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Algebra 1 Final Review Guide
To prepare for your final exam, please follow these suggested steps. The more practice you do,
the better prepared you will be for the exam. Be sure to have your calculator with WORKING
batteries, a ruler, and more than one sharpened pencil. Do not expect to borrow materials.
1. Review key vocabulary terms at the beginning of each chapter or use the list at the end of the
chapter in the review.
2. Read the chapter summary at the end of each chapter several times. Write down any ideas that
are unclear.
3. ***Review the quizzes and tests you have already taken and be sure that you would get 100% if
you took the same test today.***
4. Complete the lesson-by-lesson review in the Study Guide and Review section at the end of
each chapter.
5. Complete the practice test at the end of each chapter.
6. Use pages 827-844 for extra practice problems for each section of each chapter. This is the
EXTRA PRACTICE section of the back of your book.
7. Use pages 850-856 for extra practice word problems for each section of each chapter. This is the
MIXED PROBLEM SOLVING section of the back of your book.
8. For additional practice on areas you may use previous homework assignments and worksheets.
These should be a solution key to check your work.
9. Use the guiding questions in the remainder of this packet for a general review. However, do not
rely solely on these questions.
*REMINDER: We started with chapter 6 after the midterm and went up through Chap 9
We also DID Probability (13.6 and 13.10 Packets) and Counting Principle (13.8 Packet).
We did NOT do sections 6.6, 6.7, 6.8, 9.3, 9.4, 9.8, 9.9.
Chapter 6 – Systems
1) If a system is consistent independent,
(a) how many solutions does it have?
(b) what does the graph look like?
(c) comparing the 2 equations, tell me about their slopes and y-intercepts…
(Are they the same or different?)
2) If a system is consistent dependent,
(a) how many solutions does it have?
(b) what does the graph look like?
(c) comparing the 2 equations, tell me about their slopes and y-intercepts…
(Are they the same or different?)
3) If a system is inconsistent,
(a) how many solutions does it have?
(b) what does the graph look like?
(c) comparing the 2 equations, tell me about their slopes and y-intercepts…
(Are they the same or different?)
4) Solve the given system by graphing.
y = -2x – 3
y=x–3
5) Solve the given system by substitution.
3x + 4y = -3
x = -2y – 1
6) Solve the given systems by elimination using addition or subtraction.
a) 8x + 5y = 38
b) 7f + 3g = -6
-8x + 2y = 4
7f – 2g = -31
7) Solve the given systems by elimination using multiplication.
a) 12x – 3y = -3
b) 4x + 2y = -14
6x + y = 1
5x + 3y = -17
~Remember word problems that you have to solve using systems…
(1st write your system, then solve it.)
8) A used book store started selling CD’s (x) and videos (y). In the first week, the store sold and
total of 40 CD’s and videos and earned a total of $180. CD’s costs $4 per CD and videos costs
$6 per video. Find how many CD’s and videos the store sold that first week.
9) In order for Joe and Marty to compete against each other during the wrestling season next year
they will need to be in the same weight category. Joe weighs 180 pounds (y) and plans to gain 2
pounds per week (x). Marty weighs 249 pounds (y) and plans to lose 1 pound per week(x). Find
how many weeks it would take for them to weigh the same amount.
Chapter 7 – Polynomials
1) Give an example of each. (a) monomial, (b) binomial, (c) trinomial, (d) polynomial
2) What are polynomials not allowed to have? Give examples of expressions that are not
polynomials.
3) When do you add the exponents? Give an example.
4) When do you multiply the exponents? Give an example.
5) When do you distribute the exponent? Give an example.
6) When do you subtract the exponents? Give an example.
7) How do you make a negative exponent positive? Give an example.
8) How do you find the degree of a monomial? Of a polynomial?
9) What does it mean for a polynomial to be written in Standard Form and what is the leading
coefficient?
10) Give an example of a polynomial that is written in standard form, then give one that is not
written in standard form.
11) When adding or subtracting monomials, what do you need to have in order to consider them
like terms?
12) When adding or subtracting monomials, you obviously add or subtract the coefficients, but
3
3
what do you do with the exponents? For example, 3x  5x .
13) What do the letters in FOIL stand for?
14) What is the special product of the square of a sum,
a b 
15) What is the special product of the square of a difference,
2
a b 
2
16) What is the special product of the product of a sum and difference,
a b(a b) =
17) In order to properly write a number in scientific notation, you need ______________
Chapter 7 Examples:
Simplify #s 1-3.
1) (9t3n5)(–2tn2)
2) (w5y4)3
3)
4) Express 0.000000607 in scientific notation.
5) Evaluate each product or quotient. Express the results in both scientific notation and standard
form.
a) (2.8
10–4)(7.7
109)
b)
6) Find the degree of the polynomial 2x3y3 + 4xy – 10x3y.
7) Write 4 + 3x3 – x5 + x in standard form. Identify the leading coefficient.
8) Find each sum or difference.
a) (5n2 – 2ny + 3y2) – (9n2 – 8ny – 10y2)
b) (11m2 – 2mt + 8t2) + (8m2 + 4mt – 2t2)
Simplify #s 9-12.
9) 5hk2(2h2k – hk3 + 4h2k2)
10) (4x2 + 2y2)(2x2 – y2)
11) (5c – 4)2
12) (3r + 5)(2r2 – 8r + 6)
13) Solve the given equation.
–6(3n – 2) = 4(–3 – 2n)
Chapter 8: Factoring and Quadratic Equations
1) What does it mean to factor?
2) How do you find the GCF of two or more monomials?
3) What do you do to factor a polynomial using the distributive property? When should you use
the distributive property to factor?
4) How many terms should a polynomial have to factor by grouping?
5) In order to solve a polynomial, you must set it equal to ____________.
6) What is the standard form of a quadratic equation?
7) When factoring x 2  bx  c , the two factors need to add to ___________ and multiply to
____________.
8) If there is a coefficient in front of x 2 , the two factors need to add to _____________ and
multiply to the ____________________________.
9) When c is positive, and b is positive, the factors are _____________.
10) When c is positive and b is negative, the factors are _____________.
11) When c is negative, the factors have _________________ signs.
12) What does it mean for a polynomial to be prime?
13) What are the three things that must be true for a polynomial in order to factor using the
difference of squares method?
14) What are the three things that must be true for a polynomial to be a perfect square trinomial?
15) What is the square root property? How many answers must you have when using the square
root property?
Chapter 8: Examples
1) Factor 95xy 2 completely.
2) Find the GCF of each set of monomials.
a. 30 gh 2 ,42 g 2 h,66 g
3) Use the distributive property to factor
a. 2k 2  4k
b. 4a 2 b 2  2a 2 b  10ab 2
4) Factor each polynomial. If the polynomial cannot be factored, write prime.
a. a 2  4a  24  6a
b. 21th  3t  35h  5
c. x 2  17 x  42
d. x 2  17 x  72
e. x 2  8 x  48
f. x 2  2 x  35
g. 5 x 2  34 x  24
h. 2 x 2  3 x  9
i. 4 x 2  5 x  7
j. 64 x 2  y 2
k. y 4  1
l. 9 x 2  24 x  16
5) Solve each equation
a. b 2  3b
b. 3b(9b  27)  0
c. x 2  7 x  12  0
d. x 2  18  11x
e. 2 x 2  9 x  18  0
f.  2 x 2  13 x  15
g. x 2 
9
0
16
h. 9 x 2  48 x  64  0
6) A rectangle has an area represented by x 2  4 x  12 square feet. If the length is x + 2 feet,
what is the width of the rectangle?
7) Solve (a  10) 2  121
Chapter 9: Quadratic and Exponential Functions
1) What is the standard form of a quadratic equation?
2) What is the shape of a quadratic equation graph?
3) What is the axis of symmetry? How do you find it from a graph? From a quadratic eqn?
4) What is the vertex and how do you find the vertex of a quadratic equation?
5) How do you find the y-intercept from a quadratic equation?
6) When a > 0, the graph of the parabola will point ______ and have a ________________,
when a < 0, the graph of the parabola will point ______ and have a ________________.
7) How do you graph a quadratic equation?
8) What does the graph of a quadratic equation look like if there are two roots? One root?
Or no roots?
9) Write the quadratic formula.
10) What is the expression for the discriminant and what is it used for?
11) If the discriminant is negative, there will be ________ solutions, if the discriminant is
zero, there will be __________ solution, if the discriminant is positive, there will be
__________ solutions.
12) What does an exponential equation look like? Exponential growth equation? Exponential
decay equation?
13) What does an exponential growth graph look like? An exponential decay graph?
Chapter 9: Examples
1) Graph the given quadratic equation: y  2 x 2  8 x  1 . State the roots. (Solve)
2) Graph the given quadratic equation: y  2 x 2  4 x  3 State the roots.
3) Find the vertex, the equation of the axis of symmetry, the y-intercept, if the function has a
minimum or maximum, and what is the domain and range of each function
a. y  x 2  4 x  5
b. y  3x 2  6 x  7
4) Solve each quadratic equation using the quadratic formula.
a. 4 x 2  5 x  6  0
b. 5 x 2  21x  18
c. x 2  10 x  16  0
d. 2 x 2  5 x  7
5) State the value of the discriminant and then determine the number of real solutions of the
equation.
a. 2 x 2  5 x  20  0
6) Graph y  2 x
x
y
-2
-1
0
1
2
b. y  x 2  9 x  21
c. y  0.2 x 2  1.5x  2.9
1
7) Graph y   
3
x
y
-2
-1
0
1
2
x
Probability and the Counting Principle:
1) How do you find the probability of an event (formula)?
2) What are the two types of compound probabilities and how do you find each one?
3) What is the counting principle and how do you find the answer?
4) How do you draw a tree diagram?
Examples:
1) What is the probability of rolling a number greater than 4 on a 6 sided die?
2) What is the probability of picking a red king, putting it back, and then picking an ace?
3) What is the probability of picking a club and a red queen without replacement?
4) What is the probability of rolling an odd number on a die or rolling a 5?
5) How many different sandwiches with one meat and one cheese can you make if you have 3
different meats and 4 different cheeses to choose from? AND draw a tree diagram.
.