JAMB UTME - Mathematics - 1982
Question 1 Report
A world congress of mathematicians were held in Nice in 1970 with 800 people participating. There were 300 from Europe, 200 from America, 150 from Asia, 45 from Africa and 105 from Australia. Representing the above on a pie chart, the angle of the sector representing the participant is
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Question 2 Report
The quantity y is partly constant and partly varies inversely as the square of x. With P and Q as constants, a possible relationship between x and y is
Question 3 Report
Seven years ago, the age of a father was three times that of his son, but in six years time the age of the son will be half that of his father, representing the present ages of the father and son by x and y, respectively, the two equations relating x and y are
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Question 4 Report
Given that p:q = \(\frac{1}{3}\):\(\frac{1}{2}\) and q:r = \(\frac{2}{5}\), find p:r
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Question 5 Report
The currency used in a country is called 'Matimalik'(M) and is of base seven. A lady in that country bought 4 bags of rice at M56 per bag and and 3 tins of milk at M4 per tin. What is the total cost of the item she bought?
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Question 6 Report
The arithmetic mean of the ages of 30 pupils in a class is 15.3 years. One boy leaves the class and one girl is enrolled, and the new average age of 30 pupils in the class becomes 15.2 years. How much older is the boy than the girl?
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Question 7 Report
A side of a rhombus is 2cm in length. An angle of the rhombus is 60o. What is the length of the diagonal facing this angle?
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Question 8 Report
If K is a constant, which of the following equations best describes the parabola?
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Question 9 Report
If sin \(\theta\) = \(\frac{m - n}{m + n}\); Find the value of 1 + tan2\(\theta\)
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Question 10 Report
In the figure, QRST is a rectangle; PT// QM, angle P = 60o. Find angle MUR
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Question 11 Report
PQRS is a parallelogram with area 50 square cm and the side PQ is 10cm long. T is a point on RS and TF is the altitude of the triangle TPQ. Find TF
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Question 12 Report
Express 37.05 x 0.0042 in standard form
Question 13 Report
The area of the curved surface of the cone generated by the sector of a circle radius 6cm and are length 22cm is (\(\pi\) = \(\frac{22}{7}\))
Question 14 Report
A variable y is inversely proportional to x2, when y = 10, x = 2. What is y when x = 10?
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Question 15 Report
In the fiqure where PQRTU is a circle, ISTI = IRSI and angle TSR = 52o. Find the angle marked m
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Question 17 Report
Write the equation 2 log2x - x log2(1 + y) = 3 in a form not involving logarithms
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Question 18 Report
Find \(\alpha\) and \(\beta\) such that x\(\frac{3}{8}\) x y\(\frac{-6}{7}\) x (\(\frac{y^{\frac{9}{7}}}{x^{\frac{45}{8}}}\))\(\frac{1}{9}\) = \(\frac{y^{\alpha}}{y^{\beta}}\)
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Question 19 Report
Solve for x, If \(\frac{\frac{2}{x}}{\frac{p^2 + p^2}{p^2 + p^2}}\) = m
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Question 20 Report
Which of the following lines is not parallel to the line 3y + 2x + 7 = 0?
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Question 21 Report
What is the least possible value of \(\frac{9}{1 + 2x^2}\) if 0 \(\geq\) x \(\geq\) 2?
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Question 22 Report
Determine the mean monthly salary of 50 employees of a company from the following frequency distribution.
\(\begin{array}{c|c} \text{Monthly salary} & \text{Frequency}\\\hline N200.00 & 10\\ N325.00 & 5\\N100.00 & 20\\N120.00 & 2\\ N60.00 & 10\\ N80.00 & 3\end{array}\)
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Question 23 Report
Two distinct sectors i the same circle substend 100o and 30o respectively at the centre of the circle. Their corresponding arcs are in ratio
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Question 24 Report
If the function y = 5x is graphed, what would be its intercept on the y-axis?
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Question 26 Report
A sector of a circle is bounded by two radii 7cm long and an arc length 6cm. Find the area of the sector.
Question 27 Report
The graphical method of solving the equation x3 + 3x2 + 4x - 28 = 0 is by drawing the graphs of the curves
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Question 28 Report
If N560.70 is shared in the ratio 7 : 2 : 1, what is the smallest share?
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Question 29 Report
Find the median of the set set of numbers 110, 116, 113, 119, 118, 127, 118, 117, 113
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Question 30 Report
A stone Q is tied to a point P vertically above Q by an inelastic string of length 2 meters. How high does the stone rise when the string is inclined at an angle 60o to the vertical?
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Question 31 Report
In a regular polygon of n sides, each interior angle is 144o. Find n
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Question 32 Report
A housewife bought 3 kilograms of garri at N13.00 per kg. She deposited N160. 00 for half a cow and bought 24 oranges at 10k each. She came back home with N20.60. She therefore left home with
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Question 33 Report
In the diagram, angle QPR = 90o, angle PSR = 90o and PR = 5 units. Find the length of QS.
Question 36 Report
The diameter of a metal rod is measured as 23.40 cm to four significant figures. What is the maximum error in the measurement?
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Question 37 Report
Find the values of x for which the expression \(\frac{(x - 3)(x - 2)}{x^2 + x - 2}\)
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Question 39 Report
If \(\frac{3e + f}{3f - e}\) = \(\frac{2}{5}\), find the value of \(\frac{e + 3f}{f - 3e}\)
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Question 40 Report
The square base of a pyramid of side 3cm has height 8cm. If the pyramid is cut into two parts by a plane parallel to the base midway between the base and the vertex, the volumes of the two sections are
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Question 41 Report
TP and TQ are tangents to a circle centre 0 and r is a point on the circumference of the circle as shown in the figure. If angle PTQ = 45o, what is the magnitude of the angle PRO?
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Question 42 Report
The diagram is the distance time graph of a vehicle. Find its average speed in kilometers per hour during the journey
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Question 43 Report
A man bought wrist watch for N150 but was only able to sell it for N120. Find the loss per cent on the transaction
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Question 45 Report
The solution of the quadratic equation bx2 + cx + a = 0 is given by
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Question 46 Report
The solution to the simultaneous equations 3x + 5y = 4, 4x + 3y = 5 is
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Question 47 Report
Simplify f\(\frac{1}{2}\)g2h\(\frac{1}{2}\) \(\div\) f\(\frac{5}{2}\)goh\(\frac{7}{3}\)
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