Download California Algebra 1 Unit 2 - Math Tutor 6-8

Algebra 1 Unit 2
1.
Students will be able to solve equations with variables on both sides of the
equation. (Section 2.3)
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1 – 14
2.
Students will be able to identify the hypothesis and conclusion in conditional
statements and determine if statements are true or false.
Worksheet 2
1 - 14
3.
Students will be able to translate sentences to algebraic equations and then solve.
Worksheet 3
1 - 10
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Quiz 1
4.
Students will be able to solve word problems about consecutive integers and
perimeter. (Section 2.5)
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1–8
5.
Students will be able to solve word problems that involve comparisons involving 2
or more items.
Worksheet 5
1 – 11
6.
Students will be able to solve inequalities. (Section 3.1, 3.2, 3.4)
Worksheet 6
1 – 26
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1 – 35 odd, 44 – 49
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Quiz 2
Review
Worksheet
Algebra 1 Unit 2
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Worksheet 2
Definition:
A conditional statement in math is a statement in the if-then form.
Example:
Definition:
If
x = 4,
then
2x = 8.
The “if” part is called the hypothesis
The “then” part is called the conclusion
Example:
Fact:
hypothesis:
conclusion:
x=4
2x = 8
Some conditional statements are true, and some are false.
In problems 1 – 4 tell whether the conditional statement is true or false.
1.
If x + 3 = 5, then x = 2.
2.
If 2x + 6 = x – 8, then x = – 14.
3.
If 3(x + 5) = 18, then 3x + 5 = 18.
4.
If 5 + 3(x + 1) = 12, then 8(x + 1) = 12.
In problems 5 – 10 state a) the hypothesis b) the conclusion
x
5.
If
= 6, then x = 18.
3
6.
If 4x – 20 = 0,
7.
If x = 12, then x2 = 144.
Algebra 1 Unit 2
then x = 5.
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8.
If x = –7, then x2 = 49.
9.
If k = –7
10.
If
then
k = 7.
1
(6x – 10) = 12, then 3x – 5 = 12.
2
Solve:
11.
4 5x  7  6x  + 2 = 2(x – 6)
13.
2 – 3x = 5 2(x  3)  x
Identify at which step the error occurred in solving the following problem:
6(x – 4) = -4(x + 1)
Step 1
6x – 24 = -4x – 4
Step 2
2x –24 =
-4
Step 3
2x = 20
Step 4
x = 10
A.
14.
12.
Step 1
B.
Step 2
C.
Step 3
D.
Step 4
Jordan solved the equation as shown.
3(x – 5) = 48
Step 1
3x – 15 = 48
Step 2
3x = 63
Step 3
x = 21
What property did he use in Step 1?
A. the multiplicative inverse property
B. the additive inverse property
C. the distributive property
Algebra 1 Unit 2
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Worksheet 3
Write an algebraic word problem for the following and then solve.
1.
The cost of renting a jet ski is $40 per day plus $50 per hour of use. How many
hours was a jet ski rented if the total cost was $390?
2.
When an alligator is born it is about 8 inches long. Each year they grow about 12
inches. Determine how old an alligator is that is 116 inches long.
3.
Membership at the Healthy You Gym is a $40 initial fee and $5 a visit. If
Sanjaya’s bill was $105, how many times had he visited the gym?
4.
Membership to a video game club is $50 a year and $3 per game rented. At the
end of the year Harvey had spent $296. How many games had he rented?
5.
Danielle wants to paint a ceramic planter. The total price is the cost of the
planter plus an hourly painting rate of $6. Determine how many hours Danielle
painted if she spent $9 on the planter and her total bill was $33.
Algebra 1 Unit 2
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6.
Jackson Intermediate School is doing a fund raiser selling magazine subscriptions.
The magazine publisher will pay the school a starting bonus of $500 and then $4
for each magazine subscription sold. At the end of the fund raiser the school is
paid a total of $1360. How many subscriptions did they sell?
7.
The lengths of the sides of a triangle are x, 2x + 1, 5x + 4 inches. If the
perimeter is 53 inches, what is the value of x ?
x+6
8.
The perimeter of the quadrilateral shown is 45 inches.
Find the value of x .
2x – 1
5x + 4
4x
9.
The sides of a square are all the same length. If the perimeter
3x + 2
of the square shown below is 56 cm., find the value of x.
3x + 2
3x + 2
3x + 2
10.
The length of a rectangle is 50 cm. longer than the width. If the perimeter of
the rectangle is 220 cm., find the width and length.
x + 50
x
Algebra 1 Unit 2
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Worksheet 5
Solve the following word problems by writing an equation and then solving algebraically.
1.
Alison has a piece of board 70 inches long. She cuts it into three pieces. The
longest piece is twice the length of the middle-sized piece, and the shortest piece
is 10 inches shorter than the middle-sized piece. Find the length of the longest
piece. (Let x = length of the middle-sized piece)
2.
During the 2007 baseball season, Wade was up to bat 10 more times than
his teammate Dwight. Dwight batted 17 fewer times than another
teammate, Ellis. The three players were up to bat a total of
1650 times. How many times did Ellis come to bat?
3.
There are a total of 20 lions, tigers and bears. If the number of tigers is 2 more
than the number of lions and the number of bears is 1 more than the
number of tigers, find the number of each.
4.
Debbie is one year older than Dave. James is twice as old as Dave. Joelle is
twice as old as Debbie. Altogether their ages total 33. Find each person’s age.
(Let x = Dave’s age)
Algebra 1 Unit 2
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5.
Tom performed a total of 100 hours of community service. He served at three
charities – Salvation Army, Red Cross and Rescue Mission. The number of hours
he served at the Red Cross was 19 hours more than at the Salvation Army.
The number of hours he served at the Rescue Mission was 8 hours more than
what he served at the Red Cross. Find the number of hours he volunteered at
each charity.
6.
Rainbo Bread Company delivered a total of 180 loaves of bread to three markets.
Savemart received 12 more loaves than Vons. Ralphs received 6 more loaves than
Savemart. Find the number of loaves delivered to each market.
7.
Hungry Bear Cookies baked a total of 98 cookies of three kinds – chocolate chip,
oatmeal raisin, and peanut butter. The number of oatmeal raisin was twice the
number of peanut butter. The number of chocolate chip was 3 more than the
number of oatmeal. Find the number of cookies of each type.
8.
State the hypothesis and conclusion of:
Algebra 1 Unit 2
If x = 7, then 9x + 1 = 64
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Worksheet 6
Solve each inequality and graph.
3.
x
<8
4
6.
5 – 3x >-10
9.
9x + 18 < 0
1.
x + 5 > -3
2.
2> 6+x
4.
x – 6 + 10 > -8
5.
–
7.
72 > 6x + 2x
8.
–(6x + 3) < 27
10.
-3(x – 3) > 5 – 2x
11.
5x – 2(x + 1) < 28 + x
12.
7 – 3(x + 8) > 19
13.
3
x>0
7
Algebra 1 Unit 2
2
x < 24
3
14.
– (9 – x) > 0
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Select the correct multiple choice response:
15.
Which of the following is the graph of -2 < x ?
A.
B.
–2
0
2
4
6
8
C.
0
2
4
0
2
4
6
–2
8
2
0
4
A. 4 £ x
B. 4 < x
0
C. 4 ³ x
2
4
D. 4 > x
Which of the following is the graph of 20 < x ?
A.
B.
–20 –10
0
10
20 30
C.
–20 –10
0
10
20 30
D.
–20 –10
18.
8
6
Which inequality below is represented by the graph
–2
17.
8
6
D.
–2
16.
–2
0
10
20 30
0
–20 –10
Which of the following is equivalent to
A.
x < -12
B.
x > -12
C.
-12 > x
x < 12
19.
Which number is in the solution set of
A.
0
B.
-2
C.
10
20 30
?
D.
x > 12
3x + 8 < -1
-3
D.
-4
20.
Which number is in the solution set of
2 – 4x < -6
A.
-2
B.
-1
C.
0
D.
2
21.
Solve:
-23 < 5 – 4(x – 2)
A.
x > -21
B.
x<9
D.
x < -21
Algebra 1 Unit 2
C.
x>9
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6
8
22.
In which step did the error occur in the following?
12 > 2x + 18
Step 1
-6 > 2x
Step 2
-3 > x
Step 3
x > -3
A. Step 1
B. Step 2
C. Step 3
D. no error was made
23.
Which of the following are correct steps to use in solving the inequality
-2x > -16
A.
Add 2 to both sides and leave the sign >
B.
Divide both sides by -2 and leave the sign >
C.
Divide both sides by -2 and reverse the sign to <
D.
Multiply both sides by -2 and reverse the sign to <
24.
Which inequality is equivalent to:
A. 9x < -18
B. 9x > -18
25.
Which one of the following are correct steps to find the solution of the inequality
x
—
> 18
6
A. Divide both sides by -6 and leave the sign >
B. Divide both sides by -6 and reverse the sign to <
C. Multiply both sides by -6 and leave the sign >
D. Multiply both sides by -6 and reverse the sign to <
26.
Which one of the following are correct steps to find the solution of the inequality
3
x < -12
4
4
A. Multiply both sides by
and leave the sign <
3
4
B. Multiply both sides by
and reverse the sign to >
3
3
C. Multiply both sides by
and leave the sign <
4
3
D. Multiply both sides by
and reverse the sign to >
4
Algebra 1 Unit 2
9x – 5 < -23
C. 9x < -28
D. 9x > -28
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Review
Solve the following equations:
1.
12x – 36 = 3x
2.
7x + 23 = 3x – 29
3.
4 + 4(x – 5) = 12x
Solve the following inequalities:
4.
8 – 5x < -17
5. 2y – 3 < 3y
7.
10 – 2(x + 6) > 2
8.
6.
8x – x + 2 < 4x – (3 – 2x)
5
x < -1
8
Write an equation for each problem below and then solve it.
9.
The lengths of the sides of a triangle are 2x, x + 4, and 13 inches. If the
perimeter of the triangle is 35 inches, what is the value of x?
10.
The cost to hire an electrician is $50 plus $65 per hour. How many hours
did the electrician work if his bill was $505?
11.
A piece of string that is 132 inches long is cut into 3 pieces. The second piece of
string is twice as long as the first piece. The third piece of string is three times
as long as the first piece. Find the length of the longest piece of string.
Algebra 1 Unit 2
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12.
Three consecutive odd integers have a sum of 99. Find the three integers.
13.
A bakery makes three flavors of bagels – strawberry, cinnamon-raisin, and
blueberry. This morning they made a total of 52 bagels. They made two more
cinnamon-raisin than strawberry. The number of blueberry is 9 more than the
number of cinnamon-raisin. How many of each flavor did they make?
State the hypothesis and conclusion in problems 14 and 15.
14.
If 2x + 8 = 20, then x = 6.
15.
If x = 5, then 7x – 1 = 34.
Select the correct multiple choice response:
16.
Identify at which step the error occurred in solving the equation below:
6(x + 4) – 2 = 4x
A.
17.
Step 1
Step 2
Step 3
Step 4
6x + 24 – 2 = 4x
6x + 22 = 4x
2x + 22 = 0
x = 11
Step 1
B.
Which is equivalent to
A.
C.
21x – 28 = 12x + 1
15x – 22 = 12x + 1
Algebra 1 Unit 2
Step 2
C.
Step 3
D.
Step 4
2 + 5(3x – 4) = 12x + 1
B.
D.
15x – 18 = 12x + 1
21x – 4 = 12x + 1
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18.
Identify at which step the error occurred in solving the equation below:
34(x  2)  10 = 14
A.
19.
20.
12(x – 2) – 10
12x – 24 – 10
12x – 34
12x
x
Step 1
B.
Step 2
= 14
= 14
= 14
= 48
= 4
C.
Step 3
D.
Step 4
The perimeter of the rectangle shown is 80 inches. Which equation could be
used to represent this?
x + 10
A.
(x) + (x + 10) = 80
B.
x(x + 10) = 80
C.
(x) + (x + 10) + (x) + (x + 10) = 80
D.
x + 10 = 80
x
The sum of 3 consecutive integers is 45. Which equation represents this?
A.
(x) + (x) + (x) = 45
B.
(x) + (x + 1) + (x + 2) = 45
C.
21.
Step 1
Step 2
Step 3
Step 4
Step 5
(x) + (x + 2) + (x + 4) = 45
D.
(x) + (x + 1) + (x + 3) = 45
Jordan is going bowling. He must rent shoes for $3 and then pay $5 for each
game bowled. Which equation represents this if ‘g’ represents the number of
games bowled and ‘C’ represents cost.
A.
C = 3g + 5g
B.
C = 3g + 5
C.
C = 3 + 5g
D.
C=8+g
Algebra 1 Unit 2
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22.
The equation
Step 1
Step 2
Step 3
3(x – 5) =
3x – 15 =
3x
=
x
=
60 is solved as follows:
60
75
25
What property was used to go from step 1 to step 2?
23.
A.
The multiplicative inverse property
B.
The additive inverse property
C.
The distributive property
The equation
Step 1
Step 2
Step 3
5x + 10 + 5 =
5x + 15 =
5x
=
x
=
40 is solved as follows:
40
25
5
What property was used to go from step 2 to step 3?
24.
A.
The multiplicative inverse property
B.
The additive inverse property
C.
The distributive property
Which of the following is the graph of -2 > x ?
A.
B.
–2
0
2
4
6
8
C.
0
2
4
6
8
D.
–2
25.
–2
0
2
4
6
–2
8
0
2
4
6
8
What is the conclusion of the statement in the box?
If x = 4, then x2 + 2x = 24
A.
x=4
Algebra 1 Unit 2
B.
x2 + 2x
C.
= 24
D.
x2 + 2x = 24
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