Download Algebra 1 Unit 1 1. Students will be able to add, subtract, multiply

Algebra 1 Unit 1
1.
Students will be able to add, subtract, multiply and divide positive and negative
numbers and evaluate expressions using positive and negative numbers.
They will be able to give a counterexample to show an assertion is false.
(Section 1.4, 1.5, 1.6)
Worksheet 1
1 - 34
2.
Students will be able to use proper order of operations to simplify an expression
using positive and negative numbers. (Section 1.3)
Worksheet 2
1 - 29
3.
Students will be able to use the distributive property and combine similar terms.
(Section 1.7)
Worksheet 3
1 - 40
(optional)Page 48 - 50
15, 20, 25, 27- 29, 39 – 43, 55 – 57, 81 – 86, 90 – 97
*
Quiz 1
4.
Students will be able to translate words into variable expressions. (Section 1.1)
Worksheet 4
1 - 35
5.
Students will be able to solve one-step equations using reciprocals (multiplicative
inverses) and opposites (additive inverses).
Worksheet 5
1 – 26
6.
Students will be able to solve two-step equations. (Section 2.1)
Worksheet 6
1 - 22
(optional)
page 72
1 – 15, 18 – 23, 28 – 31, 55 – 60
*
Quiz 2
7.
Students will be able to solve word problems by substituting data into a given
equation.
Worksheet 7
1 – 12
8.
Students will be able to solve multi-step equations that involve the distributive
property and/or combining like terms on each side of the equation. (Section 2.2)
Worksheet 8
1 - 22
(optional)Page 79
1 – 19
*
Quiz 3
Review Worksheet 1
Review Worksheet 2
Algebra 1 Unit 1
1 – 30
1 - 19
1
Worksheet 1
Simplify:
1.
47 + (-86)
2.
-6 – (-13)
3.
-12(12)
4.
-42 ÷ -3
5.
(–2)(–5)(–6)
6.
(12)(-2)(-5)
7.
-9 + 15 – 7 – (-13) + 4
8.
0
10
9.
10
0
10.
(-6)2
11.
-62
12.
–42 + (–4)2
13.
12  18
2
14.
(4)(5)
10
15.
12(5)
13
Evaluate each expression for x = 2, y = -5, z = -6
16.
x y2
17.
(xy)2
18.
-z + y2
19.
y–z
20.
x2 + y2
21.
(x + y)2
22.
-z + 2y2 – x
23.
x2 – y2
24.
(x – y)2
25.
(2y)3
26.
z2 – y
27.
xz
4
Algebra 1 Unit 1
2
Complete each table
28.
n work -4n
-5
-1
0
8
29.
30.
p work 9–p
15
4
-2
-7
m work -3m+4
-4
-2
5
6
31.
A scuba diver is 74 feet below sea level. He begins to rise and ascends 12 feet.
Find the new depth after rising.
32.
A football team loses 9 yards on their first play. On the next two
plays they gain 4 yards and then gain 15 more. What is the end
result? (How many total yards have they either gained or lost?)
33.
The chart shows an expression evaluated for four different
values of x. Looking at the chart Carol concluded that x2 > x.
Which value of x serves as a counterexample to prove Carol’s
conclusion false?
A.
–9
B.
8
C.
0
D.
11
34.
Which number serves as a counterexample to the statement below?
x
–12
–5
2
10
The value of x2 – 4 is always positive.
A.
B.
C.
D.
7
–6
3
1
Algebra 1 Unit 1
3
x2
144
25
4
100
Unit 1 Worksheet 2
Simplify each expression using proper order of operations.
1.
22 – 8 ÷ 2
2.
–92
3.
(–9)2
4.
–72 + 72
5.
2 • 32
6.
(2 • 3)2
7.
3 • 52 + (3 • 5)2
8.
6 + 2(4)
9.
4 + 5(8 + 1)
10.
12 – 6(5)2
11.
6 – 2(1 + 4)
12.
3 + 6(10 – 4)
14.
[8 + 2(3 – 5)] – 6
15.
13.
5  8  5  8
20  8  11
Explain the error in the following problems and then work the problem correctly.
16.
16 + 16 ÷ 4
17.
17 – 3 + 2
18.
3(2 + 7)
= 32 ÷ 4
= 17 – 5
= 6+ 7
=
8
=
12
=
13
19.
–12 ÷ 2 + 2
= 6 + 2
=
8
Algebra 1 Unit 1
20.
4 + 3(6 + 4)
= 7(6 + 4)
=
7 (10)
=
70
21.
4(–3) + (–6)(2)
= –12 + (–6)(2)
=
–18(2)
=
–36
4
22.
Four students simplified the problem below. Which student worked it correctly
using proper order of operations?
Alice
4 + 2(3 + 5)
=
6(3 + 5)
=
6(8)
=
48
Beth
4 + 2(3 + 5)
=
6(3 + 5)
=
18 + 5
=
23
Cathy
4 + 2(3 + 5)
= 4 + 2 (8)
= 4 + 16
=
20
Darla
4 + 2(3 + 5)
= 4+ 6 + 5
= 10 + 5
=
15
Answer the following statements as true or false. If false give one counterexample to
support your answer.
23.
The order in which two numbers are added does not affect the sum.
24.
The order in which two numbers are subtracted does not affect the difference.
25.
The order in which two numbers are divided does not affect the quotient.
26.
The sum of zero and a number will equal the number.
27.
The order in which two numbers are multiplied does not affect the product.
28.
The product of zero and a number will equal the number.
29.
The product of one and a number will equal the number.
Algebra 1 Unit 1
5
Unit 1 Worksheet 3
Simplify the following expressions by combining like terms:
1.
3a + 2a
2.
7e – 5e
3.
8y + 3y – 5y
4.
2a + 3 + 4a + 5
5.
3d – 2 + 18 + 4d
6.
x + 3x + 6
7.
9 + 6x + 2x
8.
9x + 3 + 7x + 4
9.
2y + 7 + y + 9y + 4
10.
9 + 6u – 31 + 8u
11.
x+2+x+9
12.
–x + 3 + 4x – 12
Use the distributive property and simplify each of the following:
13.
–2(x + 3)
14.
7(3y – 8)
15.
–3(4m – 6)
16.
5( –x + 7)
17.
–(–5h – 9)
18.
6(x – 4)
19.
1
(10x + 12)
2
20.
1
(18x – 24)
3
21.
3
(4x + 8)
4
22.
3(x + 4) + 5(2x + 7)
23.
9(x + 3) – 7(x – 2)
24.
3(4p + 3) + 4(p – 1)
25.
-3(2x + 4) +
26.
4(x + 2) – (x + 6)
27.
1
(10x – 5) – (2x–3)
5
Algebra 1 Unit 1
1
(2x – 4)
2
6
28.
5(2m + 5) – 6
29.
9(8x – 5) – 10
30.
5(2 + x) + 7x
31.
2 + 5(3x – 4)
32.
4 + 2(7x + 1)
33.
7 – 3(x + 9)
34.
8 – (10x – 5)
35.
10 – 8(x – 3)
36.
5+
1
(8x + 6)
2
Select the correct multiple choice response:
37.
Which shows the proper use of the distributive property?
A.
–3(x + 2) = –3x + 2
B.
–3(x + 2) = –3x + 6
C.
–3(x + 2) = –3x – 2
D.
–3(x + 2) = –3x – 6
38.
Which shows the proper use of the distributive property?
A.
– (y – 7) = –y + 7
B.
– (y – 7) = –y – 7
C.
– (y – 7) = y + 7
D.
– (y – 7) = y – 7
39.
Is the equation 5(7x – 6) = 2 equivalent to 35x – 30 = 2 ?
A.
No, they are not equivalent. It should be 35x – 6 = 2
B.
Yes, they are equivalent by the Distributive Property
C.
No, they are not equivalent. It should be 35x – 30 = 10
D.
No, they are not equivalent. It should be 12x – 6 = 2
40.
What should be done first when simplifying 6 + 3(2x – 1) ?
A.
Add the 6 and 3
B.
Subtract the 2x and 1
C.
Distribute the 3 to the 2x – 1
Algebra 1 Unit 1
7
Worksheet 4
In problems 1 – 19, translate each phrase into a mathematical expression:
1.
Twice a number, w
2.
The square of v
3.
The cube of m
4.
Triple k
5.
Double y
6.
Five less than x
7.
The quotient of c and 4
8.
Four more than half a number
9.
Two less than the cube of x
10.
Six decreased by the triple of d
11.
Square a number and diminish by 2
12.
The product of 8 and the cube of k
13.
5 less than the product of 3 and m
14.
The square of x diminished by the cube of y
15.
The reciprocal of x increased by twice x
16.
The sum of x and the opposite of d
17.
The product of 5 and the reciprocal of y
18.
The additive inverse of 5 diminished by m
19.
The product of y and its reciprocal
Answer the questions in problems 20 - 22
20.
What is another word for reciprocal?
21.
What is another word for opposite?
22.
What number does not have a reciprocal?
Algebra 1 Unit 1
8
Complete the chart for problems 23 – 28.
Additive inverse Multiplicative inverse
(opposite)
(reciprocal)
23. 5
24. –7
25. 2
3
26. 0
27. 3
5
28. 1
Select the correct multiple choice response in problems 29 – 32.
29.
Which is an algebraic expression for: the sum of 7 and x?
A.
30.
31.
7x
B.
7–x
C.
What is the additive inverse of –w ?
1
A.
B.
w
C.
w
What is the multiplicative inverse of 0?
A.
1
B.
–1
C.
7
x
7+x
D.
–w
D.
–
0
D.
none of these
32.
What is the sum of a number, x, and its opposite?
A.
1
B.
–1
C.
0
D.
x
33.
What is the product of a number, x, and its reciprocal?
A.
1
B.
–1
C.
0
D.
x
34.
Which shows the proper use of the distributive property?
A.
2(3x + 6) = 5x + 5
B.
2(3x + 6) = 5x + 12
C.
2(3x + 6) = 6x + 6
D.
2(3x + 6) = 6x + 12
35.
What is the reciprocal of 12p ?
12
A.
B.
–12p
p
Algebra 1 Unit 1
C.
–12 – p
D.
1
w
1
12p
9
Worksheet 5
Solve using the additive inverse (opposite)
1.
x+4=–9
2.
x + 8 = -5
Solve using the multiplicative inverse (reciprocal)
2
4.
-5x = -20
5.
x = 24
3
Solve using the additive inverse or multiplicative inverse.
x
7.
x – -9 = 12
8.
= 6
3
3.
21 + x = 14
6.
-8 =
9.
3x = 6
x
2
10.
3+x= 1
11.
-x = 30
12.
x
5
13.
x
= -12
4
14.
2
x = 6
3
15.
3
x=1
4
16.
-5x = 30
17.
4
x=1
5
18.
–
Algebra 1 Unit 1
= 10
4
x = 12
3
10
19.
18x = 0
20.
3
x=1
7
21.
x
= 0
4
22.
3
x = -24
4
23.
-x = -7
24.
x
= 7
7
25
What is the solution to –
A.
9
7
B.
–
C.
D.
26.
7
= 1
9
9
7
7
1
9
2
9
Which multiple choice describes the correct way to solve the equation:
2
x = -40
5
A.
Add the opposite to both sides
B.
Subtract the opposite from both sides
C.
Multiply both sides by the multiplicative inverse
D.
Divide both sides by -40
Algebra 1 Unit 1
11
Worksheet 6
Solve:
1.
2x + 1 = 9
2.
3x + 4 = – 11
3.
4x – 5 = –9
4.
7x – 2 = 19
5.
x
+ 1 = 15
2
6.
x
+ 1 = 8
7
7.
5x + 8 = 0
8.
–8 +
9.
5 
10.
1
x+3=9
2
11.
3x + 42 = 0
12.
9x – 7 = 0
13.
3 – 2x = 17
14.
12 = 6 – 3x
15.
–3x – 4 = 1
Algebra 1 Unit 1
x
= 12
4
x
= –7
6
12
In problems 16 – 27, select the correct multiple choice answer.
16.
Which equation is equivalent to
17.
3x – 2 = - 12
A.
3x = - 24
B.
3x = - 6
C.
3x = - 14
D.
3x = - 10
?
Max is solving the equation 3x – 2 = 10
Which of the following are correct steps to find the solution?
A.
B.
C.
Divide both sides by 3. Then add 2 to both sides.
Add 2 to both sides. Then divide both sides by 3.
Subtract 2 from both sides. Then divide both sides by 3.
1
Multiply both sides by . Then subtract 2 from both sides.
3
D.
18.
Which of the following are correct steps to find the solution of the following
equation?
8 = 18 – 2x
A.
Subtract 18 from both sides and divide by 2.
B.
Subtract 8 from both sides and divide by 2
C.
Subtract 18 from both sides and divide by – 2
D.
Subtract 8 from both sides and divide by – 2.
19.
Four students worked the following equation. Their work is shown below.
x
Identify which one student did the work correctly.
+ 4 = 7
3
Alice
x
+ 4 = 7
3
Bill
x
+ 4 = 7
3
Chu
x
+ 4 = 7
3
x
3
= 11
x
3
=
3
x
3
=
x
=
x
=
1
x
= 9
33
Algebra 1 Unit 1
3
Danielle
x
+ 4 = 7
3
x + 4 = 21
x
= 17
13
20.
21.
Which of the following are correct steps to find the solution of the following
x
equation?
5 +
= 9
2
A.
Multiply both sides by 2 and subtract 5.
B.
Multiply both sides by -2 and subtract 5.
C.
Subtract 5 from both sides and multiply by 2
D.
Subtract 5 from both sides and divide by 2.
What is the multiplicative inverse of
A.
B.
C.
22.
–
7
?
8
8
7
–
8
7
7
8
What is the value of x in the equation 6x + 5 = 0 ?
A.
5
6
B.
6
5
C.
–
6
5
D.
–
5
6
Algebra 1 Unit 1
14
Worksheet 7
1.
The total number of cups of flour (f) that McKenna has left after baking (c)
number of cakes is given by the equation f = –9c + 80
a)
If McKenna bakes 3 cakes how much flour will she have left?
b)
2.
The amount of time (t) in seconds it takes a cashier to ring up a customer is
related to (n) the number of items they purchase. The equation is
t = n + 12
a)
How long does it take to ring up a customer with 5 items?
b)
3.
If it took 30 seconds to ring up a customer, how many items did they
purchase?
The number of pictures (p) that Lola takes depends on the number of days (d)
she is on vacation. The equation is p = 5d + 2
a)
If Lola took 37 pictures, how many days was she on vacation?
b)
4.
If McKenna has 17 cups of flour how many cakes did she bake?
If Lola vacations for 10 days, how many pictures will she take?
The equation below is used to how the number of napkins that Ken has left
is related to the number of tables that he has set.
n = –8t + 200
a)
If Ken has 120 napkins left, how many tables did he set?
b)
If Ken sets 25 tables, how many napkins will he have left?
Algebra 1 Unit 1
15
5.
The distance (d) in miles that Cecil runs depends on the number of track
practices (p) he attends.
d = 2p + 3
How many miles would Cecil run if he attended 5 practices?
6.
The amount of fabric (f) in yards used to sew n number of shirts can be found
3
using the equation f = n
4
If 12 yards of fabric were used, how many shirts were sewn?
7.
The number of fish (f) Bill catches is related to the number of days (d) he goes
fishing.
f = 2d + 2
If Bill fishes for 8 days, how many fish will he catch?
8.
The height of a plant in inches (i) is related to the number of days (d) you care
1
for and water the plant.
i= d+2
2
If a plant is 10 inches tall how many days was it cared for?
9.
When digging into the earth, the temperature (t) in Celsius rises according to the
1
depth (d) in meters.
t = 15 +
d
100
a)
What will the temperature be at 100 meter?
b)
At what depth would the temperature be 24° C ?
Algebra 1 Unit 1
16
10.
A faucet drips (d) ounces of water every m minutes as shown in the equation
2
d = m + 10
5
a)
How many ounces of water will it have dripped after 20 minutes?
b)
11.
How long will it take for it to drip 30 ounces?
Many times the actual temperature outside is much colder than what the
thermometer says if it is a windy day. The wind chill makes it colder than the
thermometer reads. Using the formula below determine
the wind chill temperature (w) if the thermometer reading ‘t ‘
reads 50°.
13
w = -22 +
t
10
12.
Algebra 1 Unit 1
Moselle is riding a roller coaster that is 155 feet high.
He is at the very top and he wants to know how far he is from
the bottom after 2 seconds. Use the formula below to find
out how far from the bottom he is. (s represents seconds)
distance from bottom = 155 – 16s2
17
Worksheet 8
Solve the following:
1.
4x + 5x = 45
2.
3x + 2x + 6 = 71
3.
3x + 4x + 2 = –57 + 3
4.
6(x + 5) = 12
5.
4(2x – 7) = 12
6.
1
(6x + 18) = –24
3
7.
1
(4x + 6) = 0
2
8.
1
(12x – 4) = –13
4
9.
2 + 3(x – 5) = 5
10.
3 + 5(m – 3) = –2
12.
2x – 4(x – 1) = 10
11.
4 – (9g – 5) = – 18
Algebra 1 Unit 1
18
13.
6 – 4(x + 2) = 9 – 35
14.
5 – 2(x + 6) = -15
15.
2 + 4(x – 2) + 6x = –96
16.
6 + 2(x – 5) + 4x = 44
17.
2(3x + 5) + 3(2x + 5) = 1
18.
–
19.
4 5x  7  8x  + 2 = –18
20.
5 2(x  3)  x = –15
21.
2 4  (x  1)  3x = 14
22.
2 + 3 2(x  4)  7  = 35
Algebra 1 Unit 1
1
(6x – 4) + 5(x + 2) = 0
2
19
Review 1
Simplify problems 1 – 9.
1.
6 + 3(2 + 1)
2.
5
0
3.
0
5
4.
–82 + (–8)2
5.
2 • 52 + (2 • 5)2
6.
4 + 3(7 + 1)
7.
–5(3x + 7y) – 8(2x – 3y) 8.
2
(6x + 9y) – (5x – 10y)
3
9.
5 – 2(4x + 5)
Answer individual questions in problems 10 – 16.
What is the reciprocal of 9w ?
11.
12.
State the additive inverse of – 4k
13. State the multiplicative inverse of –8k
14.
What number does not have a reciprocal?
15.
What is the sum of a number and its opposite?
16.
What is the product of a number and its reciprocal?
Find the value of x in problems 17 – 25
x
3
17.
= –10
18.
x=1
10
4
20.
3
x – 12 = 36
4
Algebra 1 Unit 1
21.
State the opposite of
4
5
10.
19.
7 – (x + 4) = 0
9x + 5 = 0
22.
2(x – 6) + 8 = 20
20
23.
4 + 2(x + 3) = 24
25.
2[6x – 5(x – 3)] + 4 = 40
24.
4(2x – 3) – 9(x + 2) = 0
In problems 26 – 28, write an equation and solve.
26.
The grams of medicine (g) prescribed for a child weighing p pounds can be found
using the equation
g = 4 + 2w
How much does a child weigh if he was prescribed 54 grams of medicine?
27.
The cost (c) in dollars to rent a chain saw for h hours is found using the equation
c = 3h + 6
How much would it cost to rent the saw for 12 hours?
28.
A rock is thrown vertically upward into the air. The height (h) in feet of the rock
after t seconds can be found using the equation h = –16t2 + 128t
Find the rock’s height after 3 seconds.
In problems 29 – 30 give a counterexample to the statement.
29.
The sum of two numbers is always positive.
30.
When x2 + 2x is evaluated for all numbers the answer will always be an even
number.
Algebra 1 Unit 1
21
Review 2
Select the correct multiple choice response:
1.
2.
3.
Max is solving the equation 3x – 2 = 10. Which of the following are the correct
steps in finding the solution?
1
A.
Multiply both sides by . Then subtract 2 from both sides.
3
1
B.
Multiply both sides by . Then subtract 2 from both sides.
3
C.
Subtract 2 from both sides. Then divide both sides by 3.
D.
Add 2 to both sides. Then divide both sides by 3.
The solution of this equation has an error. Identify at which step the error
occurred.
5x + 2 – 2x = 9 + 7
Step 1:
5x + 2 – 2x = 16
Step 2:
7x + 2 = 16
Step 3:
7x = 14
Step 4:
x=2
A.
Step 1
B.
Step 2
C.
Step 3
D.
Step 4
The solution of this equation has an error. Identify at which step the error
occurred.
2(x + 4) + 6 = 14
Step 1:
Step 2:
Step 3:
Step 4
A.
4
Step 1
2x + 4 + 6 = 14
2x + 10 = 14
2x = 4
x=2
B.
Step 2
C.
Step 3
D. Step 4
Jason solved this equation as shown below:
x
 4  52
3
x
Step 1:
47
3
x
3
Step 2:
3
Step 3:
x=1
Which statement is true about his solution?
A.
Jason solved it correctly.
B.
Jason made an error in step 1
C.
Jason made an error in step 2
D.
Jason made an error in step 3
Algebra 1 Unit 1
22
5.
6.
7.
8.
9.
5 + 2(x + 3) = 17 is equivalent to which selection?
A.
2x + 11 = 17
B.
2x + 8 = 17
C.
7x + 6 = 17
D.
7x + 3 = 17
Which of the following is equivalent to
3(2x + 1) = – 9
A.
5x + 1 = 9
B.
5x + 4 = – 9
C.
6x + 3 = – 9
D.
6x + 1 = – 9
2
What is the additive inverse of
?
3
3
A.
2
3
B.
–
2
2
C.
3
2
D.
–
3
Which statement is true?
A.
x + x = x2
B.
x + x = 2x
C.
–x2 = x2
1
D.
x( )=x
x
A student worked the following problem:
Solve:
?
8x + 10 – 6x + 4 = 24
Their work is shown below:
Step 1
2x + 14 = 24
Step 2
2x = 38
Step 3
x = 19
Which statement is correct?
A.
There is an error in Step 1
B.
There is an error in Step 2
C.
There is an error in Step 3
D.
No errors were made. The problem was worked correctly.
Algebra 1 Unit 1
23
10.
Solve
A.
B.
C.
D.
for x:
5
–5
–7
7
3[4x – 2(x –6)] + 6 = 0
11.
Amy simplified the expression below. In which step did she first make a mistake?
2 + 3(1 + 4)
Step 1
Step 2
Step 3
A.
B.
C.
D.
2 + 3 (5)
5 (5)
25
Step 1
Step 2
Step 3
Amy did not make a mistake
12.
Simplify:
-2(x – 3y) + 4(5x + 6y)
A.
18x + 30y
B.
18x + 18y
C.
-22x + 18y
D.
-18x + 18y
13.
What is the multiplicative inverse of –9k ?
A.
9k
1
B.
9k
1
C.
–
9k
D.
1
14.
x2 is never negative
When is this statement true?
A.
This statement is never true
B.
This statement is only true for positive numbers.
C.
This statement is always true.
D.
There is not enough information to tell
Algebra 1 Unit 1
24
15.
Which number serves as a counterexample to the statement below?
When evaluating (2x + 5) your
answer is always greater than 0
A.
B.
C.
D.
16.
What is the value of x?
18.
19.
5
x=1
8
5
8
3
B.
8
8
C.
5
5
D.
–1
8
Solve for x:
–7 – (x + 3) = 12
A.
22
B.
–22
C.
16
D.
–16
The total cost (c) in dollars to work on a computer at Kinkos for h hours is given
by the equation
c = 2h + 4
A.
17.
5
–7
–1
0
1
If Jeremiah worked on the computer for 12 hours, how much did it cost him?
A.
$4
B.
$24
C.
$2
D.
$28
Solve for x:
6 – 2(x – 8) = 24
A.
–1
B.
1
C.
14
D.
–14
Algebra 1 Unit 1
25