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Mathematics
UTME / JAMB 2016
Geometry and Trigonometry
Solution
Evaluate \(\int\)(cos4x + sin3x)dx
A
sin4x - cos3x + k
B
sin4x + cos3x + k
C
\(\frac{1}{4}\)sin4x - \(\frac{1}{3}\)cos3x + k
D
\(\frac{1}{4}\)sin4x + \(\frac{1}{3}\)cos3x + k
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\int (\cos 4x + \sin 3x) \mathrm d x\)
= \(\frac{1}{4} \sin 4x - \frac{1}{3} \cos 3x + k\)
Source: Myschool Past Questions Archive (Record #44769)
Mathematics
UTME / JAMB 2016
Number and Numeration
Solution
If x10 = 235. Find x
A
15
B
12
C
14
D
13
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
x10 = 235
x10 = 2 x 51 + 3 x 50
= 10 + 3
= x10 = 13
Source: Myschool Past Questions Archive (Record #44770)
Mathematics
UTME / JAMB 2016
Geometry and Trigonometry
Diagram
Solution
The pie chart above shows the distribution of subjects offered by students in SSS III level. If 80 students enrolled in the class. What is the size of the angle of the sector in economics?
Attached Figure / Diagram
A
24o
B
39o
C
32o
D
36o
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
xo + 36o + 54o + 28o + 90o + 120o = 360o
x + 328o = 360o
x = 360o - 328o
x = 32o
Source: Myschool Past Questions Archive (Record #44771)
Mathematics
UTME / JAMB 2016
Number and Numeration
Solution
Calculate the range of 20, -6, 25, 30, 21, 28, 32, 33, 34, 5, 3, 2, and 1.
A
32
B
36
C
33
D
40
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Range = 34 - (-6) = 34 + 6 = 40
Source: Myschool Past Questions Archive (Record #44772)
Mathematics
UTME / JAMB 2016
Number and Numeration
Diagram
Solution
The bar chart above shows the number of visitors received in a week. How many visitors were received on Friday, Tuesday and Sunday?
Attached Figure / Diagram
A
17
B
22
C
20
D
16
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
No of visitors = 10 + 5 + 1 = 16
Source: Myschool Past Questions Archive (Record #44773)
Mathematics
UTME / JAMB 2016
Number and Numeration
Solution
Factorize k2 - 2kp + p2.
A
(k +p)2
B
(k - p)2
C
k2 + p2
D
k2 - p2
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
k2 - 2kp + p2 = (k - p)2
Source: Myschool Past Questions Archive (Record #44774)
Mathematics
UTME / JAMB 2016
Geometry and Trigonometry
Solution
Calculate the perimeter of a sector of a circle of raduis 12cm and angle 60o.
A
(12 + 4\(\pi\))cm
B
(24 + 4\(\pi\))cm
C
(12 + 6\(\pi\))cm
D
(24 + 6\(\pi\))cm
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Perimeter = 2r + \(\frac{\theta}{360}\) x 2\(\pi\)r
= 2(12) + \(\frac{60}{360}\) x 2 x \(\pi\) x 12
= (24 + 4\(\pi\))cm
Source: Myschool Past Questions Archive (Record #44775)
Mathematics
UTME / JAMB 2016
Number and Numeration
Solution
Given U = {x: x is a positive integer less than 15} and P = {x: x is even number from 1 to 14}. Find the compliment of P.
A
{1, 3, 5, 7, 9, 11, 13, 15}
B
{2, 3, 5, 7, 9, 11, 13}
C
{1, 3, 5, 7, 9, 11, 13}
D
{2, 3, 5, 7, 11, 15}
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
U = {1, 2, 3, 4, 5......14}
P = {2, 4, 6, 8, 10, 12, 14}
P' = {1, 3, 5, 7, 9, 11,13}
Source: Myschool Past Questions Archive (Record #44777)
Mathematics
UTME / JAMB 2016
Geometry and Trigonometry
Solution
Simplify \(\frac{0.026 \times 0.36}{0.69}\). Leave your answer in standard form
A
1.36 x 10-4
B
1.36 x 10-3
C
1.36 x 10-1
D
1.36 x 10-2
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{0.026 \times 0.36}{0.69}\) = \(\frac{26 \times 10^-3 \times 36 \times 10^-2}{69 \times 10^-2}\)
= 0.01356 = 1.36 x 10-2
Source: Myschool Past Questions Archive (Record #44827)
Mathematics
UTME / JAMB 2016
Number and Numeration
Solution
A number of pencils were shared out among Bisi, Sola and Tunde in the ratio of 2:3:5 respectively. If Bisi got 5, how many were shared out?
A
15
B
25
C
30
D
50
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Let x represent total number of pencils shared
B : S : T
2 : 3 : 5
2+3+5 = 10
\(\frac{2}{10}\) x x = 5
\(\frac{2x}{10}\) = 5
2x = 50
x = 25
Source: Myschool Past Questions Archive (Record #44828)
Mathematics
UTME / JAMB 2016
Geometry and Trigonometry
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
Number and Numeration
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 and Probability
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
Number and Numeration
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
Number and Numeration
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)