This test consists of a total of 10 questions. You are given 30 minutes to complete it. You are to complete this test by yourself and you may not use mathematical tools other than a pen/pencil, an eraser, a ruler and a compass. You should have rough paper handy while doing the test. Only your final answer is required. Select your final answer among the 4 options given. Each question is worth 1 mark.
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.
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?
Answer
69
75
87
107
Question 5
Question
How many 2-digit numbers have the property that the sum of the digits is a perfect square?
Answer
15
17
18
19
Question 6
Question
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?
Answer
68
48
70
69
Question 7
Question
How many real solutions are there to the equation |x-2|+|x+3|=1?
Answer
0
1
3
∞
Question 8
Question
Given that m=|x+2|+|x-1|-|2x-4|, find the maximum value of m.
Answer
1
5
7
0
Question 9
Question
Given that the area of ΔBDE=1, the area of ΔCDE=3 and DE//AC, find the area of ΔACD.