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Mathematics
UTME / JAMB 2002
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
Calculate the mean deviation of the set of numbers 7, 3, 14, 9, 7, and 8.
A
13/6
B
5/2
C
7/6
D
7/3
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
x
7
3
14
9
7
8
Total
\(x - \bar{x}\)
-1
-5
6
1
-1
0
\(|x - \bar{x}|\)
1
5
6
1
1
0
14
Mean : \(\frac{7 + 3 + 14 + 9 + 7 + 8}{6} = \frac{48}{6} = 8\)
Mean deviation : \(\frac{\sum |x - \bar{x}|}{n} = \frac{14}{6} = \frac{7}{3}\)
Source: Myschool Past Questions Archive (Record #3396)
Mathematics
UTME / JAMB 2002
Indices, Logarithms & Surds
Diagram
Solution
In the diagram above , XZ is the diameter of the circle XZW, with center O and radius 15/2 cm. If XY = 12 cm, find the area of the triangle XYZ
Attached Figure / Diagram
A
54 cm2
B
45 cm2
C
27 cm2
D
75 cm2
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Since radius = \(\frac{15}{2}\) diameter = 2 * (\(\frac{15}{2}\)) = 15cm
XYZ is a right-angled triangle (since
Source: Myschool Past Questions Archive (Record #7728)
Mathematics
UTME / JAMB 2002
Sets, Logic & Venn Diagrams
Diagram
Solution
The venn diagram above shows the numbers of students offering music and history in a class of 80 students. If a student is picked at random from the class, what is the probability that he offers Music only?
Attached Figure / Diagram
A
0.38
B
0.13
C
0.50
D
0.25
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
30 - x + x + 40 - x = 80 - 20
70 - x = 60
- x = 60 - 70
- x = - 10
∴ x = 10
Music only = 30 - x
= 30 - 10
20
P(music only) = 20/80
= 1/4
= 0.25
Source: Myschool Past Questions Archive (Record #7734)
Mathematics
UTME / JAMB 2002
Inequalities & Linear Programming
Diagram
Solution
Use the graph above to find the values of p and q if px + qy \(\geq\) 4
Attached Figure / Diagram
A
p = 2, q = -1
B
p = -1, q = 2
C
p = 2, q = 2
D
p = 1, q = 2
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
m = \(\frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 0}{0 - (4)} = \frac{2}{4} = \frac{1}{2}\)
\(\frac{y_2 - y_1}{x_2 - x_1} \geq m\)
\(\frac{y - 0}{x + 4} \geq \frac{1}{2}\)
2y \(\geq\) x + 4, -x + 2y \(\geq\) 4 = px + qy \(\geq\) 4
p = -1, q = 2
Source: WAEC / JAMB / NECO Classroom Archive (Record #33102)
Mathematics
NECO SSCE 2002
Mensuration (Areas, Perimeters & Volumes)
Solution
A wire was shaped to form a square of area 81cm\(^2\). An equilateral triangle was formed by the same wire,What is the length of a side of the triangle formed?
A
3cm
B
6cm
C
9cm
D
12cm
E
27cm
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Area of a square = L X L = 81
: L = 9
Perimeter of square = 4 X L
4 X 9 = 36cm
An equilateral triangle with equal sides:
36/3 = 12cm
Source: WAEC / JAMB / NECO Classroom Archive (Record #42139)
Mathematics
NECO SSCE 2002
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
The mean and the range of the set of numbers: 1.20, 1.00, 0.90, 1.40, 0.80, 0.80, 1.20 and 1.10 are p and q respectively. What is the value of p ÷ q?
A
1.11
B
65
C
1.85
D
2.45
E
3.85
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Mean of 1.20, 1.00, 0.90, 1.40, 0.80, 0.80, 1.20 and 1.10
→ \(\frac{8.4}{8}\) = 1.05 → p
Range = 1.40 - 0.80 = 0.60 → q
p \div q = 1.05 \div 0.60
= 1.75
Source: WAEC / JAMB / NECO Classroom Archive (Record #42203)
Physics
WAEC / WASSCE 2002
Temperature, Thermometry & Thermal Expansion
Solution
One common characteristics of solids, liquids and gasses is that?
A
all the three has fixed volume
B
their molecule have the same size
C
their molecules are always in motion
D
all the three have the same inter molecular forces
medium Difficulty
Verified Correct Answer: Option C
Physical Principles & Numerical Solution
The kinetic theory of matter (particle theory) says that all matter consists of many, very small particles which are constantly moving or in a continual state of motion.
Source: WAEC / JAMB / NECO Classroom Archive (Record #33964)
Physics
NECO SSCE 2002
Circular Motion, Gravitation & Simple Harmonic Motion
Solution
What is the escape velocity of a satellite launched from the earth’s surface? (Take g as 10ms\(^{-2}\) and the radius of the earth as 6.4 × 10\(^6\)m)
A
7.80 × 10kms-1
B
11.2 × 10kms-1
C
3.56 × 107ms-1
D
6.00 × 107ms-1
E
1.20 × 108ms-1
medium Difficulty
Verified Correct Answer: Option B
Physical Principles & Numerical Solution
V\(_e\) = \(\sqrt{2gr}\)
V\(_e\) = \(\sqrt{2 \times 10 \times 6.4 \times 10^6}\) = 11.313km/s
The escape speed from Earth's surface is about 11.186 km/s
Source: WAEC / JAMB / NECO Classroom Archive (Record #42866)
Physics
UTME / JAMB 2002
Magnetism, Electromagnetism & AC Circuits
Solution
Which of the following statements is true of the properties of a moving coil galvanometer?
A
THe coil has a small area
B
There are strong hair springs to gives a large control panlel
C
There is a strong permanent magnet to give high magnetic flux
D
it has a small number of turns of coil
medium Difficulty
Verified Correct Answer: Option C
Physical Principles & Numerical Solution
The galvanometer possesses a rectangular coil mounted on a soft iron core rotating on a magnetic field induced by a permanent magnet.
Source: WAEC / JAMB / NECO Classroom Archive (Record #12263)
Physics
NECO SSCE 2002
Current Electricity & Electric Circuits
Solution
When a current of 1 .0A flows in an electrolyte for 3.0h, a mass of 1 .0g is deposited. What mass will be deposited in 10.0h if a current of 3.0A flows through the electrolyte?
A
30.0g
B
24.0g
C
10.0g
D
6.0g
E
0.4g
medium Difficulty
Verified Correct Answer: Option C
Physical Principles & Numerical Solution
Q = charge
i = current
t = time in sec
Mass(M1)
3hours to sec
60*60*3= 10800
Mass(M2)
10hours to sec
60*60*10 = 36,000
36,000 * 3.0A = 108,000
if it takes 10800 current to discharge 1g
how much will it take 108000
10800---->1
108000---x
= 108000/10800
=10
Source: WAEC / JAMB / NECO Classroom Archive (Record #42888)
Physics
WAEC / WASSCE 2002
Magnetism, Electromagnetism & AC Circuits
Diagram
Solution
Calculate the inductance L, of the coil in the circuit diagram shown above
Attached Figure / Diagram
A
3.8H
B
0.6H
C
0.4H
D
0.2H
medium Difficulty
Verified Correct Answer: Option B
Physical Principles & Numerical Solution
XL = \(\frac{V}{I} = \frac{240}{2} = 120\Omega\)
L = \(\frac{X_L}{2 \pi f}\)
= \(\frac{120 \times \pi}{2 \times \pi \times 100}\)
= 0.6H
Source: WAEC / JAMB / NECO Classroom Archive (Record #34114)
Physics
WAEC / WASSCE 2002
Atomic, Quantum, Nuclear Physics & Electronics
Solution
In a model of the hydrogen atom, the energy levels Wn are given by the formula Wn = -\(\frac{R}{n^2}\), where n is an integer and R is a constant. Determine the energy released in the transition from n = 3 to n = 2.
A
\(\frac{R}{5}\)
B
-\(\frac{R}{4}\)
C
\(\frac{5R}{36}\)
D
\(\frac{-5R}{36}\)
medium Difficulty
Verified Correct Answer: Option C
Physical Principles & Numerical Solution
Given that W = -\(\frac{R}{n^2}\)
from n = 3 to n = 2.
-\(\frac{R}{3^2}\) - (-\(\frac{R}{2^2}\))
-\(\frac{R}{9}\) - (-\(\frac{R}{4}\))
-\(\frac{R}{9}\) + \(\frac{R}{4}\);
with LCM 36
\(\frac{-4R + 9R}{36}\)
= \(\frac{5R}{36}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #34120)
Physics
NECO SSCE 2002
Reflection, Refraction & Dispersion of Light
Solution
Which colour is deviated least when white light passes through a triangular prism?
A
green
B
indigo
C
red
D
violet
E
yellow
medium Difficulty
Verified Correct Answer: Option C
Physical Principles & Numerical Solution
violet color will deviate the most.
Red light shows the least amount of deviation
Source: WAEC / JAMB / NECO Classroom Archive (Record #42859)
Chemistry
UTME / JAMB 2002
Acids, Bases, pH & Salts
Solution
Three drops of a 1.0 mol dm-3 solution of NaOH are added to 20 cm3 of a solution of pH 8.4. The pH of the resulting solution will?
A
Close to that of pure water
B
Unaltered
C
Greater than 8.4
D
Less than 8.4
medium Difficulty
Verified Correct Answer: Option C
Chemical Principles & Mechanism
A strong base is one that fully dissociates to give ions in solution. Weak bases only partially dissociate in a solution,
while the strong bases dissociate fully in a solution. Weak bases have pH 7.3 – 10, strong ones have pH 10 – 14.
Source: WAEC / JAMB / NECO Classroom Archive (Record #1757)
Chemistry
WAEC / WASSCE 2002
Acids, Bases, pH & Salts
Solution
Which of following acids forms normal salts only?
A
Tetraoxosulphate (VI) acid
B
Trioxosulphate (IV) acid
C
Acetic acid
D
Tetraoxophosphate (V) acid
medium Difficulty
Verified Correct Answer: Option C
Chemical Principles & Mechanism
So we can determine that the basicity of Acetic acid is 1 because it releases one hydrogen ion in an aqueous solution.
Due to this they act as very weak acids. When weak acid reacts with strong base, they tend to form normal salt.
Source: WAEC / JAMB / NECO Classroom Archive (Record #39998)