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Mathematics
UTME / JAMB 1986
Number and Numeration
Solution
Simplify \(\frac{1}{5x + 5}\) + \(\frac{1}{7x+ 7}\)
A
\(\frac{12}{35x + 1}\)
B
\(\frac{1}{35(x + 1)}\)
C
\(\frac{12x}{35(x + 7)}\)
D
\(\frac{12}{35x + 35}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{1}{5x + 5}\) + \(\frac{1}{7x+ 7}\) = \(\frac{1}{5(x + 1)}\) + \(\frac{1}{7(x + 1)}\)
= \(\frac{7 + 5}{35(x + 1)}\)
= \(\frac{12}{35(x + 1)}\)
Source: Myschool Past Questions Archive (Record #32090)
Mathematics
UTME / JAMB 1986
Number and Numeration
Solution
Factorize (4a + 3)2 - (3a - 2)2
A
(a + 1)(a + 5)
B
(a - 5)(7a - 1)
C
(a + 5)(7a + 1)
D
a(7a + 1)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
(4a + 3)2 - (3a - 2)2 = a2 - b2
= (a + b)(a - b)
= [(4a + 3) + (3a - 2)][(4a + 3) + (3a - 2)]
= [(4a + 3 + 3a - 2)][(4a + 3 - 3a + 2)]
= (7a + 1)(a + 5)
∴ (a + 5)(7a + 1)
Source: Myschool Past Questions Archive (Record #32105)
Mathematics
UTME / JAMB 1986
Number and Numeration
Solution
Simplify \(\frac{1}{x - 2}\) + \(\frac{1}{x + 2}\) + \(\frac{2x}{x^2 - 4}\)
A
\(\frac{2x}{(x - 2)(x + 2)(x^2 - 4)}\)
B
\(\frac{2x}{x^2 - 4}\)
C
\(\frac{x}{x^2 - 4}\)
D
\(\frac{4x}{x^2 - 4}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{1}{x - 2}\) + \(\frac{1}{x + 2}\) + \(\frac{2x}{x^2 - 4}\)
= \(\frac{(x + 2) + (x - 2) + 2x}{(x + 2)(x - 2)}\)
= \(\frac{4x}{x^2 - 4}\)
Source: Myschool Past Questions Archive (Record #32113)
Mathematics
UTME / JAMB 1986
Number and Numeration
Solution
make v the subject of the formula S = \(\sqrt{\frac{6}{v} - \frac{w}{2}}\)
A
v = \(\frac{12}{2s^2}\)
B
v = \(\frac{12}{2s+ w}\)
C
v = \(\frac{12}{2s^2 + w}\)
D
v = \(\frac{12}{2s^2}\) + w
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
S = \(\sqrt{\frac{6}{v} - \frac{w}{2}}\)
S = \(\frac{12 - vw}{2v}\)
2vs\(^2\) = 12 - vw
v(2s\(^2\) + w) = 12
v = \(\frac{12}{2s^2 + w}\)
Source: Myschool Past Questions Archive (Record #32114)
Mathematics
UTME / JAMB 1986
Number and Numeration
Solution
If \(\frac{a}{b}\) = \(\frac{c}{d}\) = k, find the value of \(\frac{3a^2 - ac + c^2}{3b^2 - bd + d^2}\) in terms of k
A
3k2
B
3k - k2
C
\(\frac{17k^2}{4}\)
D
k2
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Given that
\(\frac{a}{b} = \frac{c}{d} = k\)
we can express \(a\) and \(c\) as:
\(a = kb, \quad c = kd\)
We want to find the value of
\(\frac{3a^2 - ac + c^2}{3b^2 - bd + d^2}\)
Substituting \(a\) and \(c\) into the expression gives:
\(3a^2 - ac + c^2 = 3k^2b^2 - k^2bd + k^2d^2 = k^2(3b^2 - bd + d^2)\)
Thus, the expression simplifies to:
\(\frac{k^2(3b^2 - bd + d^2)}{3b^2 - bd + d^2} = k^2\)
Therefore, the value is: \(k^2\)
Source: Myschool Past Questions Archive (Record #32154)
Mathematics
UTME / JAMB 1986
Number and Numeration
Solution
A girl walks 45 meters in the direction 050o from a point Q to a point X. She then walks 24 meters in the direction 140o from X to a point Y. How far is she then from Q?
A
69m
B
57m
C
51m
D
21m
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
QY = 452 + 242 = 2025 + 576
= 2601
QY = \(\sqrt{2601}\)
= 51
Source: Myschool Past Questions Archive (Record #32159)
Mathematics
UTME / JAMB 1986
Number and Numeration
Solution
Find the total surface area of solid cone of radius 2\(\sqrt{3}\)cm and slanting side 4\(\sqrt{3}\)
A
8\(\sqrt{3}\pi \)cm2
B
24\(\pi \)cm2
C
15\(\sqrt{3}\pi \)cm2
D
36\(\pi \)cm2
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Total surface area of a solid cone
r = 2\(\sqrt{3}\)
= \(\pi r^2\) + \(\pi\)rH
H = 4\(\sqrt{3}\), \(\pi\)r(r + H)
∴ Area = \(\pi\)2\(\sqrt{3}\) [2\(\sqrt{3}\) + 4\(\sqrt{3}\)]
= \(\pi\)2\(\sqrt{3}\)(6\(\sqrt{3}\))
= 12\(\pi\) x 3
= 36\(\pi \)cm2
Source: Myschool Past Questions Archive (Record #32165)
Mathematics
UTME / JAMB 1986
Number and Numeration
Diagram
Solution
The people in a city with a population of 0.9 million were grouped according to their ages. Use the diagram to determine the number of people in the 15 - 29 years group
Attached Figure / Diagram
A
29 x 104
B
26 x 104
C
16 x 104
D
13 x 104
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
15 - 29 years is represented by 104o
Number of people in the group is \(\frac{104}{360}\) x 0.9m
= 260000 = 26 x 104
Source: Myschool Past Questions Archive (Record #32845)
Mathematics
UTME / JAMB 1985
Number and Numeration
Solution
Find x if log\(_9\)x = 1.5
A
72.0
B
27.0
C
36.0
D
3.5
E
24.5
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
If log\(_9\)x = 1.5,
9\(^1.5\) = x
9^\(\frac{3}{2}\) = x
(\sqrt9)\(^3\) = 3
∴ x = 27
Source: WAEC / JAMB / NECO Classroom Archive (Record #32213)
Mathematics
UTME / JAMB 1985
Number and Numeration
Solution
The ratio of the length of two similar rectangular blocks is 2 : 3. If the volume of the larger block is 351cm\(^3\), then the volume of the other block is?
A
234.00 cm3
B
526.50 cm3
C
166.00 cm3
D
687cm3
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Let x represent total vol. 2 : 3 = 2 + 3 = 5
\(\frac{3}{5}\)x = 351
x = \(\frac{351 \times 5}{3}\)
= 585
Volume of smaller block = \(\frac{2}{5}\) x 585
= 234.00cm\(^3\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #32260)
Mathematics
UTME / JAMB 1985
Number and Numeration
Solution
If three numbers P, Q, R are in ratio 6 : 4 : 5, find the value of \(\frac{3p - q}{4q + r}\)
A
\(\frac{3}{2}\)
B
\(\frac{2}{3}\)
C
2
D
3
E
18
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
P : Q : r = 6 : 4 : 5
5 = 6 + 4 + 5
= 15
P = \(\frac{6}{15}\), q = \(\frac{4}{15}\), r = \(\frac{5}{15}\) = \(\frac{1}{3}\)
To find \(\frac{3p - q}{4q + r}\)
3p - q = 3 x \(\frac{6}{15}\) - \(\frac{4}{15}\)
\(\frac{18}{15}\) - \(\frac{4}{15}\) = \(\frac{14}{15}\)
∴ 4q + r = 4 x \(\frac{4}{15}\) + \(\frac{5}{15}\)
\(\frac{16}{15}\) = \(\frac{16}{15}\) + \(\frac{5}{15}\)
= \(\frac{21}{15}\)
\(\frac{14}{15}\) x \(\frac{15}{21}\) = \(\frac{14}{21}\)
= \(\frac{2}{3}\)
Source: Myschool Past Questions Archive (Record #32180)
Mathematics
UTME / JAMB 1985
Number and Numeration
Solution
Arrange the following numbers in ascending order of magnitude \(\frac{6}{7}\), \(\frac{13}{15}\), 0.8650
A
\(\frac{6}{7}\) < 0.865 < \(\frac{13}{15}\)
B
\(\frac{13}{15}\) < \(\frac{6}{7}\) < 0.865
C
\(\frac{6}{7}\) < \(\frac{13}{15}\) < 0.865
D
0.865 < \(\frac{6}{7}\) < \(\frac{13}{15}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\frac{6}{7}\), \(\frac{13}{15}\), 0.8650
In ascending order, we have 0.8571, 0.8650, 0.8666
i.e. \(\frac{6}{7}\) < 0.8650 < \(\frac{13}{15}\)
Source: Myschool Past Questions Archive (Record #32191)
Mathematics
UTME / JAMB 1985
Number and Numeration
Solution
A sum of money was invested at 8% per annum simple interest. If after 4 years the money amounts to N330.00. Find the amount originally invested
A
N180.00
B
N165.00
C
N150.00
D
N250.00
E
N200.00
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
S.I = \(\frac{PTR}{100}\)
T = 4yrs, R = 8%, a = N330.00
330 - P = \(\frac{PTR}{100}\), A = P + I
i.e. A = P + \(\frac{PTR}{100}\)
330 = P + \(\frac{P(4) (8)}{100}\)
33000 = 32P + 100P
132P = 33000
P = N250.00
Source: Myschool Past Questions Archive (Record #32197)
Mathematics
UTME / JAMB 1985
Number and Numeration
Solution
In the equation below, Solve for x if all the numbers are in base 2: \(\frac{11}{x}\) = \(\frac{1000}{x + 101}\)
A
101
B
11
C
110
D
111
E
10
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\frac{11}{x}\) = \(\frac{1000}{x + 101}\) = 11(x + 101)
1000x = 11x + 1111
1000x - 11x = 1111
101x = 1111
x = \(\frac{1111}{101}\)
x = 11
Source: Myschool Past Questions Archive (Record #32200)
Mathematics
UTME / JAMB 1985
Number and Numeration
Solution
Find correct to two decimals places 100 + \(\frac{1}{100}\) + \(\frac{3}{1000}\) + \(\frac{27}{10000}\)
A
100.02
B
1000.02
C
100.22
D
100.01
E
100.51
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
100 + \(\frac{1}{100}\) + \(\frac{3}{1000}\) + \(\frac{27}{10000}\)
\(\frac{1000,000 + 100 + 30 + 27}{10000}\) = \(\frac{1,000.157}{10000}\)
= 100.02
Source: Myschool Past Questions Archive (Record #32204)