Download CA ALG 1 Standard 04

CA ALG 1 Standard 4
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Fill in the missing justifications.
Procedure
Justification
Definition of subtraction
?
?
?
Simplify.
Definition of subtraction
____
2.
____
3.
____
4.
____
5.
____
6.
a. Distributive Property; Associative Property; Commutative Property
b. Associative Property; Commutative Property; Distributive Property
c. Commutative Property; Distributive Property; Associative Property
d. Commutative Property; Associative Property; Distributive Property
Simplify.
5(5a + 4)
a. 25a – 20
c. 10a + 9
b. 25a + 4
d. 25a + 20
Simplify.
9(4t + 6) + 3t
a. 33t + 54
c. 39t – 54
b. 39t + 54
d. 39t + 6
Simplify.
7(x + 7) – 6x
a. x + 49
c. x – 49
b. 13x + 49
d. x + 7
Solve –2z + 3 + 7z = –12.
a. z = –3
c. z = 1
b. z = –15
d. z = –1.8
Solve 5h + 15 – 3h = 32.
a. h = 16
c. h = 8 1
2
b. h = 23 1
2
____
____
____
7. Solve
.
a.
b.
8. Solve
.
a.
=4
b.
= –11
9. Solve 3(a + 5) + 6 = 27.
a. a = 5
b. a = –2
d. h = 2 1
8
c.
d.
c.
d.
= –1
=5
c. a = –5
d. a = 2
____ 10. Simplify and solve.
a.
c.
b.
d.
____ 11. A family travels to Bryce Canyon for three days. On the first day, they drove 150 miles. On the second day,
they drove 190 miles. What is the least number of miles they drove on the third day if their average number of
miles per day was at least 180?
a. 540 mi
c. 201 mi
b. 180 mi
d. 200 mi
____ 12. Sara needs to take a taxi to get to the movies. The taxi charges $4.00 for the first mile, and then $2.75 for each
mile after that. If the total charge is $20.50, then how far was Sara’s taxi ride to the movie?
a. 6 miles
c. 5.1 miles
b. 7 miles
d. 7.5 miles
____ 13.
a.
c.
b.
d.
____ 14.
a. x > 5.6
b. x > –3
____ 15. Solve and graph.
n – 8  3n  –4
a. n  –3
–10 –8
c. x > 0.4
d. x > 12
–6
–4
–2
0
2
4
6
8
10
–6
–4
–2
0
2
4
6
8
10
–6
–4
–2
0
2
4
6
8
10
–6
–4
–2
0
2
4
6
8
10
b. n  –3
–10 –8
c. n  1
–10 –8
d. n  1
–10 –8
____ 16. Solve  3 a – 2  3 a  –5 and graph.
1
2
a. a  3
–10 –8
–6
–4
–2
0
2
4
6
8
10
–6
–4
–2
0
2
4
6
8
10
b. a  3
–10 –8
c. a  7
–10 –8
–6
–4
–2
0
2
4
6
8
10
–6
–4
–2
0
2
4
6
8
10
d. a  7
–10 –8
Numeric Response
17. A volleyball team scored 14 more points in its first game than in its third game. In the second game, the team
scored 28 points. The total number of points scored was less than 80. What is the greatest number of points
the team could have scored in its third game?
Short Answer
18. Mr. Johnson bought a new television. He paid 6% sales tax on his purchase. After paying a portion of the bill
with a $25 gift certificate, he still owed $187 for the purchase. What was the original price of the television
without sales tax? Show all work.
CA ALG 1 Standard 4
Answer Section
MULTIPLE CHOICE
1. ANS: D
Procedure
Justification
Definition of subtraction
Commutative Property
Associative Property
Distributive Property
Simplify.
Definition of subtraction
Feedback
A
B
C
D
What is the difference between the Commutative Property and the Distributive
Property?
The Associative Property involves grouping of numbers. What does the Commutative
Property state?
What is the difference between the Associative Property and the Distributive Property?
Correct!
PTS: 1
DIF: Advanced
OBJ: Simplifying Polynomials
NAT: 12.5.2.e
STA: 1A4.0
TOP: Simplifying Algebraic Expressions
2. ANS: D
Use the Distributive Property to simplify. Distribute the constant term to both terms inside the parentheses.
Feedback
A
B
C
D
Check the sign of the second term.
Distribute the constant term to both terms inside the parentheses.
Use the Distributive Property.
Correct!
PTS: 1
DIF: Average
OBJ: Simplifying Polynomials by Using the Distributive Property
STA: 1A4.0
TOP: Simplifying Polynomials
KEY: polynomial | simplify | Distributive Property
3. ANS: B
Example:
Simplify 9(10a – 7) + 5a.
90a – 63 + 5a
Multiply.
(90a + 5a) – 63
Group like terms.
95a – 63
Add or subtract the coefficients.
Feedback
A
After grouping like terms did you add and subtract the coefficients correctly?
B
C
D
Correct!
Did you use the proper sign for the number that has no variable?
Did you multiply through for all the terms in the parentheses?
PTS: 1
DIF: Average
OBJ: Using the Distributive Property to Simplify
NAT: 8.1.5.e
STA: 1A4.0
TOP: Simplifying Algebraic Expressions
KEY: like terms | simplify | combine | algebraic expression
4. ANS: A
Example:
Simplify 9(10a – 7) + 5a.
90a – 63 + 5a
Distributive Property
90a + 5a – 63
Commutative Property
(90a + 5a) – 63
Associative Property
95a – 63
Combine like terms.
Feedback
A
B
C
D
Correct!
Check that you combined like terms correctly.
Check your signs.
Check that you multiplied both terms inside the parentheses when you used the
Distributive Property.
PTS: 1
DIF: Average
OBJ: Using the Distributive Property to Simplify
NAT: 8.1.5.e
STA: 1A4.0
TOP: Simplifying Algebraic Expressions
KEY: like terms | simplify | combine | algebraic expression
5. ANS: A
To solve this equation, combine like terms and use the inverse operation to isolate the variable from the
addition/subtraction. Then use division as the inverse operation to isolate the variable from the multiplication.
Feedback
A
B
C
D
Correct!
How do you combine like terms?
Did you use inverse operations to solve?
How do you solve multi-step equations?
PTS: 1
DIF: Basic
OBJ: Solving Equations That Contain Like Terms
NAT: 8.5.4.a
STA: 1A4.0
TOP: Solving Multi-Step Equations
KEY: equation | like terms | solving
6. ANS: C
To solve this equation, combine like terms and then follow the order of operations in reverse. First, add or
subtract to isolate the term with the variable. Then, divide to isolate the variable.
Feedback
A
B
C
D
First, combine like terms. Then, add or subtract to isolate the term with the variable.
Finally, divide to isolate the variable.
Use inverse operations to solve.
Correct!
Combine like terms first.
PTS:
NAT:
KEY:
7. ANS:
1
DIF: Average
OBJ: Combining Like Terms to Solve Equations
8.5.4.a
STA: 1A4.0
TOP: Solving Multi-Step Equations
addition | combine | division | like terms | multiplication | solving | subtraction | multi-step equations
A
Use the Commutative Property of Addition.
Combine like terms.
Since 10 is added to 17a, subtract 10 from both sides to undo
the addition.
Since a is multiplied by 17, divide both sides by 17 to undo the
multiplication.
Feedback
A
B
C
D
Correct!
Check your signs.
Combine like terms, and then solve.
Combine like terms, and then solve.
PTS: 1
NAT: 12.5.3.c
8. ANS: C
DIF: Average
STA: 1A4.0
OBJ: Simplifying Before Solving Equations
TOP: Solving Multi-Step Equations
Distribute –4.
Add
to both sides.
Divide by
.
Feedback
A
B
C
D
Distribute over all the terms inside the parentheses.
Distribute before solving the equation.
Correct!
To isolate the variable after distributing, add the opposite of the constant term to both
sides of the equation.
PTS: 1
NAT: 12.5.4.a
9. ANS: D
3(a + 5) + 6 = 27
3a + 15 + 6 = 27
3a + (15 + 6) = 27
3a + 21 = 27
3a+ 21 = 27
– 21– 21
3a= 6
DIF: Average
STA: 1A4.0
OBJ: Simplifying Using the Distributive Property
TOP: Solving Multi-Step Equations
Distributive Property
Associative Property of Addition
Combine like terms.
Addition or Subtraction Property of Equality
Additive Inverse Property/Addition or subtraction
Division Property of Equality
a=2
Division
Feedback
A
B
C
D
Use the Distributive Property first.
Check the signs.
First, multiply each term inside the parentheses by the factor that is outside the
parentheses. Then, combine like terms and solve.
Correct!
PTS: 1
NAT: 8.5.4.a
10. ANS: B
3(9
8x
27
24x
DIF: Average
STA: 1A4.0
4x)
12x
+
+
8(3x
24x
OBJ: Using the Distributive Property to Solve Equations
TOP: Solving Multi-Step Equations
+
+
4)
32
=
=
59
12x
=
59
12x
=
12x
=
=
x
=
11
11 Distributive Property
Combine Coefficients.
11
11 Subtract 59 from both
sides.
–48 Simplify.
Divide both sides by 12.
4 Simplify.
Feedback
A
B
C
D
After removing the parenthesis and combining like terms, isolate the variable x.
Correct!
A negative number minus a negative number is the sum of two negative numbers.
First use the distributive property to remove the parentheses.
PTS: 1
DIF: Advanced
OBJ: Using the Distributive Property to Solve Equations
NAT: 8.5.4.a
STA: 1A4.0
TOP: Solving Multi-Step Equations
KEY: multi-step | solve
11. ANS: D
Let d represent the distance the family drove on the third day. The average number of miles is the sum of the
miles of each day divided by 3.
( 150
plus
190
plus
d)
divided
3
is at
180
by
least
( 150
+
190
+
d)
÷
3
180
Since
is divided by 3, multiply both sides by 3
to undo the division.
Combine like terms.
Since 340 is added to d, subtract 340 from both sides to undo
the addition.
The least number of miles the family drove on the third day is 200.
Feedback
A
B
C
D
First, set up an inequality where the average number of miles is the sum of the miles of
each day divided by 3. Then, solve the inequality.
First, set up an inequality where the average number of miles is the sum of the miles of
each day divided by 3. Then, solve the inequality.
First, set up an inequality where the average number of miles is the sum of the miles of
each day divided by 3. Then, solve the inequality.
Correct!
PTS: 1
DIF: Average
OBJ: Application NAT: 12.5.3.c
STA: 1A4.0
TOP: Solving Two-Step and Multi-Step Inequalities
KEY: inequality
12. ANS: B
Let d be the distance (in miles) to the movies, then
is the number of miles after the first mile. So a
formula for the total charge could be
first mile
charge
4.00
+
+
rate after first
mile
2.75
=
total charge
=
20.50
2.75
2.75
=
=
Subtract 4.00
from each side.
20.50 4.00
16.5
Divide both sides
by 2.75.
=
d
d
=
6
=
=
6+1
7
Add 1 to both
sides.
Feedback
A
B
C
D
Add one for the first mile.
Correct!
The mileage rate is the charge for each mile after the first mile.
Subtract the charge for the first mile.
PTS: 1
NAT: 12.5.3.b
13. ANS: C
DIF: Average
STA: 1A4.0
OBJ: Problem-Solving Application
TOP: Solving Two-Step and Multi-Step Equations
Use the Distributive Property.
Since 48 is subtracted from 6s, add 8 to both sides to undo the
subtraction.
Simplify.
Since 6 is multiplied by s, divide 6 from both sides to undo the
multiplication.
Simplify.
Feedback
A
B
C
D
Check your division.
Distribute before solving the equation.
Correct!
After distributing, use inverse operations to isolate the variable.
PTS: 1
STA: 1A4.0
14. ANS: A
DIF: Average
OBJ: Solving Multi-Step Inequalities
TOP: Solve Multi-Step Inequalities
KEY: inequalities | multistep
Evaluate powers.
–4____
–4
Combine like terms and simplify.
Since 4 is added to 5x, subtract 4 from both sides to undo the
addition.
Since x is multiplied by 5, divide both sides by 5 to undo the
multiplication.
Feedback
A
B
C
D
Correct!
Check your signs and arithmetic.
Check that you simplified powers correctly.
Check that you simplified powers correctly.
PTS: 1
DIF: Average
OBJ: Solving Multi-Step Inequalities
STA: 1A4.0
TOP: Solve Multi-Step Inequalities
KEY: multistep inequalities
15. ANS: C
Example:
Solve the inequality
and graph the solutions.
Combine like terms.
Subtract 1 from both sides to undo addition.
Divide both sides by
to isolate z. When you divide by a negative
number, reverse the inequality.
–3
–2
–1
0
1
2
3
4
5
6
7
8
9

Use a closed circle when the value is included in the graph, such as with or Use an open circle when
the value is not included, such as with > or <.
Feedback
A
B
C
D
What inverse operations are needed to isolate the variable?
Be careful with your calculations when using inverse operations to isolate the variable.
Correct!
If you divide both sides of the inequality by a negative number, reverse the inequality
sign. If you divide by a positive number, do not reverse the sign.
PTS: 1
DIF: Average
NAT: 8.5.4.a
STA: 1A4.0
KEY: multi-step inequality | solving
16. ANS: A
Example:
Solve the inequality
OBJ: Solving Two-Step Inequalities
TOP: Solving Two-Step Inequalities
and graph the solutions.
Combine like terms. Simplify fractions.
Subtract 1 from both sides to undo addition.
Divide both sides by 2 to isolate z. If you divide by a negative
number, reverse the inequality.
–9
–8
–7
–6
–5
–4
–3
–2
–1
0
1
2
3

Use a closed circle when the value is included in the graph, such as with or Use an open circle when
the value is not included, such as with > or <.
Feedback
A
B
C
D
Correct!
If you divide both sides of the inequality by a negative number, reverse the inequality
sign. If you divide by a positive number, do not reverse the sign.
What inverse operations are needed to isolate the variable?
Be careful with your calculations when using inverse operations to isolate the variable.
PTS: 1
DIF: Average
NAT: 8.5.4.a
STA: 1A4.0
KEY: multi-step inequality | solving
NUMERIC RESPONSE
OBJ: Solving Inequalities That Contain Fractions
TOP: Solving Two-Step Inequalities
17. ANS: 18
PTS: 1
DIF: Advanced
OBJ: Application NAT: 12.5.4.c
STA: 1A4.0
TOP: Solving Two-Step and Multi-Step Inequalities
KEY: inequality | application
SHORT ANSWER
18. ANS:
b = $200
Let b represent the original bill before the gift certificate.
bill + sales tax – gift certificate = amount paid
Scoring Rubric:
4
The solution is correct, and all of the work is shown as above.
or
A different logical method is used to find the correct solution.
3
The solution is correct, but not all of the work is shown.
2
The solution is incorrect, but the work shows understanding of the concept.
1
The solution is incorrect, and the work shows no understanding of the concept.
PTS: 1
STA: 1A4.0
DIF: Average
OBJ: Application
TOP: Solving Multi-Step Equations
NAT: 8.5.4.a
KEY: multi-step equation | solving