## 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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