Unit 3 Test – Quadratic Functions
MCR 3U1
Name:
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Date:
MCR 3U1 – Unit 3 Test: Quadratic Functions
K/U
/18
App
/14
Th
/13
Comm
/9
PART A: KNOWLEDGE – Multiple Choice (12 Marks)
Multiple Choice - COMPLETE ON YOUR SCANTRON ONLY.
PART B: KNOWLEDGE - Short Answer (8 Marks)
For full marks, show all your work for the questions that follow.
11. Simplify each of the following radical expressions. Express your answers in simplest radical form.
18
5 2  3 8  32
a)
b) 2 (4 5  3 2 )
c)
2



PART C: APPLICATION – (14 Marks)
12. Shondra has 120 m of fencing to enclose a rectangular pen for a children’s play area.
a) Determine a function to represent the area of the playground. (2 marks)
b) Determine the maximum area for the play area. (3 marks)
MCR 3U1
Unit 3 Test – Quadratic Functions
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c) Determine the dimensions of the rectangle with the maximum area. (2 marks)
13. Calculate the exact area of a circle with radius (1  2 ) . (3 marks)
14. Stephanie owns a business that sells greeting cards. The profit function for her business can be
modelled by the equation , P( x)  0.5 x 2  8 x  24 where x is the quantity sold, in thousands, and
P(x) is the profit in thousands of dollars. How many cards must Stephanie sell in order for her
business to break even? (4 marks)
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Unit 3 Test – Quadratic Functions
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PART D: THINKING – (13 Marks)
15. A quadratic function is defined by
. A linear function is defined by
g(x) = –0.5x + k. Determine the value of k so that the line intersects the parabola at exactly one
point. Write your answer to the nearest hundredth. (3 marks)
16. The function
models the production expenses for a bicycle company in
thousands of dollars where t represents time in years.
a) Restrict the domain of the function, so that its inverse is also a function. (Think carefully,
there is only one correct answer) (3 marks)
b) Using your restricted domain, determine the model that describes time in terms of expenses.
(2 marks)
MCR 3U1
Unit 3 Test – Quadratic Functions
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17. A rectangular pool is to be built on a lot that measures 20 m by 12 m. A wooden deck of uniform
width, equal to the area of the pool, must surround it. How wide is the deck? Round your
answer to one decimal place. Include a diagram with your solution. (5 marks)
PART E: COMMUNICATION – (9 Marks)
18. Explain how you would determine algebraically, the number of times any quadratic function
crosses the x-axis. Provide an example. (2 marks)
19. Does the parabola for the function
Explain your answer. (3 marks)
open up or down? What is the range?
Unit 3 Test – Quadratic Functions
MCR 3U1
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20. Write the equation of a quadratic function that has zeroes 2  5 and contains the point (1, -12).
(4 marks)
BONUS QUESTION
Simplify
. (2 marks)
RANDOM QUESTION
What is your favourite TV show? ______________________