IM 3 Course Assessment
Name:_______________________
Date:_______________________
______________________________________________________________________________
1
Simplify by combining like terms.
A
B
C
D
2
Evaluate the expression for the given value of the variable.
x = –3
A
B
C
D
3
Solve the equation.
A
B
C
D
4
–76
62
32
30
7
6
5
4
Solve the equation.
A
B
C
D
–0.5
–2
0.5
2
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IM 3 Course Assessment
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5
What is the graph of the relation? Find the domain and range.
A
domain:
range:
B
domain:
range:
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IM 3 Course Assessment
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C
domain:
range:
D
domain:
range:
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6
Choose the correct mapping diagram for the relation.
{(–1, –3), (0, 1), (3, –1), (4, –6)}
A
B
C
D
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7
Choose an equation that represents the equation below translated 4 units down.
A
B
C
D
8
Choose the correct equation for the translation of the equation.
A
B
C
D
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9
What is the graph of the equation?
A
B
C
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D
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IM 3 Course Assessment
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10
What is the graph of the absolute value equation?
A
B
C
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D
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11
Choose the graph of the absolute-value inequality.
y < |x + 2| – 2
A
B
C
D
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IM 3 Course Assessment
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12
Choose the inequality shown in the graph.
A
B
C
D
–6x + 5y –30
–6x + 5y –30
5x – 6y –30
5x – 6y –30
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13
Choose the correct graph of the system. Identify the solution(s).
A
, solution: (–5, –4)
B
, solution: (–10, –19)
C
, solution: (–4, –5)
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D
, solution: (–1, –8)
14
A rental car agency charges a flat fee of $32.00 plus $3.00 per day to rent a certain car.
Another agency charges a fee of $30.50 plus $3.25 per day to rent the same car.
a.
Choose the system of equations that represents the cost c for renting a car at each
agency for d days.
b
.
Find the number of days for which the costs are the same. Round your answer to the
nearest whole day.
A
B
C
D
a.
b. 11
a.
b. 6
a.
b. 6
a.
b. 11
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15
Use the elimination method to solve the system.
A
B
C
D
16
Solve the system by using the substitution method.
A
B
C
D
17
infinite solutions
(–5, 2)
(5, –2)
no solutions
(–1, –6, –1)
(1, –6, 1)
(–1, –6, 1)
(–1, 6, 1)
A food store makes a 9-lb mixture of peanuts, cashews, and raisins. Peanuts cost $1.50
per pound, cashews cost $2.00 per pound, and raisins cost $1.00 per pound. The mixture
calls for twice as much peanuts than cashews. The total cost of the mixture is $13.00. How
much of each ingredient did the store use?
A
B
C
D
6 lb peanuts, 1 lb cashews, 2 lb raisins
2 lb peanuts, 4 lb cashews, 3 lb raisins
4 lb peanuts, 2 lb cashews, 3 lb raisins
6 lb peanuts, 2 lb cashews, 1 lb raisins
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18
Which is the graph of the equation?
A
B
C
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D
19
A manufacturer determines that the number of drills it can sell is given by the formula,
where p is the price of the drills in dollars.
a. At what price will the manufacturer sell the maximum number of drills?
b. What is the maximum number of drills that can be sold?
A
B
C
D
20
$60; 285 drills
$30; 2,415 drills
$31; 2,418 drills
$90; 8,385 drills
Factor the expression.
A
B
C
D
21
Factor the polynomial.
81x2 + 18x – 35
A
B
C
D
(9x + 5)(9x – 7)
(9x – 5)(9x – 7)
(9x + 5)(9x + 7)
(9x – 5)(9x + 7)
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22
Solve by factoring.
4x2 + 28x – 32 = 0
A
B
C
D
23
8,
–8, 4
–8,
,
For the equation, complete the square. That is, write it in the form
numbers k and D.
for some
A
B
C
D
24
The function models the daily profit a barbershop makes from haircuts that include a
shampoo. Here P is the profit in dollars, and h is the price of a haircut with a shampoo.
What is this function in vertex form? Use the vertex form to find the price that yields the
maximum daily profit and the amount of the daily profit.
A
; $50; $300
B
; $30; $500
C
; $60; $300
D
; $30; $600
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25
Use the Quadratic Formula to solve the equation.
A
B
C
D
26
Find the roots of the equation. Round to the nearest hundredth.
A
B
C
D
27
–5.61 and –1.61
1.61 and –5.61
5.61 and –1.61
5.61 and 1.61
Solve and check:
A
B
C
D
(2,4) and (7,5)
(2,4) and (5,7)
(4,2) and (7,5)
(4,2) and (5,7)
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28
Solve by graphing.
A
B
C
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D
29
The table shows the number of hybrid cottonwood trees planted in tree farms in Oregon
since 1995. Find a cubic function to model the data and use it to estimate the number of
cottonwoods planted in 2006.
Years since 1995
1
3
5
7
9
Trees planted
(in thousands)
1.3
18.3
70.5
177.1
357.3
A
B
C
D
30
What is 4x2(–2x2 + 5x3) expressed in standard form? Classify it by degree and number of
terms.
A
B
C
D
31
; 630.3 thousand trees
; 630.3 thousand trees
; 618.1 thousand trees
; 618.1 thousand trees
2x + 9x4; quintic binomial
20x5 – 8x4; quintic binomial
2x5 – 8x4; quintic trinomial
20x5 – 10x4; quartic binomial
Solve the equation.
A
B
C
D
3
–3
–3, 3
no solution
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IM 3 Course Assessment
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32
Factor the expression.
A
B
C
D
33
Which point is on the graph of
A
B
C
D
?
(0, 0)
(–1, 0.3)
(2, –32)
(4, 16)
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34
Match the exponential function to its graph.
A
B
C
D
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IM 3 Course Assessment
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35
Suppose you invest $1600 at an annual interest rate of 4.6% compounded continuously.
How much will you have in the account after 4 years?
A
B
C
D
36
Due to inflation, the cost of a box of cereal increases 1% per year. This year the cost is
$2.99. How much will a box of cereal cost in 17 years?
A
B
C
D
37
$800.26
$6,701.28
$10,138.07
$1,923.23
$3.51
$3.50
$3.54
$3.58
What is the logarithmic form of
?
A
B
C
D
38
Expand the logarithmic expression.
A
B
C
D
39
What is the value of
A
B
C
D
? Use the Change of Base Formula.
about 1.65
about 0.6
about 0.19
about 1.4
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40
Find all solutions to the equation.
A
B
C
D
41
What is the solution of
A
B
C
D
42
about
about 2978.96 or 1357.60
about 146.41 or 150.41
about 1357.60
–1.664
0.073
0.168
0.190
Find the mean and standard deviation of the data set. Round to the nearest tenth.
62, 37, 48, 67, 44, 58, 47, 47
A
B
C
D
44
?
Use natural logarithms to solve the equation. Round to the nearest thousandth.
A
B
C
D
43
6
12
–6
0
mean = 51.3; standard deviation = 9.4
mean = 51.3; standard deviation = 88.9
mean = 47.5; standard deviation = 9.4
mean = 47.5; standard deviation = 88.9
A set of data has mean 66 and standard deviation 7. Find the z-score of the value 32.
A
B
C
D
0.4
4.9
–34
–4.9
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IM 3 Course Assessment
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45
Which of the following sampling methods would result in the least biased presidential
opinion poll?
A
B
C
D
46
The bar graph shows the rents paid per month for apartments in an urban neighborhood.
The curve shows that the rents are normally distributed. Estimate the percent of apartment
residents who pay from $600 to $749 per month.
A
B
C
D
47
You call 2,000 randomly selected registered Democrats nationwide.
You call 2,000 randomly selected registered voters in the Northeast.
You call 2,000 randomly selected registered voters throughout all sections of the
United States.
You call 2,000 randomly selected registered voters who attended the Republican
national convention.
93%
68%
43%
25%
In any data set, 68% of the data ____ falls within one standard deviation of the mean.
A
B
C
always
sometimes
never
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48
Find the measure of an angle between 0° and 360° coterminal with an angle of –110° in
standard position.
A
B
C
D
250°
20°
110°
70°
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49
Which graph shows the angle in standard position?
250
A
B
C
D
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50
Find the exact values of the following.
A
B
C
D
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51
Which graph shows one cycle of the function?
A
B
C
D
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52
Identify the graph of the function for
.
A
B
C
D
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53
Use a graphing calculator to find the solution to the equation.
Interval:
(Hint: graph the following on the same grid)
A
B
C
D
54
no solution
about 63°
45°
30°
Identify the period for the function.
Tell where two asymptotes occur for the function.
A
period =
B
period = ; two asymptotes at x =
and x =
C
period = ; two asymptotes at x =
and x = 2
D
period = ; two asymptotes at x = 0 and x =
; two asymptotes at x = –
and x =
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55
Identify the graph of the function for
.
A
B
C
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D
56
Given:
Find the following.
A
120
B
C
D
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57
Suppose you are building a rain shelter for a local park. The function models the length of
rafters y needed if the peak is 4 feet above the top of the wall.
The angle symbol below is formed by the rafters and top of the wall.
Use a graphing calculator. Find the length of the rafters needed to make the roof with the
following.
Round to the nearest tenth of a foot.
A
B
C
D
58
3.8 feet
1.3 feet
4.2 feet
12.3 feet
Simplify the trigonometric expression.
A
B
C
D
tan
1
cot
sin
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59
Find the length x. Round to the nearest tenth.
A
B
C
D
60
78.8
36.8
40.6
205.9
In triangle ABC, angle C is a right angle, a = 3, and c = 19. Find the remaining angles and
side. Round your answers to the nearest tenth.
A
B
C
D
= 9.1°,
= 80.9°,
= 14.5°,
= 75.5°,
= 80.9°, b = 18.8
= 9.1°, b = 18.8
= 75.5°, b = 18.8
= 14.5°, b = 18.8
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