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Mathematics
WAEC / WASSCE 2018
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
Marks
10
20
30
40
50
60
70
80
90
Frequency
1
1
x
5
y
1
4
3
1
The frequency distribution shows the marks distribution of a class of 30 students in an examination.
The mean mark of the distribution is 52.
(a) Find the values of x and y.
(b) Construct a group frequency distribution table starting with a lower class limit of 1 and class interval of 10.
(c) Draw a histogram for the distribution
(d) Use the histogram to estimate the mode.
medium Difficulty
Verified Correct Answer: Option
Step-by-Step Mathematical Solution
(a)
Marks(x)
Frequency (f)
fx
10
1
10
20
1
20
30
x
30x
40
5
200
50
y
50y
60
1
60
70
4
280
80
3
240
90
1
90
Total
16 + x + y
900 + 30x + 50y
\(\sum f = 16 + x + y = 30\)
\(\implies x + y = 14 ... (1)\)
\(\bar{x} = \frac{\sum fx}{\sum f}\)
\(52 = \frac{900 + 30x + 50y}{30}\)
\(1560 = 900 + 30x + 50y \implies 30x + 50y = 660\)
\(3x + 5y = 66 .... (2)\)
Solving equation (1) and (2),
From (1), x = 14 - y
\(3(14 - y) + 5y = 42 - 3y + 5y = 66\)
\(2y = 24 \implies y = 12\)
\(x = 14 - y = 14 - 12 = 2\)
(x, y) = (2, 12).
(b)
Class interval
Frequency
Upper class boundary
1 - 10
1
10.5
11 - 20
1
20.5
21 - 30
2
30.5
31 - 40
5
40.5
41 - 50
12
50.5
51 - 60
1
60.5
61 - 70
4
70.5
71 - 80
3
80.5
81 - 90
1
90.5
(c)
(d) From the histogram, Mode = 44.
Source: Myschool Past Questions Archive (Record #52323)
Mathematics
UTME / JAMB 2018
Permutations, Combinations & Probability
Solution
If X, Y can take values from the set (1, 2, 3 ,4), find the probability that the product of X and Y is not greater than 6
A
\(\frac{5}{8}\)
B
\(\frac{5}{16}\)
C
\(\frac{1}{2}\)
D
\(\frac{3}{8}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
x
1
2
3
4
1
1*
2*
3*
4*
2
2*
4*
6*
8
3
3*
6*
9
12
4
4*
8
12
16
The numbers that are not greater than 6 are either less than 6 or equal to 6.
P(picking a number not greater than 6) = \(\frac{10}{16}\)
= \(\frac{5}{8}\)
Source: Myschool Past Questions Archive (Record #54912)
Mathematics
UTME / JAMB 2018
Plane Geometry, Polygons & Circle Theorems
Solution
If \(N = \begin{pmatrix} 3 & 5 & -4 \\ 6 & -3 & -5 \\ -2 & 2 & 1 \end{pmatrix}\), find \(|N|\).
A
65
B
23
C
17
D
91
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\begin{vmatrix} 3 & 5 & -4 \\ 6 & -3 & -5 \\ -2 & 2 & 1 \end{vmatrix}\)
= \(3(-3 - (-10)) - 5(6 - 10) + (-4)(12 - 6)\)
= \(21 + 20 - 24\)
= 17
Source: Myschool Past Questions Archive (Record #54913)
Physics
UTME / JAMB 2018
Current Electricity & Electric Circuits
Solution
The density of 400cm\(^3\) of palm oil was 0.9gcm-3 before frying. If the density of the oil was 0.6gcm-3 after frying, assuming no loss of oil due to spilling, its new volume was?
A
1360cm\(^3\)
B
600cm\(^3\)
C
240cm\(^3\)
D
8000m\(^3\)
medium Difficulty
Verified Correct Answer: Option B
Physical Principles & Numerical Solution
\(Density= \frac{mass}{volume}\)
⇒ \(0.9gcm^{-3} = \frac{mass}{400cm^{3}} = 360g\)
without any loss in the frying process, we have
\(0.6gcm^{-3} = \frac{360g}{v}\)
\(v = \frac{360g}{0.6gcm^{-3}} = 600cm^{3}\)
Source: Myschool Past Questions Archive (Record #47376)
Physics
UTME / JAMB 2018
Atomic, Quantum, Nuclear Physics & Electronics
Solution
Natural radioactivity consists of the emission of
A
α- particles and β-rays
B
α- particles and X-rays
C
α- particles, β - rays and y-rays
D
γ- rays and X-rays
medium Difficulty
Verified Correct Answer: Option C
Physical Principles & Numerical Solution
Radioactivity is the spontaneous emission of radiation from atomic nuclei. This radiation can consist of alpha, beta, and gamma radiation.
Source: Myschool Past Questions Archive (Record #47378)
Physics
UTME / JAMB 2018
Current Electricity & Electric Circuits
Which of the following is true of an electrical charge?
A
Positive charge means deficit electrons
B
Negative charge means excess of electrons
C
electric current means movement of electrons
D
All of the above
medium Difficulty
Verified Correct Answer: Option D
Physical Principles & Numerical Solution
No expanded working has been attached for this question yet. The verified answer is Option D.
Source: Myschool Past Questions Archive (Record #47380)
Physics
UTME / JAMB 2018
Reflection, Refraction & Dispersion of Light
Solution
Which of the following does NOT describe the Image formed by a plane minor?
A
Erect
B
Laterally inverted
C
Same distance from mirror as object
D
Magnified
medium Difficulty
Verified Correct Answer: Option D
Physical Principles & Numerical Solution
The image formed by a plane mirror is always virtual (the light rays do not actually come from the image), upright, and of the same shape and size as the object it is reflecting.
Source: Myschool Past Questions Archive (Record #47381)
Physics
UTME / JAMB 2018
Current Electricity & Electric Circuits
Diagram
Solution
What is the resultant resistance of the circuit in the image shown?
Attached Figure / Diagram
A
8Ω
B
11Ω
C
4Ω
D
3.6Ω
medium Difficulty
Verified Correct Answer: Option A
Physical Principles & Numerical Solution
First, the two 2-ohm resistors are in parallel
R\(_T\) = \(\frac{2 \times 2}{2 + 2}\) = 1 ohm
Now, the 3, 4, and 1 ohm resistors are in series
Therefore, R\(_eq\) = 3 + 4 + 1 = 8 ohms.
Source: Myschool Past Questions Archive (Record #47382)
Physics
UTME / JAMB 2018
Reflection, Refraction & Dispersion of Light
A narrow beam of white light can be split up into different Colours by a glass prism. The correct explanation is that
A
white light Is an electromagnetic wave
B
the prism has all the colours of the white light
C
different colours of white light travel with different speeds in glass
D
white light has undergone total Internal reflection in the prism
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 #47385)
Physics
UTME / JAMB 2018
Atomic, Quantum, Nuclear Physics & Electronics
What type of reaction is represented by the following scheme?
\(_{1} ^{2} X\) + \(_{1} ^{2} Y\) -----> \(_{2} ^{3} Z\) + \(_{0} ^{1} n\) + energy
A
fusion reaction
B
fission reaction
C
Chain reaction
D
radioactive decay
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 #47387)
Physics
UTME / JAMB 2018
Calorimetry, Latent Heat & Change of State
Solution
The amount of heat needed to raise the temperature of 10kg of Copper by 1K is its
A
specific heat capacity
B
latent heat
C
heat capacity
D
internal energy
medium Difficulty
Verified Correct Answer: Option C
Physical Principles & Numerical Solution
The heat capacity of a defined system is the amount of heat (usually expressed in calories, kilocalories, or joules) needed to raise the system's temperature by one degree (usually expressed in Celsius or Kelvin).
Source: Myschool Past Questions Archive (Record #47388)
Physics
UTME / JAMB 2018
Reflection, Refraction & Dispersion of Light
Shadows and eclipses result from the
A
refraction of light
B
reflection of light
C
defraction of light
D
rectilinear propagation of light
medium Difficulty
Verified Correct Answer: Option D
Physical Principles & Numerical Solution
No expanded working has been attached for this question yet. The verified answer is Option D.
Source: Myschool Past Questions Archive (Record #47390)
Physics
UTME / JAMB 2018
Current Electricity & Electric Circuits
Which of the following has the lowest internal resistance when new?
A
Leclanche cell
B
Daniell cell
C
Torch battery
D
Accumulator
medium Difficulty
Verified Correct Answer: Option D
Physical Principles & Numerical Solution
No expanded working has been attached for this question yet. The verified answer is Option D.
Source: Myschool Past Questions Archive (Record #47396)
Physics
UTME / JAMB 2018
Current Electricity & Electric Circuits
The pitch of an acoustic device can be increased by
A
decreasing the loudness
B
increasing the intensity
C
increasing the frequency
D
decreasing the intensity
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 #47397)
Physics
UTME / JAMB 2018
Atomic, Quantum, Nuclear Physics & Electronics
One of the features of the fission process is that
A
it leads to chain reaction
B
its products are not radioactive
C
neutrons are not released
D
the of the masses of the reactants equals the sum of the masses of the products
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 #47398)