JAMB Mathematics 1997 Past Questions

Evaluate 64.764² - 35.2362 correct to 3 significant figures

Find the value of (0.006)³ + (0.004)³ in standard form

Given that log_a2 = 0.693 and log_a3 = 1.097, find log_a 13.5

If 8^{\(\frac{x}{2}\)} = (2^{\(\frac{3}{8}\)})(4\(\frac{3}{4}\)), find x

Simplify \(\frac{2\sqrt{3} + 3\sqrt{5}}{3\sqrt{5} - 2\sqrt{3}}\)

Find the simple interest rate percent per annum at which N1,000 accumulates to N1,240 in 3 years

If U = (s, p, i, e, n, d, o, u, r), X = (s, p, e, n, d) Y = (s, e, n, o, u), Z = (p, n, o, u, r) find X ∩ Y ∪ Z

A survey of 100 students in an institution shows that 80 students speak Hausa and 20 students speak Igbo, while only 9 students speak both language. How many students speak neither Hausa nor Igbo?

If the function f(fx) = x³ + 2x² + qx - 6 is divisible by x + 1, find q

Solve the simultaneous equations \(\frac{2}{x} - {\frac{2}{x}}\) = 2, \(\frac{4}{x} + {\frac{3}{y}}\) = 10

Find the minimum value of X² - 3x + 2 for all real values of x

Make F the subject of the formula t = \(\sqrt{\frac{v}{\frac{1}{f} + \frac{1}{g}}}\)

What value of g will make the expression 4x² - 18xy + g a perfect square?

Find the value of k if \(\frac{5 + 2r}{(r + 1)(r - 2)}\) expressed in partial fraction is \(\frac{k}{r - 2}\) + \(\frac{L}{r + 1}\) where K and L are constants

Let f(x) = 2x + 4 and g(x) = 6x + 7 here g(x) > 0. Solve the inequality \(\frac{f(x)}{g(x)}\) < 1

Find the range of values of x which satisfies the inequality 12x² < x + 1

S_n is the sum of the first n terms of a series given by S_n = n₂n - 1. Find the nth term

The nth term of a sequence is given 3^{1 - n} , find the sum of the first terms of the sequence.

Two binary operations \(\ast\) and \(\oplus\) are defines as m \(\ast\) n = mn - n - 1 and m \(\oplus\) n = mn + n - 2 for all real numbers m, n.

Find the value of 3 \(\oplus\) (4 \(\ast\) 50)

If X \(\ast\) Y = X + Y - XY, find x when (x \(\ast\) 2) + (x \(\ast\) 3) = 68

Determine x + y if \(\begin{pmatrix} 2 & -3 \\ -1 & 4 \end{pmatrix}\) \(\begin{pmatrix} x \\ y \end{pmatrix}\) = \(\begin{pmatrix}-1 \\ 8 \end{pmatrix}\)

Find the non-zero positive value of x which satisfies the equation \(\begin{vmatrix} x & 1 & 0 \\ 1 & x & x \\ 0 & 1 & x\end{vmatrix}\) = 0

Each of the base angles of a isosceles triangle is 59^o and the verticles of the triangle lie on a circle. Determine rhe angle which the base of the triangle subtends at the centre of the circle.

A chord of a circle of a diameter 42cm subtends an angle of 60^o at the centre of the circle. Find the length of the mirror arc

An arc of a circle subtends an angle 70^o at the centre. If the radius of the circle is 6cm, calculate the area of the sector subtended by the given angle.(\(\pi\) = \(\frac{22}{7}\))

A cone with the sector angle of 45^o is cut out of a circle of radius of the cone.

The angle between the positive horizontal axis and a given line is 135^o. Find the equation of the line if it passes through the point (2,3)

A point P moves so that is equidistant from point L and M. If LM is 6cm, find the distance of P from LM when P is 10cm from L

Find the distance between the point Q (4,3) and the point common to the lines 2x - y = 4 and x + y = 2

The angle of elevation of a building from a measuring instrument placed on the ground is 30^o. If the building is 40m high, how far is the instrument from the foot of the building?

In a triangle XYZ, if < ZYZ is 60, XY = 3cm and YZ = 4cm, calculate the length of the sides XZ.

Differentiate \(\frac{6x^3 - 5x^2 + 1}{3x^2}\) with respect to x

\(\frac{d}{dx}\) cos(3x² - 2x) is equal to

Integrate \(\frac{1}{x}\) + cos x with respect to x

If y = x(x4 + x + 1), evaluate ∫\(^{1}_{0}\) ydx

\(\begin{array}{c|c} Age & 20 & 25 & 30 & 35 & 40 & 45\\
\hline Number of people & 3 & 5 & 1 & 1 & 2 & 3\end{array}\)
Find the median age of the frequency distribution in the table above.

Find the difference between the range and the variance of the following set of numbers 4, 9, 6, 3, 2, 8, 10, 5, 6, 7 where \(\sum d^2\) = 60

In a basket of fruits, there are 6 grapes, 11 bananas and 13 oranges, if one fruit is chosen at random, what is the probability that the fruit is either a grape or a banana?

A number is selected at random between 10 and 20, both numbers inclusive. Find the probability that the number is an even number

Find the standard derivation of the following data -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5

The figure shows circles of radii 3cm and 2cm with centres at X and Y respectively. The circles have a transverse common tangent of length 25cm. Calculate XY

Find the volume of the prism

In the figure, XYZ is a triangle with XY = 5cm, XZ = 2cm and XZ is produced to E making the angle < YZE = 150^o. If the angle XYZ = \(\theta\), calculate the value of sin\(\theta\)

The pie chart shows the income of a civil servant in a month. If his monthly income is N600, find his monthly basic salary

In an examination, the result of a certain school is as shown in the histogram above. How many candidates did the school present?