Infinite Algebra 2

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Infinite Algebra 2
Secondary Math 2
END-OF-YEAR REVIEW
Complete the following packet. While in class, you may use this
paper packet, BUT DO NOT WRITE IN IT!!! When working at
home, please use the online version. All answers can be found
online. The work (just answers will not be accepted!) for this
packet will be due the day of the SAGE test and is worth 210
points AND WILL NOT BE ACCEPTED LATE!
UNIT 1 REVIEW
Name___________________________________
Period___________
Part I(Multiple Choice): Choose the best answer(s) for each of the following questions.
_______1.
Simplify the radical expression √24.
(a)
_______2.
(b)
Natural
Rational
(b)
(e)
Natural
Rational
(b)
(e)
123⁄2
(b)
(2)4⁄5
(b)
√105
(b)
1
3
√()2
(b)
Simplify the expression
(a)
______10.
4 2  3 √−2
−32√
(c)
−8√
(d)
8√
Whole
Irrational
(c)
Integer
Whole
Irrational
(c)
Integer
122⁄3
(c)
(2√3)
3
10 4
(c)
32 4
√50
(c)
5
√100
Rewrite the following exponential expression in radical form:
(a)
_______9.
6√2
Rewrite the following exponential expression in radical form:
(a)
_______8.
(d)
Rewrite the following radical expression in exponential form:
(a)
_______7.
2√12
Rewrite the following radical expression in exponential form:
(a)
_______6.
(c)
To which of the following set(s) does −11 belong? (Choose all that apply.)
(a)
(d)
_______5.
2√4
To which of the following set(s) does √5 belong? (Choose all that apply.)
(a)
(d)
_______4.
(b)
Simplify the radical expression −2√16 2  3 .
(a)
_______3.
2√6
6 8
(b)
Simplify the expression
(a)
8 5
(b)
−
3
√()
(√12)
(d)
3
8√27
4
√(2)5
(d)
(2)5⁄4
105⁄2
(d)
5
√20
()−3⁄2
1
(c)
−3√
(d)
(c)
5 8
(d)
6 15
(c)
15 5
(d)
15 6
√()3
(2 5 )3
8 15
3 3 ∙ 5 2
8 6
Part II (Work-Out Problems): Show all work if you expect to receive any partial credit for incorrect answers.
For Problems 11 and 12: State the set(s) to which the number belongs:
̅̅̅̅
11.
17
12.
−3. 66
For Problems 13 and 14: Rewrite the expression in exponential form.
13.
3
( √ )
4
14.
1
5
√(2)2
For Problems 15 and 16: Rewrite the expression in radical form.
15.
 4⁄3
16.
(2)6⁄5
For Problems 17 – 20: Simplify the expression.
17.
√8 3
√805  3
19.
(56 )−1⁄3
18.
20.
10 2  3  4
2 5   5
UNIT 2 REVIEW
Part 1 (Multiple Choice): Choose the best answer(s) for each of the following questions.
________1. Simplify the expression (5 2 + 2 4) ) − ( 5 3 + 2 4 )
(a) −5 3 + 5 2
(b)  3 + 4 4
(c) 4 4
(d) −5 3 + 4 4 + 5 2
________2. Simplify the expression (5 2 + 4) + ( 3 − 3)
() 5 2 + 7 − 3
(b) 9v + 3 2 - 1
(c) 9 2 + 3v - 3
(d) 5 2 + 1 − 3
_______ 3. Find the GCF of 18 , 30
(a)
6
(b)
2
(c)
4
(d)
7
(c)
m
(d)
13nm
________4. Find the GCF of 132  , 39n2
(a)
13
(b)
3nm
________5. Factor the common factor out of the expression : 12 2 + 18v
(a)
2v ( 6v + 9 )
(b)
12v (v + 18)
(c)
6v ( 2v + 3) (d)
6v ( 3v + 2)
________6. Factor the common factor out of the expression : −6 2 − 18
(a)
-6 ( x + 3)
(b)
−6  ( − 12 )
(c)
−6 ( x + 3 )
−4 ( 2 − 2)
(d)
________7. Find the product of −5 (  + 4 )
(a)
- 5s + 1
(b) 5 s - 20
(c) - 5s + 4
(d)
- 5s - 20
________8. Factor 10 2  2  5 − 40 2 + 20
(a)
10 (  4 − 4 + 2 )
(b) 10 (  4 − 4 + 10 )
(c)
 ( 10 4 − 40 + 20 )
(d) 2 ( 5 4 − 20 + 10 )
________9. Find the product of ( x – 5 ) ( x + 5)
(a)  2 + 10 − 10
(b)  2 + 10 − 20
(c)  2 − 10 − 25
(d)  2 − 25
________10. Find the product of ( 8 − 2 ) ( 6 + 3)
(a)
482 + 12p + 1
(b) 142 + 12 + 6
(c) 242 −  + 1
(d) 482 + 12p – 6
________11. Factor completely 2 + 2 − 80
(a) ( m + 16 )( m – 5 ) (b) ( m + 5 ) ( m – 16 )
(c) (  + 10 ) (  − 8 )
(d) (  − 10 ) (  + 8 )
(c) (8  + 5 ) ( 2 − 5 )
(d) ( 8 − 5)2
________12. Factor completely 252 − 60 + 36
(a)
( 5m + 6 )( 5m – 6 )
(b) (5 − 6)2
Part II (Work - Out Problems): Show all work, if you expect to receive any partial credit for incorrect answers.
For problems 11-12: Factor
13. 4 − 16
14. 15 − 25
For problems 13-14: Find the product.
15. ( m + 7 ) ( 3m – 4 )
16. ( 7x – 2 ) ( 6x – 3 )
For problems 15 – 16: Factor completely.
17. 2 + 8 + 15
18.  2 − 4 − 32
For problems 17-18: Factor completely
19. 62 + 7 − 49
20. 32 − 13 − 10
For problems 19-20: Factor by Grouping
21. 12 3 − 21 2 + 28 − 49
22. 28 3 + 16 2 − 21 − 12
For problems 23-25: Simplify
23. ( 4 − 2 ) − ( −7 −  )
24. (−5 + 8 ) + (5) − (3)
25. −3 (−6) (7)
26. (−2 − 8)( −7 + 7)
Unit 3 REVIEW
In this unit six functions have been studied and reviewed: Line y = mx + b, Quadratic (parabola)  =  2 , square root y =
3
√ , Absolute Value y = || , Cubic Equation y =  3 , Cube Root y = √ . Each function can be translated using vertical
shift, horizontal shift, stretch, and reflection about the x – axis.
For Problems 1-3: Answer the following Questions about each graph.
a) What type of function is this graph? (b) What is the equation of this function? (c) What is the domain? (d) What is the
range? (e) Where (x-values in the interval notation) is the function increasing? (f) Where is the function decreasing? (g)
Where is the function positive? (h) Where is the function negative? (i) Are there any minimums? If so, where (x,y)?
(j) Are there any maximums? If so where (x,y)?
1.
2.
3.
a) _____________________
a) _____________________
a) _____________________
b) _____________________
b) _____________________
b) _____________________
c) _____________________
c) _____________________
c) _____________________
d) _____________________
d) _____________________
d) _____________________
e) _____________________
e) _____________________
e) _____________________
f) _____________________
f) _____________________
f) _____________________
g) _____________________
g) _____________________
g) _____________________
h) _____________________
h) _____________________
h) _____________________
i) _____________________
i) _____________________
i) _____________________
j) _____________________
j) _____________________
j) _____________________
For Problems 4-12: Graph the following functions. Plot points as necessary.
4.  = 3| − 1| + 4
7.  = √ + 3
10.  = 2
5.  = 3 x + 3
11.  = 3+1
9.  = 2√ − 2 +2
8.  = −( − 2)3 + 2
6.  = ( + 2)2 − 3
12.  = 2(.5)
2
13. Is the given function exponential? If so, does it represent a growth ro a decay model?
(a)  = 2(3)+4
(b)  = 6 2 + 1
(c)  = 4− − 3
14. What is the average rate of change of the given function over the given interval?
1
(a)  = 2  + 3, [0, 3]
(b)  =  2 − 2, [−1, 3]
(c)  = 2√ + 4, [−3, 5]
Unit 5 REVIEW
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Solve each equation.
1) x 2 - 6 x = 0
2) m 2 + 4m - 25 = - 4
3) 3 x 2 + 2 x - 8 = - 7
4) 9r 2 - 3r - 2 = 3
5) 10 x 2 + 2 x - 21 = - 5
Sketch the graph of each function.
2
2
6) y = - 2 ( x + 1 ) + 2
7) y = - ( x + 4 ) - 1
y
y
1
3
2
-7
-6
-5
-4
-3
-2
x
-1
1
-1
-9
-8
-7
-6
-5
-4
-3
-2
1 x
-1
-2
-1
-2
-3
-3
-4
-4
-5
-5
-6
-6
-7
-7
8) y = x 2 + 6 x + 8
9) y = x 2 + 8 x + 18
y
y
4
7
3.5
6
3
2.5
5
2
1.5
4
1
3
0.5
-5
-4
-3
-2
1 x
-1
2
- 0.5
-1
1
- 1.5
-2
-6
-5
-4
-3
-2
-1
1 x
Solve each equation.
10) 4 x 2 + 15 x = - 21 - 4 x
11) 3k 2 + 23k = 8
Worksheet by Kuta Software LLC
-1-
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12) 5 p 2 + 3 = 3 p - 9
13) - 3m 2 + 18m + 2 = - 12m 2 + 12m
14) 7n 2 - 16n - 24 = 5n 2 - 3n
15) 9 x 2 - 6 = 6 x
Find the intercepts and the vertex and sketch a graph of the equation.
2
2
16) y = - x + 3 x + 4
17) y = 2 x + x - 6
vertex: _____________
vertex: _____________
x-intercepts: _____________
x-intercepts: _____________
y-intercepts: _____________
y-intercepts: _____________
y
-8
-6
-4
y
8
8
6
6
4
4
2
2
-2
2
4
6
8 x
-8
-6
-4
-2
2
-2
-2
-4
-4
-6
-6
-8
-8
4
6
8 x
2
18) y = - x + 2 x + 3
vertex: _____________
x-intercepts: _____________
y-intercepts: _____________
y
8
6
4
2
-8
-6
-4
-2
2
4
6
8 x
-2
-4
-6
-8
Worksheet by Kuta Software LLC
-2-
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Unit 6 Review
Match the given equation to the picture of the parabola
1. _________  =
−1
2
B.
A.
(  + 1)(  − 4)
(-1, 0)
(4, 0)
2. _________ y = 2( + 4 )2 − 2
(5, 0)
3. _________  = − (  − 1)2 + 6
4 . _________  = ( − 5 ) (  − 6 )
(6, 0)
D.
C.
(1, 6)
(-6, 6)
(3, 2)
(-4, -2)
Solve the following inequalities. Match the given equation with its solution in interval notation.
5. _______  2 − 6 < 0
A.
[− ∞ , −2.712 ] ∪ [ 2.2122
6. _______  2 + 3 ≤ 10
B.
( 0 ,6 )
7. _______ 2 2 + 5 − 12 ≥ 0
C.
(−∞, 0) ∪ (6, ∞)
D.
[− 5 , 2 ]
8. ______
2 2 > 12
,∞ ]
For each of the following problems (9 – 10), write a quadratic equation, and solve. (Hint: Draw the picture)
9.
The length of a rectangular room is 1 foot more than twice its width. The area is 78 square feet. Find the
dimensions of the room.
10.
A rectangular enclosure at a zoo is 35 feet long, by 18 feet wide. The zoo wants to double the area of the
enclosure by adding the same distance x to the length and the width. Write and solve an equation to find the
value of x. What are the new dimensions of the enclosure?
11.
A snowboarder in the terrain park at Powder Mountain hits a jump at 39.6 feet per second. The equation of the
boarders height is modeled by  () = −16 2 + 39.6. How high did the boarder jump?
12.
While playing rec basketball this weekend, Frank shoots an air-ball. The height h in feet of the ball is given by
ℎ() = −16 2 + 32 + 8. What is the maximum height of the ball?
What is the degree of the polynomial that has the following zeros?
13.
3, 8, 9
14.
1, 3(multiplicity 2), 6
State the number of complex roots and then list the possible rational roots for the following function.
15.
() = 2 4 −  3 − 7 2 + 4 − 4
Solve each equation for the variable specified.
1
16.
 = 2 ℎ , for (b)
17.
E = m 2 , for (c)
Unit 7 REVIEW
1. Which point lies on the x-axis?
a. (0, 1)
b. (2, 5)
c. (-3, 0)
d. (-1, 1)
2. Which of the following models suggests a plane?
a. bowling ball
b. garage door c. beam of a flashlight d. fence post
3. What is the coordinate of the midpoint of AD?
a. -5
b. -2
c. -1
d. 5
4. Find the distance between J(8, 3) and K (3, 15).
a. 5
b. 12
c. 13
d. 18
For Questions 5-6, refer to the figure at the right.
5. Use a protractor to find the measure of ∠TAC.
a. 125
b. 55
c. 150
d. 35
6. Use a protractor to classify ∠CAQ .
a. acute
b. right
c. obtuse
d. complementary
7. Find the slope of the line passing through the points (0, 5) and (-1. 2).
1
1
a. −3
b. − 3
c. 3
d. 3
8. What is the slope of a line that is parallel to the line  = −4 + 1 ?
1
1
a. 1
b. − 4
c. 4
d. −4
9. In which figure are ∠1 and ∠2 alternate interior angles?
a.
b.
c.
10. Find the value of x so that
a. 5
b. 12
c. 60
d. 125
d.
a ǀǀ b
11. The coordinates of the endpoints of a segment are (5, 8) and (-7, 16) Find the midpoint of the segment.
12. A triangle has vertices at A (1, -3), B (15, -1) and C (7,5).
Which two sides of the triangle have the same length?
13. Name the angle in four ways, and classify
the angle as acute, right or obtuse.
14. If the measure of ∠B is 55, find the measure of an angle that is complementary to ∠B and find the measure of an
angle that is supplementary to ∠B . (be sure to specify which answer is for complementary/supplementary)
15. Graph the equation  =
3

2
−3
16. Find the slope of the line shown below.
17. Using the picture below determine the measure of ∠3, ∠6 and ∠8; if the measure of ∠2 = 40
18. Using the picture from problem 17:
Name two angles that are Vertical angles:
Name two angles that are Consecutive Interior angles:
Name two angles that are Corresponding angles:
19.Find the value of x so that
a ǀǀ b
20. In the figure below, M is the midpoint of LN.
Find the value of x, and find the length of LM
3x + 16
L
7x
M
N
Unit 8 Review
______ 1. In ∆ ∠A is 78°, ∠B is 41°, find ∠C.
a. 51
b. 63
c. 32
d. 61
________ 2. ∆DEF , ∠ = 48°,  ∠ = 24°. What type of triangle is triangle DEF?
a. acute
b. right
c. obtuse
d. isosceles
________ 3. If two sides of an isosceles triangle measure 7 and 7. Which of the following could be the measure of the
base angles?
a. 45, 35
b. 25, 26
c. 102, 45,
d. 65, 65
________ 4. The triangles are congruent. State which postulate applies.
a. Side-Angle-Side
(SAS)
b. Angle-Side-Angle
(ASA)
c. Angle-Angle-Side
(AAS)
d. Side-Side-Side
(SSS)
_________5. Which postulate can be used to prove the triangles congruent?
a. ASA
b. SSS
c. Not Possible
d. SAS
_________6. In triangle ABC, m∠A = 60, and m∠B = 40. Which side of the triangle ABC is the longest?
a. AC
b. AB
c. BC
d. BC ≅ AB
_________7. Which of the following lengths are the sides of a right triangle?
a. 3, 4, 5
b. 6, 8, 10
d. 9, 12, 15
d. All of the above
_________8. Find the length of the hypotenuse of a right triangle with legs of 9 cm and 12 cm.
a. 17.3 cm
b. 15 cm
c. 7.9 cm
d. 21 cm
_________9. The side opposite the right angle of a right triangle is called the leg.
a. True
b. False
________10. In the diagram DE is parallel to AC, BD = 4, DA = 6 and EC = 8. Find BC to the
nearest tenth.
a. 4.3
b. 5.3
c. 8.3
d.13.3
11. Solve for “x”.
12. Classify the triangle by its sides and angles.
13. State if the triangles are congruent. If they are
state how you know.
14. State if the triangles are congruent. If they are state how
you know.
15. State if the triangles in each pair are similar.
If so , state how you know they are similar and
complete the similarity statement.
16. State if the triangles are similar.
Find the missing side of the triangle for questions 17-18.
Round your answer to the nearest tenth if necessary.
17.
18.
Story Problems (round answer to the nearest tenth)
19. A ladder leans against a building. The foot of the
Ladder is 6 feet from the building. The ladder
reaches a height of 14 feet on the building. Find the
length of the ladder to the nearest foot.
(Hint: Draw the pic)
20. A young boy is flying a kite. A strong wind came along
and blew the kite onto the top edge of a shed 12 ft. high.
The boy wanted to retrieve his kite. He leaned a 15 ft.
ladder against the shed. How far away from the base of
the shed was the ladder? (Hint: Draw the pic)
Unit 9 REVIEW
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Find the value of each trigonometric ratio.
1) sin X
2) sin A
41
X
9
A
Z
40
Y
34
30
B
3) cos Z
C
16
4) sin Z
41
X
Z
29
Z
40
20
Y
40
41
9
C)
41
40
9
41
D)
9
A)
X
9
21
Y
B)
20
21
29
C)
20
21
20
21
D)
29
A)
B)
Find the measure of the indicated angle to the nearest degree.
5)
6)
28
?
?
16
8
7
7)
8)
3
4
?
6
A) 34°
C) 56°
7
B) 42°
D) 66°
?
A) 17°
C) 67°
B) 23°
D) 25°
Worksheet by Kuta Software LLC
-1-
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Find the missing side. Round to the nearest tenth.
9)
10)
x
59°
63°
14
x
13
11)
12)
11
x
x
27°
39°
A) 9.4
C) 4.7
20
B) 8.9
D) 13.6
A) 17.8
C) 17.3
B) 22.4
D) 16.4
13) The tallest building in the world is the Burj
Kalifa. If you are on level ground exactly
5280 feet (one mile) from the base of the
tower, the angle of elevation to the top of
the skyscraper would be 27.7°. How tall is
the tower?
14) In rhombus ABCD with sides 3 inches long,
diagonals AC and BD meet at point E. If the
length of EB is 1.17 inches, what is the
measure of angle DAB?
15) A communications tower is built on top of a
building with the following specifications:
from a point 150 meters from the base of the
building, the angle of elevation to the top of
the building is 16° and the angle of
elevation to the top of the tower is 24°. Find
the height of the tower.
16) A fire department’s longest ladder is 110
feet long, and the safety regulation states
that they can use it at a maximum angle of
elevation of 65.3°. W hat is the maximum
heightn for the rescue ladder?
17) A 9 meter flagpole casts a 12 meter shadow.
Find the angle of elevation of the sun.
18) A swimming pool is 20 meters long and 10
meters wide. The bottom of the pool is
slanted so that the water depth is 1.5 meters
at the shallow end and 5 meters at the deep
end. Find the angle of depression of the
bottom of the pool.
Worksheet by Kuta Software LLC
-2-
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Unit-10 REVIEW
Part 1:
1. Data was taken for two hospitals for a one month period of time. Assume all patients had an equal chance of going to
either hospital and, on average, the patients that attended either hospital had about the same health histories. Fill in the
blanks on the 2-way table below:
Died
Survived
total
Hospital A
63
Hospital B
Total
79
784
2100
2. Build a Venn Diagram for the data in the completed table above. Label your ovals. Include the relevant numbers in
your diagram.
3. For the data provided in problem 1 (above), calculate the following probabilities:
a. P(Died) = _____
b. P(patient went to Hospital A) = ____
c. P(did not survive and was at hospital B) = ____
d. P(Survived given that the patient was at Hospital A) = ____
e. P(went to hospital A and survived OR went to hospital B and died) = ____
f. Which hospital would you rather go to? Justify your answer with at least two of your own probability statements (with
numbers) that “proves” your opinion is correct.
4. Build a tree diagram for the data above. Choose the first branches so that you can use your table to answer the
following probability statement: P(Died given that you went to Hospital B) = _____
Part 2:
The following probability statements are given:
P(green eyes) = 40/110
P(blue and male) = 15/110
P(male) = 40/110
P(female given that the person doesn’t have blue or green eyes) = 12/25
5. (6 points) Fill in the following table using the numbers from the probability statements above:
Blue eyes
Green eyes
Other colored eyes
total
Male
Female
total
6. Build a tree diagram for the data above. Make your first branches so that you can answer the following question:
P(Green eyes / male) = ____
7. Build a Venn diagram
8. Calculate the following probabilities:
a. P(female and blue eyes) = ____
b. P(other colored eyes given that the person is a male) = ____
c. P(male OR has green eyes) = _____
9. 5 different books will be displayed in the library window. How many different arrangements are there?
10. In a talent show, the top 3 performers of 12 will advance to the next round. In how many ways can this be done?
Unit 11 REVIEW
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Find the measure of the arc or angle indicated.
1)
2)
X
C
?
?
W
D
76 °
E
A) 73°
C) 55°
V
82 °
110 °
A) 182°
C) 126°
B) 57°
D) 77°
B) 186°
D) 153°
Find the measure of the arc or central angle indicated. Assume that lines which appear to be
diameters are actual diameters.
3) m RPT
4) m IJH
H
Q
G
56°
R
P
I
76°
J
59°
F
59°
U
S
E
T
Find the length of each arc (remember to change the degrees to radians).
5)
6)
240°
270°
6 in
11 m
Find the area of each sector.
7)
8)
60° 13 in
19 in
90°
Worksheet by Kuta Software LLC
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Find the volume of each figure. Round your answers to the nearest tenth, if necessary.
9)
12 ft
10)
10 ft
11 ft
7 cm
11 ft
6 cm
10 ft
11)
12)
9m
5.7 yd
4m
Find the volume of each figure. Round your answers to the nearest hundredth, if necessary.
13)
7 cm
3 cm
3 cm
Find the volume.
14) A silot is formed by a 15ft tall cylinder with
a radius of 2.1 ft, and topped by a 3ft tall
cone. W hat is the volume of the rocket?
Find the measure of the indicated angle to the nearest degree.
15)
47
?
28
Worksheet by Kuta Software LLC
-2-
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Find the missing side. Round to the nearest tenth.
16)
20°
x
10
Find the value of each trigonometric ratio.
17) tan A
C
41
40
B
9
A
Find the measure of the indicated angle to the nearest degree.
18)
26
19) Jordon has finally made it to Paris for her
summer vacation, she is so excited to visit
the Eifeel Tower. The day she visit this
iconic giant, she looks up at the Eifeel
Tower at an angle of elevation of 84.6° and
is standing 100 ft from its base. How tall is
the Eifeel Tower?
25
?
Find the probability of each event.
20) A gambler places a bet on a horse race. To
win, he must pick the top three finishers in
order. Twelve horses of equal ability are
entered in the race. Assuming the horses
finish in a random order, what is the
probability that the gambler will win his
bet?
1
» 1.111%
90
1
C)
» 0.076%
1320
A)
21) Kristin and Dan each purchase one raffle
ticket. If a total of fourteen raffle tickets are
sold and two winners will be selected, what
is the probability that both Kristin and Dan
win?
1
» 0.139%
720
1
C)
» 4.762%
21
A)
1
» 2.222%
45
1
D)
» 0.909%
110
B)
1
» 0.833%
120
1
D)
» 1.099%
91
B)
Worksheet by Kuta Software LLC
-3-
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