Download Topics to study for your Algebra II final exam

Topics to Study for Your Algebra II Final Exam
Chapter 1
 Recursive formula
o Arithmetic Sequences
(1.1)
o Geometric Sequences
(1.1)
 Percentages (1.2)
Chapter 3
 Slope (3.2)
 Writing linear equations
o Slope-intercept form
(3.1, 3.2)
o Point-slope form (3.3)
o Line of best fit (3.3)
 System of Linear Equations
o Solve by substitution
(3.6)
o Solve by elimination
(3.7)
Chapter 4
 Function vs. Relation (4.2)
 Function notation (4.2)
 Composition of functions (4.8)
 Equations of transformed
(4.4) functions (linear,
absolute value, quadratics)
o Translations
o Reflections over x-axis
o Dilations
Chapter 5
 Properties of Exponents (5.2)
 Rational Exponents (5.3)
 Solving power equations (5.2)
 Solving exponential equations
(5.2)
 Logarithms (5.6)
Chapter 6
 Add and subtract matrices
(6.2)
 Scalar multiply matrices (6.2)
 Multiply matrices (6.2)
Chapter 7
 Add, subtract, multiply
polynomials (7.0)
 Factor polynomials (7.0, 7.2)
 Classify polynomials (7.1)
 Polynomial vs. not polynomial
(7.1)
 Solve quadratic equations
(7.2, 7.4, 7.5)
o Square root
o Factoring
o Quadratic formula
 Complex numbers (7.5)
o Plotting
o Arithmetic
o Simplifying
Chapter 10
 Basic Probability (10.0)
 Compound probability (10.2)
 Combinations (10.6)
 Permutations (10.5)
 Counting Principle (10.5)
Chapter 12
 Pythagorean Theorem (12.0)
 Right triangle Trigonometry
(12.1)
o Solve for sides
o Solve for angles.
Chapter 1
1) Consider the arithmetic sequence 5, 8, 11, 14, . . . .
Write an expression for the nth term of the sequence.
2) An equilateral triangle can be made using 3 toothpicks. If the pattern below is
continued, how many toothpicks are needed to make 24 equilateral triangles of
this size?
3) The price of a $45,000 automobile is reduced by 14% and then the price is
further cut by $2,393. What is the new price?
4) Write a recursive formula for the sequence. 40, 20, 10, 5, . . .
5) Use the recursive formula to write the first four terms of the sequence defined
1
by u1  81, un  F
Hun 1 IKwhere n  2.
3
6) You deposit $800 in an account that pays 6% annual interest compounded
annually. Write a recursive function to model the situation.
Chapter 3
1) Write an equation in intercept form for each line in the graphs.
y
10
y
10
l1
l2
–10
10 x
–10
–10
–10
2) Solve the system of equations.
a.
b.
 6 x  3 y  – 10
R
S
T4 x  9 y  5
c.
2x  2 y  4
R
S
Ty   x
x  4 y  27.2
R
S
Tx  2 y  15.2
e.
10 x
f.
2 y   2 x  16.2
R
S
T2 y   4 x  22.8
d.
3x  2 y   20
R
S
Tx  5y   37
g.
7 x  8 y   21
R
S
Tx  y   2
9 x  8 y  68
R
S
T3x  5y  32
3) Determine the slope and equation of the line passing through (-7, 8) and (5, -7)
4) Write an equation for the line in the graph. Is the slope positive, negative, zero,
or undefined?
10 y
–10
10
x
–10
5) Bob has two job offers at the same shoe store. Job A will pay $15,000 base
salary and then a commission of $20.00 per sale. Job B will pay $20,000 base
salary with $10 per sale.
a. If x equals the number of sales and y equals yearly income, write a
system of equations.
b. Solve the system of equation using any method.
c. Interpret the solution to this system of sales and salary.
Chapter 4
1) How does the graph of y  x  3  2 compare with the graph of y  x 2 ?
b g
2
2) The graph below shows the amount of gas in Sharon’s tank during a trip to her
mom’s house. She stopped twice for 15 minute breaks, once at a rest stop and
once at a gas station. When did she stop at the rest stop?












5:00
PM
6:00
PM
7:00
PM
Time
8:00
PM
9:00
PM
bg
4) Find the x-values corresponding to hbg
x  4 and hbg
x  6 for the
, 2, 3gb
, 3, 4gb
, 4, 5gb
, 5, 6gb
, 6, 7g
relation h  m
b1, 2gb
r.
5) Consider the relation defined by the set of points m
, – 6, 5gb
, 1, 5g
b– 4, 5gb
r. Is the
bg
3) Given g x  3x 2  6 x  9. Find g – 3 .
relation a function?
6) The graph of the function y  x 2 is translated left 7 units. Write the equation of
the resulting graph.
7) (Multiple choice) f(x) = 3x – 4 and g(x) = 2x + 1
i. Find g(2)
a. 5
b. 2
c. 7
d.1
ii. Find f(x) – g(x)
a. x – 5
b. –x + 5
c. 5x – 3
d. –5x + 3
iii. Find f(3 + 2) – 5
a. 0
b. 10
c. 1
d. 6
iv. Find f(g(2))
a. 1
b. 11
c. 5
d. 7
v. Find f(g(x))
a. 5x – 3
b. 6x2 – 5x – 4
c. 6x – 7
d. 6x – 1
vi. Given the relations s = {(0, 1), (1, 3), (2, 5)} and t ={(1, 7), (2, 3), (5, 0)}
Find t(s(2))
a. 0
b. 1
c. 2
d. 3
8) (Multiple Choice) Describe how the graph j(x + 4) – 5 would translate j(x).
a. j(x) will translate right 4, up 5
b. j(x) will translate right 4, down 5
b. j(x) will translate left 4, up 5
c. j(x) will translate left 4, down 5
9) f(x) = 5x + 2 and g(x) = –4x + 5. Find each of the following.
a. f(4)
b. f(x) – g(x)
c. g(4 + 2) – 6
c. f(g(4))
10) Given p = {(0, 1), (2, –5), (3, 7)} and t = {(–5, 4), (1, 3), (0.10)}. Find each of
the following.
a. Find t(p((–5))
b. Find p(t(1))
Chapter 5
1) Solve each equation.
1
a. 27   
9
x
5
e. 5x  160  0
b.
8 x5  1312
f.
x
d. 3  6  87
g.
h.
2) Simplify each of the following.
a.  4 x 5  3x 3
x4
x –9
i. 3 3  5 8
b.
144x12
21x 6
9
f. 7 x
j.
28
5
 
c. 2x8
3
3
343
g.
k.
x  9
k. 3x – 4 = 361
j. logx5 = 25
i.
e.
c. 273x  94 x 2 .
20
6
3) Write as a radical expression and evaluate if possible.
1 2
16
d.
48x12
h.
80
Chapter 6
Simplify
1.
2.
 3 4
5 7 310 6 
12 11
3.
3 1
L
M
7 2
M
M
N1 8
1 1
O
L
4P
+ M
3 7
P
M
3P
2 4
QM
N
–5
O
0P
P
 1P
Q
2
4
L
M
5
M
M
–8
N
–6
O
L
P
M
1P
M
0
– 6P
–4
QM
N
–4
–9
O
L
P
M
1P
M
7
– 1P
QM
N4
2
O
– 6P
P
3P
Q
–5
Chapter 7
1) Simplify.
a.
b1  2igb8  2ig
b.
c.
d.
 1  7i g
b 4  igb
 12  9i g
b4  5igb
e.
2  5i
 4  9i
2) The height of a baseball thrown into the air can be represented by the equation
h(t) = -4.9t2 + 32t + 6 where h ( t ) is the height of the ball in meters after t seconds.
a. Find h(0) and give a real-world meaning for this value.
b. How high is the ball when t = 3 seconds?
c. When does the ball hit the ground? (Round your answer to the
nearest hundredth.)
3) How many terms are in the polynomial?
1
3x 5 y  x 6 y 7 z 9  x 2  6 x 5 y 8 z 4
8
4) Write the polynomial 7 x 3  x10  2 x 6 in standard form. Identify the leading
coefficient of the polynomial
5) . Solve each equation. Check your solutions.
a. x  5 2 x  1  0
b. 4 x 5x  2  0
b gb g
d. 0  2 x 2  6 x  8
b g
e.
2
c. 16x  5  0
f.
i 11
Chapter 10
1) You go to a restaurant where you can select one main course from 2 maincourse choices, one vegetable from 2 vegetable choices, and one beverage from 2
beverage choices. How many different combinations can you order?
2) Jane has a 4-digit combination lock on her suitcase and has forgotten the
combination. If she knows that the first digit is a 5 and the second digit is prime,
how many numbers must Jane try before the lock is sure to open?
3) Each student is asked to create a 5-digit password when registering for an
online account.
a. How many different 5-digit passwords can be formed from the digits 1, 2,
3, 4, 5 if each digit is used only once in each number?
b. What is the probability the number ends in a 5?
4) The combination for a lock consists of three different integers from 1 to 24,
inclusive, in a particular order. Use permutation notation to represent the number
of three-integer codes that are possible.
5) In how many different ways can you arrange four songs on a CD? Use
permutation notation to represent the different ways.
6) In an electronics experiment 1 white cord is connected to 6 black cords. Each
black cord is connected to 4 gray cords. Each gray cord is connected to 7 blue
cords. How many blue cords are there?
7) A committee is to consist of four members. If there are seven men and six
women available to serve on the committee, how many different committees can
be formed?
8) A teacher must choose 3 teams from 9 students. The teams will be selected by
choosing one student at a time for each team.
a. In how many ways can the teacher choose 3 students in different orders?
b. How many different possible 3-student teams are there?
9) What is the probability of rolling a die twice in a row and getting a four both
times?
10) What is the probability of rolling a die and getting an even number, then rolling
a die and getting a four?
11) What is the probability of rolling a die and getting an even number then rolling
a die and getting a 5 or 6?
12) Given a 8 digit code using the numbers 0-9
a. How many digit codes can be made if no number is repeated in the
code
b. How many digit codes can be made if there can be repeats
13) Eight friends take a placement test for Brookdale. Assume there are no ties.
a. How many different orders can they finish in?
c. How many different orders can the top three finish in?
d. What is the probability of Bob finishing in first or 2nd?
14) You and thirteen friends enter in a contest to win a free trip. Three people are
going to win the free trip.
a. How many combinations are possible for this trip?
b. What is the probability you will be with your two best friends on the trip
15) Each student is asked to create a 3-digit password when registering for an
online account.
a. How many different 3-digit passwords can be formed from the digits 0,
3, 5, 6, 8 and 9 if each digit is used only once in the password?
b. What is the probability the number ends in a 5?
c. What is the probability the number starts with a 5?
d. What is the probability that the number starts with a 3 then a 4
e. What is the probability the number ends in a 5 or a 6?
Chapter 12
1. Refer to the right triangle below to calculate the values for the sine, cosine, and
tangent of angle T.
T
34
16
U
30
V
2. In the right triangle below, what trigonometric function does
B
5
A
4
3
C
4
represent?
5