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Mathematics
UTME / JAMB 2016
Geometry and Trigonometry
Solution
An arc subtends an angle of 30º at the centre of a circle radius 12cm. Calculate the length of the arc.
A
6\(\pi\)cm
B
2\(\pi\)cm
C
3\(\pi\)cm
D
9\(\pi\)cm
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Length or arc = \(\frac{\theta}{360}\) x 2\(\pi\)r
= \(\frac{30}{360}\) x 2 x \(\frac{22}{7}\) x 12
= \(\frac{1}{12}\) x 2 x \(\pi\) x 12 = 2\(\pi\)cm
Source: Myschool Past Questions Archive (Record #44834)
Mathematics
UTME / JAMB 2016
Geometry and Trigonometry
Solution
Evaluate \(\int\limits_0^\frac{\pi}{2}\) sin xdx
A
2
B
-1
C
1
D
-2
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\int\limits_0^\frac{\pi}{2}\) sin xdx = -cosx|\(\frac{\pi}{2}\)
= -(cos\(\frac{\pi}{2}\) - cos0) = -(0-1) = 1
Source: Myschool Past Questions Archive (Record #44835)
Mathematics
UTME / JAMB 2016
Geometry and Trigonometry
Solution
An arc of the length 16\(\pi\)cm subtends an angle of 80o at the centre of the circle. Find the radius of the circle.
A
24cm
B
28cm
C
36cm
D
32cm
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
L = \(\frac{\theta}{360}\) x 2\(\pi\)r
16\(\pi\) = \(\frac{80}{360}\) x 2\(\pi\)r
\(\frac{16\pi \times 360}{80 \times 2\pi}\) = r
r = 36cm
Source: Myschool Past Questions Archive (Record #44836)
Mathematics
UTME / JAMB 2016
Statistics and Probability
Solution
The mean of 2-t, 4+t, 3-2t, 2+t and t-1 is
A
2
B
t
C
-t
D
-2
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Mean = \(\frac{2 - t + 4 + t + 3 - 2t + 2 + t + t - 1}{5}\)
= \(\frac{10}{5}\) = 2
Source: Myschool Past Questions Archive (Record #44838)
Mathematics
UTME / JAMB 2016
Number and Numeration
Solution
Evaluate \(\frac{12.02 \times 20.06}{26.04 \times 60.06}\), correct to three significant figures.
A
0.157
B
0.154
C
0.155
D
0.158
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\frac{12.02 \times 20.06}{26.04 \times 60.06}\) = \(\frac{241.1212}{15698.96}\) = 0.154
Source: Myschool Past Questions Archive (Record #44848)
Mathematics
UTME / JAMB 2016
Number and Numeration
Solution
If y = 2x3 + 6x2 + 6x + 1, Find \(\frac{dy}{dx}\)
A
6x2 + 12x + 1
B
6x2 + 6x + 1
C
6x2 + 6x + 6
D
6x2 + 12x + 6
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
y = 2x3 + 6x2 + 6x + 1
\(\frac{dy}{dx}\) = 6x2 + 12x + 6
Source: Myschool Past Questions Archive (Record #44851)
Mathematics
UTME / JAMB 2016
Algebra
Solution
The nth term of the sequence 3, 9, 27, 81.....is
A
3 x 3n-2
B
3 x 3n-1
C
3 x 3n+2
D
3 x 3n+1
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
3,9,27,81,.....
r = \(\frac{9}{8}\) = 3
Tn = arn-1
Tn = 3(3)n-1 = \(\frac{3(3^2)}{3}\)
Source: Myschool Past Questions Archive (Record #44853)
Mathematics
UTME / JAMB 2016
Number and Numeration
Solution
Simplify 1 - (\(\frac{1}{7}\) x 3 \(\frac{1}{2}\)) \(\div\) \(\frac{3}{4}\)
A
2
B
\(\frac{1}{3}\)
C
1
D
\(\frac{2}{3}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
1 - (\(\frac{1}{7}\) x 3 \(\frac{1}{2}\)) \(\div\) \(\frac{3}{4}\)
1 - (\(\frac{1}{7}\) x \(\frac{7}{2}\)) x \(\frac{4}{3}\)
1 - \(\frac{1}{2}\) x \(\frac{4}{3}\)
1 - \(\frac{2}{3}\) = \(\frac{1}{3}\)
Source: Myschool Past Questions Archive (Record #44856)
Mathematics
UTME / JAMB 2016
Number and Numeration
Solution
If a car travels 120km on 45 litres of petrol, how much petrol is needed for a journey of 600km?
A
720 litres
B
160 litres
C
225 litres
D
960 litres
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
120km \(\to\) 45litres
1km \(\to\) \(\frac{45}{120}\)litres
600km \(\to\) \(\frac{45}{120}\) x 600 = 225litres
Source: Myschool Past Questions Archive (Record #44857)
Mathematics
UTME / JAMB 2016
Number and Numeration
Solution
Find \(\frac{dy}{dx}\). If y = 3x3 + 2x2 + 3x + 1
A
9x2 + 4x + 3
B
9x2 - 4x - 3
C
9x2 + 4x - 3
D
9x2 - 4x + 3
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
y = 3x3 + 2x2 + 3x + 1
\(\frac{dy}{dx}\) = 9x2 + 4x + 3
Source: Myschool Past Questions Archive (Record #44860)
Mathematics
UTME / JAMB 2016
Geometry and Trigonometry
Solution
Evaluate \(\int\)(sinx - 5x2)dx
A
-cosx - 10x + k
B
cosx - \(\frac{5x^3}{3}\) + k
C
-cosx - \(\frac{5x^3}{3}\) + k
D
cosx - 10x + k
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\int\)(sin x - 5x^2) = -cosx - \(\frac{5x^3}{3}\) + k
Source: Myschool Past Questions Archive (Record #44861)
Mathematics
UTME / JAMB 2016
Number and Numeration
Solution
If N = \(\frac{p}{2}\)(\(\frac{T_1 - T_2}{T_1}\)). Find P when N = 12, T1 = 27 and T2 = 24.
A
48
B
108
C
54
D
216
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
N = \(\frac{p}{2}\)(\(\frac{T_1 - T_2}{T_1}\))
12 = \(\frac{p}{2}\)(\(\frac{27 - 24}{27}\))
24 = P(\(frac{3}{27}\)
P = 24 x 9 = 216
Source: Myschool Past Questions Archive (Record #44862)
Mathematics
UTME / JAMB 2016
Number and Numeration
Solution
Solve for x and y respectively
3x - 5y = 9
6x - 4y = 12
A
\(\frac{3}{4}\), 1
B
\(\frac{4}{3}\), 1
C
\(\frac{3}{4}\), -1
D
\(\frac{4}{3}\), -1
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
3x - 5y = 9 ------x2
6x - 4y = 12 -----x1
6x - 10y = 18
-6x - 4y = 12
____________
\(\frac{6y}{-6}\) = \(\frac{6}{6}\)
y = -1
in eq (1) 3x - 5y = 9
3x - 5(-1) = 9
3x + 5 = 9
3x = 4
x = \(\frac{4}{3}\)
Source: Myschool Past Questions Archive (Record #44863)
Mathematics
UTME / JAMB 2016
Number and Numeration
Solution
If Q is a factor of 18 and T is prime numbers between 2 and 18. What is Q\(\cap\)T?
A
(2,3)
B
(2,3,18)
C
(2,3,9)
D
(2,3,6)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Q = {1,2,3,6,9,18}, T = {2,3,5,7,11,13,17}
Q\(\cap\)T = {2,3}
Source: Myschool Past Questions Archive (Record #44865)
Mathematics
UTME / JAMB 2016
Number and Numeration
Diagram
Solution
From the cyclic quadrilateral above, find < TSV
Attached Figure / Diagram
A
60o
B
80o
C
70o
D
50o
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
< TVS = 180o - (80 + 20)
= 180 - 100 = 80o
Source: Myschool Past Questions Archive (Record #44870)