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Mathematics
UTME / JAMB 2014
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
\(\begin{array}{c|c}
Numbers & 1 & 2 & 3 & 4 & 5 & 6 \\
\hline
Frequency & 18 & 22 & 20 & 16 & 10 & 14
\end{array}\)
The table above represents the outcome of throwing a die 100 times. What is the probability of obtaining at least a 4?
A
\(\frac{1}{5}\)
B
\(\frac{1}{2}\)
C
\(\frac{2}{5}\)
D
\(\frac{3}{4}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Let E demote the event of obtaining at least a 4
Then n(E) = 16 + 10 + 14 = 40
Hence, prob (E) = \(\frac{n(E)}{n(S)}\)
\( = \frac{40}{100}\)
\( = \frac{2}{5}\)
Source: Myschool Past Questions Archive (Record #27036)
Mathematics
UTME / JAMB 2014
Permutations, Combinations & Probability
Solution
A number is chosen at random from 10 to 30 both inclusive. What is the probability that the number is divisible by 3?
A
\(\frac{2}{15}\)
B
\(\frac{1}{10}\)
C
\(\frac{1}{3}\)
D
\(\frac{2}{5}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Sample space S = {10, 11, 12, ... 30}
Let E denote the event of choosing a number divisible by 3
Then E = {12, 15, 18, 21, 24, 27, 30} and n(E) = 7
Prob (E) = \(\frac{n(E)}{n(S)}\)
Prob (E) = \(\frac{7}{21}\)
Prob (E) = \(\frac{1}{3}\)
Source: Myschool Past Questions Archive (Record #27037)
Mathematics
UTME / JAMB 2014
Sets, Logic & Venn Diagrams
Diagram
From the venn diagram above, the shaded parts represent
Attached Figure / Diagram
A
(P\(\cap\)Q)\(\cup\)(P\(\cap\)R)
B
(P\(\cup\)Q)\(\cap\)(P\(\cap\)R)
C
(P\(\cup\)Q)\(\cup\)(P\(\cup\)R)
D
(P\(\cap\)Q)\(\cup\)(P\(\cup\)R)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option A.
Source: Myschool Past Questions Archive (Record #33156)
Mathematics
UTME / JAMB 2014
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the figure above, KL//NM, LN bisects o and angle MKN is 35o, calculate the size of angle KMN.
Attached Figure / Diagram
A
91o
B
89o
C
37o
D
19o
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
In the diagram above, \(\alpha\) = 54o(alternate angles; KL||MN) o
35o + o = 180o(sum of angles of \(\bigtriangleup\))
o = 180o
o - 143o
= 37o
Source: Myschool Past Questions Archive (Record #33157)
Mathematics
UTME / JAMB 2014
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
From the figure above, what is the value of p?
Attached Figure / Diagram
A
135o
B
90o
C
60o
D
45o
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
In the figure above, qo = 30o (vertically opposite angles)
(P + 2q)o + 30o = 180o(angles on a straight line)
p + 2 x 30o + 30o = 180o
p + 60o + 30o = 180o
p + 90o = 180o
p = 180o - 90o
= 90o
Source: Myschool Past Questions Archive (Record #33158)
Mathematics
UTME / JAMB 2014
Indices, Logarithms & Surds
Diagram
Solution
Find the value of x in the figure above
Attached Figure / Diagram
A
20\(\sqrt{3}\)cm
B
10\(\sqrt{3}\)cm
C
5\(\sqrt{3}\)cm
D
4\(\sqrt{3}\)cm
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
In the figure above, \(\frac{x}{\sin 60^o} = \frac{10}{\sin 30^o}\) (Sine rule)
x = \(\frac{10 \sin 60^o}{\sin 30^o}\)
= 10 x \(\frac{\sqrt{3}}{2} \times \frac{1}{2}\)
= 10 x \(\frac{\sqrt{3}}{2} \times \frac{2}{1}\)
= 10\(\sqrt{3}\)cm
Source: Myschool Past Questions Archive (Record #33159)
Mathematics
UTME / JAMB 2014
Coordinate Geometry
Diagram
Solution
in the figure above, what is the equation of the line that passes the y-axis at (0,5) and passes the x-axis at (5,0)?
Attached Figure / Diagram
A
y = x + 5
B
y = -x + 5
C
y = x - 5
D
y = -x - 5
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
(x1, y1) = (0,5)
(x2, y2) = (5, 0)
Using \(\frac{y - y_1}{y_2 - y_1} = \frac{x - x_1}{x_2 - x_1}\)
\(\frac{y - 5}{0 - 5} = \frac{x - 0}{5 - 0}\)
\(\frac{y - 5}{-5} = \frac{x}{5}\)
5(y - 5) = -5x
y - 5 = -x
x + y = 5
y = -x + 5
Source: Myschool Past Questions Archive (Record #33160)
Mathematics
UTME / JAMB 2014
Statistics (Data Representation, Central Tendency & Dispersion)
Diagram
Solution
The pie chart above shows the monthly distribution of a man's salary on food items. If he spent N8,000 on rice, how much did he spent on yam?
Attached Figure / Diagram
A
N42,000
B
N18,000
C
N16,000
D
N12,000
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Angle of sector subtended by yam
= 360o - (70 + 80 + 50)o
= 360o - 200o
= 160o
But \(\frac{80^o}{360^o}\) x T = 8000
T = \(\frac{8000 \times 360^o}{80^o}\)
= N36,000
Hence the amount spent on yam = \(\frac{160^o}{260} \times N36,000\)
= N16,000
Source: Myschool Past Questions Archive (Record #33161)
Mathematics
UTME / JAMB 2014
Mensuration (Areas, Perimeters & Volumes)
Solution
If the angle of a sector of a circle with radius 10.5 cm is 120^\circ, find the perimeter of the sector. [Take \(\pi = \frac{22}{7}\)]
A
48 cm
B
40 cm
C
43 cm
D
45 cm
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Perimeter of the sector = \(2r + \frac{\theta}{360^\circ} \times 2\pi r\)
= \(2(10.5) + \frac{120}{360} \times 2 \times \frac{22}{7} \times 10.5\)
= \(21 + 22\)
= 43 cm
Source: Myschool Past Questions Archive (Record #54929)
Physics
UTME / JAMB 2014
Current Electricity & Electric Circuits
What is the least possible error encountered when taking measurement with a meter rule?
A
0.1mm
B
1.0mm
C
0.5mm
D
0.2mm
medium Difficulty
Verified Correct Answer: Option C
Physical Principles & Numerical Solution
No expanded working has been attached for this question yet. The verified answer is Option C.
Source: Myschool Past Questions Archive (Record #26954)
Physics
UTME / JAMB 2014
Scalars, Vectors & Relative Motion
Solution
A quantity which requires magnitude and direction to be specified is
A
Temperature
B
Distance
C
Displacement
D
Mass
medium Difficulty
Verified Correct Answer: Option C
Physical Principles & Numerical Solution
Displacement is a vector quantity
Source: Myschool Past Questions Archive (Record #26955)
Physics
UTME / JAMB 2014
Equilibrium of Forces, Moments & Flotation
I Electrical potential, II Torque, III Kinetic Energy, IV Momentum. Which of the quantities listed are vectors?
A
II and IV
B
I and II
C
I and III
D
II and III
medium Difficulty
Verified Correct Answer: Option A
Physical Principles & Numerical Solution
No expanded working has been attached for this question yet. The verified answer is Option A.
Source: Myschool Past Questions Archive (Record #26956)
Physics
UTME / JAMB 2014
Current Electricity & Electric Circuits
Solution
Which type of motion do the wheels of a moving car undergo?
A
Vibratory and translational motion
B
Random and translational motion
C
Rotational mand oscillatory motion
D
Translational and rotational motion
medium Difficulty
Verified Correct Answer: Option D
Physical Principles & Numerical Solution
The tyre in motion makes a rotation and it translates in a straight line alongside. if the wheels is turned it continued further in a translational straight line through rotational motion.
Source: Myschool Past Questions Archive (Record #26957)
Physics
UTME / JAMB 2014
Current Electricity & Electric Circuits
Solution
A car accelerates uniformly from rest at 3ms-2. its velocity after traveling a distance of 24m is
A
12ms-1
B
144ms-1
C
72ms-1
D
36ms-1
medium Difficulty
Verified Correct Answer: Option A
Physical Principles & Numerical Solution
V2 = U2 x 2ax
V2 = 0 x 2(3)(24)
V2 = 144
V = \(\sqrt{144}\)
V = 12ms-1
Source: Myschool Past Questions Archive (Record #26958)
Physics
UTME / JAMB 2014
Circular Motion, Gravitation & Simple Harmonic Motion
Solution
Calculate the escape velocity of a satellite launched from the earth's surface if the radius of the earth is 6.4x106m
A
25.3kms-1
B
4.2kms-1
C
4.0kms-1
D
11.3kms-1
medium Difficulty
Verified Correct Answer: Option D
Physical Principles & Numerical Solution
Vescape = \(\sqrt{2gR}\)
Vescape = \(\sqrt{2\times10\times6.4\times10^6}\)
Vescape = \(\sqrt{128000000}\)
Vescape = 11313.7085mS-1
Vescape = 11.313kmS-1
Source: Myschool Past Questions Archive (Record #26959)