JAMB UTME - Mathematics - 1997

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

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

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 \( \sum d^2 = 60 \)

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

Find the range of values of \(x\) for which \(3x - 7 \le 0\) and \(x + 5 > 0\)

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 \( 3 \oplus (4 \ast 50) \)

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

The table above shows that the scores of a group of students in a test. If the average score is 3.5, find the value of x

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.

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

If y = x(x4 + x + 1), evaluate \( \int_{0}^{1} y\,dx \)

Find the volume of the prism.

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

Evaluate 64.7642 - 35.2362 correct to 3 significant figures

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

Find the non-zero positive value of x which satisfies the equation

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?

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

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

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

Find the median age of the frequency distribution in the table above.

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

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

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