JAMB - Mathematics (1995)

1
Calculate \(3310_5 - 1442_5\)
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(A)
1313₅
2
Convert 3.1415926 to 5 decimal places
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(B)
3.14159
3
The length of a notebook 15cm, was measured as 16.8cm. Calculate the percentage error to 2 significant figures.
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(A)
12.00%
4
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?
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(B)
N29,040
5
Express the product of 0.0014 and 0.011 in standard form
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(D)
1.54 x 10^-5
6
Evaluate \(\frac{(81)^{\frac{3}{4}} - (27)^{\frac{1}{3}}}{3 \times 2^3}\)
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(B)
1
7
Simplify \(\frac{\sqrt{12} - \sqrt{3}}{\sqrt{12} + \sqrt{3}}\)
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(A)
\(\frac{1}{3}\)
8
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?
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(B)
21
9
If S = (x : x\(^2\) = 9, x > 4), then S is equal to
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(C)
\(\emptyset\)
10
If x - 1 and x + 1 are both factors of the equation x\(^3\) + px\(^2\) + qx + 6 = 0, evaluate p and q
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(A)
-6, -1
11
Finds a positive value of p if the expression 2x² - px + p leaves a remainder 6 when divided by x - p and q
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(B)
2
12
Find T in terms of K, Q, and S if S = 2r\(\sqrt{\pi(QT + K)}\)
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(C)
\(\frac{S^2}{4 \pi r^2Q} - \frac{k}{Q}\)
13
The graph of f(x) = x² - 5x + 6 crosses the x-axis at the points
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(D)
(2, 0), (3, 0)
14
Factorize completely the expression \(abx^2 + 6y - 3ax - 2byx\)
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(A)
(ax - 2y)(bx - 3)
15
Solve the inequality (x - 3)(x - 4) \(\leq\) 0
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(A)
3 \(\leq\) x \(\leq\) 4
16
The 4th term of an A.P. is 13 while the 10th term is 31. Find the 21st term.
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(C)
64
17
Simplify \(\frac{x^2 - 1}{x^3 + 2x^2 - x - 2}\)
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(A)
\(\frac{1}{x + 2}\)
18
Express \(\frac{5x - 12}{(x - 2)(x - 3)}\) in partial fractions
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(B)
\(\frac{2}{x - 2} + \frac{3}{x - 3}\)
19
Which of the following binary operations is cumulative on the set of integers?
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(B)
a \(\ast\) b = a + b - ab
20
If a \(\ast\) b = + \(\sqrt{ab}\), evaluate 2 \(\ast\)(12 \(\ast\) 27)
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(C)
6
21
Find the sum to infinity of the following sequence \(1, \frac{9}{10}, (\frac{9}{10})^{2}, (\frac{9}{10})^{3}\)
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(D)
10
22
\(\begin{vmatrix} -2 & 1 & 1 \\ 2 & 1 & k \\1 & 3 & -1 \end{vmatrix}\) = 23
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(B)
2
23
If x = \(\begin{pmatrix} 1 & 2 \\ 0 & 3 \end{pmatrix}\) and y = \(\begin{pmatrix} 2 & 1 \\ 4 & 3 \end{pmatrix}\). Find xy.
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(A)
\(\begin{pmatrix} 10 & 7 \\ 12 & 9 \end{pmatrix}\)
24
In a triangle XYZ, < YXZ = 44° and < XYZ = 112°. Calculate the acute angle between the internal bisectors of < XYZ and < XZY.
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(C)
68^o
25
Find the distance between two towns P(45°N, 30°W) and Q(15°S, 30°W) if the radius of the earth is 7000km. [\(\pi = \frac{22}{7}\)]
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(C)
\(\frac{22000}{3}\)km
26
Two perpendicular lines PQ and QR intersect at (1, -1). If the equation of PQ is x - 2y + 4 = 0, find the equation of QR
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(D)
2x + y - 1 = 0
27
P is on the locus of points equidiatant from two given points X and Y. UV is a straight line throuh Y parallel to the locus. If < PYU is 40°, find < XPY.
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(B)
80 ^o
28
A school boy lying on the ground 30m away from the foot of a water tank tower observes that the angle of elevation of the top of the tank 60^o. Calculate the height of the water tank.
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(B)
30 \(\sqrt{3}\)m
29
The derivative of cosec x is
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(B)
-cot x cosec x
30
For what value of x is the tangent to the curve y = x\(^2\) - 4x + 3 parallel to the x-axis?
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(B)
2
31
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
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(B)
2x² - 3x + 3
32
Find the area bounded by the curve y = 3x\(^2\) - 2x + 1, the ordinates x = 1 and x = 3 and the x-axis.
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(D)
20
33
\(\begin{array}{c|c} \text{Age in years} & 13 & 14 & 15 & 16 & 17 \\ \hline \text{No. of students} & 3 & 10 & 30 & 42 & 15\end{array}\)
The frequency distribution above shows the ages of students in a secondary school. In a pie chart constructed to represent the data, the angles corresponding to the 15 years old is
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(D)
108^o
34
The pie chart shows the distribution of students in a secondary school class. If 30 students offered French, how many offered C.R.K?

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(C)
10
35
\(\begin{array}{c|c} class& 1 - 3 & 4 - 6 & 7 - 9\\ \hline Frequency & 5 & 8 & 5\end{array}\)
Find the standard deviation of the data using the table above
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(D)
\(\sqrt{5}\)
36
The variance of the scores 1, 2, 3, 4, 5 is
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(C)
2.0
37
\(\begin{array}{c|c} \text{Class Interval} & Frequency & \text{Class boundaries} & Class Mid-point \\ \hline 1.5 - 1.9 & 2 & 1.45 - 1.95 & 1.7\\ 2.0 - 2.4 & 1 & 1.95 - 2.45 & 2.2\\ 2.5 - 2.9 & 4 & 2.45 - 2.95 & 2.7 \\ 3.0 - 2.9 & 15 & 2.95 - 3.45 & 3.2\\ 3.5 - 3.9 & 10 & 3.45 - 3.95 & 3.7\\ 4.0 - 4.4 & 5 & 3.95 - 4.45 & 4.2\\ 4.5 - 4.9 & 3 & 4.45 - 4.95 & 4.7\end{array}\)
Find the mode of the distribution.
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(B)
3.3
38
\(\begin{array}{c|c} \text{Class Interval} & Frequency & \text{Class boundaries} & Class Mid-point \\ \hline 1.5 - 1.9 & 2 & 1.45 - 1.95 & 1.7\\ 2.0 - 2.4 & 21 & 1.95 - 2.45 & 2.2\\ 2.5 - 2.9 & 4 & 2.45 - 2.95 & 2.7 \\ 3.0 - 2.9 & 15 & 2.95 - 3.45 & 3.2\\ 3.5 - 3.9 & 10 & 3.45 - 3.95 & 3.7\\ 4.0 - 4.4 & 5 & 3.95 - 4.45 & 4.2\\ 4.5 - 4.9 & 3 & 4.45 - 4.95 & 4.7\end{array}\)
The median of the distribution above is
پاسخ دهید
(B)
3.4
39
Let p be a probability function on set S, where S = (a₁, a₂, a₃, a₄). Find P(a₁) if P(a₂) = \(\frac{1}{3}\), p(a₃) = \(\frac{1}{6}\) and p(a₄) = \(\frac{1}{5}\)
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(D)
\(\frac{3}{10}\)
40
A die has four of it's faces coloured white and the remaining two coloured black. What is the probability that when the die is thrown two consecutive time, the top face will be white in both cases?
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(C)
\(\frac{4}{9}\)
41
Use the graph of the curve y = f(x)to solve the inequality f(x) \(\leq\) 0
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(B)
x \(\leq\) -1, 1 \(\geq\) x \(\geq\) 2
42
Determine the value of x in the figure
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(A)
134^o
43
PT is a tangent to the circle TYZX. YT = YX and < PTX = 50o. Calculate < TZY
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(B)
65^o
44
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.[\(\pi \frac{22}{7}\)]
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(A)
836cm²
45
In the diagram, find PQ if the area of triangle PQR is 35cm\(^2\)
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(C)
14cm