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Mathematics
UTME / JAMB 2016
Differentiation & Applications
Solution
Find the derivative of y = ( \(\frac{1}{3}\)X + 6)\(^2\)
A
2( \(\frac{1}{3}\)X + 6
B
\(\frac{2}{3}\) ( \(\frac{1}{3}\)X + 6)
C
\(\frac{2}{3}\) ( \(\frac{1}{3}\)X + 6)2
D
\(\frac{1}{3}\) ( \(\frac{1}{3}\)X + 6)2
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Y = ( \(\frac{1}{3}\)X + 6)\(^2\)
\(\frac{dy}{dx}\) = 2( \(\frac{1}{3}\)X + 6) \(\frac{1}{3}\)
= \(\frac{2}{3}\) ( \(\frac{1}{3}\)X + 6)
Source: Myschool Past Questions Archive (Record #44746)
Mathematics
UTME / JAMB 2016
Sets, Logic & Venn Diagrams
Solution
In a school of 150 students, 80 offer French while 60 offer Arabic and 20 offer neither. How many students offer both subjects?
A
45
B
10
C
35
D
30
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
80 - x + x + 60 - x + 20 = 150
160 - x = 150
x = 160 - 150 = 10
Source: Myschool Past Questions Archive (Record #44747)
Mathematics
UTME / JAMB 2016
Sequences & Series (AP & GP)
Solution
If the 2nd term of a G.P is \(\frac{8}{9}\) and the 6th term is 4\(\frac{1}{2}\). Find the common ratio.
A
2
B
\(\frac{3}{2}\)
C
\(\frac{2}{3}\)
D
3
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
T2 = \(\frac{8}{9}\), T6 = 4\(\frac{1}{2}\)
ar = \(\frac{8}{9}\)
ar5 = \(\frac{9}{2}\)
\(\frac{ar}{ar^5}\) = \(\frac{8}{9}\) x \(\frac{2}{9}\)
\(\frac{1}{r^4}\) = \(\frac{16}{81}\)
r = \(\sqrt[4]{\frac{18}{16}}\) = \(\frac{3}{2}\)
Source: Myschool Past Questions Archive (Record #44748)
Mathematics
UTME / JAMB 2016
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
From the diagram above, find the value of < OTQ
Attached Figure / Diagram
A
230o
B
55o
C
115o
D
65o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
o
Source: Myschool Past Questions Archive (Record #44749)
Mathematics
UTME / JAMB 2016
Plane Geometry, Polygons & Circle Theorems
Solution
The sum of the interior angles of a polygon is a given as 1080o. Find the number of the sides of the polygon.
A
5
B
7
C
6
D
8
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{(n - 2) 180}{180}\) = \(\frac{1080}{180}\)
(n - 2) = 6
n = 6 + 2 = 8
Source: Myschool Past Questions Archive (Record #44750)
Mathematics
UTME / JAMB 2016
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram above, l1 is parallel to l2, Find the value of < PMT
Attached Figure / Diagram
A
82o
B
36o
C
72o
D
118o
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
o - 118o = 62o
o ( Alternative angle)
y + 2y + 10o + 62o = 180o (Angles on a straight line)
3y = 180 - 72
\(\frac{3y}{3}\) = \(\frac{108}{3}\)
y = 36o
o
Source: Myschool Past Questions Archive (Record #44751)
Mathematics
UTME / JAMB 2016
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
From the diagram above, Find the value of < ROP
Attached Figure / Diagram
A
110o
B
70o
C
95o
D
85o
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
o (Exterior angle of cyclic quadrilateral)
Source: Myschool Past Questions Archive (Record #44755)
Mathematics
UTME / JAMB 2016
Plane Geometry, Polygons & Circle Theorems
Solution
If line p = 5x + 3 is parallel to line p = wx + 5. Find the value of w.
A
7
B
3
C
6
D
5
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
P = 5x + 3, P = wx + 5
M1 = 5, M2 = w
M1 = M2 (parallel lines)
w = 5
Source: Myschool Past Questions Archive (Record #44768)
Mathematics
UTME / JAMB 2016
Trigonometry, Elevation & Bearings
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
Plane Geometry, Polygons & Circle Theorems
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
Statistics (Data Representation, Central Tendency & Dispersion)
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
Plane Geometry, Polygons & Circle Theorems
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
Statistics (Data Representation, Central Tendency & Dispersion)
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
Algebraic Expressions, Polynomials & Factorisation
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
Mensuration (Areas, Perimeters & Volumes)
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)