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Mathematics
NECO SSCE 2005
Geometry and Trigonometry
Solution
Find the standard deviation of the numbers 6, 9, 10, 8 and 7
A
1.4
B
2
C
2.4
D
5
E
8
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
6, 9, 10, 8 and 7
S.D = \(\sqrt{V}\)
S.D = standard deviation, V = variance
V = \(\frac{\sum({x - \overline{x})^2}}{n}\)
Mean(\(\overline{x}\)) = \(\frac{6 + 9 + 10 + 8 + 7}{5}\) = 8
x
x - \(\overline{x}\)
(x - \(\overline{x}\))\(^2\)
6
6 - 8 = -2
4
9
9 - 8 = 1
1
10
10 - 8 = 2
4
8
8 - 8 = 0
0
7
7 - 8 = -1
1
TOTAL = 10
V = \(\frac{\sum({x - \overline{x})^2}}{n}\) = \(\frac{10}{5}\) = 2
S.D = \(\sqrt{V}\) = \(\sqrt{2}\) = 1.414 ≈ 1.4
Source: Myschool Past Questions Archive (Record #42451)
Mathematics
NECO SSCE 2005
Number and Numeration
Simplify P-6 × P3 × P2 ÷ P4 × P0
A
p5
B
p4
C
p3
D
p-3
E
p-5
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option E.
Source: Myschool Past Questions Archive (Record #42454)
Mathematics
NECO SSCE 2005
Number and Numeration
Solution
3 - 7, 8 - 12, 13 - 17, 18 - 22. Which of the following is/are true?
I. The class Interval is 4
II. The class boundaries are 2.5, 7.5, 12.5, 18.5, 22.5
III. The mid-marks are 5, 10, 15, and 20
A
I only
B
II only
C
III only
D
I and II only
E
I and III only
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
Given the class intervals: \(3 - 7\), \(8 - 12\), \(13 - 17\), and \(18 - 22\):
The class interval is \(4\):
\(7 - 3 = 4 \quad \text{(True)}\)
Class boundaries are \(2.5, 7.5, 12.5, 18.5, 22.5\):
- Correct boundaries: \(2.5, 7.5, 12.5, 17.5, 22.5\) False.
Mid-marks are \(5, 10, 15, 20\):
\(\text{Mid-mark} = \frac{\text{Lower} + \text{Upper}}{2}\)
- \(3 - 7: 5\)
- \(8 - 12: 10\)
- \(13 - 17: 15\)
- \(18 - 22: 20\) True.
Source: Myschool Past Questions Archive (Record #42455)
Mathematics
NECO SSCE 2005
Number and Numeration
Solution
T varies directly as D and inversely as A. Given that T = 6, D = 3, and A = 2, find A when T = 3 and D = 6.
A
4
B
6
C
8
D
12
E
24
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
T = \(\frac{ \text{KD}}{\text{A}}\)
6 = \(\frac{3K}{2}\)
3K = 12
K = 4
T= \(\frac{4D}{A}\)
but T = 3, D = 6 and A =?
T = \(\frac{4D}{A}\)
A = \(\frac{4D}{T}\)
A = \(\frac{4 \times 6}{3}\) = 8
Source: Myschool Past Questions Archive (Record #42456)
Mathematics
NECO SSCE 2005
Geometry and Trigonometry
A chord 20cm long subtends an angle of 60° at the circumference of a circle, what is the diameter of the circle the nearest cm?
A
12cm
B
20cm
C
23cm
D
60cm
E
80cm
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option C.
Source: Myschool Past Questions Archive (Record #42458)
Mathematics
NECO SSCE 2005
Number and Numeration
If 25a2 = 5-1 × 125. Find the value of a?
A
a = -1
B
a = 1
C
a = ±1
D
a = ±5
E
a = 25
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option C.
Source: Myschool Past Questions Archive (Record #42460)
Mathematics
NECO SSCE 2005
Geometry and Trigonometry
The parallel sides of a trapezium are 13cm and 7cm. If the area of the trapezium is 50cm2, find the perpendicular distance between the parallel sides.
A
5cm
B
6cm
C
7cm
D
10cm
E
12cm
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 #42462)
Mathematics
NECO SSCE 2005
Statistics and Probability
Two fair dice are tossed together once. What is the probability of getting a total of at least 9 from the outcome?
A
\(\frac{1}{9}\)
B
\(\frac{1}{6}\)
C
\(\frac{5}{18}\)
D
\(\frac{1}{3}\)
E
\(\frac{13}{18}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option C.
Source: Myschool Past Questions Archive (Record #42465)
Mathematics
NECO SSCE 2005
Number and Numeration
If 2x : ( x + 1) = 3 : 2, what is the value of x?
A
\(\frac{1}{2}\)
B
1
C
1\(\frac{1}{2}\)
D
3
E
3\(\frac{1}{2}\)
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 #42467)
Mathematics
NECO SSCE 2005
Number and Numeration
Solution
If y\(^2\)+ 14y + k is a perfect square, then k =
A
4
B
7
C
28
D
49
E
196
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
y\(^2\)+ 14y + k
let a = 1, b = 14, c = k (where a and b represent the coefficient of y and y\(^2\) respectively)
4ac = b\(^2\)
4 x 1 x c = 14 x 14 = 196
4c = 196
c = \(\frac{196}{4}\) = 49
Source: Myschool Past Questions Archive (Record #42469)
Physics
NECO SSCE 2005
Electricity and Magnetism
The angle between the geographic and the magnetic meridians at a place on the earth’s surface is the
A
angle of declination
B
angle of depression
C
angle of dip.
D
latitude of the place
E
longitude of the place
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 #42996)
Physics
NECO SSCE 2005
Mechanics and Properties of Matter
A body moves along a circular path with uniform angular speed of 0.6 rad s-1 and at a constant speed of 3.0 ms-1.
Calculate the acceleration of the body towards the centre of the circle.
A
0.2.ms-2
B
1.8 ms-2
C
5.0 ms-2
D
5.4 ms-2
E
25.0 ms-2
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 #42998)
Physics
NECO SSCE 2005
Mechanics and Properties of Matter
Which of the statements is/are true of two bodies involved in an inelastic collision? After collision.
I. the kinetic energy increases
II. The momentum decreases
III. Their velocities are the same.
A
I only
B
II Only
C
III only
D
I and II only
E
II and III only
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 #42999)
Physics
NECO SSCE 2005
Heat Energy & Temperature
491 K is equivalent to
A
273 °C
B
218 °C
C
373 °C
D
491 °C
E
764 °C
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 #43000)
Physics
NECO SSCE 2005
Thermal Physics
An atom radiates 1.5 × 10-19J when an electron jumps from one level to another. What is the wavelength of the emitted radiation? (Planck’s constant 6.6 × l0-34Js ; Speed of light in vacuum = 3.0 × 108ms-1)
A
1.32 × 10-6m
B
2.97 × 10-6m
C
3.30 × 10-6m
D
6.82 × 10-6m
E
8.01 × 10m-6
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 #43001)