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Mathematics
UTME / JAMB 1995
Number and Numeration
Solution
Convert 3.1415926 to 5 decimal places
A
3.14160
B
3.14159
C
0.31415
D
3.14200
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
3.1415926 \(\approxeq\) 3.14159 (to 5 d.p)
Source: Myschool Past Questions Archive (Record #30873)
Mathematics
UTME / JAMB 1995
Number and Numeration
Solution
The length of a notebook 15cm, was measured as 16.8cm. Calculate the percentage error to 2 significant figures.
A
12.00%
B
11.00%
C
10.71%
D
0.12%
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Error = (16.8cm - 15cm = 1.8cm\)
\(\text{% error} = \frac{1.8}{15} \times 100% = \frac{180}{15}\)
= \(12.00%\)
Source: Myschool Past Questions Archive (Record #30875)
Mathematics
UTME / JAMB 1995
Number and Numeration
Solution
A worker's present salary is N24,000 per annum. His annual increment is 10% of his basic salary. What would be his annual salary at the beginning of the third year?
A
N28,800
B
N29,040
C
N31,200
D
N31,944
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Present salary = N24,000.
Increment after first year = \(\frac{10}{100} \times N24,000 = N2,400\)
Salary at the beginning of second year = N(24,000 + 2,400)
= N26,400.
Increment after second year = \(\frac{10}{100} \times N26,400 = N2,640\)
Salary at the beginning of third year = N(26,400 + 2,640)
= N29,040.
\(\therefore\) His salary at the beginning of the third year = N29,040.
Source: Myschool Past Questions Archive (Record #30876)
Mathematics
UTME / JAMB 1995
Number and Numeration
Solution
Evaluate \(\frac{(81)^{\frac{3}{4}} - (27)^{\frac{1}{3}}}{3 \times 2^3}\)
A
27
B
1
C
\(\frac{1}{3}\)
D
\(\frac{1}{8}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\frac{(81)^{\frac{3}{4}} - (27)^{\frac{1}{3}}}{3 \times 2^3}\)
= \(\frac{(3^{4})^{\frac{3}{4}} - (3^{3})^{\frac{1}{3}}}{3 \times 2^{3}}\)
= \(\frac{3^{3} - 3^{1}}{24}\)
= \(\frac{27 - 3}{24} = 1\)
Source: Myschool Past Questions Archive (Record #30878)
Mathematics
UTME / JAMB 1995
Number and Numeration
Solution
Simplify \(\frac{\sqrt{12} - \sqrt{3}}{\sqrt{12} + \sqrt{3}}\)
A
\(\frac{1}{3}\)
B
9
C
16cm
D
3
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\frac{\sqrt{12} - \sqrt{3}}{\sqrt{12} + \sqrt{3}}\)
\(\sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}\)
\(\therefore \frac{\sqrt{12} - \sqrt{3}}{\sqrt{12} + \sqrt{3}} = \frac{2\sqrt{3} - \sqrt{3}}{2\sqrt{3} + \sqrt{3}}\)
= \(\frac{\sqrt{3}}{3\sqrt{3}}\)
= \(\frac{1}{3}\)
Source: Myschool Past Questions Archive (Record #30881)
Mathematics
UTME / JAMB 1995
Number and Numeration
Solution
Four members of a school first eleven cricket team are also members of the first fourteen rugby team. How many boys play for at least one of the two teams?
A
25
B
21
C
16
D
3
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Number of people playing both rugby and cricket = 4
Number that play cricket only = 11 - 4 = 7
Number that play rugby only = 14 - 4 = 10.
Number that play for at least one of the teams = 4 + 7 + 10 = 21.
Source: Myschool Past Questions Archive (Record #30882)
Mathematics
UTME / JAMB 1995
Number and Numeration
If S = (x : x\(^2\) = 9, x > 4), then S is equal to
A
4
B
{0}
C
\(\emptyset\)
D
{\(\emptyset\)}
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 #30884)
Mathematics
UTME / JAMB 1995
Number and Numeration
Solution
Finds a positive value of p if the expression 2x2 - px + p leaves a remainder 6 when divided by x - p and q
A
1
B
2
C
3
D
4
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
x - p,x = p
2p2 - p2 + p = 6
= p2 + p - 6
= 0
p = 3, 2
Source: Myschool Past Questions Archive (Record #30894)
Mathematics
UTME / JAMB 1995
Number and Numeration
Solution
Find T in terms of K, Q, and S if S = 2r\(\sqrt{\pi(QT + K)}\)
A
\(\frac{S^2}{2 \pi r^2Q} - \frac{k}{Q}\)
B
\(\frac{S^2}{2 \pi r^2Q}\) - k
C
\(\frac{S^2}{4 \pi r^2Q} - \frac{k}{Q}\)
D
\(\frac{s^2}{4 \pi r^2Q}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{s^2}{4r^2}\) = \(\pi\)(QT + K)
\(\frac{s^2}{4r^2}\) - k\(\pi\) = QT\(\pi\)
T = \(\frac{s^2}{4Q\pi r^2}\) - \(\frac{k}{Q}\)
Source: Myschool Past Questions Archive (Record #30903)
Mathematics
UTME / JAMB 1995
Number and Numeration
Solution
The graph of f(x) = x2 - 5x + 6 crosses the x-axis at the points
A
(-6, 0), (-1, 0)
B
(-3, 0), (-2,0)
C
(-6, 0),(1, 0)
D
(2, 0), (3, 0)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
When X = 3, Y = 0(3, 0),
When x = 2, y = 0(2, 0)
Source: Myschool Past Questions Archive (Record #30904)
Mathematics
UTME / JAMB 1995
Number and Numeration
Solution
Factorize completely the expression \(abx^2 + 6y - 3ax - 2byx\)
A
(ax - 2y)(bx - 3)
B
(bx + 3)(2y - ax)
C
(bx + 3)(ax - 2y)
D
(ax - 2y)(ax - b)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(abx^{2} + 6y - 3ax - 2byx\)
Collecting like terms, we have
\(abx^{2} - 3ax + 6y - 2byx\)
= \(ax(bx - 3) + 2y(3 - bx)\)
= \(ax(bx - 3) - 2y(bx - 3)\)
= \((ax - 2y)(bx - 3)\)
Source: Myschool Past Questions Archive (Record #30905)
Mathematics
UTME / JAMB 1995
Number and Numeration
Solution
Simplify \(\frac{x^2 - 1}{x^3 + 2x^2 - x - 2}\)
A
\(\frac{1}{x + 2}\)
B
\(\frac{x - 1}{x + 1}\)
C
\(\frac{x - 1}{x + 2}\)
D
\(\frac{1}{x - 2}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\frac{x^2 - 1}{(x - 1)(x + 2)(x + 1)}\) = \(\frac{(x -
1)(x + 1)}{(x - 1)(x + 2)(x + 1)}\)
= \(\frac{1}{x + 2}\)
Source: Myschool Past Questions Archive (Record #30912)
Mathematics
UTME / JAMB 1995
Number and Numeration
Solution
Express \(\frac{5x - 12}{(x - 2)(x - 3)}\) in partial fractions
A
\(\frac{2}{x + 2} - \frac{3}{x - 3}\)
B
\(\frac{2}{x - 2} + \frac{3}{x - 3}\)
C
\(\frac{2}{x - 3} - \frac{3}{x - 2}\)
D
\(\frac{5}{x - 3} - \frac{4}{x - 2}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\frac{5x - 12}{(x - 2)(x - 3)} = \frac{A}{x - 2} + \frac{B}{x - 3}\)
= \(\frac{A(x - 3) + B(x - 2)}{(x - 2)(x - 3)}\)
\(\implies 5x - 12 = Ax - 3A + Bx - 2B\)
\(A + B = 5 ... (i)\)
\(-(3A + 2B) = -12 \implies 3A + 2B = 12 ... (ii)\)
From (i), \(A = 5 - B\)
\(3(5 - B) + 2B = 12\)
\(15 - 3B + 2B = 12 \implies B = 3\)
\(A + 3 = 5 \implies A = 2\)
\(\frac{5x - 12}{(x - 2)(x - 3)} = \frac{2}{x - 2} + \frac{3}{x - 3}\)
Source: Myschool Past Questions Archive (Record #30913)
Mathematics
UTME / JAMB 1995
Number and Numeration
Solution
Which of the following binary operations is cumulative on the set of integers?
A
a \(\ast\) b = a + 2b
B
a \(\ast\) b = a + b - ab
C
a \(\ast\) b = a2 + b
D
a \(\ast\) b = \(\frac{a(b + 1)}{2}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(a \ast b = a + b - ab\)
\(b \ast a = b + a - ba\)
On the set of integers, the two above are cumulative as multiplication and addition are cumulative on the set of integers.
Source: Myschool Past Questions Archive (Record #30916)
Mathematics
UTME / JAMB 1995
Number and Numeration
Solution
If a \(\ast\) b = + \(\sqrt{ab}\), evaluate 2 \(\ast\)(12 \(\ast\) 27)
A
12
B
9
C
6
D
2
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(2 \ast (12 \ast 27)\)
\(12 \ast 27 = + \sqrt{12 \times 27}\)
= \(+ \sqrt{324} = 18\)
\(2 \ast 18 = + \sqrt{2 \times 18}\)
= \(+ \sqrt{36} = 6\)
Source: Myschool Past Questions Archive (Record #30918)