PreAP Algebra II Summer Work 2018 The summer work
PreAP Algebra II Summer Work 2018 The summer work for PreAP Algebra II is the 1st Chapter in our book. It is a review of Algebra I. If you get stuck go to https://www.khanacademy.org . There are worksheets and information for you there. Please show all your work on the worksheets to get credit.
I hope you have a great summer. Summer work will be due the Aug. 27, 2018 at the beginning of the period. Be ready to take a test over the material the First Friday Aug. 31, 2018.
Christine Smyers [email protected]
NAME _____________________________________________ DATE ____________________________ PERIOD _____________
1 Student-Built Glossary This is an alphabetical list of key vocabulary terms you will learn in Chapter 1. Use the internet to find the definitions. Please use the mathematical definition. Draw a picture or write an example of each term
Vocabulary Term
Picture/example
Definition/Description
absolute value
algebraic expressions
compound inequality
empty set
equation
formula
integers
intersection
irrational numbers
natural numbers
(continued on the next page)
Chapter 1
1
Glencoe Algebra 2
NAME _____________________________________________ DATE ____________________________ PERIOD _____________
1 Student-Built Glossary Vocabulary Term
Picture/example
Definition/Description
open sentence
order of operations
rational numbers
real numbers
set-builder notation
solution
union
variable
whole numbers
Chapter 1
2
Glencoe Algebra 2
NAME _____________________________________________ DATE ____________________________ PERIOD _____________
1-1 Study Guide and Intervention Expressions and Formulas Order of Operations Step 1 Evaluate expressions inside grouping symbols. Step 2 Evaluate all powers. Step 3 Multiply and/or divide from left to right. Step 4 Add and/or subtract from left to right.
Order of Operations
Example 1: Evaluate [18 β (6 + 4)] Γ· 2.
Example 2: Evaluate πππ + π(π β π)
[18 β (6 + 4)] Γ· 2 = [18 β 10] Γ· 2
if x = 3 and y = 0.5.
=8Γ·2
Replace each variable with the given value.
=4
3π₯ 2 + π₯(π¦ β 5) = 3 β’ (3)2 + 3(0.5 β 5) = 3 β’ (9) + 3(β4.5) = 27 β 13.5 = 13.5
Exercises Evaluate each expression. 1. 14 + (6 Γ· 2)
2. 11 β (3 + 2)2
3. 2 + (4 β 2)3 β 6
4. 9(32 + 6)
5. (5 + 23 )2 β 52
6. 52 +
16 + 23 Γ· 4 1 β 22
8. (7 β 32 )2 + 62
9. 20 Γ· 22 + 6
10. 12 + 6 Γ· 3 β 2(4)
11. 14 Γ· (8 β 20 Γ· 2)
12. 6(7) + 4 Γ· 4 β 5
13. 8(42 Γ· 8 β 32)
14.
7.
6+4Γ·2 4Γ·6β1
1 4
+ 18 Γ· 2
15.
6 + 9 Γ· 3 + 15 8β2
17. 5(6c β 8b + 10d)
18.
π2 β 1 πβπ
20. (π β π)2 + 4a
21. π + 6b β 5c
π
Evaluate each expression if a = 8.2, b = β3, c = 4, and d = β π. 16.
ππ π
19. ac β bd π
π
π
22. 3(π)β b
23. cd + π
24. d(a + c)
25. a + b Γ· c
26. b β c + 4 Γ· d
27. π + π β d
Chapter 1
π
5
Glencoe Algebra 2
NAME _____________________________________________ DATE ____________________________ PERIOD _____________
1-1 Study Guide and Intervention (continued) Expressions and Formulas Formulas A formula is a mathematical sentence that expresses the relationship between certain quantities. If you know the value of every variable in the formula except one, you can use substitution and the order of operations to find the value of the remaining variable.
Example: The formula for the number of reams of paper needed to print n copies of a booklet that is p pages long ππ
is r = πππ, where r is the number of reams needed. How many reams of paper must you buy to print 172 copies of a 25-page booklet? ππ
r = 500
Formula for paper needed
=
(172)(25) 500
n = 172 and p = 25
=
4300 500
Evaluate (172)(25).
= 8.6
Divide.
You cannot buy 8.6 reams of paper. You will need to buy 9 reams to print 172 copies.
Exercises 1. For a science experiment, Sarah counts the number of breaths needed for her to blow up a beach ball. She will then find the volume of the beach ball in cubic centimeters and divide by the number of breaths to find the average volume of air per breath. a. Her beach ball has a radius of 9 inches. First she converts the radius to centimeters using the formula C = 2.54I, where C is a length in centimeters and I is the same length in inches. How many centimeters are there in 9 inches? 4
b. The volume of a sphere is given by the formula V = 3 ππ 3 , where V is the volume of the sphere and r is its radius. What is the volume of the beach ball in cubic centimeters? (Use 3.14 for Ο.) c. Sarah takes 40 breaths to blow up the beach ball. What is the average volume of air per breath? 2. A personβs basal metabolic rate (or BMR) is the number of calories needed to support his or her bodily functions for one day. The BMR of an 80-yearold man is given by the formula BMR = 12w β (0.02)(6)12w, where w is the manβs weight in pounds. What is the BMR of an 80-year-old man who weighs 170 pounds?
Chapter 1
6
Glencoe Algebra 2
NAME
DATE
1-2
PERIOD
Practice Properties of Real Numbers
Name the sets of numbers to which each number belongs. 1. 6425
5.
25 β β 36
2. β 7
3. 2Ο
4. 0
6. - β 16
7. -35
8. -31.8
Name the property illustrated by each equation. 9. 5x (4y + 3x) = 5x (3x + 4y) 11. 5(3x + y) = 5(3x + 1y)
10. 7x + (9x + 8) = (7x + 9x) + 8 12. 7n + 2n = (7 + 2)n
13. 3(2x)y = (3 2)(xy)
14. 3x 2y = 3 2 x y
15. (6 + -6)y = 0y
1 4y = 1y 16. β
17. 5(x + y) = 5x + 5y
18. 4n + 0 = 4n
4
Find the additive inverse and multiplicative inverse for each number. 19. 0.4
5 6
22. 5 β
Simplify each expression. 23. 5x - 3y - 2x + 3y
24. -11a - 13b + 7a - 3b
25. 8x - 7y - (3 - 6y)
26. 4c - 2c - (4c + 2c)
27. 3(r - 10t) - 4(7t + 2r)
1 1 28. β (10a - 15b) + β (8b + 4a)
29. 2(4z - 2x + y) - 4(5z + x - y)
5 3 1 βx + 12y - β 30. β (2x - 12y)
5
2
(
6 5
)
4
31. TRAVEL Olivia drives her car at 60 miles per hour for t hours. Ian drives his car at 50 miles per hour for (t + 2) hours. Write a simplified expression for the sum of the distances traveled by the two cars. 32. NUMBER THEORY Use the properties of real numbers to tell whether the following
( )
( )
1 > b 1 . Explain statement is true or false: If a and b β 0 and a > b, it follows that a β β a b your reasoning.
Chapter 1
14
Glencoe Algebra 2
Copyright Β© Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
11 16
21. - β
20. -1.6
NAME _____________________________________________ DATE ____________________________ PERIOD _____________
1-3 Skills Practice Solving Equations Write an algebraic expression to represent each verbal expression. 1. 4 times a number, increased by 7
2. 8 less than 5 times a number
3. 6 times the sum of a number and 5
4. the product of 3 and a number, divided by 9
5. 3 times the difference of 4 and a number 6. the product of β11 and the square of a number Write a verbal sentence to represent each equation. 7. n β 8 = 16
8. 8 + 3x = 5
9. b + 3 = π 2
10. 3 = 2 β 2y
π¦
Name the property illustrated by each statement. 11. If a = 0.5b, and 0.5b = 10, then a = 10.
12. If d + 1 = f, then d = f β 1.
13. If β7x = 14, then 14 = β7x.
14. If (8 + 7)r = 30, then 15r = 30.
Solve each equation. Check your solution. 15. 4m + 2 = 18
16. x + 4 = 5x + 2
17. 3t = 2t + 5
18. β3b + 7 = β15 + 2b
19. β5x = 3x β 24
20. 4v + 20 β 6 = 34
21. a β
2π 5
=3
22. 2.2n + 0.8n + 5 = 4n
Solve each equation or formula for the specified variable. 23. I = prt, for p
25. A =
π₯+π¦ , 2
Chapter 1
for y
1
24. y = 4x β 12, for x 26. A = 2ππ 2 + 2Οrh, for h
19
Glencoe Algebra 2
NAME _____________________________________________ DATE ____________________________ PERIOD _____________
1-4 Skills Practice Solving Absolute Value Equations Evaluate each expression if w = 0.4, x = 2, y = β3, and z = β10. 1. |5w|
2. |β9y|
3. |9y β z|
4. β |17z|
5. β |10z β 31|
6. β |8x β 3y| + |2y + 5x|
7. 25 β |5z + 1|
8. 44 + |β2x β y|
9. 2|4w|
10. 3 β |1 β 6w|
11. |β3x β 2y| β 4
12. 6.4 + |w β 1|
Solve each equation. Check your solutions. 13. |y + 3| = 2
14. |5a| = 10
15. |3k β 6| = 2
16. |2g + 6| = 0
17. 10 = |1 β c|
18. |2x + x| = 9
19. |p β 7| = β14
20. 2|3w| = 12
21. |7x β 3x| + 2 = 18
22. 4|7 β y| β 1 = 11
1
23. |3n β 2| = 2
24. |8d β 4d| + 5 = 13
25. β5|6a + 2| = β15
26. |k| + 10 = 9
Chapter 1
26
Glencoe Algebra 2
I hope you have a great summer. Summer work will be due the Aug. 27, 2018 at the beginning of the period. Be ready to take a test over the material the First Friday Aug. 31, 2018.
Christine Smyers [email protected]
NAME _____________________________________________ DATE ____________________________ PERIOD _____________
1 Student-Built Glossary This is an alphabetical list of key vocabulary terms you will learn in Chapter 1. Use the internet to find the definitions. Please use the mathematical definition. Draw a picture or write an example of each term
Vocabulary Term
Picture/example
Definition/Description
absolute value
algebraic expressions
compound inequality
empty set
equation
formula
integers
intersection
irrational numbers
natural numbers
(continued on the next page)
Chapter 1
1
Glencoe Algebra 2
NAME _____________________________________________ DATE ____________________________ PERIOD _____________
1 Student-Built Glossary Vocabulary Term
Picture/example
Definition/Description
open sentence
order of operations
rational numbers
real numbers
set-builder notation
solution
union
variable
whole numbers
Chapter 1
2
Glencoe Algebra 2
NAME _____________________________________________ DATE ____________________________ PERIOD _____________
1-1 Study Guide and Intervention Expressions and Formulas Order of Operations Step 1 Evaluate expressions inside grouping symbols. Step 2 Evaluate all powers. Step 3 Multiply and/or divide from left to right. Step 4 Add and/or subtract from left to right.
Order of Operations
Example 1: Evaluate [18 β (6 + 4)] Γ· 2.
Example 2: Evaluate πππ + π(π β π)
[18 β (6 + 4)] Γ· 2 = [18 β 10] Γ· 2
if x = 3 and y = 0.5.
=8Γ·2
Replace each variable with the given value.
=4
3π₯ 2 + π₯(π¦ β 5) = 3 β’ (3)2 + 3(0.5 β 5) = 3 β’ (9) + 3(β4.5) = 27 β 13.5 = 13.5
Exercises Evaluate each expression. 1. 14 + (6 Γ· 2)
2. 11 β (3 + 2)2
3. 2 + (4 β 2)3 β 6
4. 9(32 + 6)
5. (5 + 23 )2 β 52
6. 52 +
16 + 23 Γ· 4 1 β 22
8. (7 β 32 )2 + 62
9. 20 Γ· 22 + 6
10. 12 + 6 Γ· 3 β 2(4)
11. 14 Γ· (8 β 20 Γ· 2)
12. 6(7) + 4 Γ· 4 β 5
13. 8(42 Γ· 8 β 32)
14.
7.
6+4Γ·2 4Γ·6β1
1 4
+ 18 Γ· 2
15.
6 + 9 Γ· 3 + 15 8β2
17. 5(6c β 8b + 10d)
18.
π2 β 1 πβπ
20. (π β π)2 + 4a
21. π + 6b β 5c
π
Evaluate each expression if a = 8.2, b = β3, c = 4, and d = β π. 16.
ππ π
19. ac β bd π
π
π
22. 3(π)β b
23. cd + π
24. d(a + c)
25. a + b Γ· c
26. b β c + 4 Γ· d
27. π + π β d
Chapter 1
π
5
Glencoe Algebra 2
NAME _____________________________________________ DATE ____________________________ PERIOD _____________
1-1 Study Guide and Intervention (continued) Expressions and Formulas Formulas A formula is a mathematical sentence that expresses the relationship between certain quantities. If you know the value of every variable in the formula except one, you can use substitution and the order of operations to find the value of the remaining variable.
Example: The formula for the number of reams of paper needed to print n copies of a booklet that is p pages long ππ
is r = πππ, where r is the number of reams needed. How many reams of paper must you buy to print 172 copies of a 25-page booklet? ππ
r = 500
Formula for paper needed
=
(172)(25) 500
n = 172 and p = 25
=
4300 500
Evaluate (172)(25).
= 8.6
Divide.
You cannot buy 8.6 reams of paper. You will need to buy 9 reams to print 172 copies.
Exercises 1. For a science experiment, Sarah counts the number of breaths needed for her to blow up a beach ball. She will then find the volume of the beach ball in cubic centimeters and divide by the number of breaths to find the average volume of air per breath. a. Her beach ball has a radius of 9 inches. First she converts the radius to centimeters using the formula C = 2.54I, where C is a length in centimeters and I is the same length in inches. How many centimeters are there in 9 inches? 4
b. The volume of a sphere is given by the formula V = 3 ππ 3 , where V is the volume of the sphere and r is its radius. What is the volume of the beach ball in cubic centimeters? (Use 3.14 for Ο.) c. Sarah takes 40 breaths to blow up the beach ball. What is the average volume of air per breath? 2. A personβs basal metabolic rate (or BMR) is the number of calories needed to support his or her bodily functions for one day. The BMR of an 80-yearold man is given by the formula BMR = 12w β (0.02)(6)12w, where w is the manβs weight in pounds. What is the BMR of an 80-year-old man who weighs 170 pounds?
Chapter 1
6
Glencoe Algebra 2
NAME
DATE
1-2
PERIOD
Practice Properties of Real Numbers
Name the sets of numbers to which each number belongs. 1. 6425
5.
25 β β 36
2. β 7
3. 2Ο
4. 0
6. - β 16
7. -35
8. -31.8
Name the property illustrated by each equation. 9. 5x (4y + 3x) = 5x (3x + 4y) 11. 5(3x + y) = 5(3x + 1y)
10. 7x + (9x + 8) = (7x + 9x) + 8 12. 7n + 2n = (7 + 2)n
13. 3(2x)y = (3 2)(xy)
14. 3x 2y = 3 2 x y
15. (6 + -6)y = 0y
1 4y = 1y 16. β
17. 5(x + y) = 5x + 5y
18. 4n + 0 = 4n
4
Find the additive inverse and multiplicative inverse for each number. 19. 0.4
5 6
22. 5 β
Simplify each expression. 23. 5x - 3y - 2x + 3y
24. -11a - 13b + 7a - 3b
25. 8x - 7y - (3 - 6y)
26. 4c - 2c - (4c + 2c)
27. 3(r - 10t) - 4(7t + 2r)
1 1 28. β (10a - 15b) + β (8b + 4a)
29. 2(4z - 2x + y) - 4(5z + x - y)
5 3 1 βx + 12y - β 30. β (2x - 12y)
5
2
(
6 5
)
4
31. TRAVEL Olivia drives her car at 60 miles per hour for t hours. Ian drives his car at 50 miles per hour for (t + 2) hours. Write a simplified expression for the sum of the distances traveled by the two cars. 32. NUMBER THEORY Use the properties of real numbers to tell whether the following
( )
( )
1 > b 1 . Explain statement is true or false: If a and b β 0 and a > b, it follows that a β β a b your reasoning.
Chapter 1
14
Glencoe Algebra 2
Copyright Β© Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
11 16
21. - β
20. -1.6
NAME _____________________________________________ DATE ____________________________ PERIOD _____________
1-3 Skills Practice Solving Equations Write an algebraic expression to represent each verbal expression. 1. 4 times a number, increased by 7
2. 8 less than 5 times a number
3. 6 times the sum of a number and 5
4. the product of 3 and a number, divided by 9
5. 3 times the difference of 4 and a number 6. the product of β11 and the square of a number Write a verbal sentence to represent each equation. 7. n β 8 = 16
8. 8 + 3x = 5
9. b + 3 = π 2
10. 3 = 2 β 2y
π¦
Name the property illustrated by each statement. 11. If a = 0.5b, and 0.5b = 10, then a = 10.
12. If d + 1 = f, then d = f β 1.
13. If β7x = 14, then 14 = β7x.
14. If (8 + 7)r = 30, then 15r = 30.
Solve each equation. Check your solution. 15. 4m + 2 = 18
16. x + 4 = 5x + 2
17. 3t = 2t + 5
18. β3b + 7 = β15 + 2b
19. β5x = 3x β 24
20. 4v + 20 β 6 = 34
21. a β
2π 5
=3
22. 2.2n + 0.8n + 5 = 4n
Solve each equation or formula for the specified variable. 23. I = prt, for p
25. A =
π₯+π¦ , 2
Chapter 1
for y
1
24. y = 4x β 12, for x 26. A = 2ππ 2 + 2Οrh, for h
19
Glencoe Algebra 2
NAME _____________________________________________ DATE ____________________________ PERIOD _____________
1-4 Skills Practice Solving Absolute Value Equations Evaluate each expression if w = 0.4, x = 2, y = β3, and z = β10. 1. |5w|
2. |β9y|
3. |9y β z|
4. β |17z|
5. β |10z β 31|
6. β |8x β 3y| + |2y + 5x|
7. 25 β |5z + 1|
8. 44 + |β2x β y|
9. 2|4w|
10. 3 β |1 β 6w|
11. |β3x β 2y| β 4
12. 6.4 + |w β 1|
Solve each equation. Check your solutions. 13. |y + 3| = 2
14. |5a| = 10
15. |3k β 6| = 2
16. |2g + 6| = 0
17. 10 = |1 β c|
18. |2x + x| = 9
19. |p β 7| = β14
20. 2|3w| = 12
21. |7x β 3x| + 2 = 18
22. 4|7 β y| β 1 = 11
1
23. |3n β 2| = 2
24. |8d β 4d| + 5 = 13
25. β5|6a + 2| = β15
26. |k| + 10 = 9
Chapter 1
26
Glencoe Algebra 2
