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Mathematics
NECO SSCE 2005
Indices, Logarithms & Surds
Solution
If x + \(\frac{1}{x}\) = 8, find x\(^2\) + \(\frac{1}{x^2}\)
A
64
B
62
C
32
D
16
E
4
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Given that \(x + \frac{1}{x} = 8\)
We want to find
\(x^2 + \frac{1}{x^2}\)
We can use the identity:
\(x^2 + \frac{1}{x^2} = \left( x + \frac{1}{x} \right)^2 - 2\)
Substituting the given value:
\(x^2 + \frac{1}{x^2} = 8^2 - 2\)
Calculating \( 8^2 \):
\(8^2 = 64\)
Now substituting back:
\(x^2 + \frac{1}{x^2} = 64 - 2 = 62\)
Thus, the final answer is \(x^2 + \frac{1}{x^2} = 62\)
Source: Myschool Past Questions Archive (Record #42419)
Mathematics
NECO SSCE 2005
Indices, Logarithms & Surds
Solution
Evaluate 0.0025 \times 2.5 \times 10\(^2\) to 2 significant figures.
A
0.625 × 10-3
B
0.63 × 10-2
C
6.25 × 10-3
D
6.3 × 10-2
E
6.3 × 10-1
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
0.0025 \times 2.5 \times 10\(^2\)
0.0025 \times 2.5 \times 10\(^2\) = 0.0025 x 2.5 x 100 = 0.625 ≈ 0.63 to 2 significant figures.
6.3 \times 10\(^{-1}\)
Source: Myschool Past Questions Archive (Record #42422)
Mathematics
NECO SSCE 2005
Trigonometry, Elevation & Bearings
A ship sails 6km from a port on a bearing 070° and then 8km on a bearing of 040°. Find the distance from the port.
A
7.21km
B
13.53km
C
16.86km
D
44.57km
E
67.17km
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option B.
Source: Myschool Past Questions Archive (Record #42431)
Mathematics
NECO SSCE 2005
Trigonometry, Elevation & Bearings
Calculate without using tables Tan 45° + Cos 60°
A
\(\sqrt{\frac{3}{2}}\) - 1
B
\(\frac{1}{2}\)
C
1\(\frac{1}{2}\)
D
\(\sqrt{\frac{3}{2}}\) + 1
E
2
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 #42438)
Mathematics
NECO SSCE 2005
Fractions, Decimals, Percentages & Approximations
A is at 50°N and B is at 10°N, If A and B are on the same longitude, find the distance AS. Correct your answer to Four significant figures. (Earth radius = 6400km)
A
6468km
B
5469km
C
4470km
D
3470km
E
2488km
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 #42441)
Mathematics
NECO SSCE 2005
Inequalities & Linear Programming
Solution
If a = {x : 1 < x < 9} ; b = {x : 0 < x < 9} ; C = {x : 2 x < 9} and a, b, c U, what are the elements in U?
A
U = {-1 < x < 9}
B
U = {0 < x < 9}
C
U = {1 < x < 9}
D
U = {1 < x < 10}
E
{2 < x < 10}
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
a = {x : 1 < x < 9}: a = {2, 3, 4, 5, 6, 7, 8}
b = {x : 0 < x < 9}: b = {1, 2, 3, 4, 5, 6, 7, 8}
C = {x : 2 < x < 9}; c = {3, 4, 5, 6, 7, 8}
U = {1, 2, 3, 4, 5, 6, 7, 8} = {0 < x < 9}.
Source: Myschool Past Questions Archive (Record #42442)
Mathematics
NECO SSCE 2005
Indices, Logarithms & Surds
If log 3 = 0.4771 and log 2 = 0.3010, what is the value of log 12?
A
0.0432
B
0.4322
C
1.0791
D
1.2552
E
1.5225
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 #42449)
Mathematics
NECO SSCE 2005
Inequalities & Linear Programming
Solution
If 7 is subtracted from twice a certain number x, the result is at most 5. What is the range of the number?
A
x < 2
B
x < 3
C
x < 4
D
x < 5
E
x < 6
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
At most 5 = less than or equal to 5
2x - 7 \le 5
2x \le 5 + 7
2x \le 12
divide through by 2
x \le 6
Source: Myschool Past Questions Archive (Record #42450)
Mathematics
NECO SSCE 2005
Statistics (Data Representation, Central Tendency & Dispersion)
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
Plane Geometry, Polygons & Circle Theorems
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
Plane Geometry, Polygons & Circle Theorems
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
Variations
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
Plane Geometry, Polygons & Circle Theorems
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
Plane Geometry, Polygons & Circle Theorems
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
Plane Geometry, Polygons & Circle Theorems
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)