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Mathematics
UTME / JAMB 2008
Trigonometry, Elevation & Bearings
Solution
If sin\theta = 3/5. Find Tan\theta
A
3/4
B
3/5
C
2/5
D
1/4
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
sin\theta = 3/5
x2 = 52 - 32
Source: Myschool Past Questions Archive (Record #9286)
Mathematics
UTME / JAMB 2008
Differentiation & Applications
Solution
Find the derivative of \(y=\frac{x^7 - x^5}{x^4}\)
A
x(x2-1)
B
3x(x2-1)
C
3x2-1
D
7x6-5x4
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(y=\frac{x^7 - x^5}{x^4}\)
y = \(\frac{x^7}{x^4} \div \frac{x^5}{x^4}\)
y = x\(^3\) - x
\(\frac{dy}{dx}\) = 3x\(^2\) - 1
Source: Myschool Past Questions Archive (Record #9288)
Mathematics
UTME / JAMB 2008
Differentiation & Applications
Solution
Differentiate sin x - x cos x
A
x cos x
B
x sin x
C
-x cos x
D
-x sin x
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
sin x - x cos x
dy/dx = cos x - [1.cos x + x -sin x]
= co x - [cos x - x sin x]
= cos x - cos x + x sin x
= x sin x
Source: Myschool Past Questions Archive (Record #9289)
Mathematics
UTME / JAMB 2008
Differentiation & Applications
Solution
Find the minimum value of the function y = x(1+x)
A
-1/4
B
-1/2
C
1/4
D
1/2
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
y = x(1+x)
= x + x2
dy/dx = 1 + 2x
As dy/dy → 0
1 + 2x = 0
2x = -1
X = -1/2
Y = x(1+x)
= -1/2(1 - 1/2) at x = -1/2
= -1/2(1/2)
= -1/4
Source: Myschool Past Questions Archive (Record #9290)
Mathematics
UTME / JAMB 2008
Integration & Applications
Solution
Evaluate \(\int_1 ^2(6x^2-2x)dx\)
A
16
B
13
C
12
D
11
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\int_1 ^2(6x^2-2x)\)dx = \(\frac{6x^3}{3}-\frac{2x^2}{2}]_1 ^2\)
= \(2x^3 - x^2)_1^2\)
= [2(2)3 - (2)2] – [2(1)3 - (1)2]
= [16-4] – [2-1]
= 12 – 1
= 11
Source: Myschool Past Questions Archive (Record #9291)
Mathematics
UTME / JAMB 2008
Integration & Applications
Solution
Evaluate \(\int^{\frac{\pi}{2}} _{\frac{-\pi}{2}} cos x dx\)
A
zero
B
1
C
2
D
3
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\int^{\frac{\pi}{2}} _{\frac{-\pi}{2}} cos x dx = [sinx]^{\frac{\pi}{2}} _{\frac{-\pi}{2}}\)
=sin\(\frac{\pi}{2} - sin\frac{-\pi}{2}\)
= sin90 – sin(-90)
= sin90 – sin270
= 1 – (-1)
= 1+1
= 2
Source: Myschool Past Questions Archive (Record #9292)
Mathematics
UTME / JAMB 2008
Fractions, Decimals, Percentages & Approximations
Solution
On a pie chart there are six sectors of which four angles are 30^\circ, 45^\circ, 60^\circ, 90^\circ and the remaining two angles are in the ratio 2:1. Find the smallest angles of the remaining two angles.
A
15o
B
30o
C
45o
D
60o
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
30 + 45 + 60 + 90 + 2x + x = 360^\circ
225 + 3x = 360
3x = 360 - 225
3x = 135
x = 45^\circ
Source: Myschool Past Questions Archive (Record #9293)
Mathematics
UTME / JAMB 2008
Fractions, Decimals, Percentages & Approximations
Diagram
Solution
The bar chart above shows the number of times the word "a, and , in, it, the ,to" appear in a paragraph in a book.
What is the ratio of the least frequent word to the most frequent word?
Attached Figure / Diagram
A
1/6
B
1/3
C
2/3
D
3/4
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Ratio of least to most = 2:12
= 2/12
= 1/6
Source: Myschool Past Questions Archive (Record #9294)
Mathematics
UTME / JAMB 2008
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
What is the mean of the data t, 2t-1, t-2, 2t -1, 4t and 2t+2?
A
2t
B
2t-1
C
2/3t+1
D
2t-1/3
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(Mean = \frac{t+2t-1+t-2+2t-1+4t+2t+2}{6}\)
Mean = \(\frac{12t-2}{6}\)
=\(\frac{2(6t-1)}{6}\)
=\(\frac{6t-1}{3}\)
=\(\frac{6t}{3}- \frac{1}{3}\)
=2t-\(\frac{1}{3}\)
Source: Myschool Past Questions Archive (Record #9295)
Mathematics
UTME / JAMB 2008
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
Find the median of 4, 1, 4, 1, 0, 4, 4, 2 and 0
A
zero
B
1
C
2
D
4
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
4, 4, 1, 0, 4, 4, 2, 0
Arrange in ascending order:
0, 0, 1, 1, 2, 4, 4, 4, 4
Position of median = N+1 / 2 = 9+1 / 2 = 5th
Median = 2
Source: Myschool Past Questions Archive (Record #9296)
Mathematics
UTME / JAMB 2008
Plane Geometry, Polygons & Circle Theorems
Solution
If x > 0, find the range of number x-3, 3x+2,x-1, 4x, 2x-1, x-2, 2x-2, 3x and 3x+1
A
3x+3
B
3x+1
C
2x+5
D
2x+1
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
x-3, 3x+2,x-1, 4x, 2x-1, x-2, 2x-2, 3x, 3x+1
Range = 3x + 2 - (x-3)
= 2x + 5
(Assuming x = 1, since x > 0)
Source: Myschool Past Questions Archive (Record #9297)
Mathematics
UTME / JAMB 2008
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
Find the mean deviation of 2, 4, 5, and 9
A
1
B
2
C
5
D
7
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
X = 20/4
= 5
mean deviation = 8/4 = 2
Source: Myschool Past Questions Archive (Record #9298)
Mathematics
UTME / JAMB 2008
Permutations, Combinations & Probability
Solution
In how many ways can the letters of the word ACCEPTANCE be arranged?
A
\(\frac{10!}{(2!2!3!)}\)
B
\(\frac{10!}{( 2!3!)}\)
C
\(\frac{10!}{(2!2!)}\)
D
10!
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
ACCEPTANCE = 10 Letters
A = 2 letters
C = 3 letters
E = 2 letters
It can be arranged in \(\frac{10!}{(2!3!2!)}\) ways
Source: Myschool Past Questions Archive (Record #9299)
Mathematics
UTME / JAMB 2008
Permutations, Combinations & Probability
Solution
Find the number of ways of selecting 6 out of 10 subjects for an examination
A
128
B
216
C
215
D
210
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(^{10}C_6 = \frac{10!}{(10-6)!6!}\)
= \(\frac{10!}{4!6!}\)
=\(\frac{10\times 9\times 8 \times 7 \times 6!}{4\times 3\times 2\times 1 \times 6!}\)
= 210.
Source: Myschool Past Questions Archive (Record #9300)
Mathematics
UTME / JAMB 2008
Permutations, Combinations & Probability
Solution
The probability of picking a letter T from the word OBSTRUCTION is?
A
1/11
B
2/11
C
3/11
D
4/11
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
OBSTRUCTION
Total possible outcome = 11
Number of chance of getting T = 2
P(picking T) = 2/11
Source: Myschool Past Questions Archive (Record #9301)