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Mathematics
UTME / JAMB 2019
Indices, Logarithms & Surds
Solution
Find the distance between the points C(2, 2) and D(5, 6).
A
13 units
B
7 units
C
12 units
D
5 units
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
= \(\sqrt{(5 - 2)^2 + (6 - 2)^2}\)
= \(\sqrt{3^2 + 4^2}\)
= \(\sqrt{9 + 16}\)
= \(\sqrt{25}\)
= 5 units
Source: Myschool Past Questions Archive (Record #55435)
Mathematics
WAEC / WASSCE 2019
Indices, Logarithms & Surds
Solution
(a) If logo a = 1.3010 and log\(_{10}\)b - 1.4771. find the value of ab
(b)
In the diagram. O is the centre of the circle,< ACB = 39\(^o\) and < CBE = 62\(^o\). Find: (i) the interior angle AOC;
(ii) angle BAC.
medium Difficulty
Verified Correct Answer: Option
Step-by-Step Mathematical Solution
(a) finding a = 10\(^{1.3010}\) and b = 10\(^{1.4771}\)
Then, ab = 10\(^{1.3010}\) x 10\(^{1.4771}\) = 10\(^{2.4771}\) = 599.9
(b)(i) they were expected to find < ABC = 180^\circ - 62^\circ = 118^\circ
Exterior < AOC a 2 x 118^\circ - 236^\circ (< at centre is twice angle at the circumference)
Interior < AOC = 360^\circ - 236^\circ = 124^\circ(angle at a point) as required.
(b)(ii) < BAC in 180^\circ - 39^\circ - 118^\circ = 23^\circ (sum of angles of a triangle)
Source: Myschool Past Questions Archive (Record #56422)
Mathematics
WAEC / WASSCE 2019
Indices, Logarithms & Surds
Solution
(a) Without using mathematical tables or calculator, simplify: \(\frac{log_28 + \log_216 - 4 \log_22}{\log_416}\)
(b) If 1342\(_{five}\) - 241\(_{five}\) = x\(_{ten}\), find the value of x.
medium Difficulty
Verified Correct Answer: Option
Step-by-Step Mathematical Solution
(a) \(\frac{\log_28 + \log_216 - 4\log_22}{\log_416}\) = \(\frac{\log_22^3 + \log_2 2^4 - 4\log_22}{\log_44^2}\)
= \(\frac{3 \log_2 2 + 4\log_22 - 4 \log_2^2}{2 \log 4^4}\)
But log\(_2\) 2 = \(\log_44 = 1\)
Then, \(\frac{\log_28+\log_216 - 4 \log_2^2}{\log_416}\) = \(\frac{3 + 4 - 4}{2}\) = 1\(\frac{1}{2}\)
(b) Subtract 241\(_{five}\) to get 1101\(_{five}\). Thereafter, converting to base ten to find the value of x = (5\(^3\) x 1) + (5\(^2\) x 1 + (5\(^1\) x 0) + (5\(^o\) x 1) = 125 + 25 + 0 + 1 = 151
(b) They subtracted 241\(_{five}\) from 1342\(_{five}\) to get 1101\(_{five}\). Thereafter, converting to base ten to find the value of x = (5\(^3\) x 1) + (5\(^2\) x 1) + (5\(^1\) x 0) + (5^\circx 1) = 125 + 25 + + 1 = 151.
Source: Myschool Past Questions Archive (Record #56424)
Mathematics
WAEC / WASSCE 2019
Indices, Logarithms & Surds
Solution
(a) Given that 110\(_x\) - 40\(_{five}\). find the value of x
(b) Simplify \(\frac{15}{\sqrt{75}} + \(\sqrt{108}\) + \(\sqrt{432}\), leaving the answer in the form a\(\sqrt{b}\), where a and b are positive integers.
medium Difficulty
Verified Correct Answer: Option
Step-by-Step Mathematical Solution
(a)110\(_x\) - 4\(0_5\)
1 x \(x^2}\) + 1 x \(x^1\) + 0 x \(x^o\)
x = 4 x 5\(^1\) + 0 x 5\(^o\)
x\(^2\) + x = 4 x 5 + 0
x\(^2\) + x - 20 = 0
(x - 4)(x + 5) = 0
x - 4 = 0 or x + 5 = 0
x = 4 or x = -5
x = 4
(b) Simplify \(\frac{15}{\sqrt{75}}\) + \(\sqrt{108}\) + \(\sqrt{432}\)
= \(\frac{15}{\sqrt{25 \times 3}}\) + \(\sqrt{36 \times 3}\)
= \(\frac{15}{5 \sqrt{3}\) + 6\(\sqrt{3}\) + 12\(\sqrt{3}\)
= \(\frac{15 \sqrt{3}}{15 \times \sqrt{3} \times \sqrt{3}}\) + 18\(\sqrt{3}\)
= \(\frac{15\sqrt{3}}{15}\) + 18\(\sqrt{3}\)
\(\sqrt{3}\) + 18\(\sqrt{3}\) = 19\(\sqrt{3}\)
Source: Myschool Past Questions Archive (Record #56486)
Mathematics
WAEC / WASSCE 2019
Indices, Logarithms & Surds
Solution
Evaluate; \(\frac{\log_3 9 - \log_2 8}{\log_3 9}\)
A
-\(\frac{1}{3}\)
B
\(\frac{1}{2}\)
C
\(\frac{1}{3}\)
D
-\(\frac{1}{2}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{\log_3 9 - \log_2 8}{\log_3 9}\)
= \(\frac{\log_3 3^2 - \log_2 2^3}{\log_3 3^2}\)
= \(\frac{2 -3}{2}\)
= \(\frac{-1}{2}\)
Source: Myschool Past Questions Archive (Record #57125)
Mathematics
WAEC / WASSCE 2019
Indices, Logarithms & Surds
Solution
Evaluate: 2\(\sqrt{28} - 3\sqrt{50} + \sqrt{72}\)
A
4\(\sqrt{7} - 21 \sqrt{2}\)
B
4\(\sqrt{7} - 11 \sqrt{2}\)
C
4\(\sqrt{7} - 9 \sqrt{2}\)
D
4\(\sqrt{7} + \sqrt{2}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
2\(\sqrt{28} - 3\sqrt{50} + \sqrt{22}\)
4\(\sqrt{7} - 15\sqrt{2} + 6\sqrt{2}\)
6\(\sqrt{7} - 9\sqrt{2}\)
Source: Myschool Past Questions Archive (Record #57156)
Mathematics
WAEC / WASSCE 2019
Indices, Logarithms & Surds
Solution
If m : n = 2 : 1, evaluate \(\frac{3m^2 - 2n^2}{m^2 + mn}\)
A
\(\frac{4}{3}\)
B
\(\frac{5}{3}\)
C
\(\frac{3}{4}\)
D
\(\frac{3}{5}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
m = 2, n = 1
\(\frac{3m^2 - 2n^2}{m^2 _ mn}\)
= \(\frac{3(2)^2 - 2(1)^2}{2^2 + 2(1)}\)
= \(\frac{12 - 2}{4 + 2} = \frac{10}{6}\)
= \(\frac{5}{3}\)
Source: Myschool Past Questions Archive (Record #57161)
Mathematics
WAEC / WASSCE 2019
Indices, Logarithms & Surds
Solution
Simplify: \(\log_{10}\) 6 - 3 log\(_{10}\) 3 + \(\frac{2}{3} \log_{10} 27\)
A
3 \(\log_{10}^2\)
B
\(\log_{10}^2\)
C
\(\log_{10}^3\)
D
2 \(\log_{10}^3\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
log\(_{10}\) 6 - log\(_{10}\)3\(^3\) + log\(_{10}\) (\(\sqrt[3]{27}\))\(^2\)
= log \(_{10}\) 6 - log \(_{10}\) 27 + log\(_{10}\) 9
= log\(_{10}\) \(\frac{6 \times 9}{27}\)
= log\(_{10}\)2
Source: Myschool Past Questions Archive (Record #57197)
Mathematics
WAEC / WASSCE 2019
Indices, Logarithms & Surds
Solution
If (0.25)\(^y\) = 32, find the value of y.
A
y = - \(\frac{5}{2}\)
B
y = -\(\frac{3}{2}\)
C
y = \(\frac{3}{2}\)
D
y = \(\frac{5}{2}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
(0.25)\(^y\) = 32
2\(^{-2y}\) = 3\(^{2}\)
2 - 2y = 5
y = - \(\frac{5}{2}\)
Source: Myschool Past Questions Archive (Record #57211)
Mathematics
WAEC / WASSCE 2019
Indices, Logarithms & Surds
Solution
If 2\(^{a}\) = \(\sqrt{64}\) and \(\frac{b}{a}\) = 3, evaluate a\(^2 + b^{2}\)
A
250
B
160
C
90
D
48
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
2\(^a\) = \(\sqrt{64}\)
2\(^a\) = 8
2\(^a\) = 2\(^3\)
a = 3
b = 3\(^a\)
b = 3 x 3 = 9
a\(^2\) + b\(^2\) = 3\(^2\) + 9\(^2\)
= 9 + 81 = 90
Source: Myschool Past Questions Archive (Record #57238)
Mathematics
WAEC / WASSCE 2019
Indices, Logarithms & Surds
Solution
If log\(_x\) 2 = 0.3, evaluate log\(_x\) 8.
A
2.4
B
1.2
C
0.9
D
0.6
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
log\(_x\)2 = 0.3
log\(_x\)8 = log\(_x\)2\(^3\) = 3 log\(_x\)2
= 3 x 0.3
= 0.9
Source: Myschool Past Questions Archive (Record #57255)
Mathematics
WAEC / WASSCE 2019
Indices, Logarithms & Surds
Solution
The foot of a ladder is 6m from the base of an electric pole. The top of the ladder rest against the pole at a point 8m above the ground. How long is the ladder?
A
14m
B
12m
C
10m
D
7m
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
H\(^2\) = 8\(^2\) + 6\(^2\) + 6\(^2\)
H\(^2\) = 64 + 36 = 100
H = \(\sqrt{100}\) = 10m
Source: Myschool Past Questions Archive (Record #57361)
Mathematics
UTME / JAMB 2018
Indices, Logarithms & Surds
\(\frac{0.00256 \times 0.0064}{0.025 \times 0.08}\)
A
8.8 x 10\(^{-1}\)
B
8.8 x 10\(^{-2}\)
C
8.2 x 10\(^{-3}\)
D
8.8 x 10\(^{3}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option C.
Source: Myschool Past Questions Archive (Record #47007)
Mathematics
UTME / JAMB 2018
Indices, Logarithms & Surds
Solution
Evaluate (2\sqrt3 - 4) (2\sqrt3 + 4)
A
-4
B
-2
C
2
D
4
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
2\sqrt3 - 4) ( 2\sqrt3 + 4)
= 12 + 8\sqrt3 - 8\sqrt3 – 16
= 12 – 16
= -4
The two expressions in the bracket are conjugate of each other
Source: Myschool Past Questions Archive (Record #47565)
Mathematics
UTME / JAMB 2018
Indices, Logarithms & Surds
Solution
Evaluate log\(_2\) 8 – log\(_3\) \(\frac{1}{9}\)
A
-1 1\(\frac{1}{2}\)
B
-1
C
1
D
5
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
log\(_2\) 8 – log\(_3\) \(\frac{1}{9}\)
= log \(_2\) 2\(^3\) – log\(_3\) 9\(^{-1}\)
= log\(_2\) 2\(^3\) – log\(_3\) 3\(^{-2}\)
Based on law of logarithm
= 3 log\(_2\) 2 – (-2 log\(_3\) 3)
But log\(_2\) 2 = 1,
log\(_3\) 3 = 1
So, = 3 + 2
= 5
Source: Myschool Past Questions Archive (Record #47571)