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 16–30 of 543 verified questions
Sort by:
Mathematics
UTME / JAMB 2024
Indices, Logarithms & Surds
Solution
PQR is a triangle such that |PQ| = |QR| = 8cm and QPR = 60º. Find the area of \(\angle\) PQR
A
16\(\sqrt{3}cm^2\)
B
16\(\sqrt{2}cm^2\)
C
8\(\sqrt{3}cm^2\)
D
16\(\sqrt{2}cm^2\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
The area of a triangle given two sides and the included angle = \(\frac{1}{2}\) x a x b x Sin\(\theta\)
a = b = 8cm
\(\theta\) = 60º
Area = \(\frac{1}{2}\) x 8 x 8 x Sin 60º = \(\frac{1}{2}\) x 64 x \(\frac{\sqrt{3}}{2}\) ( Sin 60º = \(\frac{\sqrt{3}}{2}\) )
= \(\frac{64\sqrt{3}}{4}\) = 16\(\sqrt{3}cm^2\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #70195)
Mathematics
UTME / JAMB 2024
Indices, Logarithms & Surds
Diagram
Solution
In the diagram above, T represents the construction of angle .....
Attached Figure / Diagram
A
15\(^0\)
B
30\(^0\)
C
45\(^0\)
D
60\(^0\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
The construction of angle 30º
(If you take a 60º angle and bisect it, you would divide it into two angles of 30º each.)
Source: WAEC / JAMB / NECO Classroom Archive (Record #70266)
Mathematics
UTME / JAMB 2024
Indices, Logarithms & Surds
Solution
Solve 16\(^x\) = 0.25
A
-\(\frac{1}{2}\)
B
\(\frac{1}{4}\)
C
-\(\frac{1}{4}\)
D
\(\frac{1}{2}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
16\(^x\) = 0.25
16\(^x\) = \(\frac{25}{100} = \frac{1}{4}\)
4(\(^2)^x\) = 4\(^{-1}\)
2x = -1
x = \(\frac{-1}{2}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #70177)
Mathematics
UTME / JAMB 2024
Indices, Logarithms & Surds
Solution
Simplify \(\frac{ 5 + \sqrt{7}}{3 + \sqrt{7}}\)
A
17 - \(\sqrt{7}\)
B
4 - \(\sqrt{7}\)
C
7 - \(\sqrt{7}\)
D
15 - \(\sqrt{7}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\frac{ 5 + \sqrt{7}}{3 + \sqrt{7}}\)
multiply the denominator and the numerator by the conjugate of 3 + \(\sqrt{7}\) → 3 - \(\sqrt{7}\)
\(\frac{ 5 + \sqrt{7}}{3 + \sqrt{7}}\) x \(\frac{3 - \sqrt{7}}{3 - \sqrt{7}}\)
\(\frac{15 - 5\sqrt{7} + 3\sqrt{7} - 7}{3^2 - (\sqrt{7})^2}\)
\(\frac{8 - 2\sqrt{7}}{9 - 7}\) = \(\frac{ 8 - 2\sqrt{7}}{2}\)
= 4 - \(\sqrt{7}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #70251)
Mathematics
UTME / JAMB 2024
Indices, Logarithms & Surds
Solution
(\(\sqrt{a} +\sqrt{8a})^2\) = 54 + b\(\sqrt{2}\), a and b are positive integers. Find the value of a and the value of b.
A
a = 24, b = 6
B
a = 6, b = 2
C
a = 6, b = 24
D
a = 2, b = 6
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
(\(\sqrt{a} +\sqrt{8a})^2\) = 54 + b\(\sqrt{2}\)
(\(\sqrt{a} + \sqrt{8a}\))(\(\sqrt{a} + \sqrt{8a}\))
a + 4a\(\sqrt{2} + 8a = 54 + b\sqrt{2}\)
9a + 4a\(\sqrt{2}\) = 54 + b\(\sqrt{2}\)
comparing both sides
9a = 54, so that a = 6
4a = b
b = 4 x 6 = 24.
Source: Myschool Past Questions Archive (Record #71530)
Mathematics
WAEC / WASSCE 2024
Indices, Logarithms & Surds
Solution
Multiply 3.4 x 10\(^{-5}\) by 7.1 x 10\(^8\) and leave the answer in standard form.
A
2.414 x 10\(^2\)
B
2.414 x 10\(^3\)
C
2.414 x 10\(^4\)
D
2.414 x 10\(^5\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
3.4 x 10\(^{-5}\) by 7.1 x 10\(^8\) = ( 3.4 x 7.1) x 10\(^{-5 + 8}\)
= 24.14 x 10\(^3\)
= 2.414 x 10\(^4\)
Source: Myschool Past Questions Archive (Record #71740)
Mathematics
WAEC / WASSCE 2024
Indices, Logarithms & Surds
Solution
Express in index form: log\(_a^x\) + log\(_a^y\) = 3
A
x + y = 3
B
xy = 3
C
xy = a\(^3\)
D
x + y = a\(^3\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
According to the laws of logarithms: log\(_a^x\) + log\(_a^y\) = 3
= log\(_a^{xy}\) =3 and this in index form
= xy = a\(^3\)
Source: Myschool Past Questions Archive (Record #71751)
Mathematics
WAEC / WASSCE 2024
Indices, Logarithms & Surds
Solution
If (3 - 4\(\sqrt{2}\))(1 + 3\(\sqrt{2}\)) = a + b\(\sqrt{2}\), find the value of b
A
-5
B
5
C
-21
D
21
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
(3 - 4\(\sqrt{2}\))(1 + 3\(\sqrt{2}\)) = a + b\(\sqrt{2}\),
3 + 9\(\sqrt{2} - 4\sqrt{2} - (4\sqrt{2} \times 3\sqrt{2}) = a + b\sqrt{2}\)
3 + 5\(\sqrt{2} - (4 \times 3\sqrt{2} \times \sqrt{2}) = a + b\sqrt{2}\)
3 + 5\(\sqrt{2} - (12 \times 2) = a + b\sqrt{2}\)
3 + 5\(\sqrt{2} - 24 = a + b\sqrt{2}\)
-21 + 5\(\sqrt{2}\) = a + b\(\sqrt{2}\)
Comparing both sides, we have b = 5
Source: Myschool Past Questions Archive (Record #71760)
Mathematics
WAEC / WASSCE 2024
Indices, Logarithms & Surds
Solution
If log\(_3^{2x - 1}\) = 5, find the value of x
A
8
B
16
C
64
D
122
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
log\(_3^{2x - 1}\) = 5 in index form becomes 3\(^5\) = 2x - 1
2x - 1 = 243
2x = 243 + 1 = 244
x = \(\frac{244}{2}\) = 122
Source: Myschool Past Questions Archive (Record #71765)
Mathematics
WAEC / WASSCE 2024
Indices, Logarithms & Surds
Diagram
Solution
In the diagram above, O is the centre of the circle. If | \(\overline{OA}\) = 25 cm and |\(\overline{AB}\) = 40 cm, find |\(\overline{OH}\)|
Attached Figure / Diagram
A
15 cm
B
20 cm
C
25 cm
D
30 cm
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Line OH divides Line AB into two halves, therefore, Line AH = Line HB = 20cm
Considering \(\triangle\) AOH
(\(\overline{OH})^2\) = 25\(^2\) - 20\(^2\) = 625 - 400 = 225
Taking the square root of both sides
(\(\overline{OH}\) = \(\sqrt{225}\) = 15 cm
Source: Myschool Past Questions Archive (Record #71802)
Mathematics
WAEC / WASSCE 2024
Indices, Logarithms & Surds
Diagram
Solution
In the diagram above, < SQR = 52º and < PRT = 16º. Find the value of the angle marked y
Attached Figure / Diagram
A
64\(^0\)
B
68\(^0\)
C
112\(^0\)
D
128\(^0\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Source: Myschool Past Questions Archive (Record #71824)
Mathematics
WAEC / WASSCE 2024
Indices, Logarithms & Surds
Diagram
Solution
Find, correct to the nearest whole number, the value of h in the diagram above.
Attached Figure / Diagram
A
15 m
B
22 m
C
23 m
D
18 m
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
From the diagram on the right-hand side above,
x\(^2\) = 20\(^2\) - 19\(^2\) = 39 ( from Pythagoras theorem)
x = \(\sqrt{39}\) = 6.245m
As can be seen from the diagram on the right-hand side above,
h = x + 17 = 6.245 + 17 = 23.245 m ≈ 23 m(to the nearest whole number)
Source: Myschool Past Questions Archive (Record #71828)
Mathematics
UTME / JAMB 2023
Indices, Logarithms & Surds
Diagram
Solution
Find the value of the angle marked x in the diagram above
Attached Figure / Diagram
A
60\(^0\)
B
45\(^0\)
C
90\(^0\)
D
30\(^0\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(PR^2 = PQ^2 + RQ^2 - 2(PQ)(RQ)cos Q\)
\(\implies cos Q = \frac{PQ^2 + RQ^2 - PR^2}{2(PQ)(RQ)}\)
\(\implies cos Q = \frac{8^2 + 5^2 - 7^2}{2\times8\times5}\)
\(\implies cos Q = \frac{64 + 25 - 49}{80}\)
\(\implies cos Q = \frac{40}{80} = 0.5\)
\(\implies Q = cos^{-1} (0.5) = 60^0\)
\(\therefore x = 60^0\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #67385)
Mathematics
UTME / JAMB 2023
Indices, Logarithms & Surds
Solution
Evaluate: 16\(^{0.16}\) × 16\(^{0.04}\) × 2\(^{0.2}\)
A
2
B
0
C
2\(^0\)
D
\(\frac{1}{2}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
16\(^{0.16}\) \times 16\(^{0.04}\) \times 2\(^{0.2}\)
=2\(^{4(0.16)}\) \times 2\(^{4(0.04)}\) \times 2\(^{0.2}\)
=2\(^{0.64}\) \times 2\(^{0.16}\) \times 2\(^{0.2}\)
=2\(^{0.64\times0.16\times0.2}\)
=2\(^1\)
2
Source: WAEC / JAMB / NECO Classroom Archive (Record #67244)
Mathematics
WAEC / WASSCE 2023
Indices, Logarithms & Surds
Solution
Solve \(2^{5x} \div 2^x = \sqrt[5]{2^{10}}\)
A
\(\frac{3}{2}\)
B
\(\frac{1}{2}\)
C
\(\frac{1}{3}\)
D
\(\frac{5}{3}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(2^{5x} \div 2^x = \sqrt[5]{2^{10}}\)
applying the laws of indices
\(2^{5x - x} = 2^{10(1/5)}\)
\(2^{4x} = 2^{10(1/5)}\)
\(2^{4x} = 2^2\)
Equating the powers
then 4x = 2
therefore, x = \(\frac{2}{4}\) = \(\frac{1}{2}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #69048)