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Mathematics
UTME / JAMB 2010
Number and Numeration
Solution
Determine the value of x for which (x\(^2\) - 1)>0
A
x 1
B
-1 < x < 1
C
x > 0
D
x < -1
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
(x\(^2\) - 1) > 0
x\(^2\) > 1
Taking the square root of both sides
x >1 or x < -1
Source: WAEC / JAMB / NECO Classroom Archive (Record #29653)
Mathematics
UTME / JAMB 2010
Number and Numeration
Solution
A cylindrical pipe 50m long with radius 7m has one end open. What is the total surface area of the pipe?
A
749\(\pi\)m2
B
700\(\pi\)m2
C
350\(\pi\)m2
D
98\(\pi\)m2
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Total surface area of the cylindrical pipe = area of circular base + curved surface area
= \(\pi\)r\(^2\) + 2\(\pi\)rh
= \(\pi\) x 7\(^2\) + 2\(\pi\) x 7 x 50
= 49\(\pi\) + 700\(\pi\)
= 749\(\pi\)m\(^2\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #29579)
Mathematics
UTME / JAMB 2010
Number and Numeration
Solution
At what value of X does the function y = -3 - 2x + X2 attain a minimum value?
A
-1
B
14
C
4
D
1
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Given that y = -3 - 2x + X2
then, \(\frac{dy}{dx}\) = -2 + 2x
At maximum value, \(\frac{dy}{dx}\) = O
therefore, -2 + 2x
2x = 2
x = 2/2 = 1
Source: WAEC / JAMB / NECO Classroom Archive (Record #29563)
Mathematics
UTME / JAMB 2010
Number and Numeration
Solution
Evaluate \(\int^{2}_{0}(x^3 + x^2)\)dx.
A
4\(\frac{5}{6}\)
B
6\(\frac{2}{3}\)
C
1\(\frac{5}{6}\)
D
2\(\frac{5}{6}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\int^{2}_{0}(x^3 + x^2)\)dx = \(\int^{2}_{0}\)(\(\frac{x^4}{4} + {\frac {x^3}{3}}\))
= (\(\frac{2^4}{4} + {\frac {2^3}{3}}\)) - (\(\frac{0^4}{4} + {\frac {0^3}{3}}\))
= (\(\frac{16}{4} + {\frac {8}{3}}\)) - 0
= \(\frac{80}{12}
= {\frac {20}{3}}\) or 6\(\frac{2}{3}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #29586)
Mathematics
UTME / JAMB 2010
Number and Numeration
Solution
In how many ways can a committee of 2 women and 3 men be chosen from 6 men and 5 women?
A
100
B
200
C
30
D
50
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
A committee of 2 women and 3 men can be chosen from 6 men and 5 women, in \(^{5}C_{2}\) x \(^{6}C_{3}\) ways
= \(\frac{5!}{(5 - 2)!2!} \times {\frac{6!}{(6 - 3)!3!}}\)
= \(\frac{5!}{3!2!} \times {\frac{6!}{3 \times 3!}}\)
= \(\frac{5 \times 4 \times 3!}{3! \times 2!} \times {\frac{6 \times 5 \times 4 \times 3!}{3! \times 3!}}\)
= \(\frac{5 \times 4}{1 \times 2} \times {\frac{6 \times 5 \times 4}{1 \times 2 \times 3}}\)
= 10 x \(\frac{6 \times 20}{6}\)
= 200
Source: WAEC / JAMB / NECO Classroom Archive (Record #29608)
Mathematics
UTME / JAMB 2010
Number and Numeration
Solution
Solve for x and y if x - y = 2 and x\(^2\) - y\(^2\) = 8
A
(-1, 3)
B
(3, 1)
C
(-3, 1)
D
(1, 3)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
x - y = 2 ...........(1)
x\(^2\) - y\(^2\) = 8 ........... (2)
x - 2 = y ............ (3)
Put y = x - 2 in (2)
x\(^2\) - (x - 2)\(^2\) = 8
x\(^2\) - (x\(^2\) - 4x + 4) = 8
x\(^2\) - x\(^2\) + 4x - 4 = 8
4x = 8 + 4 = 12
x = \(\frac{12}{4}\)
= 3
from (3), y = 3 - 2 = 1
therefore, x = 3, y = 1
Source: Myschool Past Questions Archive (Record #29568)
Mathematics
WAEC / WASSCE 2010
Number and Numeration
Solution
Factorize: x + y - ax = ay
A
(x - y)(1 - a)
B
(x + y)(1 + a)
C
(x + y)(1 - a)
D
(x - y)(1 + a)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
x + y - ax = ay
= (x + y) -a(x + y) = (x + y)(1 - a)
Source: Myschool Past Questions Archive (Record #36516)
Mathematics
WAEC / WASSCE 2010
Number and Numeration
Correct 0.002473 to 3 significant figure
A
0.002
B
0.0024
C
0.00247
D
0.0025
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 #36518)
Mathematics
WAEC / WASSCE 2010
Number and Numeration
Solution
Simplify 1\(\frac{1}{2} + 2\frac{1}{3} \times \frac{3}{4} - \frac{1}{2}\)
A
-2\(\frac{1}{3}\)
B
-2\(\frac{1}{4}\)
C
2\(\frac{1}{8}\)
D
2\(\frac{3}{4}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
1\(\frac{1}{2} + 2\frac{1}{3} \times \frac{3}{4} - \frac{1}{2}\)
\(\frac{3}{2} + \frac{7}{3} \times \frac{3}{4} - \frac{1}{2} = \frac{3}{2} + \frac{7}{4} - \frac{1}{2}\)
= \(\frac{6 + 7 - 2}{4} = \frac{11}{4}\)
= 2\(\frac{3}{4}\)
Source: Myschool Past Questions Archive (Record #36519)
Mathematics
WAEC / WASSCE 2010
Number and Numeration
Solution
A casting is made up of Copper and Zinc. If 65% of the casting is Zinc and there are 147g of Copper. What is the mass of the casting?
A
320g
B
420g
C
520g
D
620g
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
%Zinc + %Copper = 100%
65% + %Copper = 100%
%Copper = 100% - 65% = 35%
%Copper = \(\frac{\text{Mass of % Copper}}{\text{Mass of Casting}}\) x 100%
Mass of Casting = \(\frac{147}{35}\) x 100%
= 420g
Source: Myschool Past Questions Archive (Record #36521)
Mathematics
WAEC / WASSCE 2010
Number and Numeration
Solution
Given that P = {x : 1 \(\leq x \leq 6\)}, and Q = {x : 2 \(\leq x \leq 10\)} where x is an integer. Find n(P \(\cap\) Q)
A
5
B
6
C
8
D
10
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
P = {1, 2, 3, 4, 5, 6}; Q = {3, 4, 5, 6, 7, 8, 9}
P \(\cap\) Q) = {2, 3, 4, 5, 6}
n(P \(\cap\) Q) = 5
Source: Myschool Past Questions Archive (Record #36522)
Mathematics
WAEC / WASSCE 2010
Number and Numeration
Solution
The sum of 6 and one-third of x is one more than twice x, find x
A
x = 7
B
x = 5
C
x = 3
D
x = 2
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
6 = \(\frac{1}{3}x\) = 1 + 2x
6 = 1 = \(\frac{2x}{1} - \frac{x}{3}\)
5 = \(\frac{6x - x}{3} = \frac{5x}{3}\)
5 = \(\frac{5x}{3}\)
3 x 5 = 5x
15 = 5x
x = \(\frac{15}{5}\)
= 3
Source: Myschool Past Questions Archive (Record #36523)
Mathematics
WAEC / WASSCE 2010
Number and Numeration
Solution
Given that = {x: -2 < x \(\leq\) 9}, where x is an integer what is n(T)?
A
9
B
10
C
11
D
12
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
T = {-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
n(T) = 11
Source: Myschool Past Questions Archive (Record #36524)
Mathematics
WAEC / WASSCE 2010
Number and Numeration
Solution
Given that \(\frac{5^{n +3}}{25^{2n -3}}\) = 5º, find n
A
n = 1
B
n = 2
C
n = 3
D
n = 5
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{5^{n +3}}{25^{2n -3}} = 5^0\)
\(\frac{5^{n + 3}}{5^{2(2n - 3)}} = 5^0\)
n + 3 - 4n + 6 = 0
-3n + 9 = 0
-3n = -9
n = \(\frac{-9}{-3}\)
n = 3
Source: Myschool Past Questions Archive (Record #36529)
Mathematics
WAEC / WASSCE 2010
Number and Numeration
Solution
Simplify 2\(\sqrt{3}\) - \(\frac{6}{\sqrt{3}} + \frac{3}{\sqrt{27}}\)
A
1
B
\(\frac{1}{3}\sqrt{3}\)
C
2\(\sqrt{3} - 5\frac{2}{3}\)
D
6\(\sqrt{3}\) - 17
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
2\(\sqrt{3}\) - \(\frac{6}{\sqrt{3}} + \frac{3}{\sqrt{27}}\)
= 2\(\sqrt{3} - \frac{6}{\sqrt{3}} + \frac{3}{\sqrt{9 \times 3}}\)
= 2\(\sqrt{3} - \frac{6}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} + \frac{3}{3\sqrt{3}}\)
= 2\(\sqrt{3} = 6 \frac{\sqrt{3}}{3} + \frac{1}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}\)
= 2\(\sqrt{3} - 2\sqrt{3} + \frac{\sqrt{3}}{3}\)
= \(\frac{\sqrt{3}}{3} = \frac{1}{3} \sqrt{3}\)
Source: Myschool Past Questions Archive (Record #36531)