Jamb Mathematics Past Paper (2015)

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

An arc of a circle subtends an angle $70^\circ$ at the centre. If the calculate the area of the subtended by the given angl

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

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

Find a two-digit number that three times the ten digit is $20$ less than twice the units digit. The number is $20$ greater than the number obtained by reversing the digits.

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

A ladder resting on a vertical wall makes an angle whose tangent is $2.4$ with the ground. If the distance between the foot of the ladder and the wall is $50\text{cm}$, what is the length of ladder?

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

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

Evaluate $\int_0^{\pi/4} (\sin x - \cos x) dx$.