8\(^{(1 - x)}\), find the value of x.
A
-4
B
4
C
1
D
-1
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
16 * 2\(^{(x + 1)}\) = 4\(^x\) * 8\(^{(1 - x)}\)
= 2\(^4\) * 2\(^{(x + 1)}\) = 2\(^{2x}\) * 2\(^{3(1 - x)}\)
--> 4 + x + 1 = 2x + 3 - 3x
collect like terms
--> x - 2x + 3x = 3 - 1 - 4
--> 2x = -2
--> x = -1
Source: WAEC / JAMB / NECO Classroom Archive (Record #61153)
Mathematics
UTME / JAMB 2021
Indices, Logarithms & Surds
Solution
Simplify 2log \(\frac{2}{5}\) - log\(\frac{72}{125}\) + log 9
A
1 - 4 log3
B
-1 + 2 log 3
C
-1 + 5 log2
D
1 - 2log 2
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
2log \(\frac{2}{5}\) - log\(\frac{72}{125}\) + log 9
[\(\frac{2}{5}\))2 x 9] = log \(\frac{4}{25}\) x \(\frac{9}{1}\) x \(\frac{125}{72}\)
= log \(\frac{72}{125}\)
= log \(\frac{5}{2}\)
= log \(\frac{10}{4}\)
= log 10 - log 4
= log10 - log2\(^2\)
= 1 - 2 log2
Source: WAEC / JAMB / NECO Classroom Archive (Record #60710)
Mathematics
UTME / JAMB 2021
Indices, Logarithms & Surds
Solution
Find x if log\(_9\)x = 1.5
A
27
B
15
C
3.5
D
32
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
If log\(_9\)x = 1.5,
9\(^{1.5}\) = x
9^\(\frac{3}{2}\) = x
(\sqrt9)\(^3\) = 3
∴ x = 27
Source: WAEC / JAMB / NECO Classroom Archive (Record #60730)
Mathematics
WAEC / WASSCE 2021
Indices, Logarithms & Surds
Solution
If log\(_{10}\) 2 = m and log\(_{10}\) 3 = n, find log\(_{10}\) 24 in terms of m and n.
A
3m + n
B
m + 3n
C
4mn
D
3mn
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
log\(_{10}\) 24 = log\(_{10}\) 8 \(\times\) log\(_{10}\) 3
where log\(_{10}\) 8 = 3 log\(_{10}\) 2 = 3 \(\times\) m
and log\(_{10}\) 3 = n
: log\(_{10}\) 24 = 3m + n
Source: WAEC / JAMB / NECO Classroom Archive (Record #61140)
Mathematics
UTME / JAMB 2021
Indices, Logarithms & Surds
Solution
Simplify \(\sqrt{27}\) + \(\frac{3}{\sqrt{3}}\)
A
4\(\sqrt{3}\)
B
\(\frac{4}{\sqrt{3}}\)
C
3\(\sqrt{3}\)
D
\(\frac{\sqrt{3}}{4}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\sqrt{27}\) + \(\frac{3}{\sqrt{3}}\)
= \(\sqrt{9 \times 3}\) + \(\frac{3 \times {\sqrt{3}}}{{\sqrt{3}} \times {\sqrt{3}}}\)
= 3\(\sqrt{3}\) + \(\sqrt{3}\)
= 4\(\sqrt{3}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #60679)
Mathematics
WAEC / WASSCE 2021
Indices, Logarithms & Surds
Solution
Simplify 2√7- \(\frac{14}{√7} + \frac{7}{√21}\)
A
\(\frac{√21}{21}\)
B
7\(\frac{√21}{21}\)
C
\(\frac{√21}{3}\)
D
3√21
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
2\sqrt7- \(\frac{14}{\sqrt7} + \frac{7}{\sqrt21}\)
L.C.M is \sqrt21
\(\frac{\sqrt21 * 2\sqrt7 - \sqrt3 *14 + 7}{\sqrt21}\)
=\(\frac{2 * 7\sqrt3 - 14\sqrt3 + 7}{\sqrt21}\)
= \(\frac{14\sqrt3 - 14\sqrt3 + 7}{\sqrt21}\)
=\(\frac{7}{\sqrt21}\)
or
\(\frac{7 \times \sqrt21}{\sqrt21 \times \sqrt21}\)
= \(\frac{7 \times \sqrt21}{21}\) or \(\frac{\sqrt21}{3}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #61165)
Mathematics
WAEC / WASSCE 2021
Indices, Logarithms & Surds
Solution
The height of an equilateral triangle of side is 10\(\sqrt{3}\)cm. Calculate its perimeter.
A
20cm
B
60cm
C
40cm
D
30cm
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Height of an equilateral triangle, h = a\(\frac{\sqrt{3}}{2}\), where a is the side of the equilateral triangle.
10\(\sqrt{3}\) = a\(\frac{\sqrt{3}}{2}\)
cross multiply--> 2 x 10\(\sqrt{3}\) = a\(\sqrt{3}\)
\(\sqrt{3}\) cancels out \(\sqrt{3}\) on both sides
20 = a
The perimeter of an equilateral triangle is: P = 3a
P = 3 * 20 = 60cm
Source: Myschool Past Questions Archive (Record #61207)
Mathematics
UTME / JAMB 2020
Indices, Logarithms & Surds
Solution
If log\(_{10}\)2 = 0.3010 and log\(_{10}\)3 = 0.4771, eventually without using the logarithm tables, log\(_{10}\)4.5
A
0.3010
B
0.4771
C
0.6532
D
0.9542
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
log\(_{10}\)2 = 0.3010 and log\(_{10}\)3 = 04771
log\(_{10} 4.5 = log_{10}\) (\(\frac{3 \times 3}{2}\))
log\(_{10}\) 3 + log\(_{10}\) 3 - log\(_{10}\)2 = 0.4471 + 0.771 - 0.3010
= 0.6532
Source: Myschool Past Questions Archive (Record #56761)
Mathematics
UTME / JAMB 2020
Indices, Logarithms & Surds
Solution
Simplify \(\frac{324 - 4x^2}{2x + 18}\)
A
2(x - 9)
B
2(9 + x)
C
81 - x\(^2\)
D
-2(x - 9)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
234 - 4x\(^2\) = 18\(^2\) - (2x)\(^2\) = (18 - 2x)(18 + 2x)
2x + 18 = 2x + 18 = (2x + 18)
18 - 2x = 2(9 - x) or -2(x - 9)
Source: Myschool Past Questions Archive (Record #56763)
Mathematics
UTME / JAMB 2020
Indices, Logarithms & Surds
Solution
What is the product of \(\frac{27}{5}\), \((3)^{-3}\) and (\(\frac{1}{5})^{-1}\)?
A
5
B
3
C
1
D
\(\frac{1}{25}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{27}{5} \times 3^{-3} \times \frac{(1)^{-1}}{5}\)
= \(\frac{27}{5} \times \frac{1}{3^3} \times \frac{1}{\frac{1}{5}}\)
\(\frac{27}{5}\) x \(\frac{1}{27}\) x \(\frac{5}{1}\) = 1
Source: Myschool Past Questions Archive (Record #56782)
Mathematics
UTME / JAMB 2020
Indices, Logarithms & Surds
Solution
Calculate the standard deviation of the following data: 7, 8, 9, 10, 11, 12, 13
A
2
B
4
C
12
D
17
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
x
x - x
(x - x)\(^2\)
7
8
9
10
11
12
13
-3
-2
-1
0
1
2
3
9
4
1
1
0
4
9
--------------
28
S.D = \(\frac{\sqrt\sum (x - x)^2}{N} = \frac{\sum d^2}{N} = \frac{\sqrt{28}}{7}\)
= \(\sqrt{4}\)
= 2
Source: Myschool Past Questions Archive (Record #56826)
Mathematics
UTME / JAMB 2020
Indices, Logarithms & Surds
Solution
Express the product of 0.0014 and 0.011 in standard form
A
1.54 x 10\(^{-2}\)
B
1.54 x 10\(^{-3}\)
C
1.54 x 10\(^{-2}\)
D
1.54 x 10\(^{-5}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
0.0014 = 1.4 \times 10\(^{-3}\)
0.011 = 1.1 \times 10\(^{-2}\)
Product = (1.4 \times 1.1) \times 10\(^{-3}\) \times 10\(^{-2}\) = 1.54 \times 10\(^{-5}\)
Source: Myschool Past Questions Archive (Record #56830)