Olympiads School MCu11 Class 1: Diagnostic test
First name: ______________ Last name: ______________
Student ID: _______
Diagnostic Test
1. The difference between 516 and half of a number is 219. What is the number?
2. Luis is five years older than Shelby. Luis is sixteen years older than Savannah. Savannah is eleven
years younger than Shelby. The sum of their ages is fifty-seven. How old is Shelby?
3. A rectangle has a larger length than width. The area of the rectangle is six thousand, eight hundred
sixty square feet. The perimeter of the rectangle is eighty-four feet more than six times its width. What
are its dimensions?
4. Four times the sum of three consecutive integers is two hundred ten less than three times the product
of the larger two numbers. What are the three integers?
5. Katherine has two types of iodine in her lab. She has brand 232 iodine, which costs thirty-six cents
per ounce. She also has brand 880 iodine, which costs $2.04 an ounce. How many ounces of each should
she use if she wants to make three hundred ninety-three ounces of iodine that cost a total of $255.72?
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Olympiads School MCu11 Class 1: Diagnostic test
6. The number of points of intersection of the circle x2 + y2 = 9 and parabola y = x2 −3 is:
7. Factor y = 2x2 – 4x – 16. Then graph it.
8. Joel, a tutor at the Math Help, decided that it would be a good
idea to drive his motorcycle off of a ramp. His height during the
jump is modeled by the equation: h = -0.2t2 + 2t + 1, where h is his
height in metres, and t is time in seconds. What is the maximum
height Joel reaches on his bike, and when does he reach this height?
9. ⊙P and ⊙Q have radii 9 and 11. Given the distance between the center of the circles P and Q is 16,
find the length of the common chord CD.
10. Dexter, after narrowly escaping from the police on his bicycle, jumps into a boat and heads south for
100m. Meanwhile, Joel, up to no good, has gone out in a boat that is 150m out from the shore and 80o
west of Dexter’s position, and is planning to fire a cannon from the 1800s directly towards the position
that Dexter is in. If Joel’s cannon can reach a distance of 200m, is there a chance that Dexter can be hit?
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