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Mathematics
NECO SSCE 2001
Algebra
Solution
Solve the equation x\(^2\) - 3x - 10 = 0
A
-2 or -5
B
-3 or -10
C
5 or -2
D
2 or 5
E
3 or 10
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
x\(^2\) - 3x - 10 = 0
Using factorisation method: x\(^2\) - 3x - 10 = 0 becomes
x\(^2\) - 5x + 2x - 10 = 0
(x\(^2\) - 5x) + (2x - 10) = 0
x(x - 5) + 2(x -5) = 0
x - 5 = 0 or x + 2 = 0
\(\therefore\) x = 5 or -2
Source: Myschool Past Questions Archive (Record #41922)
Mathematics
NECO SSCE 2001
Geometry and Trigonometry
Solution
If sin \theta = \(\frac{4}{5}\) where 0^\circ ∠ \theta ∠ 90º, what is the value of cos \theta + tan \theta?
A
\(\frac{14}{15}\)
B
\(\frac{29}{15}\)
C
\(\frac{13}{8}\)
D
\(\frac{144}{15}\)
E
\(\frac{24}{5}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
0^\circ ∠ \theta ∠ 90º,
From the diagram above, the adjacent by Pythagoras theorem = 3
Cos \theta = \(\frac{\text{adj}}{\text{hyp}}\) = \(\frac{3}{5}\)
Tan \theta = \(\frac{\text{opp}}{\text{adj}}\) = \(\frac{4}{3}\)
cos \theta + tan \theta = \(\frac{3}{5}\) + \(\frac{4}{3}\) = \(\frac{29}{15}\)
Source: Myschool Past Questions Archive (Record #41960)
Mathematics
NECO SSCE 2001
Geometry and Trigonometry
Solution
The lengths of the sides of a triangle are 15m, 21m, and 28cm. What is the size of the angle facing the side 21m (correct to one decimal place)?
A
85.7°
B
47.5°
C
41.5°
D
41.4°
E
38.2°
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
using cosine rule,
\(cos\theta\) = \(\frac{28^2 + 15^2 - 21^2}{2\times28\times15}\)
= \(\frac{568}{840}\)
\(\theta = cos^{-1}\)
= 47.5^\circ
Source: Myschool Past Questions Archive (Record #41965)
Mathematics
NECO SSCE 2001
Number and Numeration
If t varies inversely as the cube of s, and t = 24, when s = 3, find t when s = 2
A
8
B
24
C
27
D
81
E
648
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option D.
Source: Myschool Past Questions Archive (Record #41968)
Mathematics
NECO SSCE 2001
Statistics and Probability
Solution
Two fair coins are tossed at the same time. what is the probability of getting a head?
A
1
B
\(\frac{3}{4}\)
C
\(\frac{1}{2}\)
D
\(\frac{1}{3}\)
E
\(\frac{1}{4}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
T
H
T
T, T
T, H
H
H , T
H ,H
Pro(one head) = \(\frac{3}{4}\) = \(\frac{3}{4}\)
Source: Myschool Past Questions Archive (Record #41970)
Physics
NECO SSCE 2001
Waves and Optics
The invisible part of the spectrum of white light consists of
A
Infra-red and ultra-violet only
B
Infra-red, ultra-violet and blue only
C
red, orange and green only
D
red and violet only
E
yellow and indigo only
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 #42811)
Physics
NECO SSCE 2001
Mechanics and Properties of Matter
Solution
50cm\(^3\) of air at a pressure of 5Nm\(^{-2}\) is enclosed in a metal tube by a piston. If the piston is pushed in a distance of 10cm, what will the pressure of the air become, if the cross-sectional area of the tube is 2cm\(^{-2}\)? (Assume that the temperature remains constant throughout)
A
12.5 Nm-2
B
8.7 Nm-2
C
8.3 Nm-2
D
3.8Nm-2
E
3.0Nm-2
medium Difficulty
Verified Correct Answer: Option C
Physical Principles & Numerical Solution
This is an application of Boyle’s Law (since temperature is constant):
P\(_1\)V\(_1\) = P\(_2\)V\(_2\)
Given:
- Initial volume, V\(_1\) = 50 cm\(^3\)
- Initial pressure, P\(_1\) = 5 N m\(^{-2}\)
- Distance piston is pushed in = 10 cm
- Cross-sectional area of tube, A = 2 cm\(^2\)
Decrease in volume = Area \times Distance moved
= 2 cm\(^2\) \times 10 cm
= 20 cm\(^3\)
Calculate the new volume V\(_2\)
V\(_2\) = V\(_1\) − decrease in volume
= 50 cm\(^3\) − 20 cm\(^3\)
= 30 cm\(^3\)
Apply Boyle’s Law
P\(_1\)V\(_1\) = P\(_2\)V\(_2\)
5 \times 50 = P\(_2\) \times 30
P\(_2\) = \(\frac{(5 \times 50)}{ 30}\)
P\(_2\) = \(\frac{250}{30}\)
P\(_2\) = \(\frac{25}{3}\) N m\(^{-2}\)
(The pressure increases because the volume decreases at constant temperature.)
Source: Myschool Past Questions Archive (Record #42812)
Physics
NECO SSCE 2001
Heat Energy & Temperature
Which scientist discovered natural radioactivity?
A
Enrico Fermi
B
Henri Becquerel
C
Marie Curie
D
Micheal Faraday
E
Niels Bohr
medium Difficulty
Verified Correct Answer: Option B
Physical Principles & Numerical Solution
No expanded working has been attached for this question yet. The verified answer is Option B.
Source: Myschool Past Questions Archive (Record #42813)
Physics
NECO SSCE 2001
Waves and Optics
Solution
Totally reflecting prisms are preferred to mirrors in periscopes because
I. mirror gives multiple images
II. silvering on mirrors is easily damaged
III. mirrors reflect less light than totally reflecting prisms
A
I only
B
I and II only
C
I and III only
D
II and III only
E
I,II and III
medium Difficulty
Verified Correct Answer: Option E
Physical Principles & Numerical Solution
Total internal reflection in prisms occurs without loss of light, while mirrors can have some absorption and scattering. Thus, totally reflecting prisms generally reflect more light, and the silvering (reflective coating) on mirrors can be easily scratched or damaged, which makes them less durable than totally reflecting prisms.
An ordinary mirror is that it reflects from both surfaces. giving multiple reflections.
Source: Myschool Past Questions Archive (Record #42814)
Physics
NECO SSCE 2001
Mechanics and Properties of Matter
What is the energy stored in a 10μ F capacitor if the potential difference between the plates is 40 V?
A
2.0 × 10-4J
B
8.0 ×10-4J
C
4.0 × 10-3J
D
8.0 × 10-3J
E
1.6 × 10-2J
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 #42815)
Physics
NECO SSCE 2001
Waves and Optics
Solution
Notes of the same frequency sounded on a piano and on a flute may differ in
I. pitch
II. quality
III. Loudness
A
I only
B
II only
C
I and III only
D
II and III only
E
I, II and III
medium Difficulty
Verified Correct Answer: Option B
Physical Principles & Numerical Solution
Quality is that characteristic note which distinguishes the two sounds of the same loudness and same pitch but emitted by two different instruments.
Source: Myschool Past Questions Archive (Record #42816)
Physics
NECO SSCE 2001
Heat Energy & Temperature
What is X in the equation given below? 42He + 94Be → 126C + X
A
electron
B
hydrogen
C
lithium
D
neutron
E
proton
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 #42817)
Physics
NECO SSCE 2001
Mechanics and Properties of Matter
Solution
A waterfall is 630m high. What is the change in temperature of a quantity of water that falls from the top to the bottom of the waterfall? (Neglect heat losses to the surroundings, take g as 10 ms-2 and specific heat capacity of weather as 4200J kg-1K-1
A
0.015°C
B
1.50°C
C
15.00°C
D
21.00 °C
E
50.00°C
medium Difficulty
Verified Correct Answer: Option B
Physical Principles & Numerical Solution
water height as 630m, gravity = 10m/s\(^2\), specific heat capacity of weather as 4200J
Temperature change = \(\frac{gh}{c}\) = \(\frac{630 \times 10}{4200}\)
= 1.5ºC
Source: Myschool Past Questions Archive (Record #42818)
Physics
NECO SSCE 2001
Mechanics and Properties of Matter
N.N.P.C. gas cylinder containing 15kg of cooking gas was left open, and the gas emptied in 3.8 minutes, at an average speed of 20 ms-1. What force was exerted on the gas in the cylinder?
A
132N
B
13.2N
C
1.32N
D
0.132N
E
0.013N
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 #42819)
Physics
NECO SSCE 2001
Waves and Optics
An object placed 15cm from a converging lens forms a real image whose magnification is 2.0. What is the focal length of the lens?
A
5.00cm
B
10.00cm
C
15.00 cm
D
18.00 cm
E
20.00cm
medium Difficulty
Verified Correct Answer: Option B
Physical Principles & Numerical Solution
No expanded working has been attached for this question yet. The verified answer is Option B.
Source: Myschool Past Questions Archive (Record #42820)