JAMB 2014 · UTME

A woman bought a grinder for ₦60,000. She sold it at a loss of $15\%$. How much did she sell it for?

Express the product of 0.00043 and 2000 in standard form.

A man donates $10\%$ of his monthly net earnings to his church. If it amounts to ₦4,500, what is his net monthly income?

If $\log 7.5 = 0.8751$, evaluate $2\log 75 + \log 750$.

Solve for $x$ in $8x^{-2} = \frac{2}{25}$.

Simplify $\dfrac{2\sqrt2 - \sqrt3}{\sqrt2 + \sqrt3}$.

Evaluate $\log_2 8 + \log_2 16 - \log_2 4$.

If $P = \{1, 2, 3, 4, 5\}$ and $P \cup Q = \{1, 2, 3, 4, 5, 6, 7\}$, list the elements in $Q$.

From the Venn diagram, the shaded parts represent

If $gt^2 - k - w = 0$, make $g$ the subject of the formula.

Factorize $2y^2 - 15xy + 18x^2$.

Find the value of $k$ if $y - 1$ is a factor of $y^3 + 4y^2 + ky - 6$.

$y$ varies directly as $w^2$. When $y = 8$, $w = 2$. Find $y$ when $w = 3$.

$P$ varies directly as $Q$ and inversely as $R$. When $Q = 36$ and $R = 16$, $P = 27$. Find the relation between $P$, $Q$ and $R$.

What is the solution of $\dfrac{x - 5}{x + 3} < -1$?

Solve the inequality $\frac x2 + \frac34 \le \frac{5x}{6} - \frac{7}{12}$.

The 4th term of an A.P. is 13 while the 10th term is 31. Find the 24th term.

What is the common ratio of the G.P. $(\sqrt{10} + \sqrt5), (\sqrt{10} + 2\sqrt5), \ldots$?

A binary operation $*$ is defined by $x * y = xy$. If $x * x = 12 - x$, find the possible values of $x$.

Find $y$ if $\begin{pmatrix} 5 & -6 \\ 2 & -7 \end{pmatrix}\begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} 7 \\ -11 \end{pmatrix}$.

If $\begin{vmatrix} -x & 12 \\ -1 & 4 \end{vmatrix} = -12$, find $x$.

Find the value of $\begin{vmatrix} 0 & 3 & 2 \\ 1 & 7 & 8 \\ 0 & 5 & 4 \end{vmatrix}$.

How many sides has a regular polygon whose interior angles are $135^\circ$ each?

In the figure, $KL \parallel NM$ and $LN$ bisects $\angle KNM$. If $\angle KLN = 54^\circ$ and $\angle MKN = 35^\circ$, calculate $\angle KMN$.

From the figure, what is the value of $p$?

Find the value of $x$ in the figure.

A cylindrical tank has a capacity of $6160\text{ m}^3$. What is the depth of the tank if the radius of its base is $28\text{ m}$? $\left[\pi = \frac{22}{7}\right]$

The locus of a dog tethered to a pole with a rope of $4\text{ m}$ is a

Find the midpoint of $S(-5, 4)$ and $T(-3, -2)$.

The gradient of a line joining $(x, 4)$ and $(1, 2)$ is $\frac12$. Find the value of $x$.

What is the equation of the line that passes through the $y$-axis at $(0, 5)$ and the $x$-axis at $(5, 0)$?

Calculate the midpoint of the segment of the line $y - 4x + 3 = 0$ which lies between the $x$-axis and the $y$-axis.

Find the equation of the straight line through $(-2, 3)$ and perpendicular to $4x + 3y - 5 = 0$.

If $\sin\theta = \frac{12}{13}$ ($\theta$ acute), find the value of $1 + \cos\theta$.

If $y = 4x^3 - 2x^2 + x$, find $\dfrac{dy}{dx}$.

If $y = \cos 3x$, find $\dfrac{dy}{dx}$.

Find the minimum value of $y = x^2 - 2x - 3$.

Evaluate $\displaystyle\int \sin 2x\,dx$.

Evaluate $\displaystyle\int (2x + 3)^{\frac12}\,dx$.

The pie chart shows the monthly distribution of a man's salary on food items. If he spent ₦8,000 on rice, how much did he spend on yam?

Find the mode of the distribution.

Find the median of 5, 9, 1, 10, 3, 8, 9, 2, 4, 5, 5, 5, 7, 3 and 6.

Find the standard deviation of 5, 4, 3, 2, 1.

In how many ways can a team of 3 girls be selected from 7 girls?

The table represents the outcome of throwing a die 100 times. What is the probability of obtaining at least a 4?

A number is chosen at random from 10 to 30, both inclusive. What is the probability that the number is divisible by 3?