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Mathematics
UTME / JAMB 2012
Number and Numeration
Solution
The sum to infinity of a geometric progression is \(-\frac{1}{10}\) and the first term is \(-\frac{1}{8}\). Find the common ratio of the progression.
A
\(-\frac{1}{5}\)
B
\(-\frac{1}{4}\)
C
\(-\frac{1}{3}\)
D
\(-\frac{1}{2}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Sr = \(\frac{a}{1 - r}\)
\(-\frac{1}{10}\) = \(\frac{1}{8} \times \frac{1}{1 - r}\)
\(-\frac{1}{10}\) = \(\frac{1}{8(1 - r)}\)
\(-\frac{1}{10}\) = \(\frac{1}{8 - 8r}\)
cross multiply...
-1(8 - 8r) = -10
-8 + 8r = -10
8r = -2
r = -1/4
Source: Myschool Past Questions Archive (Record #27329)
Mathematics
UTME / JAMB 2012
Number and Numeration
Solution
The binary operation * is defined on the set of integers such that p * q = pq + p - q. Find 2 * (3 * 4)
A
11
B
13
C
15
D
22
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
p * q = pq + p - q
First execute for 3 * 4
==> 3(4) + 3 - 4 = 12 + 3 - 4 = 11
Now we execute for 2 * 11
==> 2(11) + 2 - 11 = 22 + 2 - 11 = 13
Source: Myschool Past Questions Archive (Record #27330)
Mathematics
UTME / JAMB 2012
Number and Numeration
Solution
The binary operation on the set of real numbers is defined by m*n = \(\frac{mn}{2}\) for all m, n \(\in\) R. If the identity element is 2, find the inverse of -5
A
\(-\frac{4}{5}\)
B
\(-\frac{2}{5}\)
C
4
D
5
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
m * n = \(\frac{mn}{2}\)
Identify, e = 2
Let a \(\in\) R, then
a * a\(^{-1}\) = e
a * a\(^{-1}\) = 2
-5 * a\(^{-1}\) = 2
\(\frac{-5 \times a^{-1}}{2} = 2\)
\(a^{-1} = \frac{2 \times 2}{-5}\)
\(a^{-1} = -\frac{4}{5}\)
Source: Myschool Past Questions Archive (Record #27331)
Mathematics
UTME / JAMB 2012
Number and Numeration
Solution
Calculate the volume of a cuboid of length 0.76cm, breadth 2.6cm and height 0.82cm.
A
3.92cm3
B
2.13cm3
C
1.97cm3
D
1.62cm3
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Volume of cuboid = L x b x h
= 0.76cm x 2.6cm x 0.82cm
= 1.62cm3
Source: Myschool Past Questions Archive (Record #27335)
Mathematics
UTME / JAMB 2012
Number and Numeration
Solution
If y = x2 - \(\frac{1}{x}\), find \(\frac{\delta y}{\delta x}\)
A
2x - \(\frac{1}{x^2}\)
B
2x + x2
C
2x - x2
D
2x + \(\frac{1}{x^2}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
y = x2 - \(\frac{1}{x}\)
y = x2 - x-1
\(\frac{\delta y}{\delta x}\) = 2x + x-2
\(\frac{\delta y}{\delta x}\) = 2x + \(\frac{1}{x^2}\)
Source: Myschool Past Questions Archive (Record #27341)
Mathematics
UTME / JAMB 2012
Number and Numeration
Solution
Find the range of 4,9,6,3,2,8,10 and 11
A
11
B
9
C
8
D
4
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Range = Highest Number - Lowest Number
Range = 11 - 2 = 9
Source: Myschool Past Questions Archive (Record #27380)
Mathematics
UTME / JAMB 2012
Number and Numeration
Solution
In how many ways can the letters of the word TOTALITY be arranged?
A
6720
B
6270
C
6207
D
6027
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\frac{8!}{3!}\)
\(\frac{8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{3 \times 2\times 1}\)
==> 8 x 7 x 6 x 5 x 4 = 6720
Source: Myschool Past Questions Archive (Record #27394)
Mathematics
UTME / JAMB 2012
Number and Numeration
Diagram
Solution
In diagram above, QR//TU, < PQR = 80^\circ and < PSU = 95^\circ. Calculate < SUT.
Attached Figure / Diagram
A
15o
B
25o
C
30o
D
80o
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
< PQR = < PTU = 80^\circ
< TSU = 85^\circ
x = 180^\circ - (80^\circ + 85^\circ)
= 15^\circ
Source: Myschool Past Questions Archive (Record #33163)
Mathematics
UTME / JAMB 2012
Number and Numeration
Diagram
Solution
Find the area of the trapezium above.
Attached Figure / Diagram
A
91 cm2
B
78 cm2
C
60 cm2
D
19 cm2
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Area of trapezium = \(\frac{1}{2} (a + b) \times h\)
= \(\frac{1}{2} (7 + 13) \times 6\)
= \(60 cm^{2}\)
Source: Myschool Past Questions Archive (Record #33165)
Mathematics
UTME / JAMB 2012
Number and Numeration
Diagram
Solution
The grades of 36 students in a class test are as shown in the pie chart above. How many students have excellent?
Attached Figure / Diagram
A
12
B
9
C
8
D
7
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Excellent = 360^\circ - (120^\circ + 90^\circ + 80^\circ)
= 70^\circ
Number of excellent students = \(\frac{70}{360} \times 36\)
= 7 students
Source: Myschool Past Questions Archive (Record #33166)
Mathematics
UTME / JAMB 2012
Number and Numeration
Diagram
Solution
The bar chart above shows the distribution of marks in a class test. If the pass mark is 5, what percentage of students failed the test?
Attached Figure / Diagram
A
10%
B
20%
C
50%
D
60%
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Number that score less than 5: 5 + 6 + 4 + 3 + 2 = 20
Total number of students: 5 + 6 + 4 + 3 + 2 + 4 + 6 + 5 + 1 + 3 + 1 = 40.
%age of students that failed: \(\frac{20}{40} \times 100% = 50%\)
Source: Myschool Past Questions Archive (Record #33167)
Mathematics
WAEC / WASSCE 2012
Number and Numeration
Express 302.10495 correct to five significant figures
A
302.10
B
302.11
C
302.105
D
302.1049
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 #36730)
Mathematics
WAEC / WASSCE 2012
Number and Numeration
Solution
In 1995, the enrollment of two schools X and Y were 1,050 and 1,190 respectively. Find the ration of the enrollments of X and Y
A
50:11
B
15:17
C
13:55
D
12:11
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Divide cash enrollment by their common factors then the answer of each division gives the required ratio. i.e. x = \(\frac{1050}{70}\) = 15
and y = \(\frac{1190}{70}\) = 17
ratio of enrollment of x to y = 15:17
Source: Myschool Past Questions Archive (Record #36733)
Mathematics
WAEC / WASSCE 2012
Number and Numeration
Convert 3510 to number in base 2
A
1011
B
10011
C
100011
D
11001
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 #36738)
Mathematics
WAEC / WASSCE 2012
Number and Numeration
Solution
If N2,500.00 amounted to N3,50.00 in 4 years at simple interest, find the rate at which the interest was charged
A
5%
B
7\(\frac{1}{2}\)%
C
8%
D
10%
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
A = 3,500, P = N2,500
A = P + I
But I = N3,500 - N2,500
I = N1,000
I = \(\frac{PRT}{100}\)
N1,000 = \(\frac{2.500 \times R \times 4}{100}\)
1000 = 100R
R = \(\frac{1000}{100}\)
= 10%
Source: Myschool Past Questions Archive (Record #36744)