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Mathematics
UTME / JAMB 1995
Number and Numeration
Solution
Two variables x and y are such that \(\frac{dy}{dx}\) = 4x - 3 and y = 5 when x = 2. Find y in terms of x
A
2x2 - 3x + 5
B
2x2 - 3x + 3
C
2x2 - 3x
D
4
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
∫dy = ∫(4x - 3)dx, y = 2x2 - 3x + C
when y = 5, x = 2, C = 3
y = 2x2 - 3x + 3
Source: Myschool Past Questions Archive (Record #30942)
Mathematics
UTME / JAMB 1995
Number and Numeration
Solution
Find the area bounded by the curve y = 3x\(^2\) - 2x + 1, the ordinates x = 1 and x = 3 and the x-axis.
A
24
B
22
C
21
D
20
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{\mathrm d y}{\mathrm d x} = 3x^{2} - 2x + 1\)
\(y = \int_{1} ^{3} (3x^{2} - 2x + 1) \mathrm d x\)
\(y = [x^{3} - x^{2} + x]_{1} ^{3}\)
= \([3^{3} - 3^{2} + 3] - [1^{3} - 1^{2} + 1]\)
= \(21 - 1 = 20\)
Source: Myschool Past Questions Archive (Record #30943)
Mathematics
UTME / JAMB 1995
Number and Numeration
Diagram
Solution
In the diagram, the base diameter is 14cm while the height is 12cm. Calculate the total surface area if the cylinder has both a base and a top.[\(\pi \frac{22}{7}\)]
Attached Figure / Diagram
A
836cm2
B
308cm2
C
528cm2
D
154cm2
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Area(S) = 2\(\pi r^2 + 2 \pi rh = 2\pi r(h + r)\)
D = 14cm, 2r = D
r = \(\frac{D}{2}\)
= 7cm
S = 2 x \(\frac{22}{7} \times [7 + 12] = 44 \times 19\)
= 836cm2
Source: Myschool Past Questions Archive (Record #33066)
Mathematics
WAEC / WASSCE 1995
Number and Numeration
Solution
(a) Factorise : \(px - 2px - 4qy + 2py\)
(b) Given that the universal set U = {1, 2, 3, 4,5, 6, 7, 8, 9, 10}, P = {1, 2, 4, 6, 10} and Q = {2, 3, 6, 9}; show that \((P \cup Q)' = P' \cap Q'\)
medium Difficulty
Verified Correct Answer: Option
Step-by-Step Mathematical Solution
(a) \(px - 2qx - 4qy + 2py\)
= \(x(p - 2q) + 2y(p - 2q)\)
= \((x + 2y)(p - 2q)\)
(b) \(U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}\)
\(P = {1, 2, 4, 6, 10} ; Q = {2, 3, 6, 9}\)
\((P \cup Q) = {1, 2, 3, 4, 6, 9, 10}\)
\((P \cup Q)' = {5, 7, 8}\)
\(P' \cap Q' = {3, 5, 7, 8, 9} \cap {1, 4, 5, 7, 8, 10}\)
= \({5, 7, 8}\)
Hence, \((P \cup Q)' = P' \cap Q'\).
Source: Myschool Past Questions Archive (Record #54521)
Mathematics
WAEC / WASSCE 1995
Number and Numeration
Solution
The frequency table shows the marks scored by 32 students in a test.
Marks scored
1
2
3
4
5
6
7
8
9
10
No of students
2
3
4
4
4
4
5
3
2
1
Find the :
(a)(i) mean ; (ii) median ; (iii) mode of the marks;
(b) percentage of the students who scored at least 8 marks.
medium Difficulty
Verified Correct Answer: Option
Step-by-Step Mathematical Solution
x
1
2
3
4
5
6
7
8
9
10
Total
f
2
3
4
4
4
4
5
3
2
1
32
fx
2
6
12
16
20
24
35
24
18
10
167
(a)(i) Mean = \(\frac{\sum fx}{\sum f} = \frac{167}{32}\)
= \(5.21875 \approxeq 5.22\)
(ii) By inspection, the average of the numbers in the 16th and 17th position give the median
= \(\frac{5 + 5}{2} = 5\)
(iii) Mode = 7 marks having the largest frequency.
(b) Students who scored at least 8 marks = Those who scored 8, 9, 10.
Total number of students that scored at least 8 = 3 + 2 + 1 = 6.
\(%age = \frac{6}{32} \times 100% = 18.75%\)
Source: Myschool Past Questions Archive (Record #54525)
Mathematics
WAEC / WASSCE 1995
Number and Numeration
Solution
(a) Using mathematical tables, find ; (i) \(2 \sin 63.35^\circ\) ; (ii) \(\log \cos 44.74^\circ\);
(b) Find the value of K given that \(\log K - \log (K - 2) = \log 5\);
(c) Use logarithm tables to evaluate \(\frac{(3.68)^{2} \times 6.705}{\sqrt{0.3581}}\)
medium Difficulty
Verified Correct Answer: Option
Step-by-Step Mathematical Solution
(a)(i) \(\sin 63.35^\circ = 0.8938\)
\(2 \sin 63.35^\circ = 2 \times 0.8938 = 1.7876\)
(ii) \(\log \cos 44.74^\circ = \bar{1}.8514\)
(b) \(\log K - \log (K - 2) = \log 5\)
\(\log (\frac{K}{K - 2}) = \log 5\)
\(\therefore \frac{K}{K - 2} = 5 \implies K = 5(K - 2)\)
\(K = 5K - 10 \implies 10 = 5K - K = 4K\)
\(K = 2\frac{1}{2}\)
(c) \(\frac{(3.68)^{2} \times 6.705}{\sqrt{0.3581}}\)
No
Log
\((3.68)^{2}\)
\(0.5658 \times 2 = 1.316\)
\(6.705\)
\(0.8264 = 0.8264\)
= \(1.9580\)
\(\sqrt{0.3581}\)
\(\bar{1}.5540 \div 2 = \bar{1}.7770\)
\(151.7\)
\(\gets 2.1810\)
\(\therefore \frac{(3.68)^{2} \times 6.705}{\sqrt{0.3581}} = 151.7\)
Source: Myschool Past Questions Archive (Record #54526)
Mathematics
UTME / JAMB 1994
Number and Numeration
Solution
Factorize a2x - b2y - b2x + a2y
A
(a - b)(x + y)
B
(y - x)(a - b)(a + b)
C
(x - y)(a - b)(a + b)
D
(x + y)(a - b)(a + b)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
a2x - b2y - b2x + a2y = a2x - b2x - b2y + a2y Rearrange
= x(a2 - b2) + y(a2 - b2)
= (x + y)(a2 - b2)
= (x + y)(a + b)(a - b)
Source: WAEC / JAMB / NECO Classroom Archive (Record #31007)
Mathematics
WAEC / WASSCE 1994
Number and Numeration
Solution
Simplify: \(2\frac{1}{3} \div 2\frac{2}{3} \times 1\frac{1}{7}\)
A
0
B
1
C
2
D
3
E
4
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(2\frac{1}{3} \div 2\frac{2}{3} \times 1\frac{1}{7}\)
= \(\frac{7}{3} \div \frac{8}{3} \times \frac{8}{7}\)
= \(\frac{7}{3} \times \frac{3}{8} \times \frac{8}{7}\)
= 1
Source: Myschool Past Questions Archive (Record #23459)
Mathematics
WAEC / WASSCE 1994
Number and Numeration
Solution
Which of the following is equal to \(\frac{72}{125}\)
A
\( \frac{2^3 \times 3^2}{5^3} \)
B
\( \frac{2^4 \times 3}{5^3} \)
C
\( \frac{2^3 \times 3}{5^3} \)
D
\( \frac{2^4 \times 3}{5^5} \)
E
\( \frac{2^2 \times 3^2 \times 4^2}{5^2} \)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\frac{72}{125} = \frac{8 \times 9}{5 \times 5 \times 5}\)
= \(\frac{2^3 \times 3^2}{5^3}\)
Source: Myschool Past Questions Archive (Record #23460)
Mathematics
WAEC / WASSCE 1994
Number and Numeration
Solution
Evaluate \( \frac{27^{\frac{1}{3}}}{16^{-\frac{1}{4}}} \)
A
6
B
5
C
4
D
3
E
2
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\frac{27^{\frac{1}{3}}}{16^{-\frac{1}{4}}} \)
= \(\frac{(3^3)^{\frac{1}{3}}}{(2^4)^{-\frac{1}{4}}}\)
= \(\frac{3}{2^{-1}}\)
= 6
Source: Myschool Past Questions Archive (Record #23463)
Mathematics
WAEC / WASSCE 1994
Number and Numeration
Solution
Simplify: 16\(^{\frac{5}{4}}\) x 2\(^{-3}\) x 3\(^0\)
A
0
B
2
C
4
D
10
E
20
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
16\(^{\frac{5}{4}}\) x 2\(^{-3}\) x 3\(^0\)
= \((2^4)^{\frac{5}{4}} \times 2^{-3} \times 1\)
= \(2^5 \times 2^{-3} \times 1\)
= \(2^2\)
= 4.
Source: Myschool Past Questions Archive (Record #23466)
Mathematics
WAEC / WASSCE 1994
Number and Numeration
Solution
simplify; 2lo\(g_3\) 6 + lo\(g_3\) 12 - lo\(g_3\) 16
A
2
B
3
C
2 - 2log32
D
3 - log32
E
4 - log32
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
2lo\(g_3\) 6 + lo\(g_3\) 12 - lo\(g_3\) 16
= \(\log_3 6^2 + \log_3 12 - \log_3 16\)
= \(\log_{3} (\frac{36 \times 12}{16})\)
= \(\log_{3} (27)\)
= \(\log_{3} 3^3\)
= \(3 \log_{3} 3\)
= 3
Source: Myschool Past Questions Archive (Record #23468)
Mathematics
WAEC / WASSCE 1994
Number and Numeration
What is the number whose logarithm to base 10 is \(\bar{3}.4771\)?
A
3.0
B
0.3
C
0.03
D
0.003
E
0.0003
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 #23471)
Mathematics
WAEC / WASSCE 1994
Number and Numeration
Solution
A house bought for N100,000 was later auctioned for N80,000. Find the loss percent.
A
20%
B
30%
C
40%
D
50%
E
60%
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Loss = N(100,000 - 80,000)
= N20,000.
Loss percentage = \(\frac{20,000}{100,000} \times 100%\)
= 20%
Source: Myschool Past Questions Archive (Record #23475)
Mathematics
WAEC / WASSCE 1994
Number and Numeration
Solution
A string is 4.8m. A boy measured it to be 4.95m. Find the percentage error.
A
\( \frac{5}{16} \)%
B
\(1\frac{5}{16} \)%
C
\( 3\frac{1}{33} \)%
D
\( 3\frac{1}{8} \)%
E
25%
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
4.95m - 4.8m = 0.15m
\(\frac{0.15}{4.8} \times 100%\)
= \(\frac{25}{8}\)
= \(3\frac{1}{8} %)
Source: Myschool Past Questions Archive (Record #23480)