MHF4U Test #1: Chapters 1-3
Name: ______________________________________
Date:
Part A – Multiple Choice [K/U – 20 marks]
1. An equation representing a function that extends from quadrant 3 to quadrant 1 is
a. y = x3
b. y = –2x5
c. y = 2x6
2. The degree of the polynomial function y = x3 – 2x2 + 5x – 1 is
a. 3
b.
4
c.
5
d. y = –5x4
d.
6
3. The function y = 6(x – 1)4(x – 2)2(x + 1) changes sign at
a. x = 1
b. x = 2
c. x = –1
d. it doesn’t change sign
4. Which of the following is not a polynomial function?
a. y = x3 –x2 + 1
b. y = x
c. y = 2x(x –1)
d.
5. Which of the following is an even function?
a. y = 2x4 + x3
b. y = 2x4 + 11
c. y = 2x4 – x
d. y = –x3 + x5
6. What is true about the function
a.
from above
as
b.
y = 2x
?
from below
c.
d. f(x) is undefined
7. The graph of the function y = x4 is transformed to the graph of the function y = –2(x – 3)4 + 1 by
a. a horizontal stretch by a factor of 2, a reflection in the x-axis, a translation of 3 to the left, and a translation of 1 unit up
b. a vertical stretch by factor of 2, a reflection in the x-axis, a translation of 3 units to the right, and a translation of 1 unit up
c. a vertical stretch by a factor of 2, a reflection in the x-axis, a translation of 3 units to the left, and a translation of 1 unit up
d. a vertical compression by a factor of
, a reflection in the x-axis, a translation of 3 to the left, and a translation of 1 unit up
8. What is the remainder when x2 + 3x is divided by x?
a. 4
b. –3
c.0
d. you cannot divide by x
9. If 2x3 – 9x2 + 4x – 7 is divided by x – 3 to give a quotient of 2x2 – 3x – 5 and a remainder of –22 , then which of the
following is true?
a. 2x3 – 9x2 + 4x – 7 = (x – 3)(2x2 – 3x – 5) + 22
b. 2x3 – 9x2 + 4x – 7 = (x – 3)(2x2 – 3x – 5) – 22
2
c. (x – 3)(2x – 3x – 5) = 22
d. (x – 3)(2x2 – 3x – 5) = –22
10. Which function is always positive?
a.
b.
c.
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d. B and C
Show all work from this point forward for full marks.
11. Solve the following:
a)
.
 & 
b)
12. Determine algebraically or graphically the intervals when the following function is negative:
. Show all steps for full marks.

Part B – Thinking and Investigation [TI – 20 marks]
1. Estimate the slope of the tangent to the graph of the function
at
.
2. The height, h, in metres, of a weather balloon above the ground after t seconds can be modelled by the function
h(t) = –2t3 + 3t2 + 149t + 410, for
. When is the balloon exactly 980 m above the ground? 
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3. (x – 1) and (x + 3) are both factors of the polynomial p(x) = ax3 + 12x2 – 11x + b. Find the values of a and b.

4. Solve the following inequality using an algebraic method:

Part C – Communication [COMM – 20 marks]
***Fully label your graphs for full marks!***
1. Determine an equation for the graph of the polynomial function shown. 
2. Determine an equation in factored form for the polynomial function with zeros 2 (order 2),
through the point (1, 6). 
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, and 3 that passes
3. Given the following information about the function y = f(x), sketch the shape of the function. 
(x-2)2 > 0 for all x
(x+1) < 0 for x< -1
(x+1) > 0 for x> -1.
4. Consider the function.
a) Determine the key features of the function:
i) domain and range
ii) intercepts
iii) equations of any asymptotes 
iv) intervals where the function is increasing and
intervals where the function is decreasing
b) Sketch a graph of the function. 
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Part D – Application [APP – 12 marks]
1. The average speed of an airplane is 11 times that of a car. It takes the airplane 20 h less than the car to travel 1500
km. Determine the average speeds of the airplane and the car. 
2. a) Use long division to divide (x3 + 3x2 – 7) by (x + 2). Express the result in quotient form. 
b) Write the corresponding statement that can be used to check the division. 
3. The volume of a rectangular box is x3 + 16x2 + 83x + 140 cm3. The box is (x + 5) cm long and (x + 7) cm wide.
How tall is the box? 
Test Summary
Knowledge &
Understanding
/20
Thinking &
Invest.
/20
Communication
/20
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Application
/12