Math Test

Given that circles with centres A and B have radii 3 and 6 respectively, CD is a common tangent that touches the circles at C and D, E is the point of intersection between AB and CD, and AE=5, find CD.

Given that ABCD and CEHG are squares, CE=14 and AB>14, find the area of ΔAEG.

A grid of squares measuring 9 units by 6 units has the two corners removed as shown in the figure below. How many squares of any size are contained within this grid?

Victor's age is a prime number. John's age has 8 factors and he is one year older than Victor. Of the following numbers, which could be the sum of their ages?

How many 2-digit numbers have the property that the sum of the digits is a perfect square?

Three positive integers have a sum of 96. The sum of any two is divisible by the third. Which is the largest of these three integers?

How many real solutions are there to the equation |x-2|+|x+3|=1?

Given that m=|x+2|+|x-1|-|2x-4|, find the maximum value of m.

Given that the area of ΔBDE=1, the area of ΔCDE=3 and DE//AC, find the area of ΔACD.

2 ordinary dice are rolled. What is the probability that the product of the two numbers obtained is a multiple of 6?