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Mathematics
UTME / JAMB 2016
Integration & Applications
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
Plane Geometry, Polygons & Circle Theorems
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
Linear, Simultaneous & Quadratic Equations
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
Sets, Logic & Venn Diagrams
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
Plane Geometry, Polygons & Circle Theorems
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)
Mathematics
UTME / JAMB 2016
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
Find the mean of 10, 8, 5, 11, 12, 9, 6, 3, 15, and 23.
A
11.2
B
10
C
10.2
D
11.3
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{10 + 8 + 5 + 11 + 12 + 9 + 6 + 3 + 15 + 23}{10}\)
= \(\frac{102}{10}\) = 10.2
Source: Myschool Past Questions Archive (Record #44871)
Mathematics
UTME / JAMB 2016
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the cyclic quadrilateral above . Find < PRO
Attached Figure / Diagram
A
70o
B
20o
C
50o
D
30o
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
< PRO = 180^\circ - (110 + 50)^\circ
= 180 - 160 = 20^\circ
Source: Myschool Past Questions Archive (Record #44872)
Mathematics
UTME / JAMB 2016
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
OGIVE is constructed using
A
Third quartile range
B
Semi-quartile range
C
Cummulative frequency table
D
Inter-quartile table
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
An ogive is constructed using the cumulative frequencies from a frequency distribution table.
Collect Data: Organize your data into a frequency distribution table.
Calculate Cumulative Frequency: Add frequencies cumulatively for each class interval.
Determine Class Boundaries: Identify the upper boundaries of the class intervals.
Plot Points: Plot cumulative frequencies against the upper class boundaries.
Draw the Ogive: Connect the points with a smooth curve, starting from (0, 0).
Label the Axes: Clearly label the x-axis (upper boundaries) and y-axis (cumulative frequency).
Source: Myschool Past Questions Archive (Record #44873)
Mathematics
UTME / JAMB 2016
Indices, Logarithms & Surds
Solution
Rationalize \(\frac{\sqrt{6} - \sqrt{4}}{\sqrt{6} + \sqrt{4}}\)
A
5 + 2 \(\sqrt{6}\)
B
5 - 4 \(\sqrt{6}\)
C
5 + 4 \(\sqrt{6}\)
D
5 - 2 \(\sqrt{6}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{\sqrt{6} - \sqrt{4}}{\sqrt{6} + \sqrt{4}}\) = \(\frac{6-2\sqrt{6} - 2\sqrt{6} + 4}{6 - 4}\)
\(\frac{10 - 4\sqrt{6}}{2}\) = 5 - 2\(\sqrt{6}\)
Source: Myschool Past Questions Archive (Record #44874)
Mathematics
UTME / JAMB 2016
Statistics (Data Representation, Central Tendency & Dispersion)
Diagram
Solution
The bar chart above shows the marks obtained by students in a mathematics test.
How many students in all took the test?
Attached Figure / Diagram
A
40
B
30
C
10
D
20
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
3 + 2 + 5 + 5 + + 5 + 10 + 4 + 3 + 1 + 2 = 40
Source: Myschool Past Questions Archive (Record #44875)
Mathematics
UTME / JAMB 2016
Statistics (Data Representation, Central Tendency & Dispersion)
Diagram
Solution
Determine the mean score of the student that took the mathematics test?
Attached Figure / Diagram
A
4.5
B
4.3
C
4.2
D
4.6
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
(3 x 0) + (1 x 2) + (5 x 2) + (5 x 3) + (5 x 4) +
(10 x 5) + (4 x 6) + (3 x 7) + (1 x 8) + (2 x 9) \(\div\) 40
= \(\frac{168}{40}\) = 4.2
Source: Myschool Past Questions Archive (Record #44878)
Mathematics
UTME / JAMB 2016
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
From the diagram above. Find the fraction of the shaded position?
Attached Figure / Diagram
A
\(\frac{1}{3}\)
B
\(\frac{1}{5}\)
C
\(\frac{1}{4}\)
D
\(\frac{1}{6}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\theta\) = 180o -(90 + 60)
\(\theta\) = 180o - 150o = 30o
Fraction of shaded position = \(\frac{30}{360}\) + \(\frac{30}{360}\)
= \(\frac{1}{12}\) + \(\frac{1}{12}\) = \(\frac{1}{6}\)
Source: Myschool Past Questions Archive (Record #44980)
Mathematics
UTME / JAMB 2016
Inequalities & Linear Programming
Diagram
Solution
From the diagram above, find the required roots/region of x.
Attached Figure / Diagram
A
x\(\leq\)-1, x \(\geq\)4
B
x\(\leq\)4
C
-1\(\leq\)x\(\leq\)4
D
x\(\leq\)-1, o\(\leq\)x\(\leq\)4
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
The required roots/region of x is -1\(\leq\)x\(\leq\)4
Source: Myschool Past Questions Archive (Record #44981)
Mathematics
WAEC / WASSCE 2016
Plane Geometry, Polygons & Circle Theorems
Solution
If 23x + 101x = 130x, find the value of x
A
7
B
6
C
5
D
4
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
23x + 101x = 130x
2 x X1 + 3 x Xo + 1 x X2 + 0 x X1 + 1 x Xo
= 1 x Xo = 1 x X2 + 3 x X1 + 0 x Xo
= X2 + 3x + 0
2x + 3 = x2 + 0 + 1 + x2 + 3x
2x - 3x + x2 - x2 = -3 - 1
- x = -4
x = 4
Source: Myschool Past Questions Archive (Record #46039)
Mathematics
WAEC / WASSCE 2016
Plane Geometry, Polygons & Circle Theorems
Solution
Simplify: (\(\frac{3}{4} - \frac{2}{3}\)) x 1\(\frac{1}{5}\)
A
\(\frac{1}{60}\)
B
\(\frac{5}{72}\)
C
\(\frac{1}{10}\)
D
1\(\frac{7}{10}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
(\(\frac{3}{4} - \frac{2}{3}\)) x 1\(\frac{1}{5}\)
= (\(\frac{9 - 8}{12} \times \frac{6}{5}\))
= \(\frac{1}{12} \times \frac{6}{5}\)
= \(\frac{1}{10}\)
Source: Myschool Past Questions Archive (Record #46042)