JAMB Mathematics 1992 Past Questions

Find n if 34_n = 10011₂

The radius of a circle is given as 5cm subject to an error of 0.1cm. What is the percentage error in the area of the circle?

Evaluate log_baⁿ if b = aⁿ

What is the value of x satisfying the equation \(\frac{4^{2x}}{4^{3x}}\) = 2?

Simplify \(\frac{(1.25 \times 10^{-4}) \times (2.0 \times 10^{-1})}{(6.25 \times 10^5)}\)

Simplify 5\(\sqrt{18}\) - 3\(\sqrt{72}\) + 4\(\sqrt{50}\)

If x = 3 - \(\sqrt{3}\), find x² + \(\frac{36}{x^2}\)

If x = (all prime factors of 44) and y = (all prime factors of 60), the elements of X ∪ Y and X ∩ Y respectively are

If U = (1, 2, 3, 6, 7, 8, 9, 10) is the universal set. E = (10, 4, 6, 8, 10) and F = is odd. Find (E ∩ F), where means x 1x² = 2⁶, x the complement of a set

Factorize 9p² - q² + 6qr - 9r²

Solve the equation: y - 11y + 24 = 0

Make t the subject of formula S = ut + \(\frac{1}{2} at^2\)

A man invested a sum of n280.00 partly at 5% and partly at 4%. if the total interest is N12.90 per annum, find the amount invested at 5%

If x + 1 is a factor of x³ + 3x² + kx + 4, find the value of k

Resolve \(\frac{3}{x^2 + x - 2}\) into partial fractions

Find all values of x satisfying the inequality -11 \(\leq\) 4 - 3x \(\leq\) 28

Find the sum to infinity to the following series 3 + 2 + \(\frac{4}{3}\) + \(\frac{8}{9}\) + \(\frac{16}{17}\) + .....

What is the n-th term of the sequence 2, 6, 12, 20...?

For an arithmetical sequence, the first term is 2 and the common difference is 3. Find the sum of the first 11 terms

If the binary operation \(\ast\) is defined by m \(\ast\) n = mn + m + n for any real number m and n, find the identity of the elements under this operation

p = \(\begin{vmatrix} x & 3 & 0 \\ 2 & y & 3\\ 4 & 2 & 4 \end{vmatrix}\)

Q = \(\begin{vmatrix} x & 2 & z \\ 3 & y & 2\\ 0 & 3 & z \end{vmatrix}\) Where p^T is the transpose P calculate /p^T/ when x = 0, y = 1 and z = 2

p = \(\begin{vmatrix} x & 3 & 0 \\ 2 & y & 3\\ 4 & 2 & 4 \end{vmatrix}\)

Q = \(\begin{vmatrix} x & 2 & z \\ 3 & y & 2\\ 0 & 3 & z \end{vmatrix}\)
PQ is equivalent to

If the angles of quadrilateral are (P + 10)^o(2P - 30)^o(3P + 20)^o and 4p^o, find p

Determine the distance on the earth's surface between two town P (lat^oN, Long 20^oN) and Q(Lat 60^oN, Long 25^oW) (Radius of the earth = 6400km)

If in the diagram, FG is parallel to KM, find the value of x

x is a point due east of point Y on a coast Z is another point on the coast but 63m due south of y. If the distance ZX is 12Km. Calculate the bearing of Z from X

The locus of a point which is equidistant from two given fixed points is the

What is the perpendicular distance of a point (2, 3) from the line 2x - 4y + 3 = 0?

find then equation line through (5, 7) parallel to the line 7x + 5y = 12

Given that \(\theta\) is an acute angle and sin \(\theta\) = \(\frac{m}{n}\), find cos \(\theta\)

Evaluate \(\frac{(x - 2)(x^2 + 3x - 2)}{x^2 - 4}\)

If y = x sin x, Find \(\frac{d^2 y}{d^2 x}\)

Ice forms on a refrigerator ice-box at the rate of (4 - 06t)g per minute after t minutes. If initially there are 2g of ice in the box, find the mass of ice formed in 5 minutes

Obtain a maximum value of the function f(x) x³ - 12x + 11

a student blows a balloon and its volume increases at a rate of \(\pi\)(20 - t²)cm³S^-1 after t seconds. If the initial volume is 0 cm³, find the volume of the balloon after 2 seconds

Evaluate the integral \(\int^{\frac{\pi}{4}}_{\frac{\pi}{12}}\) 2 cos 2x dx

A store keeper checked his stock of five commodities and arrived at the following statics
\(\begin{array}{c|c} Comoditiy & Quantity\\ \hline F & 125\\ G & 113\\ H & 108\\ K & 216 \\ M & 68\end{array}\)
What angle will commodity H represent on a pie chart?

\(\begin{array}{c|c} x & 2 & 4 & 6 & 8\\ \hline f & 4 & y & 6 & 5 \end{array}\)
If the mean of the above frequency distribution is 5.2, find y

\(\begin{array}{c|c} \text{No. of children} & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \text{No. of families} & 7 & 11 & 6 & 7 & 7 & 5 & 3 \end{array}\)
Find the mode and median respectively of the distribution above

If the scores of 3 students in a test are 5, 6 and 7, find the standard deviation of their scores

Two perfect dice are thrown together, Determine the probability of obtaining a total score of 8

The probability of an event P is \(\frac{3}{4}\) while that of another event Q is \(\frac{1}{6}\). If the probability of both P and Q is \(\frac{1}{2}\). What is the probability of either P or Q.

Five people are to be arranged in a row for a group photograph. How many arrangements are the if a married couple in the group insist on sitting next to each other?

A student has 5 courses to take from Mathematics and physics. There are 4 courses in Mathematics and 3 in Physics which he can choose his courses so that he takes exactly two courses in Physics?

The sketch is the curve of y = ax² + bx + c. Find a, b and c respectively

In the figure, TSP = 105² and PRQ = 20². Find PQR

In the figure, PQr is a semicircle while PQ and Qr are chords. QS is the perpendicular from Q to the diameter PR. What is the expression for QS?

The diagram is a circle with centre O. Find the area of the shaded portion

In the figure, if XZ is 10cm, calculate RY in cm