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Mathematics
WAEC / WASSCE 2008
Indices, Logarithms & Surds
Solution
If tan x = 1, evaluate sin x + cos x, leaving your answer in the surd form
A
2\(\sqrt{2}\)
B
\(\frac{1}{2} \sqrt{2}\)
C
\(\sqrt{2}\)
D
2
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
tan x = 1; x = tan-1(10 = 45o
sin x + cos x
= sin 45o + cos 45o
= \(\frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2}\)
= \(\frac{\sqrt{2} + \sqrt{2}}{2}\)
= \(\frac{2\sqrt{2}}{2}\)
= \(\sqrt{2}\)
Source: Myschool Past Questions Archive (Record #36363)
Mathematics
WAEC / WASSCE 2008
Indices, Logarithms & Surds
Solution
If \(2^n = 128\), find the value of \(2^{n - 1})(5^{n - 2})\)
A
5(106)
B
2(106)
C
5(105)
D
2(105)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(2^n\) = 128
\(2^n = 2^7\)
n = 7
(2\(^{n - 1}\))(5\(^{n - 2}\)), then, put n = 7
= (2\(^{7 - 1}\))(5\(^{7 - 2}\))
= (\(2^6\))(\(2^5\))
= \(2^1 \times 2^5 \times 2^5\)
= 2 x (\(2 \times 5)^5\)
= 2(\(10^5\))
Source: Myschool Past Questions Archive (Record #36366)
Mathematics
WAEC / WASSCE 2008
Indices, Logarithms & Surds
Solution
Simplify \(\frac{\log \sqrt{8}}{\log 4 - \log 2}\)
A
\(\frac{2}{3}\)
B
\(\frac{1}{2} \log 2\)
C
\(\frac{3}{2}\)
D
\(\log 2\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{\log\sqrt{8}}{\log 4 - \log 2} = \frac{\log 8\frac{1}{2}}{\log (\frac{4}{2})}\)
= \(\frac{8 \frac{1}{2}}{\log (\frac{4}{2})}\)
= \(\frac{\frac{1}{2} \log 2^3}{\log 2}\)
= \(\frac{3}{2} \frac{\log 2}{\log 2}\)
= \(\frac{3}{2}\)
Source: Myschool Past Questions Archive (Record #36368)
Mathematics
WAEC / WASSCE 2008
Indices, Logarithms & Surds
Diagram
Solution
In the diagram, o. If q2 = 25 - r2. Find the value of p
Attached Figure / Diagram
A
3
B
4
C
5
D
6
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Given q2 = 25 - r2.....(1)
from Pythagoras theorem
p2 = q2 + r2....(2)
put(1) into (2)
p2 = 25 - r2 + r2
p2 = 25
p = \(\sqrt{25}\)
Source: Myschool Past Questions Archive (Record #36405)
Mathematics
NECO SSCE 2008
Indices, Logarithms & Surds
Solution
Simplify the expression: \(Log_{4}16\) + \(Log_{3}27\) + \(Log_{8}4096\)
A
-9
B
\(\frac{1}{3}\)
C
\(\frac{1}{9}\)
D
3
E
9
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
WHERE:
\(Log_{4}16\) = 2
\(Log_{3}27\) = 3
\(Log_{8}4096\) = 4
: 2 + 3 + 4 = 9
Source: Myschool Past Questions Archive (Record #42536)
Mathematics
NECO SSCE 2008
Indices, Logarithms & Surds
Rationalize the expression \(\frac{(7 - \sqrt{3})}{(13 - \sqrt{3})}\)
A
(44 + 3\(\sqrt{3}\)) ÷ 83
B
(44 + 2\(\sqrt{3}\)) ÷ 83
C
(44 - 3\(\sqrt{3}\)) ÷ 83
D
(44 - 4\(\sqrt{3}\)) ÷ 83
E
(44 - 2\(\sqrt{3}\)) ÷ 83
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 #42649)
Mathematics
NECO SSCE 2008
Indices, Logarithms & Surds
Find the value of log\(_{\sqrt{3}}\) 81
A
81
B
16
C
8
D
3
E
\(\sqrt{3}\)
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 #42669)
Mathematics
WAEC / WASSCE 2008
Indices, Logarithms & Surds
Solution
(a) Without using calculator or tables, find the value of \(\log 3.6\) given that \(\log 2 = 0.3010, \log 3 = 0.4771\) and \(\log 5 = 0.6990\).
(b) If all numbers in the equation \(\frac{y}{y + 101} = \frac{11}{10010}\) are in base two, solve for y.
medium Difficulty
Verified Correct Answer: Option
Step-by-Step Mathematical Solution
(a) \(\log 3.6 = \log (\frac{18}{5})\)
\(\log 18 - \log 5 = \log (2 \times 3^{2}) - \log 5\)
\(\log 2 + \log 3^{2} - \log 5 = \log 2 + 2\log 3 - \log 5\)
= \(0.3010 + 2(0.4771) - 0.6990\)
= \(0.3010 + 0.9542 - 0.6990\)
= \(0.5562\).
(b) \(\frac{y}{y + 101} = \frac{11}{10010}\) (all in base 2)
Cross multiplying,
\(11(y + 101) = 10010y\)
\(11y + 1111 = 10010y\)
\(10010y - 11y = 1111\)
\(1111y = 1111\)
\(y = 1\).
Source: Myschool Past Questions Archive (Record #52935)
Mathematics
WAEC / WASSCE 2008
Indices, Logarithms & Surds
Solution
(a) A pentagon is such that one of its exterior sides is 60^\circ. Two others are (90 - m)^\circ each while the remaining angles are (30 + 2m)^\circ each. Find the value of m.
(b)
In the diagram, PQR is a straight line, \(\overline{QR} = \sqrt{3} cm\) and \(\overline{SQ} = 2 cm\). Calculate, correct to one decimal place, < PQS.
medium Difficulty
Verified Correct Answer: Option
Step-by-Step Mathematical Solution
The sum of exterior angles = 360^\circ
\(60^\circ + 2(90 - m)^\circ + 2(30 + 2m)^\circ = 360^\circ\)
\(60^\circ + 180^\circ - 2m^\circ + 60^\circ + 4m^\circ = 360^\circ\)
\(300^\circ + 2m = 360^\circ\)
\(\implies 2m = 360^\circ - 300^\circ = 60^\circ\)
\(m = 30^\circ\)
(b)
In \(\Delta QRS, \cos Q = \frac{\sqrt{3}}{2}\)
\(\cos Q = 0.8660 \implies Q = 30^\circ\)
\(\therefore < SQR = 30^\circ^\)
\(< PQS = 180^\circ - 30^\circ \) (angles on a straight line = 180^\circ)
\(< PQS = 150^\circ\)
Source: Myschool Past Questions Archive (Record #52938)
Mathematics
WAEC / WASSCE 2008
Indices, Logarithms & Surds
Solution
(a) If \(2^{x + y} = 16\) and \(4^{x - y} = \frac{1}{32}\), find the value of x and y.
(b) P, Q and R are related in such a way that \(P \propto \frac{Q^{2}}{R}\). When P = 36, Q = 3 and R = 4. Calculate Q when P = 200 and R = 2.
medium Difficulty
Verified Correct Answer: Option
Step-by-Step Mathematical Solution
(a) \(2^{x + y} = 16 \implies 2^{x + y} = 2^{4}\)
\(\implies x + y = 4 ..... (1)\)
\(4^{x - y} = \frac{1}{32} \implies (2^{2})^{(x - y)} = 2^{-5}\)
\(\implies 2x - 2y = -5 .... (2)\)
From (1), x = 4 - y.
\(\therefore 2(4 - y) - 2y = -5\)
\(8 - 2y - 2y = -5 \implies -4y = - 5 - 8 = -13\)
\(y = \frac{13}{4}\)
\(x = 4 - \frac{13}{4} \)
= \(\frac{3}{4}\)
(b) \(P \propto \frac{Q^{2}}{R}\)
\(\implies P = \frac{kQ^{2}}{R}\)
\(k = \frac{PR}{Q^{2}}\)
\(k = \frac{36 \times 4}{9} = 16\)
\(\implies P = \frac{16Q^{2}}{R}\)
\(Q^{2} = \frac{PR}{k}\)
\(Q^{2} = \frac{200 \times 2}{16}\)
\(Q^{2} = 25\)
\(Q = \pm 5\).
Source: Myschool Past Questions Archive (Record #52944)
Mathematics
UTME / JAMB 2007
Indices, Logarithms & Surds
Solution
Find y, if \(\sqrt{12}-\sqrt{147}+y\sqrt{3} = 0\)
A
5
B
1
C
7
D
3
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\sqrt{12}\) -\(\sqrt{147}\) + y\(\sqrt{3}\) = 0
\(\sqrt{4\times 3}\) - \(\sqrt{49\times 3}\) + y\(\sqrt{3}\) = 0
2\(\sqrt{3}\) - 7\(\sqrt{3}\) + y\(\sqrt{3}\) = 0
y\(\sqrt{3}\) = 7\(\sqrt{3}\) - 2\(\sqrt{3}\)
y = \(\frac{5\sqrt{3}}{\sqrt{3}}\)
y = 5
Source: Myschool Past Questions Archive (Record #9235)
Mathematics
UTME / JAMB 2007
Indices, Logarithms & Surds
Solution
Find the value of x for which 2(32x-1) = 162
A
5/2
B
3/2
C
2/5
D
1/2
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
2(32x-1) = 162
32x-1 = 162/2
32x-1 = 81
32x-1 = 32
2x - 1 = 4 (equating the indices)
2x = 5
5/2
x =
Source: Myschool Past Questions Archive (Record #9238)
Mathematics
UTME / JAMB 2007
Indices, Logarithms & Surds
Solution
A man 40 m from the foot of a tower observes the angle of elevation of the tower to be 30º. Determine the height of the tower.
A
\(\frac{40\sqrt{3}}{3}m\)
B
20 m
C
40√3 m
D
40 m
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Tan 30 = \(\frac{h}{40}\)
\(\frac{1}{\sqrt{3}}=\frac{h}{40}\)
h\(\sqrt{3}\) = 40
h = \(\frac{40}{\sqrt{3}}\)
h = \(\frac{40}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}\)
h = \(\frac{40\sqrt{3}}{3}\)
Source: Myschool Past Questions Archive (Record #9251)
Mathematics
WAEC / WASSCE 2007
Indices, Logarithms & Surds
Find the LCM of \(2^{3}\times 3\times 5^{2}, 2\times 3^{2}\times 5 \hspace{1mm}and \hspace{1mm}2^{2}\times 3^{2}\times 5\)
A
\(2^{2}\times 3^{3}\times 5^{2}\)
B
\(2^{3}\times 3^{23}\times 5\)
C
\(2^{2}\times 3^{2}\times 5^{2}\)
D
\(2^{3}\times 3^{3}\times 5^{2}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option D.
Source: Myschool Past Questions Archive (Record #26718)
Mathematics
WAEC / WASSCE 2007
Indices, Logarithms & Surds
Solution
Simplify \((0.3\times 10^{5})\div (0.4\times 10^{7})\)leaving your answer in standard form
A
\(7.5\times 10^{-4}\)
B
\(7.5\times 10^{-3}\)
C
\(7.5\times 10^{-2}\)
D
\(7.5\times 10^{-1}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\((0.3\times 10^{5})\div (0.4\times 10^{7})\\
\frac{3}{10}\times 10^{5}\div \frac{4}{10}\times 10^{7}=3\times 10^{4}\div 4\times 10^{6}\\
\frac{3\times 10^{4}}{4\times 10^{7}}=\frac{3}{4}\times 10^{-2}=0.75\times 10^{-2}\\
7.5\times 10^{-3}\)
Source: Myschool Past Questions Archive (Record #26719)