Grade 11 revision sheet
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Solve
A
B
____
.
C
or
D no real solutions
or
2. Solve
A
.
C
B
____
____
____
D
3. Solve
A
B
4. Solve
A
B
.
C
D
.
or 13
C
D
or
5. A branch breaks off the top of a giant sequoia tree and falls straight to the ground. The branch’s height in
meters is approximately
in the air?
A 8.6 s
B 4.3 s
where t is the time in seconds. About how long is the branch
C 2.2 s
D 1.1 s
____
6. Find the number and type of solutions for
A The equation has two real solutions.
B Cannot determine without graphing.
C The equation has two nonreal complex solutions.
D The equation has one real solution.
____
7. When
is written in the form
.
, what is the value of ?
A 19
B 10
C 5
D
____
8. Which of the following quadratic equations has no real solutions?
A
B
C
D
____
9. Multiply
A
B
.
C
D
____ 10. Subtract.
–
A
B
C
D
____ 11. Which polynomial represents the measure in degrees of angle PMQ?
A
B
C
D
____ 12. Write a recursive rule for the sequence.
–2, 4, –8, 16, . . .
A
;
B
;
C
;
D
;
____ 13. Write a recursive rule for the sequence.
A
B
C
D
____ 14. A company is tracking the number of complaints received on its website. During the first 4 months, they
record the following numbers of complaints: 20, 25, 30, and 35. Which is a possible explicit rule for the
number of complaints they will receive in the nth month?
A
B
____ 15. Find the first 5 terms of the sequence
A –3, –1, 3, 11, 27
B 7, 9, 13, 21, 37
.
C –4, –1, 4, 11, 20
D –3, –1, 1, 3, 5
____ 16. A city is tracking reports of identity theft. During the first 4 weeks of their study, they find the following
number of reports: 11, 22, 44, and 88. Which is a possible explicit rule for the number of reports in the nth
week?
A
C
B
D
____ 17. A conservationist is tracking the number of a rare type of tree in a forest as it recovers from a fire. During
the first 4 years after the fire, she records 2, 6, 18, and 54 trees. If this trend continues, which expression
can be used to find the number of trees after n years?
A
C
B
D
____ 18. The number of lilies a large nursery can sell each day after April 1 is modeled by a sequence whose
general term is
, where n is the number of days after April 1. Find the number of lilies that
can be sold on April 6th, 7th, and 8th.
A 1325, 1250, 1175
C 1175, 1250, 1175
B 1250, 1175, 1100
D 1400, 1325, 1250
____ 19. Write a recursive rule for the sequence.
A
B
C
D
____ 20. Find a function that describes the arithmetic sequence 16, 17, 18, 19, ... Use y to identify each term in the
sequence and n to identify each term’s position.
A y = 16n
C y = n + 15
B y = 15n +1
D y = 17n –1
____ 21. What is the 20th term in the following geometric sequence?
–2, –6, –18, –54, –162, ...
A 1,162,261,467
C 2,324,522,934
B –6,973,568,802
D –2,324,522,934
____ 22. Find an explicit function rule for the sequence –3, 3, 9, 15, . . ..
A
C
B
D
____ 23. Find an explicit function rule for the sequence
A
C
B
D
____ 24. Write a rule for the nth term of the sequence. Use your rule to find a100.
–8, 0, 8, 16, 24, . . .
A 8
C 800
B 784
D 792
____ 25. Write a rule for the nth term of the sequence. Use your rule to find a70.
–10, –8, –6, –4, –2, . . .
A 130
C 132
B 2
D 128
.
____ 26. Which function below generates the sequence
A
B
C
D
?
, where
and is an integer.
, where
and is an integer.
, where
and is an integer.
, where
and is an integer.
____ 27. Find a coordinate pair for a point on the graph of
.
A
C
1
1
(0, − )
(− , 0)
3
3
B
D 1
1
(0, )
( , 0)
3
3
for the domain D: {–8, –4, 0, 4, 8}.
y
C
____ 28. Graph
A
–8
–6
–4
8
8
6
6
4
4
2
2
–2
–2
2
4
6
8
x
–4
–6
–4
–2
–2
–4
–6
–6
–8
–8
y
–6
–8
–4
B
–8
y
8
6
6
4
4
2
2
2
4
6
8
x
4
6
8
x
2
4
6
8
x
y
D
8
–2
–2
2
–8
–6
–4
–2
–2
–4
–4
–6
–6
–8
–8
____ 29. Which of the following is not a solution of the equation represented by the graph?
y
5
4
3
2
1
–5 –4 –3 –2 –1
–1
1
2
3
4
5
x
–2
–3
–4
–5
A
B
C
D
____ 30. Which of the following data sets is best described by a linear model?
A
B
C
D
____ 31. Which of the following data sets is best described by a linear model?
A
B
C
D
____ 32. Shen is interested in joining a health and fitness club. There are four clubs in his area. The functions
,
,
, and
model the cost , in dollars, of being
a member for time , in months, at each of the four clubs. Which club charges the greatest joining fee?
A
B
C
D
Club 1 with cost
Club 2 with cost
Club 3 with cost
Club 4 with cost
____ 33. Find the x- and y-intercepts of
A
B
.
C
D
____ 34. Determine whether the function has a constant or variable rate of change.
A variable
B constant
____ 35. Use rates of change to determine whether the function is linear or nonlinear.
x
y
2
0
5
–5
A nonlinear
11
–8
17
–17
B linear
____ 36. The water level of a river is 34 feet and it is receding at a rate of 0.5 foot per day. Write an equation that
represents the water level, w, after d days. Identify the slope and y-intercept and describe their meanings.
In how many days will the water level be 26 feet?
A
The slope is 34, and this is the rate at which the water level is receding. The y-intercept is
0.5, and this is the water level after 0 days. In 16 days, the water level will be 26 feet.
B
The slope is
, and this is the rate at which the water level is receding. The y-intercept
is
, and this is the water level after 0 days. In 120 days, the water level will be 26 feet.
C
The slope is 34, and this is the rate at which the water level is receding. The y-intercept is
, and this is the water level after 0 days. In 120 days, the water level will be 26 feet.
D
The slope is
, and this is the rate at which the water level is receding. The y-intercept
is 34, and this is the water level after 0 days. In 16 days, the water level will be 26 feet.
____ 37. Which is the average rate of change over the interval [0, 10]?
Equation A
Equation B
A A: 5, B: 15
B A: 15, B: 5
____ 38. Graph the equation on a coordinate grid.
C A: 0, B: 15
D A: 15, B: 0
A
C
B
D
____ 39. What are the intercepts of the linear function shown?
y
6
4
2
–6
–4
–2
2
4
–2
–4
–6
A
B
C
D
x-intercept: ; y-intercept:
x-intercept: ; y-intercept: 4
x-intercept: 2; y-intercept: 4
x-intercept: ; y-intercept:
____ 40. Find the slope of this line.
6
x
A
C
B
D
____ 41. Which equation describes the function whose y-intercept is
A
C
B
D
and whose graph has slope 5?
____ 42. Which is a linear function?
A
B
C
D
____ 43. A health insurance plan has a $50 enrollment fee and a copayment of $5 for each doctor visit. The
function
gives the cost of x doctor visits. What is the range of this function?
A
B
C
D
____ 44. Find the slope of this line.
A
B 0
C 2
D undefined
____ 45. Find the value of y so that the points
and
A
B
lie on a line with slope
C 3
D 4
____ 46. Which equation describes the line with slope 5 that contains the point
A
B
C
D
____ 47. What is the y-intercept of
A
B
?
C 6
D 8
____ 48. Use rates of change to determine whether the function is linear or nonlinear.
x
y
3
7
4
9
6
13
A nonlinear
10
21
B linear
____ 49. What are the intercepts of the linear function shown?
y
6
4
2
–6
–4
–2
2
4
6
x
–2
–4
–6
A
B
C
D
x-intercept: ; y-intercept:
x-intercept: ; y-intercept: 4
x-intercept: 2; y-intercept: 4
x-intercept: ; y-intercept:
____ 50. Graph the linear equation
by finding the x- and y-intercepts.
?
.
y
A
y
C
10
10
–10
10
x
–10
y
10
x
y
D
10
10
–10
x
–10
–10
B
10
10
x
–10
–10
–10
____ 51. Which equations describe parallel lines?
A I and II
B I and III
C II and IV
D III and IV
____ 52. Which describes the transformation(s) from the graph of
A a reflection across the y-axis
B a reflection across the y-axis and a translation 4 units up
C a rotation (less steep) about
to the graph of
?
D a translation up 6 units
____ 53. Which equation describes the line through the points
A
C
B
D
____ 54. Which equation describes a line that passes through
and
?
and is perpendicular to the line described by
?
A
C
B
D
____ 55. Which graph below would match the situation described?
A car travelling at 23 mi/h accelerates to 45 mi/h in 5 seconds. It maintains that speed for the next 5
seconds, and then slows to a stop during the next 5 seconds.
A
C
B
____ 56. How would the graph of the function
A The graph would shift 5 units to the left.
B The graph would shift 5 units down.
C The graph would shift 5 units up.
D The graph would shift 3 units down.
D
be affected if the function were changed to
____ 57. How would you translate the graph of
to produce the graph of
A translate the graph of
down 4 units
B translate the graph of
up 4 units
C translate the graph of
left 4 units
?
D translate the graph of
right 4 units
____ 58. Which transformation from the graph of a function f(x) describes the graph of
?
A horizontal shift left 10 units
C vertical stretch by a factor of 10
B vertical shift up 10 units
D vertical shift down 10 units
____ 59. Which transformation from the graph of a function f(x) describes the graph of
A
B
horizontal shift left
vertical shift up
C
unit
D
unit
?
vertical compression by a factor of
vertical shift down
unit
____ 60. Which transformation from the graph of a function f(x) describes the graph of
A horizontal shift left 1 unit
C vertical stretch by a factor of 1
B vertical shift down 1 unit
D vertical shift up 1 unit
____ 61. Graph
A
. Find the axis of symmetry and the vertex.
y
C
–10 –8
–6
–4
12
10
10
8
8
6
6
4
4
2
(-1.5, 1.75)
2
2
(1.5, 1.75)
4
6
8
10
x
–8
–6
–4
The axis of symmetry is
. The
2
4
6
8
10
The axis of symmetry is
.
is
y
B
–2
–2
12
x
–4
–4
vertex is
y
12
–2
–2
?
. The vertex
.
y
D
12
12
10
10
8
8
6
6
4
4
2
2
(0, 4)
(4, 0)
–8
–6
–4
–2
–2
2
4
6
8
10
12
x
–4
The axis of symmetry is
is (4, 0).
–10 –8
–6
–4
–2
–2
2
4
6
8
10
x
–4
. The vertex
____ 62. Give the domain and range of the function.
The axis of symmetry is
is (0, 4).
. The vertex
y
6
4
2
2
4
x
6
A D: 0  x  7; R: 1  y  7
B D: 1  x  6; R: 1  y  7
C D: 1  x  7; R: 1  y  6
D D: 2  x  6; R: 4  y  7
____ 63. Give the domain and range of the function.
y
6
4
2
–2
2
4
6
x
–2
A D: –3  x  2; R: 0  y  4
B D: –2  x  4; R: –3  y  2
C D: –3  x  2; R: –2  y  4
D D: –3  x  2; R: –3  y  6
____ 64. The graph of the quadratic function
is shown below. What is the domain of
f(x)
6
4
2
–6
–4
–2
2
4
6
x
–2
–4
–6
A
B
C
D
The integers greater than .
The real numbers greater than
The integers
The real numbers
____ 65. Which is the inverse of
?
.
?
A
C
B
D
____ 66. Which of the following is an equation for the inverse of the function
A
1
x+
4
1
x–
4
B
C
4
3
4
3
1
x–
4
1
x+
4
D
____ 67. What is the equation of the inverse of
A
B
3
?
4
3
16
3
16
?
C
D
____ 68. An air conditioning repair service call costs $75 per hour plus a flat fee trip charge of $25. If the situation
can be represented by the function
, what do the variables represent and which is the
dependent variable?
A The repair time h depends on the repair charges r in hours.
B The repair charges h depends on the repair time r in hours.
C The repair charges r depends on the repair time h in hours.
D The repair time r depends on the repair time h in hours.
____ 69. Shen is interested in joining a health and fitness club. There are four clubs in his area. The functions
,
,
, and
model the cost , in dollars, of being
a member for time , in months, at each of the four clubs. Which club charges the greatest joining fee?
A
B
C
D
Club 1 with cost
Club 2 with cost
Club 3 with cost
Club 4 with cost
Short Answer
1. Solve
2. Solve
.
.
3. Solve
4. Solve.
5. Solve.
6. Solve the equation.
.
7. Solve the equation.
8. Solve the equation. Round the solution(s) to the nearest hundredth.
9. Solve the quadratic equation
10. Multiply
11. Write
by any method. Show your work.
.
in expanded form.
12. Write the next three terms of the arithmetic sequence. Then write a variable expression for the nth term
and evaluate it for
13. Write a rule for the nth term of the arithmetic sequence. –12, –5, 2, 9, . . .
14. Write a rule for the nth term of the arithmetic sequence with
15. Write the first five terms of the sequence.
and the common difference of
.
;
16. Consider the sequence 1, 2, 5, 10, 17, …
a. Write a quadratic function
that generates the sequence. Assume that the domain of the function
is the set of integers
.
b. Use your result from part a to determine the 15th term of the sequence.
17. Which point,
18. Which point,
or
or
, is on the graph of
?
, is on the graph of
?
19. The function
models the total cost , in dollars, for a large cheese pizza with
toppings from a local restaurant. How much does a large plain cheese pizza from this restaurant cost?
20. Graph the function. Compare the graph with the graph of
21. Graph the function.
.
y
10
–10
10
x
–10
22. Describe the transformations applied to the graph of the parent function
. Graph
used to graph
.
y
x
23. Find the slope of this line.
24. Write an equation in slope-intercept form for the function whose y-intercept is
slope
.
25. Do these ordered pairs satisfy a linear function? Explain.
and whose graph has
26. Find the value of y so that the points
and
lie on a line with slope
.
27. Write an equation in slope-intercept form for the line with slope 3 that contains the point
.
28. The graph shows the distance from its starting position of a car traveling for 8 hours.
What does the second -intercept represent in this situation?
29. Graph the function with the given domain. Classify the function as discrete or continuous. Then identify
the range of the function.
; domain
30. The function
shows the temperature in degrees Fahrenheit
temperature in degrees Celsius
graph the function.
as a function of the
. Calculate and interpret the intercepts. Then plot the intercepts and
F(C)
C
31. Use the following description to write a quadratic function in vertex form:
The parent function
is vertically compressed by a factor of
and translated 8 units right and 3
units up.
32. Find the inverse function.
33. What is the y-intercept of the graph of the inverse of
?
34. The formula for converting temperatures from kelvins K to degrees Fahrenheit F is
Find the inverse of this function, and find the equivalent temperature of
in kelvins.
.
grade 11 revision sheet
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
D
C
C
C
B
C
B
C
A
D
C
D
C
B
A
C
C
A
C
C
D
C
D
B
D
B
B
C
D
B
C
A
B
B
A
D
C
D
B
D
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
52.
53.
54.
55.
56.
57.
58.
59.
60.
61.
62.
63.
64.
65.
66.
67.
68.
69.
C
C
D
D
C
D
A
B
B
B
C
A
D
A
C
C
A
C
C
B
C
B
C
D
D
C
C
C
A
SHORT ANSWER
1.
2.
3.
4.
5.
6. 18, –18
7. 30, –30
8.
9. Possible answer: (completing the square)
Rubric
1 point for each solution; 1 point for appropriate work
10.
11.
Rubric
2 points
12.
13.
14.
15. 5, 7, 9, 11, 13
16. a.
b.
Rubric
a. 1 point
b. 1 point
17.
18.
19. A large plain cheese pizza has 0 additional toppings. Since
restaurant costs $8.50.
, a large cheese pizza from this
Rubric
2 points
20. Because the slopes of both graphs are equal, the lines are parallel. The y-intercept of g is 9 units more than
the y-intercept for f.
y
10
–10
10
x
–10
21.
22. Possible answer: The graph of
is vertically shrunk by a factor of
shifted up 3 units.
y
6
4
2
–6
–4
–2
2
4
6
x
–2
–4
–6
Rubric
3 points for transformations;
1 point for graph
23.
24.
25. No; a constant change of
in x corresponds to different changes in y.
26. 7
27.
28. After 8 hours, the car returns to its starting position.
, reflected about the -axis, and
y
20
16
12
8
4
–12 –8
–4
–4
4
8
12
16
20
24
28
x
–8
–12
–16
–20
29.
The function is continuous. The range is
30. The
-intercept is
. This means that
The F-intercept is 32. This means that it is
F(C)
40
20
–40
–20
20
40 C
–20
–40
Rubric
0.5 point each for the intercepts;
0.5 point each for the interpretations;
2 points for the graph with the intercepts
31.
32.
33.
34.
;
.
is equivalent to
is equivalent to
.
.