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Mathematics
NECO SSCE 2005
Number and Numeration
If (x - a) is a factor of bx - ax + x2 - ab, what is the other factor?
A
(x + b)
B
(b - a)
C
(x - a)
D
(a + b)
E
(a - b)
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 #42358)
Mathematics
NECO SSCE 2005
Number and Numeration
Solution
Simplify (6 - x - x2) \div (x2 - 4)
A
(3 + x) ÷ (x + 2)
B
(x - 3) ÷ (x - 2)
C
(x - 3) ÷ (x + 3)
D
(3 - x) ÷ (x + 2)
E
(3 - x) ÷ (x - 2)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
(6 - x - x2) = ( 2 - x ) ( 3 + x )
divides
( x^2 - 4 ) = ( -2 - x ) ( 2 - x )
= ( 3 + x ) / ( x + 2)
Source: Myschool Past Questions Archive (Record #42360)
Mathematics
NECO SSCE 2005
Number and Numeration
In Δ ABC, A = 60°, C = 90° and AC = 12m. Find the Length of the hypotenuse.
A
24m
B
14m
C
12m
D
7m
E
6m
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 #42364)
Mathematics
NECO SSCE 2005
Number and Numeration
For what value(s) of x is the expression (x2 + 15x + 50) ÷ (x - 5) not defined
A
-5, -10
B
-10
C
-5
D
5
E
10, 5
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 #42368)
Mathematics
NECO SSCE 2005
Number and Numeration
Solution
Evaluate log 18 + log6 - log16\(^{\frac{1}{2}}\)
A
log 3
B
log 9
C
log 20
D
3 log 2
E
3 log 3
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
To evaluate the expression \( \log 18 + \log 6 - \log 16^{\frac{1}{2}} \), we can use the properties of logarithms.
Simplify \( \log 16^{\frac{1}{2}} \)
Using the power rule of logarithms: \(\log 16^{\frac{1}{2}} = \frac{1}{2} \log 16\)
Substitute back into the expression:
Now rewrite the expression: \(\log 18 + \log 6 - \frac{1}{2} \log 16\)
Combine the logarithms:
Using the product property of logarithms: \(\log 18 + \log 6 = \log (18 \cdot 6) = \log 108\)
So we can rewrite the expression as: \(\log 108 - \frac{1}{2} \log 16\)
Rewrite \( \frac{1}{2} \log 16\)
Using the power rule again: \(\frac{1}{2} \log 16 = \log 16^{\frac{1}{2}} = \log 4\)
Substitute back;
Now we have: \(\log 108 - \log 4\)
Using the quotient property of logarithms: \(\log \left( \frac{108}{4} \right)\)
Simplify \(\frac{108}{4}\)
Calculating: \(\frac{108}{4}\) = 27
Thus, the expression simplifies to: log 27 = 3log3
NOTE: all is in base 10.
Source: Myschool Past Questions Archive (Record #42373)
Mathematics
NECO SSCE 2005
Number and Numeration
If A(I,2,3,...,10) ; B = (-5,-4,.....,-1) ; C = (-1, 0, 1, 2,....5) List all the elements in (B ∪ C) ∩ A
A
(-1,2,...5)
B
(-1,1,....5)
C
(1,2,..5)
D
(2,3,...10)
E
(1,2,...10)
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 #42382)
Mathematics
NECO SSCE 2005
Number and Numeration
What is the positive difference between the squares of 2.5 and 2.1 to 1 significant figures?
A
– 2.0
B
– 184
C
-1.84
D
2
E
18.4
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 #42385)
Mathematics
NECO SSCE 2005
Number and Numeration
Find the value of 2a - b if a + b = 8 and 4a - b = 22
A
2
B
4
C
6
D
8
E
10
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 #42388)
Mathematics
NECO SSCE 2005
Number and Numeration
Find the Iength of a diagonal of a square whose area is 288cm2.
A
24cm
B
48cm
C
95cm
D
100cm
E
124cm
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 #42394)
Mathematics
NECO SSCE 2005
Number and Numeration
A surveyor measured the length of a obtained 42.55 metres. If his measurement was more than the actual length and the percentage error of his measurement was 8%, calculate the actual length of the land
A
39.40 metres
B
46.20 metres
C
46.25 metres
D
46.50 metres
E
48.25 metres
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 #42414)
Mathematics
NECO SSCE 2005
Number and Numeration
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
Number and Numeration
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
Number and Numeration
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
Number and Numeration
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
Number and Numeration
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)