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Mathematics
UTME / JAMB 2009
Number and Numeration
Solution
A binary operation ⊗ defined on the set of integers is such that m⊗n = m + n + mn for all integers m and n. Find the inverse of -5 under this operation, if the identity element is 0?
A
-5/4
B
-5/6
C
zero
D
5
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(m \otimes n = m + n + mn\)
Let the inverse of -5 be n.
\(\therefore -5 \otimes n = 0\)
\(-5 + n + (-5n) = 0\)
\(n - 5n = 5 \implies -4n = 5\)
\(n = -\frac{5}{4}\)
Source: Myschool Past Questions Archive (Record #9323)
Mathematics
UTME / JAMB 2009
Number and Numeration
Solution
If Q is\( \left[ \begin{array}{cc}
9 & -2 \\
-7 & 4 \\
\end{array} \right]\) , then |Q| is?
A
-50
B
-22
C
22
D
50
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Q = \( \left[ \begin{array}{ccc}
9 & -2 \\
-7 & 4 \\
\end{array} \right]\)
|Q| = 9x4 - (-2 x -7)
= 36 - 14
= 22
Source: Myschool Past Questions Archive (Record #9324)
Mathematics
UTME / JAMB 2009
Number and Numeration
Solution
If P \(=\left[\begin{array}{cc}x+3 & x+2\\
x+1 & x-1\end{array}\right]\) evaluate x if |P| = -10
A
-5
B
-2
C
2
D
5
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(P=\left[\begin{array}{cc}x+3 & x+2\\
x+1 & x-1\end{array}\right]\) evaluate x if |P| = -10
(x+3)(x-1) - {(x+1)(x+2)} = -10
x2 - x + 3x - 3 - {x2 + 2x + x + 2} = -10
x2 + 2x - 3 - {x2 + 3x + 2} = -10
-x - 5 = -10
-5 + 10 = x
5 = x
∴x = 5
Source: Myschool Past Questions Archive (Record #9325)
Mathematics
UTME / JAMB 2009
Number and Numeration
Solution
If s = (2 + 3t)(5t - 4), find ds/dt when t = \(\frac{4}{5}\) secs
A
0 units per sec
B
15 units per sec
C
22 unit per sec
D
26 units per sec
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
x = (2+3t)(5t-4)
Let u = 2+3t ∴ \(\frac{\text{du}}{\text{dt}}\) = 3
and v = 5t-4 ∴ \(\frac{\text{dv}}{\text{dt}}\) = 5
dx/dt = \(\frac{\text{Vdu}}{\text{dt}}\) + \(\frac{\text{Udv}}{\text{dt}}\)
= (5t-4)3 + (2+3t)5
= 15t - 12 + 10 + 15t
= 30t - 2
= 30 x \(\frac{4}{5}\) - 2
= 24 - 2
= 22
Source: Myschool Past Questions Archive (Record #9360)
Mathematics
UTME / JAMB 2009
Number and Numeration
Solution
No. of Days
1
2
3
4
5
6
No. of students
20
2x
60
40
x
50
The distribution above shows the number of days a group of 260 students were absent from school in a particular term. How many students were absent for at least four days in the term?
A
180
B
120
C
110
D
40
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
20 + 2x + 60 + 40 + x + 50 = 260
170 + 3x = 260
3x = 260 - 170
3x = 90
x = 90/3 = 30
At least 4 days
4 days = 40
5 days = 30
6 days = 50
Total = 120
Source: Myschool Past Questions Archive (Record #9364)
Mathematics
UTME / JAMB 2009
Number and Numeration
Solution
In how many ways can a delegation of 3 be chosen from 5 men and 3 women. If at least 1 man and 1 woman must be included?
A
15
B
28
C
30
D
45
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
= \((^{5}C_{2} \times ^{3}C_{1}) + (^{5}C_{1} \times ^{3}C_{2})\)
= \((10 \times 3) + (5 \times 3)\)
= 45.
Source: Myschool Past Questions Archive (Record #9425)
Mathematics
WAEC / WASSCE 2009
Number and Numeration
Solution
If log 2 = x, log 3 = y and log 7 = z, find, in terms of x, y and z, the value of log (\(\frac{28}{3}\))
A
2x + y - z
B
2x + z - y
C
x + y - 2x
D
x + x - y
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
log (\(\frac{28}{3}) = \log (\frac{7 \times 4}{3})\)
= log 7 + log 4 - log 3
log 7 + log \(2^2\) - log 3 = log 7 + 2log2 - log 3
= z + 2x - y
= 2x + z - y
Source: WAEC / JAMB / NECO Classroom Archive (Record #36430)
Mathematics
UTME / JAMB 2009
Number and Numeration
Solution
What value of x will make the function x(4 - x) a maximum?
A
4
B
3
C
2
D
1
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
x(4 - x)
4x - x2
\(\frac{dy}{dx}\) = 4 - 2x
\(\frac{dy}{dx}\) = 0
2x = 4
x = \(\frac{4}{2}\)
= 2
Source: WAEC / JAMB / NECO Classroom Archive (Record #29712)
Mathematics
UTME / JAMB 2009
Number and Numeration
Diagram
Solution
The histogram above represents the number of candidates that sat for Mathematics examination in a school. How many candidate scored more than 50 marks?
Attached Figure / Diagram
A
80
B
95
C
100
D
115
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\begin{array}{c|c} Mark & No. of Candidate\\\hline 60 & 40\\ 70 & 25\\ 80 & 15\\ 90 & 10 \\100 & 5 \\\hline & 95 \end{array}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #33142)
Mathematics
UTME / JAMB 2009
Number and Numeration
Diagram
Solution
The cumulative frequency curve above shows the distribution of the scores of 50 students in an examination. Find the 36th percentile scores?
Attached Figure / Diagram
A
18%
B
28%
C
36%
D
50%
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
the 36th percentile i.e. 36% of the total frequency of 50.
\(\frac{36}{100}\) \(\times\) 50 = 18
= From the graph, 18 on the vertical axis corresponds to28 on the horizontal axis.
\(\therefore\) P\(_{36}\) = 28%
Source: WAEC / JAMB / NECO Classroom Archive (Record #33144)
Mathematics
WAEC / WASSCE 2009
Number and Numeration
Solution
Simplify: (3\(\frac{1}{2} + 4\frac{1}{3}) \div (\frac{5}{6} - \frac{2}{3}\))
A
1\(\frac{1}{4}\)
B
8\(\frac{1}{2}\)
C
35
D
47
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
(3\(\frac{1}{2} + 4\frac{1}{3}) \div (\frac{5}{6} - \frac{2}{3}\)) = (7\(\frac{3 + 2}{6}) \div \frac{(5 - 4)}{6}\)
7\(\frac{5}{6} \div \frac{1}{6} = \frac{47}{6} \times \frac{6}{1}\) = 47
Source: Myschool Past Questions Archive (Record #36428)
Mathematics
WAEC / WASSCE 2009
Number and Numeration
Solution
In a particular year, the exchange rate of naira (N) varies directly with the Dollars{$}. If N1122 is equivalent to $8, find the Naira equivalent of $36
A
N8976
B
N5049
C
N140.25
D
N31.17
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
N1122 = $8; x = $36
x x $8 = N1122 x $36
\(\frac{N1122 \times $36}{$8}\) = x
x = N5049
Source: Myschool Past Questions Archive (Record #36429)
Mathematics
WAEC / WASSCE 2009
Number and Numeration
Solution
Arrange the following numbers in descending orders of magnitude: 22three, 34five, 21six
A
21six, 22three, 34five,
B
21six, 34five, 22three
C
22three, 34five, 21six
D
34five, 21six, 22three
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
22three, 34five, 21six = (2 x 3)(2 x 3o), (3 x 51) = (4 x 50), (2 x 61) + (1 x 60)
= (6 + 2), (15 + 4), (12 + 1) = 8ten, 29ten, 13ten in descending order
29ten, 13ten, 8ten = 34five, 21six, 22three
Source: Myschool Past Questions Archive (Record #36433)
Mathematics
WAEC / WASSCE 2009
Number and Numeration
Solution
Find the value to which N3000.00 will amount in 5 years at 6% per annum simple interest
A
N3,900.00
B
N3,750.00
C
N3,600.00
D
N3,300
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
A = P + I
p + \(\frac{PRT}{100}\)
A = N3000 (1 + \(\frac{6 \times 5}{100}\))
= N3000(1 + 0.3)
A = N3000 (1.3)
= N3,900.00
Source: Myschool Past Questions Archive (Record #36434)
Mathematics
WAEC / WASSCE 2009
Number and Numeration
Two sets are disjoint if
A
they are both empty
B
their union is an empty set
C
their intersection is an empty set
D
one of them is a subset of the other
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 #36436)