Mathematics

 

Mathematics

 

 

1. An equation representing a function that extends from quadrant 2 to quadrant 4 is
a. y = x
3
b. y = –2x
5
c. y = 2x
6
d. y = –5x
4
2. The degree of the polynomial function is
a. 3 b. 4 c. 5 d. 6
3. The function y = –2x
2
(x –1)(x – 2)2 changes sign at
a. x = 1 b. x = 0 c. x = –1 d. it doesn’t change sign
4. Which of the following is a polynomial function?
a. y = sin x b. y = cos x c. y = 3x
d. y = x
3
5. Which of the following is an odd function?
a. y = 2x
3
+ x
2
b. y = 2x
4
+ 11 c. y = 2x
4
– x d. y = –x
3
+ x
5
6. The graph of the function y = x
4
is transformed to the graph of the function y = –[2(x + 3)]4
+ 1 by
a. Vertical stretch by a factor of 2, a reflection in the x-axis, a translation of 3 units to the right, and a translation of 1 unit up
b. Horizontal stretch by a 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. Vertical compression by a factor of , a reflection in the x-axis, a translation of 3 units to the left, and a translation of 1 unit up
d. Horizontal compression by a factor of , a reflection in the x-axis, a translation of 3 units to the left, and a translation of 1 unit up
7. If 2x
3
– 9x
2
+ 4x – 7 is divided by x – 3 to give a quotient of 2x
2
– 3x – 5 and a remainder of –22 , then which of the
following is true?
a. 2x
3
– 9x
2
+ 4x – 7 = (x – 3)(2x
2
– 3x – 5) + 22 b. 2x
3
– 9x
2
+ 4x – 7 = (x – 3)(2x
2
– 3x – 5) – 22
c. (x – 3)(2x
2
– 3x – 5) = 22 d. (x – 3)(2x
2
– 3x – 5) = –22
8. What is the maximum number of real distinct roots that a quartic equation can have?
a. infinitely many b. 4 c. 2 d. none of the above
9. Which of the reciprocal functions has a vertical asymptote at ?
a. b. c. d.
10. Which of the following is true?
a. has two vertical asymptotes. b. is always negative.
c. decreases over its entire domain. d. never increases.
Page 2 of 6
Show all work from this point forward for full marks:
11. Solve the following: ??? & ???
a)

 

 

b)

12. Determine the average rate of change of the function on the interval . ????
Part B – Thinking and Investigation [TI – 20 marks].
1. Determine the approximate slope of the tangent to the curve at , to one decimal place. ????

2. A stunt pilot is testing a new plane. The equation that models his height over time is , where x
is his the time in seconds and f(x) is his height in metres. Determine when the pilot is below 450 metres.?????
Page 3 of 6
3. The polynomial px
3
– x
2
+ qx – 2 has no remainder when divided by (x – 1) and a remainder of –18 when divided by
(x + 2). What are the values of p and q? ??????
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 a polynomial function with zeros at 1 (order 2), 0 and

 

and passes
through the point (4, 5).???

3. Write a quadratic inequality with the solution: x
?
(

 

) [<- this is the same as

 

] ???

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. ?
Part D – Application [APP – 12 marks]
1. Two resistors a and b are connected in parallel. The total resistance R in such a circuit is found by the formula
R . If R ohms and b is one more ohm than a, find the number of ohms in a and b. (answers should
be positive). ?
2. Factor fully (show your work). ? & ?
a) b)
3. The area of a triangular-shaped wall is ) m . The base of the wall is (5x + 7) m long. How tall is
the wall? ?

 

 

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