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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
Geometry and Trigonometry
Diagram
Solution
In the diagram above, PQR is a circle centre O. If < QPR is x^\circ, find < QRP.
Attached Figure / Diagram
A
x°
B
(90 – x)°
C
(90 + x)°
D
(180 – x)°
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
< PQR = 90^\circ (angle in a semi-circle)
< QRP = (90 - x)^\circ
Source: Myschool Past Questions Archive (Record #33164)
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
Algebra
Solution
The nth term of a sequence is Tn = 5 + (n - 1)2. Evaluate T4 - T6
A
30
B
16
C
-16
D
-30
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
T4 = 5 + (4 - 1)2; where n = 4
= 5 + (3)2 = 5 + 9
= 14
T = 5 + (6 - 1)2
where n = 6
= 5 + (5)2
= 5 + 25 = 30
T4 + T6 = 14 - 30
= -16
Source: Myschool Past Questions Archive (Record #36740)
Mathematics
WAEC / WASSCE 2012
Geometry and Trigonometry
Solution
Mr. Manu travelled from Accra to Pamfokromb a distance of 720km in 8 hours. What will be his speed in m/s?
A
25m/s
B
150m/s
C
250m/s
D
500m/s
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\frac{720 \times 1000}{8 \times 60 \times 60}\) = \(\frac{20 \times 10}{8}\)
= \(\frac{200}{8}\)
= 25 m/s
Source: Myschool Past Questions Archive (Record #36741)
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)
Mathematics
WAEC / WASSCE 2012
Algebra
Solution
Solve for x in the equation; \(\frac{1}{x} + \frac{2}{3x} = \frac{1}{3}\)
A
5
B
4
C
3
D
1
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\frac{1}{8} + \frac{2}{3x} = \frac{1}{3}\)
= \(\frac{1}{2}\)
\(\frac{5}{3x} = \frac{1}{3}\)
3x = 15
x = \(\frac{15}{3}\)
= 5
Source: Myschool Past Questions Archive (Record #36746)
Mathematics
WAEC / WASSCE 2012
Number and Numeration
Solution
Simplify: \(\frac{54k^2 - 6}{3k + 1}\)
A
6(1 - 3k2)
B
6(3k2 - 1)
C
6(3k - 1)
D
6(1 - 3k)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{54k^2 - 6}{3k + 1} = \frac{6(9k^2 - 1)}{3k + 1}\)
= \(\frac{6(3k + 1) - (3k - 1)}{3k + 1}\)
= 6(3k - 1)
Source: Myschool Past Questions Archive (Record #36748)
Mathematics
WAEC / WASSCE 2012
Number and Numeration
Solution
Make p the subject of the relation: q = \(\frac{3p}{r} + \frac{s}{2}\)
A
p = \(\frac{2q - rs}{6}\)
B
p = 2qr - sr - 3
C
p = \(\frac{2qr - s}{6}\)
D
p = \(\frac{2qr - rs}{6}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
q = \(\frac{3p}{r} + \frac{s}{2}\)
q = \(\frac{6p + rs}{2r}\)
6p + rs = 2qr
6p = 2qr - rs
p = \(\frac{2qr - rs}{6}\)
Source: Myschool Past Questions Archive (Record #36751)
Mathematics
WAEC / WASSCE 2012
Algebra
Solution
If x + y = 2y - x + 1 = 5, find the value of x
A
3
B
2
C
1
D
-1
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
x + y = 2y - x + 1 = 5
x + y = 2y - x + 1
x + x + y - 2y = 1
2x - y = 1....(i)
2y - x + 1 = 5
-x + 2y = 5 + 1
-x = 2y = 4
x - 2y = -4 .....(ii)
solve simultaneously (i) x 2x - y = 1
(ii) x x - 2y = -4
2x - y = 1
=2x - 4y = -8
3y = 9
y = \(\frac{9}{3}\)
y = 3
substitute y = 3 into equation (i)
2x - y = 1
2x - 3 = 1
2x = 1 + 3
2x = 4
x = \(\frac{4}{2}\)
= 2
Source: Myschool Past Questions Archive (Record #36754)