Algebra Supplement Homework Packet #1

Day 1: Fill in each blank with one of the words or phrases listed below. Distributive Real Reciprocals Absolute value Opposite Associative Inequality Commutative Whole Algebraic expression Exponent Variable

1) A(n) ___________________ is formed by numbers and variables connected by the operations of addition, subtraction, multiplication, division, raising to powers, and/or taking roots.

2) The ___________________ of a number a is –a. 3) 3(x – 6) = 3x – 18 by the ___________________ property. 4) The ___________________ of a number is the distance between that number and 0 on the

number line. 5) A(n) ___________________ is a shorthand notation for repeated multiplication of the same

factor. 6) A letter that represents a number is called a ___________________. 7) The symbols < and > are called ___________________ symbols. 8) If a is not 0, then a and 1/a are called ___________________. 9) A + B = B + A by the ___________________ property. 10) (A + B) + C = A + (B + C) by the ___________________ property. 11) The numbers 0, 1, 2, 3, 4… are called ___________________ numbers. 12) If a number corresponds to a point on the number line, we know that number is a

___________________ number.

List the elements of the set 𝟓, −𝟐

𝟑,𝟖

𝟐, 𝟗, 𝟎. 𝟑, 𝟕, 𝟏

𝟓

𝟖, −𝟏, 𝝅 that are also elements of each given set.

13) Whole Numbers 14) Natural Numbers

15) Rational Numbers 16) Irrational Numbers

17) Real Numbers 18) Integers

Simplify without the assistance of a calculator.

19) -5 + 7 – 3 – (-10) 20) 3(4 – 5)4

21) −8

15 −

2

3

2

22) −

6

158

25

23) −3

8+ 3 2 ÷ 6

24) 23 − 32 − 5 − 7 25) 23 − 32 − 5 − 7

26) 8−10 3− −4 2

2+8 2 ÷4

27) 4−9 ÷4−9

10−12÷4∙8

28) 25

4+3∙7

Simplify each expression.

29) 5xy – 7xy + 3 – 2 + xy 30) 4x + 10x – 19x + 10 – 19 31) 6x2 + 2 – 4(x2 + 1)

32) -7(2x2 – 1) – x2 – 1 33) (3.2x – 1.5) – (4.3x – 1.2) 34) (7.6x + 4.7) – (1.9x + 3.6)

Translate each statement using mathematical symbols.

35) Twelve is the product of x and negative 4. 36) The sum of n and twice n is negative

fifteen. 37) Four times the sum of y and three is -1. 38) The difference of t and five, multiplied by

six is four. 39) Seven subtracted from z is six. 40) Ten less than the product of x and nine is

five. 41) The difference of x and 5 is at least 12.

42) The opposite of four is less than the product of y and seven.

43) Two-thirds is not equal to twice the sum of n and one-fourth.

44) The sum of t and six is not more than negative twelve.

Name the property illustrated from the list provided. Distributive Property of Multiplication

Associative Property of Addition/Multiplication

Commutative Property of Addition/Multiplication

Inverse Property of Addition/Multiplication

Identity Property

Zero Product Property

45) (M + 5) + P = M +(5 + P) 46) 5(3x – 4) = 15x – 20 47) (-4) + 4 = 0 48) (3 + x) + 7 = 7 + (3 + x)

49) (XY)Z = (YZ)X

50) −3

5 −

5

3 = 1

51) 𝑇 0 = 0 52) (ab)c = a(bc)

53) A + 0 = A 54) 8(1) = 8

Complete each equation using the given property.

55) Distributive Property: 5x – 15x = ______________ 56) Commutative property: (7 + y) + (3 + x) = ______________ 57) Additive Inverse Property: 0 = ______________ 58) Multiplicative Inverse Property: 1 = ______________ 59) Associative Property: [(3.4)(0.7)]5=______________ 60) Additive Identity Property: 7 = ______________

Use <, >, or = to make each statement true.

61) -9 ____ -12 62) 0____ -6

63) -3____-1 64) 7____|-7|

65) -5____-(-5) 66) –(-2) ____-2

Simplify without the assistance of a calculator.

67) −7

11− −

1

11

68) 3−5 2+ −1 3

1+2 3− −1 2

69) 1

3 9𝑥 − 3𝑦 − 4𝑥 − 1 + 4𝑦

70) 36 ÷ 2 ∙ 3

Day 2: Solve each linear equation.

1) 4 𝑥 − 5 = 2𝑥 − 14 2) 𝑥 + 7 = −2 𝑥 + 8 3) 3 2𝑦 − 1 = −8 6 + 𝑦

4) – 𝑧 + 12 = 5 2𝑧 − 1 5) 𝑛 − 8 + 4𝑛 = 2 3𝑛 − 4 6) 4 9𝑣 + 2 = 6 1 + 6𝑣 − 10

7) 𝑥

3− 4 = 𝑥 − 2

8) 9

4𝑦 =

2

3𝑦

9) 3𝑛

8− 1 = 3 +

𝑛

6

10) 2𝑥

3−

8

3= 𝑥

11) 2𝑡−1

3=

3𝑡+2

15

12) 3𝑎−3

6=

4𝑎+1

15+ 2

Solve each equation for the specified variable.

13) 𝑉 = 𝐿𝑊𝐻 for W. 14) 5𝑥 − 4𝑦 = −12 for y. 15) 𝑦 − 𝑦1 = 𝑚 𝑥 − 𝑥1 for x.

16) 𝑆 = 𝑣𝑡 + 𝑔𝑡2 for g. 17) 𝐼 = 𝑃𝑟𝑡 + 𝑃 for P.

Solve each absolute value equation.

18) 𝑥 − 7 = 9 19) 3𝑥 − 2 + 6 = 10 20) −5 = 4𝑥 − 3 21) 6𝑥 + 1 = 15 + 4𝑥

22) 3𝑥−7

4 = 2

23) 5 + 2 6𝑥 + 1 = 15

Solve the following application problems. 24) Twice the difference of a number and 3 is the same as 1 added to three times the number. Find

the number. 25) In 2000, a record number of music CDs were sold by manufacturers in the US. By 2005, this

number had decreased to 205.4 million. If this represented a decrease of 25% find the number of music CDs sold in 2000.

26) The length of a rectangular playing field is 5 meters less than twice its width. If 230 meters of fencing goes around the field, find the dimensions of the field.

27) A car rental company charges $19.95 per day for a compact car plus 12 cents per mile for every mile over 100 miles driven per day. If Mr. Woo’s bill for 2 days use is $46.86, find how many miles he drove.

Day 3: Write inequalities.

1) Connie takes at least 54 seconds to recite a poem. Write and graph an inequality to describe this interval.

2) Tina can type at least 50 words per minute. Write and graph an inequality to describe this statement.

3) Jack can run a mile in less than minutes. Write and graph an inequality to describe this statement.

4) The width, w, of a piece of wood ranges from 70 mm to 79 mm. Write and graph an inequality to describe this interval.

5) The cost of a box of stationery ranges from $2.25 to $2.95. Write and graph an inequality to describe this statement.

6) The cost of a 5 pound bag of dog food ranges from $5.25 to $5.95. Write and graph an inequality to describe this statement.

Solve and graph the inequality. 7) −3𝑓 < 11 8) 6𝑥 − 5 < 25 9) 2𝑥 + 5 ≥ 2 − 𝑥 − 9 10) 3 1 + 𝑥 > 1 + 5𝑥 11) 5𝑥 − 4 ≤ 3 𝑥 − 7

Solve and graph the compound inequality 12) 3𝑥 < 8 𝑜𝑟 4𝑥 ≥ 4 13) 𝑥 + 5 > 𝑥 + 7 𝑜𝑟 𝑥 + 3 ≤ 3𝑥 − 4 14) 𝑥 + 5 < 10 𝑎𝑛𝑑 3𝑥 > 175 15) 𝑥 + 5 ≤ 6 𝑜𝑟 − 6𝑥 < −54 16) 5𝑥 − 6 < −16 𝑜𝑟 − 13𝑥 < 26 17) 2𝑥 ≥ 8 𝑜𝑟 − 2𝑥 + 1 > −13

Solve and graph the absolute value inequality. 18) 2𝑥 − 5 > 1 19) 3𝑥 − 2 ≤ 5 20) 2𝑥 − 3 ≤ 5 21) 3𝑥 + 4 > 5 22) 5 𝑥 + 8 > 10 23) −2𝑥 + 3 < 8 24) 4𝑥 + 5 + 7 < 4

7

Day 4 Determine whether each ordered pair is a solution of the given equation.

1) y= 3x – 5; (-1, -8) (0, 5) 2) -6x + 5y = -6; (1, 0) (2, 6/5)

3) y = 2|x|; (-1, 2) (0, 2) 4) y = x4; (-1, 1) (2, 16)

Determine whether each equation is linear or not. Then graph the equation by finding and plotting ordered-pair solutions.

5) 𝑥 + 𝑦 = 3

6) 𝑦 = 4𝑥 – 2 7) 𝑦 = |𝑥| + 2

8) 𝑦 = −2𝑥 + 3 9) 𝑦 = |𝑥 + 2|

10) 𝑦 = 𝑥3 – 2 Match each description with the graph that best illustrates it.

11) Moe worked 40 hours per week until the fall semester started. He quit and didn’t work again until he worked 60 hours a week during the holiday season starting mid-December.

12) Kawana worked 40 hours a week for her father during the summer. S he slowly cut back her hours to not working at all during the fall semester. During the holiday season in December, she started working again and increased her hours to 60 hours per week.

13) Wendy worked from July through February, never quitting. She worked between 10 and 30 hours per week.

14) Bartholomew worked from July through February. T he rest of the time, he worked between 10 and 40 hours per week. During the holiday season he worked 40 hours per week.

Answer questions using a graph. For income tax purposes, Jason Verges, owner of Copy Services, uses a method called straight-line depreciation to show the loss in value of a copy machine he recently purchased. Jason assumes that he can use the machine for 7 years. The following graph shows the value of the machine over the years.

15) What was the purchase price of the copy machine? 16) What is the depreciated value of the machine in 7

years? 17) What loss in value occurred during the first year? 18) What loss in value occurred during the second

year? 19) Why is the line tilted downward?

Find the domain and the range of each relation. Also determine whether the relation is a function.

20) {(-1, 7), (0, 6), (-2, 2), (5, 6)} 21) {(4, 9), (-4, 9), (2, 3), (10, -5)}

22) {(6, 6), (5, 6), (5, -2), (7, 6)} 23) {(1, 2), (1, 3), (1, 1), (1, 4)}

24)

25) 26)

Look at each graph and determine whether or not it is a function. Write Yes or No.

State the domain and range from each graph.

If 𝒇 𝒙 = 𝟑𝒙 + 𝟑, 𝒈 𝒙 = 𝟒𝒙𝟐 − 𝟔𝒙 + 𝟑, 𝒂𝒏𝒅 𝒉 𝒙 = 𝟓𝒙𝟐 − 𝟕, find the following: 27) 𝑓(4) 28) 𝑕(−3) 29) 𝑔(2)

30) 𝑓(−1) 31) 𝑕(0) 32) 𝑔(1)

Use the graphs to the right to answer questions 33 - 39. 33) If g(4) = 56, write the corresponding

ordered pair. 34) Find g(2) 35) Find f(-1) 36) Find g(-4) 37) Find all values of x such that f(x) = -2 38) Find all positive values of x such that g(x) = 4 39) Find all values of x such that g(x) = 0

Answer the following questions regarding functions.

40) What is the greatest number of x-intercepts a function may have? 41) What is the greatest number of y-intercepts a function may have? 42) The function f(x) = 0.42x + 10.5 can be used to predict diamond production, in billions of dollars,

for all years after 2000. What is the predicted diamond production in 2012? 2015?

Day 5: Graph the following functions.

1) y = -2x 2) y = ½ x 3) y = 1/3 x – 2 4) y = 5x + 3 5) –x + 2y = 6 6) 2x + 3y = 6 7) x = -1

8) y = 0 9) y + 7 = 0 10) x – 3 = 0 11) x – 3y > 5 12) x + 8y < 8 13) y < x 14) 4x + y > 5

15) y < 4/3x + 2 16) x > 3/2 17) y > -3 18) y = -4x + 2 19) y = 4x – 5 20) 4 > x – 3y 21) –x + 9 < -y

Find the slope between the given points or of the given line. 22) (3, 2), (8, 11) 23) (3, 1), (1, 8) 24) (4, 2), (4, 0) 25) (5, 2), (0, 5)

26) (-2, -4), (-6, -4) 27) (3, -2), (-1, -6) 28) x = 1 29) y = -3

30) -6x + 5y = 30 31) 2y – 7 = x 32) x – 7 = 0 33) 2y + 4 = 7

Determine which line has greater slope.

34)

35)

36)

37)

38)

39)

Determine if the lines are parallel, perpendicular, or neither. 40) y = -3x + 6; y = 3x + 5 41) -4x + 2y = 5; 2x – y = 7 42) y = 5x – 6; y = 5x + 2

43) 2x – y = -10; 2x + 4y = 2 44) -2x + 3y = 1; 3x + 2y = 12 45) x + 4y = 7; 2x – 5y = 0

Answer the following application questions

46) The annual average income y of an American man over 25 years with an associate’s degree is approximated by the linear equation y = 694.9x + 43,884.9, where x is the number of years after 2000.

a. Predict the average income of a man in 2009 b. Find and interpret the slope of the equation. c. Find and interpret the y-intercept of the equation.

47) With WiFi gaining popularity, the number of public wireless Internet access points, in thousands, is projected to grow from 2003 to 2008 according to the equation -66x + 2y = 84, where x is the number of years after 2003.

a. Find the slope and y-intercept of the linear equation. b. What does the slope mean in this context? c. What does the y-intercept mean in this context?

Graph the following piecewise functions.

48) 𝑓 𝑥 = 2𝑥, 𝑥 < 0

𝑥 + 1, 𝑥 ≥ 0

49) 𝑓 𝑥 = 3𝑥, 𝑥 ≤ 0

𝑥 + 2, 𝑥 > 0

50) 𝑓 𝑥 = 5𝑥 + 4 𝑥 < 21

3𝑥 − 1, 𝑥 ≥ 2

51) 𝑓 𝑥 = −4𝑥, 𝑥 < 0

3𝑥 − 2, 𝑥 ≥ 0

52) 𝑓 𝑥 = 4, 𝑥 < −3

𝑥 − 2, 𝑥 ≥ −3

53) 𝑓 𝑥 = −𝑥, 𝑥 < −1

2𝑥 + 1, 𝑥 ≥ −1

54) 𝑓 𝑥 = −𝑥, 𝑥 < −1

2𝑥 + 1, 𝑥 ≥ −1

Day 6 Write an equation of a line in slope-intercept form using the given information.

1. slope of – ½ ; y-intercept of -9 2. through (0, 4) and (-1, 3) 3. slope of ¼ ; value of f(0) = 7 4. slope of -5; through (1, 2)

5. through 1,21 and

25,3

6. values f(-5) = 3 and f(4) = -5 Write an equation of a line in point-slope form using the given information.

7. slope of – ⅖; through (3, -7) 8. through (5, -6) and (1, -7) 9. through (6, -3) and (-1, 9)

Write an equation in the given form of the line shown. 10. slope-intercept form 12. point-slope form

Write an equation in standard form using the given information.

13. y = - ⅓x – 5 14. slope of ⅛; through (16, -5) 15. through ( -4, 2) and (1, -1)

Write an equation in slope-intercept form of a line with the given characteristics.

16. parallel to y = x + 3; through (5, 0) 17. parallel to y = -2x + 8; through (-4, 1) 18. perpendicular to y = ⅔x – 4; through (-6, 1) 19. perpendicular to 3x + 5y = 10; through (-15, 6) 20. horizontal line through (9, -3) 21. vertical line through (5, 8)

Write equations to model the given situations. Then answer the related questions. 22. Marvin likes to run from his home to the recording studio. He uses his

iPod to track the time and distance he travels during his run. The table below shows the data he recorded during yesterday’s run.

a. Write an equation in slope-intercept from to model this situation.

b. What is the slope? What is the meaning of the slope in the context of the problem? c. If Marvin always runs at this pace, how long does it take him to go 12 kilometers to his

recording studio? 23. A piggy bank contains only nickels worth $0.05 and quarters worth $0.25. The total value in the

bank is $3.80. a. Write an equation in standard form that models the possible combinations of nickels

and quarters in the piggy bank. b. List two possible combinations.

24. A delivery service charges a base price for an overnight delivery of a package plus an extra

charge for each pound the package weighs. A customer is billed $18.01 for a 7-pound package and $21.30 for an 11-pound package.

a. Write an equation in slope intercept form that gives the total cost of shipping a package as a function of the weight of the package.

b. What is the meaning of the slope in context of the problem? c. What is the meaning of the y-intercept in context of the problem? d. If a customer paid $30, about how much did the package weigh?

25. You are going to a carnival and pay $7 to enter. You then have to pay $2 per ride you wish to ride.

a. Write an equation that gives the total cost of attending the carnival and riding the rides. b. Find the total cost of going if you plan on riding 8 rides. c. How many rides can you go on if you have a budget of $25?

26. A local pool has an annual membership fee and then charges your family for each visit. You

know that each time you go to the pool your family has to pay $5. You also know that after 15 visits this year you have paid a total of $174.

a. Write an equation in slope intercept form relating the cost of swimming at the pool in terms of the number of visits.

b. What is the annual membership fee for having access to the pool? c. If your family only has $150 for swimming next year, how many times can they visit the

pool? 27. The table shows the cost of mailing different weights of letters to Canada. Write an equation

that gives the cost in dollars as a function of the weight of an airmail letter.

a. What is the meaning of the slope? b. What is the meaning of the y-intercept? c. How much does it cost to mail a 15 ounce package?

Choose the best response. 28 29

30 31