Download Algebra 1 Study Guide Answer Section

Algebra 1 Study Guide
Multiple Choice
Identify the choice that best completes the statement or answers the question.
What is each expression written using each base only once?
1)
a
b
c
d
What is the simplified form of each expression?
2)
a
b
c
d
Find the simplified form of the expression. Give your answer in scientific notation.
3)
a
1.5  1012
b
5.6  1012
c
1.5  1029
d
What is the simplified form of the expression?
4)
a
b
c
d
a
b
c
d
5)
What is the simplified form of each expression?
6)
a
b
c
d
What is the simplified form of the expression?
7)
a
b
What is the sum or difference?
c
d
5.6  1029
8) 3x8 – 7x8
a
–4x16
b
–21x8
c
–4x8
c
2n3 + 6n + 8
n2 + 5n + 4
d
10x8
Simplify the product.
9) 2n(n2 + 3n + 4)
a
2n3 + 6n2 + 8n
b
2n3 + 3n + 4
d
Factor the polynomial.
10) 42w10 + 24w6
a
w6(42w4 + 24)
b
6w6(7w4 + 4)
c
d
6(7w10 + 4w6)
6w5(7w5 + 4w)
What is the factored form of the expression?
11) 15g3 + 20g2 – 18g – 24
a
(5g2 + 4)(3g – 6)
b
(5g2 – 6)(3g + 4)
c
d
(5g2 + 6)(3g – 4)
(5g2 – 4)(3g + 6)
What is the factored form of the expression? Factor completely.
12) 6x4 – 9x3 – 36x2 + 54x
a
b
3x(x2 – 6)(2x – 3)
3x(x2 + 6)(2x + 3)
c
d
6x(x2 – 6)(2x – 3)
6x(x2 + 6)(2x + 3)
What are the coordinates of the vertex of the graph? Is it a maximum or minimum?
13)
4
y
3
2
1
–4
–3
–2
–1
1
2
3
4
x
–1
–2
–3
–4
a
b
(2, 0); minimum
(0, 2); minimum
c
d
(2, 0); maximum
(0, 2); maximum
What is the solution of the system? Use substitution.
14) 3x + 2y = 7
y = –3x + 11
a
(6, –3)
b
(6, –7)
c
d
(5, –4)
d
(–9, –9)
What is the solution of the system? Use elimination.
15) 3x – 4y = 9
–3x + 2y = 9
a
(3, 9)
b
(–27, –9)
c
(–3, –6)
What is the solution of the system? Use a graph.
16) y = x + 5
y = –5x – 1
a
c
y
–4
y
4
4
2
2
–2
2
4
x
–4
–2
–2
d
17)
4
x
y
4
(–1,
4)
2
2
2
4
x
(4, –1)
–4
–2
–2
–2
–4
–4
Graph the inequality.
2
–4
(0.67, –4.35)
4
–2
x
–2
y
–4
4
(–1.5, –2.5)
–4
b
2
a
c
y
–4
–2
4
4
2
2
O
2
4
x
–2
O
–2
–4
–4
d
y
–2
–4
–2
b
–4
y
4
2
2
2
4
x
–4
–2
O
–2
–2
–4
–4
Find the GCF of the terms of the polynomial.
18) 30x3 + 16x5
a
16x
b
2x3
c
2x5
c
–3, 9
–3, –9
d
What are the solutions of the equation?
19)
a
b
3, 9
3, –9
d
Simplify the expression.
20)
a
b
Solve the equation. Check your solution.
21)
c
4
x
2
4
x
y
4
O
2
d
x3
a
6
b
36
c
3
d
6
b
16
c
58
d
23
22)
a
40
23) Solve the equation. Then check your solution.
a
b
c
11
–1
d
9
1
24) Graph the system of equations. Then determine whether the system has no solution, one solution, or
infinitely many solutions. If the system has one solution, name it.
a
c
no solution
infinitely many
y
–6
b
–4
y
6
6
4
4
2
2
–2
2
4
6
x
–6
–4
–2
–2
–2
–4
–4
–6
–6
d
one solution; (4, 1)
–4
6
x
2
4
6
x
y
6
6
4
4
2
2
–2
4
one solution; (1, 4)
y
–6
2
2
4
6
x
–6
–4
–2
–2
–2
–4
–4
–6
–6
25) Graph the system of equations. Then determine whether the system has no solution, one solution, or
infinitely many solutions. If the system has one solution, name it.
a
c
no solution
one solution; (–2, –1)
y
–6
b
–4
y
6
6
4
4
2
2
–2
2
4
6
x
–6
–4
–2
–2
–2
–4
–4
–6
–6
one solution; (–1, –2)
d
–4
6
x
2
4
6
x
y
6
6
4
4
2
2
–2
4
infinitely many
y
–6
2
2
4
6
x
–6
–4
–2
–2
–2
–4
–4
–6
–6
26) The cost of 3 large candles and 5 small candles is $6.40. The cost of 4 large candles and 6 small candles is $7.50.
Which pair of equations can be used to determine, t, the cost of a large candle, and s, the cost of a small candle?
a
c
b
d
27) The sum of two positive integers is less than 80 and their difference is more than 10.
Write a system of inequalities to represent this situation.
a
c
b
d
28) Find the degree of the polynomial.
a
b
7
4
c
d
12
8
29) Find the degree of the polynomial.
a
b
23
15
c
d
30) Find the sum or difference.
a
b
c
d
31) Find the sum or difference.
a
b
c
d
32) Solve the equation.
a
c
b
d
33) Solve the equation.
a
c
b
d
34) Solve the equation.
14
13
a
c
b
d
35) Find the product.
a
c
b
d
36) Find the product.
a
b
c
d
37) Factor the monomial completely.
a
b
c
d
38) Factor the trinomial.
a
c
b
d
39) Solve the equation. Then check your solution.
a
c
b
d
40) The Washington family is hosting a cookout. They decide to serve chicken and pork. They determine that
they will need at most 20 pounds of meat, and they want to have at least twice as much chicken as pork.
Make a graph showing the amount of each type of meat that satisfies the requirements.
a
c
pork
pork
22
22
20
20
18
18
16
16
14
14
12
12
10
10
8
8
6
6
4
4
2
2
2
b
4
6
8 10 12 14 16 18 20 chicken
2
d
pork
22
20
20
18
18
16
16
14
14
12
12
10
10
8
8
6
6
4
4
2
2
4
6
8 10 12 14 16 18 20 chicken
6
8 10 12 14 16 18 20 chicken
4
6
8 10 12 14 16 18 20 chicken
pork
22
2
4
2
Algebra 1 Study Guide
Answer Section
MULTIPLE CHOICE
1) ANS:
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11) ANS:
OBJ:
TOP:
DOK:
12) ANS:
A
PTS: 1
DIF: L2
7-3 Multiplying Powers With the Same Base
7-3.1 To multiply powers with the same base
STA: MA.912.A.4.1
7-3 Problem 1 Multiplying Powers DOK: DOK 1
B
PTS: 1
DIF: L2
7-3 Multiplying Powers With the Same Base
7-3.1 To multiply powers with the same base
STA: MA.912.A.4.1
7-3 Problem 2 Multiplying Powers in Algebraic Expressions
DOK 1
B
PTS: 1
DIF: L2
7-3 Multiplying Powers With the Same Base
7-3.1 To multiply powers with the same base
STA: MA.912.A.4.1
7-3 Problem 3 Multiplying Numbers in Scientific Notation
DOK 1
D
PTS: 1
DIF: L2
7-4 More Multiplication Properties of Exponents
OBJ: 7-4.1 To raise a power to a power
MA.912.A.4.1
TOP: 7-4 Problem 1 Simplifying a Power Raised to a Power
DOK 1
C
PTS: 1
DIF: L3
7-4 More Multiplication Properties of Exponents
OBJ: 7-4.1 To raise a power to a power
MA.912.A.4.1
TOP: 7-4 Problem 1 Simplifying a Power Raised to a Power
DOK 1
B
PTS: 1
DIF: L2
REF: 7-5 Division Properties of Exponents
7-5.1 To divide powers with the same base
STA: MA.912.A.4.1
7-5 Problem 1 Dividing Algebraic Expressions
DOK: DOK 1
A
PTS: 1
DIF: L2
REF: 7-5 Division Properties of Exponents
7-5.2 To raise a quotient to a power
STA: MA.912.A.4.1
7-5 Problem 3 Raising a Quotient to a Power
DOK: DOK 1
C
PTS: 1
DIF: L3
REF: 8-1 Adding and Subtracting Polynomials
8-1.1 To classify, add, and subtract polynomials
STA: MA.912.A.4.2
8-1 Problem 2 Adding and Subtracting Monomials
KEY: monomial | degree of a monomial
DOK 1
A
PTS: 1
DIF: L3
REF: 8-2 Multiplying and Factoring
8-2.1 To multiply a monomial by a polynomial
STA: MA.912.A.4.2| MA.912.A.4.3
8-2 Problem 1 Multiplying a Monomial and a Trinomial KEY: polynomial | trinomial | monomial
DOK 1
B
PTS: 1
DIF: L3
REF: 8-2 Multiplying and Factoring
8-2.2 To factor a monomial from a polynomial
STA: MA.912.A.4.2| MA.912.A.4.3
8-2 Problem 3 Factoring Out a Monomial
DOK: DOK 1
B
PTS: 1
DIF: L3
REF: 8-8 Factoring by Grouping
8-8.1 To factor higher-degree polynomials by grouping
STA: MA.912.A.4.3
8-8 Problem 1 Factoring a Cubic Polynomial
KEY: factoring by grouping
DOK 1
A
PTS: 1
DIF: L3
REF: 8-8 Factoring by Grouping
13)
14)
15)
16)
17)
18)
19)
20)
21)
22)
23)
OBJ: 8-8.1 To factor higher-degree polynomials by grouping
STA: MA.912.A.4.3
TOP: 8-8 Problem 2 Factoring a Polynomial Completely
KEY: factoring by grouping
DOK: DOK 1
ANS: D
PTS: 1
DIF: L3
REF: 9-1 Quadratic Graphs and Their Properties
OBJ: 9-1.1 To graph quadratic functions of the form y = ax^2 and y = ax^2 + c
STA: MA.912.A.7.1| MA.912.A.7.6| MA.912.A.7.8
TOP: 9-1 Problem 1 Identifying a Vertex
KEY: quadratic function | parabola | maximum | minimum | vertex
DOK: DOK 1
ANS: D
PTS: 1
DIF: L3
REF: 6-2 Solving Systems Using Substitution
OBJ: 6-2.1 To solve systems of equations using substitution
STA: MA.912.A.3.14| MA.912.A.3.15
TOP: 6-2 Problem 1 Using Substitution KEY: substitution method
DOK: DOK 1
ANS: D
PTS: 1
DIF: L3
REF: 6-3 Solving Systems Using Elimination
OBJ: 6-3.1 To solve systems by adding or subtracting to eliminate a variable
STA: MA.912.A.3.14| MA.912.A.3.15
TOP: 6-3 Problem 1 Solving a System by Adding Equations
KEY: elimination method
DOK: DOK 1
ANS: D
PTS: 1
DIF: L3
REF: 6-1 Solving Systems By Graphing
OBJ: 6-1.1 To solve systems of equations by graphing
STA: MA.912.A.3.13| MA.912.A.3.14| MA.912.A.3.15
TOP: 6-1 Problem 1 Solving a System of Equations by Graphing
KEY: consistent | independent | solution of a system of linear equations | system of linear equations
DOK: DOK 1
ANS: C
PTS: 1
DIF: L3
REF: 6-5 Linear Inequalities
OBJ: 6-5.1 To graph linear inequalities in two variables
STA: MA.912.A.3.5| MA.912.A.3.12
TOP: 6-5 Problem 2 Graphing an Inequality in Two Variables KEY: linear inequality
DOK: DOK 1
ANS: B
PTS: 1
DIF: L2
REF: 8-2 Multiplying and Factoring
OBJ: 8-2.2 To factor a monomial from a polynomial
STA: MA.912.A.4.2| MA.912.A.4.3
TOP: 8-2 Problem 2 Finding the Greatest Common Factor
DOK: DOK 1
ANS: C
PTS: 1
DIF: L3
REF: 9-4 Factoring to Solve Quadratic Equations
OBJ: 9-4.1 To solve quadratic equations by factoring
STA: MA.912.A.1.8| MA.912.A.7.2| MA.912.A.7.8
TOP: 9-4 Problem 2 Solving by Factoring
KEY: Zero-Product Property
DOK: DOK 2
ANS: B
PTS: 1
DIF: L3
REF: 10-3 Operations With Radical Expressions
OBJ: 10-3.1 To simplify sums and differences of radical expressions
STA: MA.912.A.6.2
TOP: 10-3 Problem 1 Combining Like Radicals
KEY: like radicals DOK: DOK 1
ANS: B
PTS: 1
DIF: L3
REF: 10-4 Solving Radical Equations
OBJ: 10-4.1 To solve equations containing radicals
STA: MA.912.A.6.2
TOP: 10-4 Problem 1 Solving by Isolating the Radical
KEY: radical equation
DOK: DOK 1
ANS: C
PTS: 1
DIF: L3
REF: 10-4 Solving Radical Equations
OBJ: 10-4.1 To solve equations containing radicals
STA: MA.912.A.6.2
TOP: 10-4 Problem 1 Solving by Isolating the Radical
KEY: radical equation
DOK: DOK 1
ANS: D
To solve an equation with more than one operation, undo operations by working backward.
Feedback
A
B
C
D
How did you undo the operation in the first step?
Be careful with sign rules.
What operation did you try to undo first?
Correct!
PTS: 1
DIF: Average
REF: Lesson 2-3
OBJ: 2-3.1 Solve equations by involving more than one operation.
STA: MA.912.A.3.1 | MA.912.A.3.5 | MA.912.A.10.3
TOP: Solve equations involving more than one operation
KEY: Solve Equations | Equations
24) ANS: D
Graph each line. The point where the two lines intersect is the solution. Check the solution by replacing x and y in
the original equations with the values in the ordered pair.
Feedback
A
B
C
D
Did you graph the second line correctly?
Remember that the x-coordinate comes first in an ordered pair.
Graph both lines.
Correct!
PTS: 1
DIF: Average
REF: Lesson 6-1
OBJ: 6-1.2 Solve systems of equations by graphing.
STA: MA.912.A.3.13 | MA.912.A.3.14 | MA.912.A.3.15 | MA.912.A.10.2 | MA.912.A.10.3
TOP: Solve systems of equations by graphing
KEY: System of Equations | Graphing
25) ANS: B
Graph each line. The point where the two lines intersect is the solution. Check the solution by replacing x and y in
the original equations with the values in the ordered pair.
Feedback
A
B
C
D
Did you graph the second line correctly?
Correct!
Remember that the x-coordinate comes first in an ordered pair.
Graph both lines.
PTS: 1
DIF: Average
REF: Lesson 6-1
OBJ: 6-1.2 Solve systems of equations by graphing.
STA: MA.912.A.3.13 | MA.912.A.3.14 | MA.912.A.3.15 | MA.912.A.10.2 | MA.912.A.10.3
TOP: Solve systems of equations by graphing
KEY: System of Equations | Graphing
26) ANS: A
Write a system of equations for the situation.
Feedback
A
B
C
D
Correct!
Check the first equation.
Check the second equation.
Check the coefficients of t and s in the first equation.
PTS: 1
DIF: Basic
REF: Lesson 6-4
OBJ: 6-4.2 Solve real-world problems involving systems of equations.
STA: MA.912.A.3.14 | MA.912.A.3.15
TOP: Solve real-world problems involving systems of equations.
KEY: System of Equations | Real-World Problems
27) ANS: C
Translate the words into mathematical symbols. The endpoints are not included in the inequalities.
Feedback
A
B
C
D
The endpoints are not included in the inequalities.
These inequalities do not fit the situation.
Correct!
These inequalities do not fit the situation.
PTS: 1
DIF: Average
REF: Lesson 6-8
OBJ: 6-8.2 Solve real-world problems involving systems of inequalities.
STA: MA.912.A.3.14 | MA.912.A.3.15 | MA.912.A.10.3
TOP: Solve real-world problems involving systems of inequalities
KEY: System of Inequalities | Real-World Problems
DOK: 1998 Lesson 8-5
28) ANS: A
Add the exponents of the variables only.
Feedback
A
B
C
D
Correct!
Add both exponents.
Add only the exponents.
Add the exponents of the variables.
PTS: 1
DIF: Basic
REF: Lesson 7-4
OBJ: 7-4.1 Find the degree of a polynomial.
STA: LA.910.1.6.1
TOP: Find the degree of a polynomial
KEY: Polynomials | Degree of Polynomial
29) ANS: C
Add the exponents of the variables for each monomial. The degree of the polynomial is the highest degree of any
of its monomials.
Feedback
A
B
C
D
Add exponents of each monomial, not each exponent in like variables.
Only add the exponents of the variables.
Correct!
Add the exponents of all 3 monomials.
PTS: 1
DIF: Average
REF: Lesson 7-4
OBJ: 7-4.1 Find the degree of a polynomial.
STA: LA.910.1.6.1
TOP: Find the degree of a polynomial
KEY: Polynomials | Degree of Polynomial
30) ANS: D
Group like terms together and then add like terms. The power stays the same.
Feedback
A
B
C
Be careful with your signs.
Group like terms together.
Subtract the other a.
D
Correct!
PTS: 1
DIF: Average
REF: Lesson 7-5
OBJ: 7-5.1 Add polynomials.
STA: MA.912.A.4.2
TOP: Add polynomials
KEY: Polynomials | Add Polynomials
31) ANS: D
Group like terms together. Subtract like terms, making sure you subtract negatives (add). The power stays the
same.
Feedback
A
B
C
D
Be careful with your signs.
Be careful with your signs.
Be careful with your signs.
Correct!
PTS:
STA:
KEY:
32) ANS:
1
DIF: Average
REF: Lesson 7-5
OBJ: 7-5.2 Subtract polynomials.
MA.912.A.4.2
TOP: Subtract polynomials
Polynomials | Subtract Polynomials
D
Feedback
A
B
C
D
Be careful subtracting 12 from both sides.
Subtract 10x from both sides.
Multiply the number outside the parentheses by EACH monomial inside.
Correct!
PTS:
OBJ:
TOP:
33) ANS:
Either
If
If
1
DIF: Basic
REF: Lesson 7-6
7-6.2 Solve equations involving polynomials.
Solve equations involving polynomials
C
or
.
, then
.
, then
.
Feedback
A
B
Watch your signs.
Remember, either r – 3 = 0 or r + 6 = 0.
STA: MA.912.A.4.2
KEY: Polynomials | Solve Equations
C
D
Correct!
Remember, either r – 3 = 0 or r + 6 = 0.
PTS:
OBJ:
STA:
KEY:
34) ANS:
1
DIF: Basic
REF: Lesson 8-2
8-2.2 Solve quadratic equations in the form ax^2 + bx = 0.
MA.912.A.1.8 | MA.912.A.4.3
TOP: Solve quadratic equations of the form ax^2 + bx = 0
Quadratic Equations | Solve Equations
A
Feedback
A
B
C
D
Correct!
Watch your division.
Watch your division.
Watch your division.
PTS:
OBJ:
STA:
KEY:
35) ANS:
1
DIF: Average
REF: Lesson 8-2
8-2.2 Solve quadratic equations in the form ax^2 + bx = 0.
MA.912.A.1.8 | MA.912.A.4.3
TOP: Solve quadratic equations of the form ax^2 + bx = 0
Quadratic Equations | Solve Equations
B
Feedback
A
B
C
D
Use the FOIL method.
Correct!
Use the FOIL method.
Watch your signs.
PTS:
OBJ:
TOP:
36) ANS:
1
DIF: Basic
REF: Lesson 7-7
7-7.1 Multiply two binomials by using the FOIL method. STA: MA.912.A.4.2
Multiply two binomials by using the FOIL method
KEY: Multiply Binomials | FOIL Method
A
Feedback
A
B
C
D
Correct!
Multiply each number in the binomial by each number in the polynomial, adding
exponents. Then add numbers of like powers.
Multiply each number in the binomial by each number in the polynomial, adding
exponents. Then add numbers of like powers.
Watch your signs.
PTS: 1
DIF: Average
REF: Lesson 7-7
OBJ: 7-7.2 Multiply two polynomials by using the Distributive Property.
STA: MA.912.A.4.2
TOP: Multiply two polynomials by using the Distributive Property
KEY: Multiply Polynomials | Distributive Property
37) ANS: B
The prime factors of 70 are
.
The prime factors of
are
.
The prime factors of
are
.
Thus,
is factored into
.
Feedback
A
B
C
D
How many b's are there?
Correct!
You want the prime factors.
How many a's are there?
PTS: 1
DIF: Average
REF: Lesson 8-1
OBJ: 8-1.1 Find prime factorizations of monomials.
STA: LA.910.1.6.1
TOP: Find prime factorizations of monomials
KEY: Prime Factorization | Monomials
38) ANS: C
Two variables, and , exist such that
.
and
.
Make a table to find the possible solutions.
The correct factors are 2 and –13.
Feedback
A
B
C
D
Remember, m + n = the middle number and m  n = the last number.
Watch your signs.
Correct!
Remember, m + n = the middle number and m  n = the last number.
PTS: 1
DIF: Average
REF: Lesson 8-3
OBJ: 8-3.1 Factor trinomials of the form x^2 + bx + c.
STA: MA.912.A.4.3 | MA.912.A.7.2 | MA.912.A.1.8 | MA.912.A.7.8 | MA.912.A.10.2
TOP: Factor trinomials of the form x^2 + bx + c
KEY: Factor Trinomials
39) ANS: C
Divide both sides of the inequality by the constant on the left. Remember to flip the inequality sign since you are
dividing by a negative number.
Feedback
A
Remember to flip the inequality sign since you are dividing by a negative number.
B
C
D
Use division instead of multiplication to solve this.
Correct!
Use division instead of subtraction to solve this.
PTS:
OBJ:
STA:
TOP:
40) ANS:
1
DIF: Average
REF: Lesson 5-2
5-2.2 Solve linear inequalities by using division.
MA.912.A.3.4 | MA.912.A.3.5 | MA.912.A.10.3
Solve linear inequalities by using division
A
Graph the inequalities
and
KEY: Linear Inequalities | Division
. The solution is the shaded area.
Feedback
A
B
C
D
Correct!
Did you use the correct inequality signs?
There must be at least twice as much chicken as pork. Double-check this inequality.
A dotted line means that the points on the line are not included in the solution.
PTS:
OBJ:
STA:
TOP:
KEY:
1
DIF: Average
REF: Lesson 6-8
6-8.2 Solve real-world problems involving systems of inequalities.
MA.912.A.3.14 | MA.912.A.3.15 | MA.912.A.10.3
Solve real-world problems involving systems of inequalities
System of Inequalities | Real-World Problems
DOK: 1998 Lesson 8-5