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Algebra II CP
Midterm Exam Review Packet
Name:______________________
Hour:______________
ALGEBRA II-CP Name___________________________________
Midterm Review - Ch. 1, 2,3
Solve each equation.
1. 8(–12y + 10) = 92 – 6(16y + 2) 2. 7x + 3 = 2(x – 1) 3. 10
4
5
x
4. 95
3 x 5. 4t – 12 = –t + 11 6. 6x – 10 – (x + 5) = 0
7. What is the slope of the line whose equation is 4x – 5y = 10?
8. What is the slope of the line passing through (2, 6) and (-9, 8)?
9. For which pair of equations are the lines perpendicular?
A. 2x – y = 1 and xy2
1 B. 6x + 3y = 10 and 3x – 6y = 10
C. y = 5x and y = -5x D. 3x + 2y = 1 and 2y = 3x + 8
10. For which pair of equations are the lines parallel?
A. y – 5 =3x and 2y – 6x = –12 B. 5x + 3y = 15 and 3x + 3y = 15
Find the equation of the line in any form satisfying the following conditions.
11. Passes through ( 2 , 6 ) and is parallel 12. m = 0 passes through ( 1 , -8 )
to -5x + 2y = 7
13. Passes through ( -1 , 2 ) and ( -5 , -3 ) 14. Passes through ( 0 , 4 ) and is perpendicular to y = 6x - 7
Solve by these systems by graphing by hand (please sketch graph).
15. –2x + y = –7 16. x + 4y = 4
3x – 4y = 8 y = -4
1x + 5
Solve by substitution
17. 2x – y = –1 18. 5x + 3y = 8 19. x + 2y = 12
y + x = 4 5x + y = 16 4x + 8y = -19
Solve by elimination 20. x – y = 7 21. 5x – 7y = –2
2x + y = 5 3x + 2y = 36
22. For which system are there infinitely many solutions?
A. 3x + 5y = 7 B. x – 5y = 7 C. 3x – y = 8 D. 2x – y = 1
6x + 10y = 14 2x = 10y + 15 3x + y = 10 y = 2x – 3
Define TWO variables, write TWO equations and solve by substitution or elimination. Show all work for full credit!
23. The sum of two numbers is 106. One number is five less than twice the other.
What are the two numbers?
24. At McDonald’s, 2 burgers and 2 fries cost $5.50. If you order 3 burgers and 4 fries it cost $9.25.
How much does one burger cost? One order of fries?
25. The perimeter of a rectangular garden is 168 ft. The length of the garden is 30 more than 5 times the width.
What are the dimensions of the garden? (You must have two equations!)
26. Ticketmaster sells pavilion and lawn tickets to Pine Knob. A total of 5,000 tickets were sold for a concert. The
pavilion tickets cost $20 each and the lawn tickets cost $15 each. The sales for all tickets totaled $82,500. How many of
each type of ticket were sold?
Algebra II: Chapter 4 Midterm Review Name _______________________________________________
Multiple Choice: Select the letter that best answers the question.
1. Determine the vertex and axis of symmetry of the
following quadratic:
12642 xy
2. Determine the vertex and the maximum or minimum
value of the following quadratic:
32
1 2 xxy
1. _____
2. _____
A. Vertex: 12,6
Axis: 6x
B. Vertex: 12,6
Axis: 12x
A. Vertex: 5.1,1
Max. Value: 5.1
B. Vertex: 3,1
Max. Value: 3
C. Vertex: 12,6
Axis: 6x
D. Vertex: 12,6
Axis: 6x
C. Vertex: 5.4,1
Min. Value: 5.4
D. Vertex: 5.3,1
Min. Value: 5.3
Determine whether the equation is in Vertex, Intercept, or Standard form. Then, find the indicated values and graph each equation. Don’t forget to draw the axis of symmetry!
3. 4123 2 xxy
4. 3105 2 xxy
Vertex or Intercept or Standard Vertex or Intercept or Standard
Opens __________ Opens __________
Vertex ,
Vertex ,
Axis of Symmetry __________
Maximum or Minimum
Value ___________
Axis of Symmetry __________
Maximum or Minimum
Value ___________
Determine whether the given equation is in Vertex, Intercept, or Standard Form.
5. 152 xxy
6. 232
1)( 2 xxxf
7. 334
1 2 xy
Vertex or Intercept or Standard Vertex or Intercept or Standard Vertex or Intercept or Standard
Multiple Choice: Select the letter that best answers the question. 8.
Simplify xx 8326 4
8. ______
A. xx248
B. xx296 C. xx96
D. xx 4192 2
9.
Simplify 526134
9. ______
A.
532026624
B.
532026624
C.
5514624
D.
532026624
10.
Simplify ii 763217
11. _____
A. i2335
B. i191 C. i923 D. i2325
11.
Simplify i
i
3
254
12. _____
A. 3
2
3
54
i
B. 3
2
3
54
i C.
3
2
3
54 ii D.
3
2
3
54 i
Use what you know about simplifying square roots and the properties of i to answer the following questions. Make sure that all denominators are rationalized and each root is completely simplified.
12. ii 3623
13. 511511
14.
54
2
15. i
i
12
153
Answer: ____________________
Answer: ____________________ Answer: ____________________ Answer: ____________________
16.
Simplify: 21
7
17.
Simplify: i
i
8
102
18.
Find the value of the discriminant and describe the zeros of: 823 2 xx
18._____
A. D = 100
2 real zeros
B. D = 100
1 double zero/root
C. D = − 94
2 imaginary zeros
D. D = 96
2 real zeros
19.
Find the solutions/zeros of: 2x2 − 4x + 3 = 0
19._____
A. 22 i B. i1 C. 22 i
D. 2
21
i
20.
Find the solutions/zeros of: 2x2 − 5x − 3 = 0
Algebra II: Chapter 5 Midterm Review Name _______________________________________________
Evaluate or simplify the expression completely. 1.
2405 57 eheh
2.
2
6
05
db
a
3.
23
56
16
34
dc
dc
Answer: ______________________________
Answer: ______________________________ Answer: ______________________________
4.
3274yx
5.
1811 310 xwxw
6.
04
73
13
39
cb
cb
Answer: ______________________________
Answer: ______________________________ Answer: ______________________________
7.
Which of the following expressions is equivalent to: cab
bca3
12
12
8
7. _____
A. 3
2 22cab
B. 223
2
cb
a C.
23
2
b
a D.
bc
a
3
2
8.
Which of the following expressions is equivalent to: 23624 223 aaaa
8. _____
A. 854 23 aaa B. 44 23 aaa C. 837 23 aa
D. 854 23 aaa
9.
Which of the following expressions is equivalent to: 4912 2 xxx
9. _____
A.
B.
C.
D.
Use the graph to describe the end behavior, determine the number of real zeros, and estimate the indicated value. 10.
______)(,
______)(,
xfxAs
xfxAs
11.
______)(,
______)(,
xfxAs
xfxAs
Number of real zeros: _________
Local Maximum: ,
Number of real zeros: _________
Local Minimum: ,
Identify all of the factors of each polynomial.
12. 18 3 y
13. xx 542 4
Factors: _________________________________
Factors: _________________________________
14. 283 24 xx
15. xxx 10122 35
Factors: _________________________________
Factors: _________________________________
Use synthetic division to divide the following polynomials.
16. 54413112 23 xxxx
17. 2101525 24 xxxx
Answer: ___________________________________________________ Answer: ____________________________________________________
Given polynomial xf and a factor of xf , factor xf completely.
18. One factor of 2425 23 xxxxf is 2x .
Find the remaining factors.
19. One factor of 673 xxxf is 1x . Find the
remaining factors.
Remaining Factors: __________________________________________ Remaining Factors: __________________________________________
20.
Find two of the zeros of the function: 362753 234 xxxxxf
20._____
A. 4,3 B. 1,3 C. 4,3i D. 4,3 i
21.
Find two of the zeros of the function: 42355 234 xxxxxf
21._____
A. 7,6 B. 5.3,1 C. 7,6 i D. 7,1 i
Write an equation in standard form with the following zeros:
22. ixandx 59
23. 74 xandix
Equation: ___________________________________________________ Equation: ___________________________________________________
24. The function whose graph is shown has _____.
24. ____
A. two local maximums B. no local maximums C. two local minimums D. one local minimum
Algebra II: Chapter 6 Midterm Review Name _______________________________________________
Evaluate the expression.
1. 3
4
27
2. 25 32
Use the properties of rational exponents to simplify. Express in simplest radical form.
3. 2
8
2
5
44
4.
5
4
5
7
m
m
5.
7
2
2
3
4
1
55
6.
7
3
3
1
5
2
xx
7.
7
12
7
4
x
x
8. 5
8
10
1
bb
9.
Which of the following expressions is equivalent to: 276752185
9. _____
A. 323 B. 38215 C. 21531054 D. 38215
10.
Which of the following expressions is equivalent to: 3 93427 zyx
10. ____
A.
33 33 xxyz B. 333 xxyz C.
33 39 xxyz D. 33 93 xxyz
Simplify the expression using the properties of radicals.
11. 4 54 8285 xx
12. 4 44 3 271096 yy
13.
If 932
xxh and ,53 32
xxxm find: xmxh ?
13. _____
A. 934 32
xx B. 934 32
xx C. 34
63 xx D. 97 37
x
14.
If 932
xxh and ,53 32
xxxm find: xhxm ?
14. _____
A. 934 32
xx B. 934 32
xx C. 34
63 xx D. 97 37
x
Let 32,95 xxgxxf . Perform the indicated operation.
15. xgf
16. xfg
Find the inverse of the function.
17. 23
4)( xxf
18. 92 xxf
Let 3,5 xxgxxf , 3
1
xxj , and 11 xxm . Find only the domain of each.
19.
)(xf
xg
20. xm
xj
Domain: ______________________ Domain: ______________________
Find the solution(s) to the equation:
21. 34 xx
22. xx 188
23. 13 xx
Algebra II: Chapter 7.1-7.3 Midterm Review Name _____________________________________________ Determine whether each function represents exponential growth, decay, or neither.
1.
x
y
3
25
2. xy 2
2
1
3. xy 410
Match the function with the graph.
4. 33
4
x
y ____
5. 23 xy ____
6. 141 1 xy ____
A.
B.
C.
Match the function with the graph.
7.
2
3
2
x
y ____
8.
x
y
2
11 + 3 ____
9. 23
22
1
x
y ____
A.
B.
C.
Determine the a, b, h, k, as well as the equation for the Horizontal Asymptote, the Domain, and the Range. Then, fill out the table
and graph the function.
10. 23 4 xy
a = _______
b = _______
Growth or Decay or Neither
h = _______
______________________
k = _______
Domain: ________________________________
Range: ________________________________
HA = _______________
x y
−1
,
0
,
1
,
2
,
11.
53
21
2
x
y
a = _______
b = _______
Growth or Decay or Neither
h = _______
______________________
k = _______
______________________
Domain: ________________________________
Range: ________________________________
HA = _______________
x y
−1
,
0
,
1
,
2
,
12. 328.0 xey
a = _______
b = _______
r = _______
Growth or Decay
h = _______
______________________
k = _______
______________________
Domain: _______________________________
Range: ________________________________
HA = _______________
x y
−2
,
−1
,
0
,
1
,
Use the formulas to solve the following story problems. You will need to have these on your notecard for the exam.
tray 1 tray 1
nt
n
rPA
1
rtPeA
13. A computer system depreciates at a rate of 15% per year. If you originally bought the computer for $4000, how much would it be worth 5 years from now?
14. Brian buys a new car for $24,000. The car depreciates in value 17% per year. How much would the car be worth 8 years from now?
15. The student enrollment of a high school was 1500 in 2010 and has increased by 8% per year since then. Let t be the number of years since 2000. How many students are enrolled in the year 2015?
16. The length l (in centimeters) of a tiger shark can be
modeled by the function, tel 178.0276337 , where t is the shark’s age (in years). Use the model to estimate the length of a shark that is 3 years old.
17. Suppose you deposit $1,000 in an account paying 6.5% annual interest compounded continuously. What is the balance after 6 years?
18. You deposit $10,000 in an account paying 6.5% annual interest compounded continuously. What is the balance after 6 years?
19. You deposit $15,000 in an account that earns 5.1% annual
interest. Find the balance after 1 year if it’s compounded daily?
20. You deposit $100 in an account that pays 6% annual interest. How much will be in the account if it’s compounded monthly?