JAMB 1994 · UME

Evaluate $\frac13 \div \left[\frac57\left(\frac{9}{10} - 1 + \frac34\right)\right]$.

Evaluate $(0.36 \times 5.4 \times 0.63) \div (4.2 \times 9.0 \times 2.4)$, correct to 2 significant figures.

Evaluate $\dfrac{\log_5 0.04}{\log_3 18 - \log_3 2}$.

Without using tables, solve the equation $8x^{-2} = \frac{2}{25}$.

Simplify $\sqrt{48} - \dfrac{9}{\sqrt3} + \sqrt{75}$.

Given that $\sqrt2 = 1.414$, find without using tables the value of $\frac{1}{\sqrt2}$.

In a science class of 42 students, each offers at least one of Mathematics and Physics. If 22 students offer Physics and 28 offer Mathematics, how many students offer Physics only?

Given that for sets $A$ and $B$ in a universal set $E$, $A \subseteq B$, then $A \cap (A \cap B)'$ is

Solve for $x$ if $25^x + 3(5^x) = 4$.

Factorize $a^2x - b^2y - b^2x + a^2y$.

Find the values of $p$ and $q$ such that $(x - 1)$ and $(x - 3)$ are factors of $px^3 + qx^2 + 11x - 6$.

The equation of the graph shown is

If $a = 1$ and $b = 3$, solve for $x$ in the equation $\dfrac{a}{a - x} = \dfrac{b}{x - b}$.

Solve for $r$ in the equation $\dfrac{1}{r - 1} + \dfrac{2}{r + 1} = \dfrac3r$.

Find $P$ if $\dfrac{x - 3}{(1 - x)(x + 2)} = \dfrac{P}{1 - x} + \dfrac{Q}{x + 2}$.

Find the range of values of $x$ for which $\frac1x > 2$ is true.

If the 6th term of an arithmetic progression is 11 and the first term is 1, find the common difference.

Find the value of $r$ if $\log_{10} r + \log_{10} r^2 + \log_{10} r^4 + \log_{10} r^8 + \log_{10} r^{16} + \log_{10} r^{32} = 63$.

Find the $n$th term of the sequence $3, 6, 10, 15, 21, \dots$

A binary operation $*$ is defined on the set of all positive integers by $a * b = ab$. Which of the following properties does NOT hold?

The table shows multiplication modulo 10 on the set $S = \{2, 4, 6, 8\}$. Find the inverse of 2.

Solve for $x$ and $y$: $\begin{pmatrix} 1 & 1 \\ 3 & y \end{pmatrix}\begin{pmatrix} x \\ 1 \end{pmatrix} = \begin{pmatrix} 4 \\ 1 \end{pmatrix}$.

The determinant of the matrix $\begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 2 & 0 & -1 \end{pmatrix}$ is

In the diagram, $O$ is the centre of the circle and $SOQ$ is a diameter. If $\angle PRS = 38^\circ$, what is the value of $\angle PSQ$?

If three angles of a quadrilateral are $(3y - x - z)^\circ$, $3x^\circ$ and $(2z - 2y - x)^\circ$, find the fourth angle in terms of $x$, $y$ and $z$.

An open rectangular box is made of wood 2 cm thick. If the internal dimensions of the box are 50 cm long, 36 cm wide and 20 cm deep, what is the volume of wood in the box?

Calculate the perimeter, in cm, of a sector of a circle of radius 8 cm and angle $45^\circ$.

In the diagram, $PTS$ is a tangent to the circle $TQR$ at $T$, $\angle QRT = 60^\circ$ and $\angle QTR = 50^\circ$. Calculate $\angle RTS$.

A triangle has base 7 cm and other sides 6 cm and 5 cm. Find its height $h$ onto the base.

In a frustum of a cone (an upturned cup shape), the top diameter is twice the bottom diameter. If the height of the frustum is $h$ cm, find the height of the cone from which it was cut.

What is the locus of a point $P$ which moves on one side of a straight line $XY$ so that the angle $XPY$ is always $90^\circ$?

If $M(4, q)$ is the midpoint of the line joining $L(p, -2)$ and $N(q, p)$, find the values of $p$ and $q$.

The equation of the line in the graph shown is

The angle of depression of a boat from the top of a cliff 10 m high is $30^\circ$. How far is the boat from the foot of the cliff?

What is the value of $\sin(-690^\circ)$?

If $y = 3t^3 + 2t^2 - 7t + 3$, find $\frac{dy}{dt}$ at $t = -1$.

Find the point $(x, y)$ where the curve $y = 2x^2 - 2x + 3$ has gradient 2.

Integrate $\dfrac{1 - x}{x^3}$ with respect to $x$.

Evaluate $\displaystyle\int_{-1}^{1} (2x + 1)^2\,dx$.

The grades A1, A2, A3, C4 and F earned by students in a course are shown in the pie chart. What percentage of the students obtained a C4 grade?

The mean of twelve positive numbers is 3. When another number is added, the mean becomes 5. Find the thirteenth number.

Find the mean deviation of the numbers 4, 5, 9.

Estimate the median of the frequency distribution below.

The table shows the number of pupils in each age group in a class. What is the probability that a pupil chosen at random is at least 11 years old?

In a survey, 20 students read newspapers and 35 read novels. If 40 of the students read either newspapers or novels, what is the probability of the students who read both newspapers and novels?