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Mathematics
WAEC / WASSCE 1999
Indices, Logarithms & Surds
Solution
Simplify log\(_7\) 8 - log\(_7\) 2 + log\(_7\) 4.
A
0
B
\(2log_7 2\)
C
\(3log_7 2\)
D
\(4log_7 2\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
log\(_7\) 8 - log\(_7\) 2 + log\(_7\) 4
= log\(_7\) (8/2 x 4)
= log\(_7\) 16
= 4 log\(_7\) 2
Source: Myschool Past Questions Archive (Record #26381)
Mathematics
WAEC / WASSCE 1999
Indices, Logarithms & Surds
Solution
If \(K\sqrt{28}+\sqrt{63}-\sqrt{7}=0\), find K.
A
-2
B
-1
C
1
D
2
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(K\sqrt{28}+\sqrt{63}-\sqrt{7}=0\\
2K\sqrt{7}+3\sqrt{7}-\sqrt{7}=0\\
2K\sqrt{7}=-2\sqrt{7}\\
K=\frac{-2\sqrt{7}}{2\sqrt{7}}\\
K=-1\)
Source: Myschool Past Questions Archive (Record #26382)
Mathematics
WAEC / WASSCE 1999
Indices, Logarithms & Surds
Solution
From a set \(A = [3, \sqrt{2}, 2\sqrt{3}, \sqrt{9}, \sqrt{7}]\), a number is selected at random. Find the probability that is a rational number
A
\(\frac{1}{5}\)
B
\(\frac{2}{5}\)
C
\(\frac{3}{5}\)
D
\(\frac{4}{5}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(A = {3, \sqrt{2}, 2\sqrt{3}, \sqrt{9}, \sqrt{7}}\)
n(A) = 5
Let the rational nos = R
n(R) = 2 (3, \(\sqrt{9}\))
P(R) = 2/5
Source: Myschool Past Questions Archive (Record #26383)
Mathematics
WAEC / WASSCE 1999
Indices, Logarithms & Surds
Solution
Given that \(81\times 2^{2n-2} = K, find \sqrt{K}\)
A
\(4.5\times 2^{n}\)
B
\(4.5\times 2^{2n}\)
C
\(9\times 2^{n-1}\)
D
\(9\times 2^{2n}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(K = 81 \times 2^{2n - 2}\)
\(\sqrt{K} = \sqrt{81 \times 2^{2n - 2}}\)
= \(9 \times 2^{n - 1}\)
Source: Myschool Past Questions Archive (Record #26396)
Mathematics
WAEC / WASSCE 1999
Indices, Logarithms & Surds
Solution
If \(tan x = \frac{1}{\sqrt{3}}\), find cos x - sin x such that \(0^o \leq x \leq 90^o\)
A
\(\frac{\sqrt{3}+1}{2}\)
B
\(\frac{2}{\sqrt{3}+1}\)
C
\(\frac{\sqrt{3}-1}{2}\)
D
\(\frac{2}{\sqrt{3}-1}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\cos x = \frac{\sqrt{3}}{2}\)
\(\sin x = \frac{1}{2}\)
\(\cos x - \sin x = \frac{\sqrt{3} - 1}{2}\)
Source: Myschool Past Questions Archive (Record #26399)
Mathematics
WAEC / WASSCE 1999
Indices, Logarithms & Surds
Solution
A pole of length L leans against a vertical wall so that it makes an angle of 60o with the horizontal ground. If the top of the pole is 8m above the ground, calculate L.
A
\(16\sqrt{3}m\)
B
\(4\sqrt{3}m\)
C
\(\frac{\sqrt{3}}{16}\)
D
\(\frac{16\sqrt{3}}{3}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(sin 60 = \frac{8}{L} = 8 \div \frac{\sqrt{3}}{2}; L = \frac{8}{sin 60}=\frac{16}{\sqrt{3}}\)
When we rationalize gives \(\frac{16\sqrt{3}}{3}\)
Source: Myschool Past Questions Archive (Record #26403)
Mathematics
WAEC / WASSCE 1999
Indices, Logarithms & Surds
Solution
Simplify 3.72 x 0.025 and express your answer in the standard form
A
\(9.3\times 10^3\)
B
\(9.3\times 10^2\)
C
\(9.3\times 10^{-2}\)
D
\(9.3\times 10^{-3}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(3.72 \times 0.025 = 0.093 = 9.3\times 10^{-2}\)
Source: Myschool Past Questions Archive (Record #26406)
Mathematics
WAEC / WASSCE 1999
Indices, Logarithms & Surds
Solution
(a) Simplify \((\frac{4}{25})^{-\frac{1}{2}} \times 2^{4} \div (\frac{15}{2})^{-2}\)
(b) Evaluate \(\log_{5} (\frac{3}{5}) + 3 \log_{5} (\frac{5}{2}) - \log_{5} (\frac{81}{8})\).
medium Difficulty
Verified Correct Answer: Option
Step-by-Step Mathematical Solution
(a) \((\frac{4}{25})^{-\frac{1}{2}} \times 2^{4} \div (\frac{15}{2})^{-2}\)
= \((\frac{25}{4})^{\frac{1}{2}} \times 2^{4} \div (\frac{2}{15})^{2}\)
= \(\frac{5}{2} \times 16 \times \frac{225}{4} = 2250\)
(b) \(\log_{5} (\frac{3}{5}) + 3\log_{5} (\frac{15}{2}) - \log_{5} (\frac{81}{8})\)
= \(\log_{5} 3 - \log_{5} 5 + 3\log_{5} 15 - 3\log_{5} 2 - \log_{5} 81 + \log_{5} 8\)
= \(\log_{5} 3 - \log_{5} 5 + 3\log_{5} (3 \times 5) - 3\log_{5} 2 - \log_{5} 3^{4} + \log_{5} 2^{3}\)
= \(\log_{5} 3 - \log_{5} 5 + 3\log_{5} 3 + 3\log_{5} 5 - 3\log_{5} 2 - 4\log_{5} 3 + 3\log_{5} 2\)
= \(2\log_{5} 5 \)
= \(2\)
Source: Myschool Past Questions Archive (Record #54376)
Mathematics
WAEC / WASSCE 1998
Indices, Logarithms & Surds
Solution
If log\(_{10}\) q = 2.7078, what is q?
A
5102
B
849.9
C
510.2
D
84.99
E
51.02
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
q = 10\(^{2.7078}\)
Antilog of 2.7078 = 510.2
Source: Myschool Past Questions Archive (Record #22095)
Mathematics
WAEC / WASSCE 1998
Indices, Logarithms & Surds
Solution
If log\(_{10}\) a = 4; what is a?
A
0.4
B
40
C
400
D
1000
E
10000
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
log\(_{10}\) a = 4
a = 10\(^4\)
= 10000
Source: Myschool Past Questions Archive (Record #22098)
Mathematics
WAEC / WASSCE 1998
Indices, Logarithms & Surds
Solution
Simplify \(\frac{8^{\frac{2}{3}} \times 27^{\frac{-1}{3}}}{64^{\frac{1}{3}}}\)
A
-3
B
\(\frac{1}{9}\)
C
\(\frac{1}{3}\)
D
\(\frac{27}{8}\)
E
4
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{8^{\frac{2}{3}} \times 27^{\frac{-1}{3}}}{64^{\frac{1}{3}}}\)
Calculating each part:
1. \(8 = 2^3 \Rightarrow 8^{\frac{2}{3}} = 4\)
2. \(27 = 3^3 \Rightarrow 27^{\frac{-1}{3}} = \frac{1}{3}\)
3. \(64 = 4^3 \Rightarrow 64^{\frac{1}{3}} = 4\)
Now substituting these values:
\(\frac{4 \times \frac{1}{3}}{4} = \frac{1}{3}\)
Thus, the simplified expression is: \(\frac{1}{3}\)
Source: Myschool Past Questions Archive (Record #24003)
Mathematics
WAEC / WASSCE 1998
Indices, Logarithms & Surds
Diagram
Solution
In the diagram above, O is the center if the two concentric circle of radii 13cm and 10cm respectively. Find the area of the shaded portion in the sector with angle 120^\circ at the center
Attached Figure / Diagram
A
\(\frac{1}{3}\pi cm^2\)
B
\(\pi cm^2\)
C
\(3\pi cm^2\)
D
\(23\pi cm^2\)
E
\(46\pi cm^2\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{120\pi}{360}(R^2 - r^2)\)
= \(\frac{1}{3}\times \pi (13^2 - 10^2)\)
= \(\frac{1}{3}\times \pi \times 69\) = 23\(\pi cm^2\)
Source: Myschool Past Questions Archive (Record #26340)
Mathematics
WAEC / WASSCE 1998
Indices, Logarithms & Surds
Solution
Evaluate \(\sqrt{20}\times (\sqrt{5})^3\)
A
10
B
20
C
25
D
50
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\sqrt{20}\times (\sqrt{5})^3\)
2\(\sqrt{5}\times \sqrt{5}\times \sqrt{5}\times \sqrt{5}=2\times 5\times 5 = 50\)
Source: Myschool Past Questions Archive (Record #26373)
Mathematics
WAEC / WASSCE 1998
Indices, Logarithms & Surds
Solution
It is observed that \(1 + 3 = 2^2, 1 + 3 + 5 = 3^2, 1 + 3 + 5 + 7 = 4^2\).
If 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = P\(^2\) find P
A
6
B
7
C
8
D
9
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = 64
where 64 = 8\(^2\)
That is, P is 8
Source: Myschool Past Questions Archive (Record #26375)
Mathematics
WAEC / WASSCE 1998
Indices, Logarithms & Surds
Solution
Evaluate \(3.0\times 10^1 - 2.8\times 10^{-1}\)leaving the answer in standard form
A
\(2\times 10^{-1}\)
B
\(2\times 10^{2}\)
C
\(2.972 \times 10^{1}\)
D
\(2.972 \times 10^{2}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(3.0\times 10^1 - 2.8\times 10^{-1}\) = 30 - 0.28 = 29.72 = 2.972 x 10\(^1\)
Source: Myschool Past Questions Archive (Record #26376)