Name: _______________________________
Teacher: __________________
Period: _______
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Assessment OF Learning (PRODUCT)
MENTOR COLLEGE JANUARY 2022
FINAL TEST (20% of mark)
Advanced Functions
Mark:
/ 53 = _________% Course: _________%
NOTE: Questions must be answered using methods and formats discussed in class.
Incomplete, sloppy or disorganized solutions will not receive full marks.
Provide exact answers whenever possible.
When necessary, round approximate answers to 2 decimal places unless otherwise stated.
Presentation 0 0.5 1
Short answer [ACK 27]
1. Solve the following (exact values):
a) 11 2x 7 5 3x 4
[KA, 3]
b) log x 1 log(x 3)
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[KA, 3]
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2. Ricky can shovel a driveway in 21 minutes by himself. Andrew can shovel the same driveway in 16 minutes
by himself. When Vikesh shovels with Ricky and Andrew, it takes the three of them only 7 minutes to shovel
the driveway. Find how long it takes Vikesh to shovel the driveway by himself. [KA, 4]
.
3. Solve using a sign chart. Provide an answer using Interval Notation
6x 3 11x 2 57x 20
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[KA, 4 marks]
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4. Factor completely.
4x 13 4x 12 4x 10 y 3 4x 9 y 3
[CK 3]
5. (x 1) is a factor of p(x) 4x 4 ax 3 bx 2 43x 15, and when p(x) is divided by (x 4) the remainder is
525. Find the values of a and b . [KA, 4]
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6. Prove the identity:
cos 2x
tan x
1 sin2x
4
[KAT 2]
7. Solve: cot x cos 2x 6 cos 2 x 2cos x 0 for all 0 x 2
2
.
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[KAT 4]
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Multiple choice: [TAK 25]
Identify the choice that best completes the statement or answers the question. Write your answer on the space provided
using CAPITAL LETTERS.
____
1. Which of the following is an even function?
A. y = 2x3(x3 – x)
B. y = x2(x2 + x)
C. y = –3x(x – 2)
D. y = –5x2(x – 2)
____
2. Determine the value of a so that the average rate of change of the function j(x) 3x 2 ax 4 over the
interval 1 x 2 is 8.
1
A. 3
C.
3
B. 5
D. 0
____
3. Which statement about f(x) 1000(1.3) x is true?
A. instantaneous rate of change is 0 for some value of x
B. instantaneous rate of change is the same for all values of x
C. instantaneous rate of change is positive for all values of x
D. instantaneous rate of change is negative for all values of x
4. Using end behaviours, turning points, and zeros, determine the polynomial equation that represents the graph
shown below.
____
A.
B.
f(x) 5x 4 3x 3 x 2 8x 2
f(x) 5x 5 x 4 3x 3 x 2 8x 2
f(x) 5x 4 3x 3 x 2 8x 2
D. f(x) 5x 5 x 4 3x 3 x 2 8x 2
C.
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____
5. What is the equation of the graph shown below?
A.
f(x) (x 3)(x 1)(x 3)
C.
f(x) (x 3)(x 3)
f(x) (x 3) 2 (x 1)
____
D.
f(x) (x 3)(x 1)(x 3)
6. The least possible degree of the polynomial function represented by the graph shown is
____
A. 3
C. 4
B. 5
D. 7
7. Which of the following graphs most likely represents a polynomial function?
B.
A.
____
C.
B.
D.
8. Which one of the following functions is divisible by x – 3?
A. h(x) 3x 3 6x 2 3x 9
C. f(x) x 3 10x 2 29x 24
B. g(x) x 3 4x 2 13x 24
D.
j(x) x 3 9x 2 15x 12
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____
9. Which of the following is a characteristic of the function f(x) x 2 2?
A. f(x) is not continuous.
B. R = {y R | y 0}
C. f(x) is decreasing on the interval (0,).
D. f(x) has two zeros.
____ 10. Determine the interval(s) on which x 2 2x 3 0 .
A. x 1
C. 3 x 1
B. x 3,x 1
D. x 3, 3 x 1,x 1
____ 11. Which graph has all four of the following characteristics?
1) The graph is symmetric with respect to the y -axis.
2) The graph has a vertical asymptote at x 1.
3) The graph has a horizontal asymptote at y 0 .
4) The graph is decreasing on the interval (3,).
A.
C.
B.
D.
cos x 1
1 have for 0 x 2 ?
____ 12. How many solutions does the equation
2
A. 4
C. 1
B. 3
D. 2
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____ 13. State the vertical asymptotes of f(x)
1
.
x 4x 12
C. x 6, x 2
D. x 6, x 2
2
A. x 6, x 2
B. x 6, x 2
11
____ 14. Convert
radians to degrees.
6
A. 98.18
C.
B. 330
D.
6
____ 15. If tan x , what is cos 2x, given that 0 x ?
8
2
8
A.
C.
5
8
B.
D.
5
98.6
300
7
25
7
25
____ 16. Determine the intervals in which the reciprocal function of f(x) x 2 + 1 is increasing.
A. (, 0)
C.
(, )
B.
(1, )
D. (0, )
____ 17. Express log8 log10 log2 as the logarithm of a product or quotient.
A. log 82
C. log 16
B. log 40
D. log 78
____ 18. State the equation of the rational function that meets these conditions:
1. Vertical asymptote at x 2
2. Horizontal asymptote at y 1
3. Increases on each interval of its domain
4. x-intercept is (3, 0)
x3
x3
A. y
C. y
x2
x2
x3
x3
B. y
D. y
x2
x2
____ 19. The function y sin x is also which of the following functions?
2
A. csc x
C. sec x
2
B. cot x
D. cos(x)
2
5
3
tan
8
8
____ 20. Simplify the expression
.
5
3
1 tan
tan
8
8
A. 1
B. 1
tan
C. undefined
D. 0
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____ 21. Which equation is represented by the following graph?
A.
2
1 sin x
C.
x
x
cos
2
2
D.
B. sin
1 tan 2 x
tan x
2 sin x sin 3 x
sin 2x
____ 22. What is the degree of the quotient for the division statement (x 4 12x 3 6x 2 9x 15) (x 2 2)?
A. 3
C. 2
B. 4
D. 1
____ 23. Evaluate log 2 3 64 .
A. 2
C. 3
B. 8
D. 16
____ 24. Identify the function that matches the graph except at x 2 .
3x 6
x2
3x 6
B. f(x)
2x
A. f(x)
3
x2
3
D. f(x)
x2
C. f(x)
____ 25. Evaluate log m m2n .
A. 2n
B. mn
C. n 2
D. n
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