JAMB 2015 · UTME

The sum of the progression $1 + x + x^2 + \ldots$ (where $|x| < 1$) is

Find a square root of $170 - 20\sqrt{30}$.

Multiply $(x + 3y + 5)$ by $(2x^2 + 5y + 2)$.

A force of 5 units acts on a particle in the direction due east and another force of 4 units acts on the particle in the direction north-east. The resultant of the two forces is

In the diagram, $PQ$ is parallel to $RS$. Calculate the value of $x$.

After getting a rise of $15\%$, a man's new monthly salary is ₦345. How much per month did he earn before the increase?

A trader goes to Ghana for $y$ days with $Y$ cedis. For the first $x$ days, he spends $X$ cedis per day. The amount he has to spend per day for the rest of his stay is

The mean of the numbers 1.2, 1.0, 0.4, 1.4, 0.8, 0.8, 1.2 and 1.1 is

A solid cylinder of radius $3\text{ cm}$ has a total surface area of $36\pi\text{ cm}^2$. Find its height.

Which formula represents the general term of the numbers $\left\{-1, \frac23, -\frac12, \frac25, \ldots\right\}$ for $n = 1, 2, 3, 4, \ldots$?

Write the decimal number 39 in base 2.

A pentagon has four of its angles equal. If the size of the fifth angle is $60^\circ$, find the size of each of the four equal angles.

In the figure, $PQ \parallel SR$, $ST \parallel RQ$, $PS = 7\text{ cm}$, $PT = 7\text{ cm}$ and $SR = 4\text{ cm}$. Find the ratio of the area of $QRST$ to the area of $PQRS$.

Find a two-digit number such that three times the tens digit is 2 less than twice the units digit, and twice the number is 20 greater than the number obtained by reversing the digits.

In $\triangle XYZ$, $XY = 3\text{ cm}$, $XZ = 5\text{ cm}$ and $YZ = 7\text{ cm}$. If the bisector of $\angle XYZ$ meets $XZ$ at $W$, what is the length of $XW$?

Marks scored by some children in an arithmetic test are 5, 3, 6, 9, 4, 7, 8, 6, 2, 7, 8, 4, 3, 2, 1, 0, 6, 9, 0, 8. The arithmetic mean of the marks is

The graphical method of solving the equation $x^3 + 3x^2 + 4x - 28 = 0$ is by drawing the graphs of the curves

A sector of a circle is bounded by two radii $7\text{ cm}$ long and an arc of length $6\text{ cm}$. Find the area of the sector.

The mean age of 30 pupils in a class is 15.3 years. One boy leaves the class and one girl is enrolled, and the new mean age of the 30 pupils becomes 15.2 years. How much older is the boy than the girl?

A world congress of mathematicians was held in Nice in 1970 with 800 people participating: 300 from Europe, 200 from America, 150 from Asia, 45 from Africa and 105 from Australia. On a pie chart, the angle of the sector representing Asia is

Find the sum to infinity of the sequence $1, \frac{9}{10}, \left(\frac{9}{10}\right)^2, \left(\frac{9}{10}\right)^3, \ldots$

Which of the following is a sketch of $y = 3\sin x$?

Given that $\log_a 2 = 0.693$ and $\log_a 3 = 1.097$, find $\log_a 13.5$.

If $f(x) = x^3 + 2x^2 + qx - 6$ is divisible by $x + 1$, find $q$.

What value of $g$ will make the expression $4x^2 - 18xy + g$ a perfect square?

An arc of a circle subtends an angle of $70^\circ$ at the centre. If the radius of the circle is $6\text{ cm}$, calculate the area of the sector. $\left[\text{Take }\pi = \frac{22}{7}\right]$

The angle of elevation of a building from a measuring instrument placed on the ground is $30^\circ$. If the building is $40\text{ m}$ high, how far is the instrument from the foot of the building?

Integrate $\dfrac1x + \cos x$ with respect to $x$.

Find $\dfrac{d}{dx}\cos(3x^2 - 2x)$.

If $\log_8 10 = x$, evaluate $\log_8 5$ in terms of $x$.

Simplify $\sqrt{\dfrac{0.0023 \times 750}{0.00345 \times 1.25}}$.

Find the matrix $T$ if $ST = I$, where $S = \begin{pmatrix} -1 & 1 \\ 1 & -2 \end{pmatrix}$ and $I$ is the identity matrix.

The first term of a geometric progression is twice its common ratio. Find the sum of the first two terms of the progression if its sum to infinity is 8.

In $\triangle MNO$, $MN = 9$ units, $MO = 6$ units and $NO = 12$ units. If the bisector of angle $M$ meets $NO$ at $P$, calculate $NP$.