JAMB UTME - Mathematics - 1982
Tambaya 1 Rahoto
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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Tambaya 2 Rahoto
If the function y = 5x is graphed, what would be its intercept on the y-axis?
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Tambaya 4 Rahoto
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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Tambaya 5 Rahoto
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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Tambaya 6 Rahoto
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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Tambaya 8 Rahoto
In the diagram, angle QPR = 90o, angle PSR = 90o and PR = 5 units. Find the length of QS.
Tambaya 10 Rahoto
Given that p:q = \(\frac{1}{3}\):\(\frac{1}{2}\) and q:r = \(\frac{2}{5}\), find p:r
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Tambaya 11 Rahoto
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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Tambaya 13 Rahoto
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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Tambaya 14 Rahoto
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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Tambaya 15 Rahoto
A variable y is inversely proportional to x2, when y = 10, x = 2. What is y when x = 10?
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Tambaya 16 Rahoto
Express 37.05 x 0.0042 in standard form
Tambaya 17 Rahoto
In the fiqure where PQRTU is a circle, ISTI = IRSI and angle TSR = 52o. Find the angle marked m
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Tambaya 19 Rahoto
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
Tambaya 20 Rahoto
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
Tambaya 21 Rahoto
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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Tambaya 22 Rahoto
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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Tambaya 23 Rahoto
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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Tambaya 25 Rahoto
If sin \(\theta\) = \(\frac{m - n}{m + n}\); Find the value of 1 + tan2\(\theta\)
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Tambaya 27 Rahoto
In the figure, QRST is a rectangle; PT// QM, angle P = 60o. Find angle MUR
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Tambaya 28 Rahoto
Find the values of x for which the expression \(\frac{(x - 3)(x - 2)}{x^2 + x - 2}\)
Tambaya 29 Rahoto
If N560.70 is shared in the ratio 7 : 2 : 1, what is the smallest share?
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Tambaya 30 Rahoto
What is the least possible value of \(\frac{9}{1 + 2x^2}\) if 0 \(\geq\) x \(\geq\) 2?
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Tambaya 31 Rahoto
Find the median of the set set of numbers 110, 116, 113, 119, 118, 127, 118, 117, 113
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Tambaya 32 Rahoto
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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Tambaya 34 Rahoto
Write the equation 2 log2x - x log2(1 + y) = 3 in a form not involving logarithms
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Tambaya 35 Rahoto
If K is a constant, which of the following equations best describes the parabola?
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Tambaya 38 Rahoto
Solve for x, If \(\frac{\frac{2}{x}}{\frac{p^2 + p^2}{p^2 + p^2}}\) = m
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Tambaya 39 Rahoto
The area of the curved surface of the cone generated by the sector of a circle radius 6cm and are length 22cm is (\(\pi\) = \(\frac{22}{7}\))
Tambaya 40 Rahoto
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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Tambaya 41 Rahoto
A sector of a circle is bounded by two radii 7cm long and an arc length 6cm. Find the area of the sector.
Tambaya 42 Rahoto
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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Tambaya 43 Rahoto
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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Tambaya 44 Rahoto
The solution to the simultaneous equations 3x + 5y = 4, 4x + 3y = 5 is
Tambaya 45 Rahoto
The graphical method of solving the equation x3 + 3x2 + 4x - 28 = 0 is by drawing the graphs of the curves
Tambaya 47 Rahoto
If \(\frac{3e + f}{3f - e}\) = \(\frac{2}{5}\), find the value of \(\frac{e + 3f}{f - 3e}\)
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Tambaya 48 Rahoto
Which of the following lines is not parallel to the line 3y + 2x + 7 = 0?
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