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Mathematics
UTME / JAMB 2008
Permutations, Combinations & Probability
Diagram
Solution
The result of rolling a fair die 150 times is as summarized in the table above. What is the probability of obtaining a 5?
Attached Figure / Diagram
A
3/10
B
1/5
C
1/6
D
1/10
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Total possible outcome
12+18+x+30+2x+45 = 105+3x
∴105+3x = 150
3x = 150-105
3x = 45
x = 15
P(obtaining 5) = \(\frac{2x}{(105+3x)}\) But x= 15
=\(\frac{2(15)}{(105+3(15))}\)
=\(\frac{30}{(105+45)}\)
=\(\frac{30}{150}\)
=\(\frac{1}{5}\)
Source: Myschool Past Questions Archive (Record #9302)
Mathematics
WAEC / WASSCE 2008
Fractions, Decimals, Percentages & Approximations
Solution
A trader bought 100 tubers at 5 for N350.00. She sold them in sets of 4 for N290.00. Find her gain percent.
A
3.6%
B
3.5%
C
3.4%
D
2.55
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Cost price, c.p = \(\frac{100}{5}\) x N350 = N7000
Selling price, s.p = \(\frac{100}{5}\) x N290 = N7250
%Gain = \(\frac{S.p - C.p}{C.p}\) x 100%
= \(\frac{7250 - 7000}{7000}\) x 100% = \(\frac{250 \times 100}{7000}\)
= 3.6% (approx.)
Source: WAEC / JAMB / NECO Classroom Archive (Record #36334)
Mathematics
UTME / JAMB 2008
Binary Operations, Matrices & Determinants
Solution
Find the values of x and y respectively if
\(\begin{pmatrix} 1 & 0 \\ -1 & -1\\ 2 & 2 \end{pmatrix}\) + \(\begin{pmatrix} x & 1 \\ -1 & 0\\ y & -2 \end{pmatrix}\) = \(\begin{pmatrix} -2 & 1 \\ -2 & -1\\ -3 & 0 \end{pmatrix}\)
A
-3, -2
B
-5, -3
C
-2, -5
D
-3, -5
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\begin{pmatrix} 1 & 0 \\ -1 & -1\\ 2 & 2 \end{pmatrix}\) + \(\begin{pmatrix} x & 1 \\ -1 & 0\\ y & -2 \end{pmatrix}\) = \(\begin{pmatrix} -2 & 1 \\ -2 & -1\\ -3 & 0 \end{pmatrix}\)
therefore, (x, y) = (-3, -5) respectively
Source: WAEC / JAMB / NECO Classroom Archive (Record #29895)
Mathematics
UTME / JAMB 2008
Binary Operations, Matrices & Determinants
Solution
\(\begin{pmatrix} -2 & 1 \\ 2 & 3 \end{pmatrix}\) \(\begin{pmatrix}p & q \\ r & s\end{pmatrix}\) = \(\begin{pmatrix} 1 & 0 \\0 & 1 \end{pmatrix}\). What is the value of r?
A
-\(\frac{1}{8}\)
B
\(\frac{3}{8}\)
C
\(\frac{5}{8}\)
D
\(\frac{1}{4}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
-2p + r = 1.......(i)
2p + 3r = 0.......(ii)
r - 1 + 2p ........(iii)
2p + 3(1 + 2p) = 0
2p + 3(1 + 2p) = 0
2p + 3 + 6p = 0
3 - 8p = 0 \(\to\) 8p = 3
p = \(\frac{3}{8}\)
6 = 1 - 2 \(\frac{3}{8}\)
= 1 - \(\frac{6}{8}\)
\(\frac{8 - 6}{8}\) = \(\frac{2}{8}\)
= \(\frac{1}{4}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #29903)
Mathematics
NECO SSCE 2008
Variations
Solution
Given that x2 + y2 + k = 60 and x = \(\sqrt{10}\) when y = 4, find the value of k.
A
56
B
34
C
32
D
-34
E
-56
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
x\(^2\) + y\(^2\) + k = 60
(\sqrt10)\(^2\) + (4)\(^2\) + k = 60
k + 10 + 16 = 60
k = 60 - 26
k = 34
Source: WAEC / JAMB / NECO Classroom Archive (Record #42529)
Mathematics
UTME / JAMB 2008
Coordinate Geometry
Solution
Calculate the distance between points L(-1, -6) and M(-3, -5)
A
√5
B
2√3
C
√20
D
√50
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
L\(\begin{pmatrix} x_1 & y_1 \\ -1 & -6 \end{pmatrix}\) m L\(\begin{pmatrix} x_2 & y_2 \\ -3 & -5 \end{pmatrix}\)
D = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)
D = \(\sqrt{(-3 - (-1)^2 + (-5 -(-6)^2}\)
D = \(\sqrt{(-3 + 1)^2 + (-5 + 6)^2}\)
D = \(\sqrt{(-2)^2 + 1^2}\)
D = \(\sqrt{4 + 1}\)
D = \(\sqrt{5}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #29962)
Mathematics
NECO SSCE 2008
Permutations, Combinations & Probability
Solution
Bello chooses a number randomly from 1 to 10. What is the probability that it is either odd or prime?
A
\(\frac{1}{10}\)
B
\(\frac{2}{5}\)
C
\(\frac{1}{2}\)
D
\(\frac{3}{5}\)
E
\(\frac{9}{10}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
the numbers from 1,2,3,4,5,6,7,8,9,10. n( total numbers) = 10
the odd numbers are 1, 3, 5, 7, 9 n( odd) = 5
the prime numbers are 2, 3, 5, 7 n( prime) = 4
but total favourable outcome = ( 1,2,3,5,7,9) = 6
Pro( odd or prime no) = \(\frac{6}{10}\) = \(\frac{3}{5}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #42655)
Mathematics
UTME / JAMB 2008
Trigonometry, Elevation & Bearings
Solution
A student sitting on a tower 68 metres high observes his principal's car at the angle of depression of 20o. How far is the car from the bottom of the tower to the nearest metre?
A
184m
B
185m
C
186m
D
187m
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Tan 20º = \(\frac{68m}{x}\)
x tan 20º = 68
x = \(\frac{68}{tan 20}\) = \(\frac{68}{0.364}\)
x = 186.8
= 187m
Source: Myschool Past Questions Archive (Record #29982)
Mathematics
WAEC / WASSCE 2008
Plane Geometry, Polygons & Circle Theorems
Solution
If x% of 240 equals 12, find x
A
x = 1
B
x = 3
C
x = 5
D
x = 7
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
x% of 240 = 12
\(\frac{x}{100} \times 240 = 12\)
x = \(\frac{12 \times 100}{240}\)
x = 5
Source: Myschool Past Questions Archive (Record #36318)
Mathematics
WAEC / WASSCE 2008
Algebraic Expressions, Polynomials & Factorisation
Solution
Evaluate \(\frac{(3.2)^2 - (4.8)^2}{3.2 + 4.8}\)
A
-0.08
B
-1.60
C
-10.24
D
-12.80
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\frac{(3.2)^2 - (4.8)^2}{3.2 + 1.8} = \frac{(3.2 - 4.8)(3.2 + 4.8)}{(3.2 + 4.8)}\)
= 3.2 - 4.8
= -1.60
Source: Myschool Past Questions Archive (Record #36323)
Mathematics
WAEC / WASSCE 2008
Indices, Logarithms & Surds
Solution
Simplify \(\sqrt{50} + \frac{10}{\sqrt{2}}\)
A
10
B
10\(\sqrt{2}\)
C
20
D
20\(\sqrt{2}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\sqrt{50} + \frac{10}}{\sqrt{2}} = \(\frac{\sqrt{50}}{1} + \sqrt{10}{\sqrt{2}}\)
= \(\frac{\sqrt{50 \times 2} + 10}{\sqrt{2}}\)
= \(\frac{\sqrt{100} + 10}{\sqrt{2}}\)
= \(\frac{10 + 10}{\sqrt{2} = \frac{20}{\sqrt{2}}\)
= \(\frac{20}{\sqrt{2}}\) \times \frac{\sqrt{2}}{\sqrt{2}}\)
= \(\frac{20\sqrt{2}}{2}\)
= 10\(\sqrt{2}\)
Source: Myschool Past Questions Archive (Record #36326)
Mathematics
WAEC / WASSCE 2008
Fractions, Decimals, Percentages & Approximations
Solution
P naira invested for 4 years invested for 4 years at r% simple interest per annum yields 0.36 p naira interest. Find the value of r
A
1\(\frac{1}{9}\)
B
1\(\frac{4}{9}\)
C
9
D
11
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
I = \(\frac{PRT}{100}\)
where r = r% p.a; I = 0.36p
0.36p = \(\frac{P \times r \times 4}{100}\)
\(\frac{0.36 \times 100}{4}\) = r
r = 9
Source: Myschool Past Questions Archive (Record #36327)
Mathematics
WAEC / WASSCE 2008
Plane Geometry, Polygons & Circle Theorems
Solution
If p-2g + 1 = g + 3p and p - 2 = 0, find g
A
-2
B
-1
C
1
D
2
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
p - 2g + 1 = g + 3p.........(1)
p - 2 = 0 .........(2)
From (2), p = 2; put p = 2 into (1);
2 - 2g + 1 = g + 3(2)
3 - 2g = g + 6
-2g - g = 6 - 3
-3g = 3
g = \(\frac{3}{-3}\)
g = -1
Source: Myschool Past Questions Archive (Record #36335)
Mathematics
WAEC / WASSCE 2008
Plane Geometry, Polygons & Circle Theorems
Solution
Simplify \(\frac{\frac{1}{x} + \frac{1}{y}}{x + y}\)
A
\(\frac{1}{x + y}\)
B
\(\frac{1}{xy}\)
C
x + y
D
xy
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\frac{\frac{1}{x} + \frac{1}{y}}{x + y}\) = \(\frac{\frac{y + x}{xy}}{x + y}\)
= \(\frac{x + y}{xy}\)
= \(\frac{x + y}{xy} \times \frac{1}{x + y}\)
= \(\frac{1}{xy}\)
Source: Myschool Past Questions Archive (Record #36336)
Mathematics
WAEC / WASSCE 2008
Indices, Logarithms & Surds
Solution
Simplify 3\(\sqrt{27x^3y^9}\)
A
9xy3
B
3xy6
C
3xy3
D
9y3
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
3\(\sqrt{27x^3y^9}\) = 3\(\sqrt{27} \times 3\sqrt{3^3} \times 3\sqrt{y^9}\)
= 3 \(\times x \times y^3\)
= 3xy3
Source: Myschool Past Questions Archive (Record #36340)