JAMB UTME - Mathematics - 2006

If \( \tan \theta = \frac{5}{4} \) find \( \sin^2 \theta - \cos^2 \theta \)

The table above shows the scores of a group of students in a physics test. If the mode is m and the number of students who scored 4 or more is n, what is (n, m)?

The solution set of the shaded area above is

Evaluate \( \int_{-4}^{0}(1-2x)\,dx \)

Find p, q for which \(\begin{pmatrix}2p & 8 \\ 3 & -5q\end{pmatrix}\) \(\begin{pmatrix}1 \\ 2\end{pmatrix}\) \(\begin{pmatrix}24 \\ -17\end{pmatrix}\)

In the diagram, the tangent MN makes an angle of 55o with the chord PS. IF O is the centre of the circle, find

he pie chart above shows the expenditure of a family whose income is ₦30,000. If the expenditure on food is twice that on housing and that on school fees is twice that on transport, how much does the family spend on food?

In the diagram P, Q, R, S are points on the circle RQS = 30o. PRS = 50o and PSQ = 20o. What is the value of xo + yo?

The solution set of the shaded area above is

In a triangle PQT, \(QR = \sqrt{3}\text{ cm}\), PR = 3cm, \(PQ = 2\sqrt{3}\text{ cm}\) and PQR = 30^o. Find angles P and R

Evaluate \( \frac{2}{6 - 5\sqrt{3}} \)

If \(T = 2\pi\sqrt{\frac{L}{g}}\), make \(g\) the subject of the formula

A binary operation * on the set of rational numbers is defined as \(x \times y = \frac{x^2-y^2}{2xy}\) find \(-5 \times 3\)

In the diagram above, |QR| is the diameter of the semicircle QR. Find the area of the figure to the nearest whole number. {\( \pi = \frac{22}{7} \)}

If \(x = \begin{vmatrix} 1 & 0 & 1 \\ 2 & -1 & 0 \\ -1 & 0 & 1 \end{vmatrix}\) and \(y = \begin{vmatrix} -1 & 1 & 2 \\ 0 & -1 & -1 \\ 2 & 0 & 1 \end{vmatrix}\)

find \(2x - y\)

simplify \( \frac{\frac{7}{9}-\frac{2}{3}}{\frac{1}{3}+\frac{\frac{2}{5}}{\frac{4}{5}}} \)

In the parallelogram PQRS given, find angle < SQR

The response of 160 pupils in a school asked to indicate their favourite subjects is given in the bar chart above. What percentage of the pupils have English English and Health education as the their favourite subjects?

In the diagram above, KLMN is a cyclic quadrilateral. /KL/ = /KN/, ∠NKM = 55o and ∠KML = 40o. Find ∠LKM.

If \(y = x^2 - x - 12\), find the range of values of \(x\) for which \(y \ge 0\)

In the diagram given PQ = 10cm, PS = 8cm and < PSR is 60 while < SRQ is a right angle. Find SR

In triangle XYZ, \(\angle XYZ = 15^\circ\), \(\angle XZY = 45^\circ\) and \(lXYl = 7\text{ cm}\). Find \(lYZl\).

In the diagram above, QR is in the diameter of the semicircle QR. Find the areas of the figure to the nearest whole number.

A binary operation \( \oplus \) on the set of rational numbers is defined as \(x \oplus y = \frac{x^2-y^2}{2xy}\). Find \(-5 \oplus 3\)

The binary operation \( \oplus \) defined on the set of real numbers is such that \( x \oplus y = \frac{xy}{6} \) for all \( x, y \in R \). Find the inverse of 20 under this operation when the identity element is 6

The table above shows the distribution of recharge cards of four major GSM operators. What is the probability that a recharge card selected at random will be GTN or Qtel?