UI Mathematics 2013/2014 Past Questions

Write the decimal number 39 to base 2.

A father is now three times as old as his son. Twelve years ago, he was six times as old as his son. How old are the son and the father'?

A steel ball of radius 1cm is dropped into a cylinder of radius 2cm and height 4cm. If the cylinder is now filled with water, what is the volume of the water in the cylinder?

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.

Find the roots of the equation $10x^2 - 13x - 3 = 0$

If a function is defined by $f(x + 1) = 3x^2 - x + 4$, find f(0).

If sin x equals cosine x, what is x in radians?

If $x^2+4=0$, then x =

In a geometric progression, the first term is 153 and the sixth term is 17/27, the sum of the first four terms is

List all integer values of x satisfying the inequality -1 < 2x - 5 ≤ 5

Make c the subject of the equation a(b + c) + 5/d - 2 = 0

Multiply (3x + 5y + 4z) by (2x - 3y + z)

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

Multiply $x^2+x+1$ by $x^2-x+1$

The factors of $6x - 5 - x^2$ are

The quantity (x +y) is a factor of

The set of values of x and y which satisfies the equations x² - y - 1 = 0 and y - 2x +2 = 0

The solution of the equation $x^2 - 2x = 8$ is

The solution of the quadratic equation $bx^2 + cx + a = 0$ is given by

The sum of the the root of a quadratic equation is 5/2 and the product of its roots is 4. The quadratic equation is

Three numbers x, y and z are connected by the relationships y = 4/9x + 1 and z = 4/9y + 1. If x = 99, find z.

What factor is common to all the expressions? $x^2 - x, 2x^2 + x - $1 and $x^2 - 1$?

A cuboid has a diagonal of length 9cm and a square base of side 4cm. What is its height?

A cylinder of height h and radius r is open at one end. Its surface area is