UI Mathematics 2017/2018 Past Questions

A die has four of its faces coloured red and the remaining two coloured blue, what is the probability that when the die is thrown twice, the top face will be blue in both cases?

List all integers satisfying the inequality -4 ≤ 3x-5<7

if the quadratic function $3x^2 - 7x + R$ is a perfect square, find R

Add the same number to the numerator and denominator of $5/9$ if the resulting fraction is $1/3$, then the number added is

$(1.28 × 10^4)$ divided by $(6.4 × 10^2)$ equals

Find the value of x for which the expression ${(x-3)(x-2)}/{x^4+x-2}$ is undefined

If the function y=5x is graphed, what would be its intercept on the y-axis?

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

the nth term of the sequence $2/2,3,16,35,74$ is

Find the value of x for which $2(3^{2x+1}) = 162$

The length , L of a simple pendulum varies as the square of the period T, A pendulum 0.4m long has a period of 2 seconds, find the equation connecting L and T

If $x*y = x/y - y/x$ for x,yεR, evaluate -3 * 4

The sum to infinity of a GP with a positive common ratio is 9 and the sum of the first two terms is 5. find the 5th term of the progression

Find constants K such that $2x^2 - 6x + 5 ≡ a(x + b)^2 + k$

Find the equation of the line which is perpendicular to 2x _ y = 1 and passes through the point (-2,-1)

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 10x² - 13x - 3 = 0

If a function is defined by f(x + 1) = 3x² - x + 4, find f(0).

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

If x² + 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