UI Mathematics 2012/2013 Past Questions

A pyramid is constructed on a cuboid. The figure has

A quadrant of a circle of radius 6cm is cut away from each corner of a rectangle 25cm long and 18cm wide. Find the perimeter of the remaining figure.

A rectangular picture 6cm by 8cm is enclosed by a frame 1/2cm wide. Calculate the area of the frame.

A regular hexagon is constructed inside a circle of diameter 12cm. the area of the hexagon is

A regular hexagon is constructed inside a circle of diameter 12cm. The area of the hexagon is

A solid cylinder of radius 3cm has a total surface area of 36πcm2. Find its height.

A square of cardboard is taped at the perimeter by a piece of ribbon 20cm long. What is the area of the board?

A triangle has angles 30°, 15° and 135°, the side opposite to the angle 30° is length 6cm. The side opposite to the angle 135° is equal to

An isosceles triangle of sides 13cm, 13cm, 10cm is inscribed in a circle. What is the radius of the circle?

Differentiate $(x^2- 1/x)^2$ with respect to x.

Find the area of the curved surface of a cone whose base radius is 6cm and whose height is 8cm (Take π = 22/7).

Find the total surface area of a solid cone of radius 2'fcm and slanting side 4i/cm

If the four interior angles of a quadrilateral are (p + 10)°, (p - 30)°, (2p - 45)° and (p + I5)°, then p is

If the hypotenuse of a right angled isosceles triangle is 2, what is the length of each of the other sides?

If the value of π is taken to be 22/7, the area of a semicircle of diameter 42m is

In a circle of radius 10cm, a cord of length 10cm is xcm from its centre where x is

The difference between the length and width of a rectangle is 6cm and the area is $135cm^2$. What is the length?

At what value of x does the function $y= -3 - 2x + x^2$ attain a minimum value?

Differentiate $(x^2 - 1/x)^2$ with respect to x.

Evaluate $∫^{3}_{2}(x^2 - 1/x)$

Find the derivative of y = sin($2x^2$ + 3x - 4).

If ${dy}/{dx}$ = x + cos x, find y.

If the maximum value of $y = 1+ hx - 3x^2 is 13,$ find h.

If s = (2+3t)(5t - 4), find ds/dt when t = 4/5 sec