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Mathematics
UTME / JAMB 2016
Mensuration (Areas, Perimeters & Volumes)
Solution
Calculate the perimeter of a sector of a circle of raduis 9cm and angle 36o.
A
18cm
B
(18 + \(\frac{9\pi}{5}\))cm
C
(9 + \(\frac{9\pi}{5}\))cm
D
\(\frac{9\pi}{5}\)cm
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Perimeter = 2r + \(\frac{\theta}{360}\) x 2\(\pi\)r
2(9) + \(\frac{36}{360}\) x 2 x \(\pi\) x 9 = 18 + \(\frac{9\pi}{5}\)
Source: Myschool Past Questions Archive (Record #44829)
Mathematics
UTME / JAMB 2016
Indices, Logarithms & Surds
Solution
Evaluate \(\frac{27^\frac{1}{3} - 8^\frac{2}{3}}{16^\frac{2}{4} \times 2}\)
A
\(\frac{23}{5}\)
B
-\(\frac{23}{5}\)
C
-\(\frac{1}{8}\)
D
\(\frac{21}{7}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{27^\frac{1}{3} - 8^\frac{2}{3}}{16^\frac{2}{4} \times 2}\)
\(\frac{27^\frac{1}{3} - 8^\frac{2}{3}}{16^\frac{2}{4} \times 2}\) = \(\frac{3\sqrt{27} - 3\sqrt{8}^2}{\sqrt{16} \times 2}\)
\(\frac{3 - 4}{4 \times 2}\)
= \(\frac{-1}{8}\)
Source: Myschool Past Questions Archive (Record #44830)
Mathematics
UTME / JAMB 2016
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
\(\begin{array}{c|c}
Scores & 3 & 6 & 5 & 2 \\
\hline
Frequency & 2 & 3 & 4 & 6
\end{array}\)
From the table above, find the median
A
3
B
5
C
4
D
6
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Listing the scores according to the number of times they occur in ascending order
2, 2, 2, 2, 2, 2,3, 3, 5, 5, 5, 5, 6, 6, 6,
Median = 3
Source: Myschool Past Questions Archive (Record #44831)
Mathematics
UTME / JAMB 2016
Differentiation & Applications
Solution
Find \(\frac{dy}{dx}\), if y = \(\frac{2}{3}\) x\(^3\) - \(\frac{4}{x}\)
A
3x2 - \(\frac{4}{x}\)
B
2x2 +\(\frac{4}{x^2}\)
C
3x2 + \(\frac{4}{x^2}\)
D
2x2 - \(\frac{4}{x}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
y = \(\frac{2}{3}\)x\(^3\) - \(\frac{4}{x}\)
\(\frac{dy}{dx}\) = 2x\(^2\) - (-4)x\(^{-2}\) = 2x\(^2\) + \(\frac{4}{x^2}\)
Source: Myschool Past Questions Archive (Record #44832)
Mathematics
UTME / JAMB 2016
Fractions, Decimals, Percentages & Approximations
Solution
Evaluate \(\frac{0.8 \times 0.43 \times 0.031}{0.05 \times 0.72 \times 0.021}\). Correct to four significant figures.
A
14.09
B
14.1
C
14.12
D
14.11
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{0.8 \times 0.43 \times 0.031}{0.05 \times 0.72 \times 0.021}\) x \(\frac{10}{10}\) = 14.11
Source: Myschool Past Questions Archive (Record #44833)
Mathematics
UTME / JAMB 2016
Plane Geometry, Polygons & Circle Theorems
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
Integration & Applications
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
Plane Geometry, Polygons & Circle Theorems
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 (Data Representation, Central Tendency & Dispersion)
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
Fractions, Decimals, Percentages & Approximations
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
Differentiation & Applications
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
Sequences & Series (AP & GP)
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
Plane Geometry, Polygons & Circle Theorems
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
Plane Geometry, Polygons & Circle Theorems
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
Linear, Simultaneous & Quadratic Equations
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)