1-1 Patterns and Expressions

Objective

A2. F.BF.A.1 Write a function that describes a relationship between two quantities.

Key Concepts

__________________ - a symbol, usually a letter, that represents one or more numbers.

_________________________________- a mathematical phrase that contains numbers

and operation symbols.

______________________________- a mathematical phrase that contains one or more

variables.

Examples

1. Look at the figures below. Do you see a pattern? What would be the next figure in the

pattern?

2. What would be the 10th number in the pattern 4, 7, 10, 13, 16…? What is an expression

that describes the number for the nth term?

3. Identify a pattern by making a table for the coordinates (1, 4), (2, 6), (3, 8), (4, 10). Then

find the next coordinate.

x rule y

n

4. Identify a pattern by making a table of the inputs and outputs. Include a process column.

a. b)

Practice 1-1: Complete your assignment on a separate sheet of paper. Show all work.

Describe each pattern using words. Draw the next figure in each pattern.

1.

Identify the pattern and find the next three numbers in the pattern.

2. 1, 4, 16, 64, . . . 3. 3, 6, 12, 24, . . .

The graph shows the number of cups of flour needed for Baking Cookies

baking cookies.

4. How many cups of flour are needed for baking 4 batches of cookies?

5. How many cups of flour are needed for baking 30 batches

of cookies? Number of batches of cookies

6. How many cups of flour are needed for baking n batches of cookies?

1-2 Properties of Real Numbers

Objective

A2. F.BF.A.1 Write a function that describes a relationship between two quantities.

Key Concepts

Subsets of the Real Numbers

Real Numbers

Name Description Examples

Natural Numbers

Whole Numbers

Integers

Rational Numbers

Irrational Numbers

Rational Numbers

Integers

Whole Numbers

Natural Numbers

Irrational

Numbers

Examples

1. Graph the numbers −4,3

2, √5, −

12

5, 𝜋

2. Which set of numbers bests describes a person’s age?

3. Which set of numbers best describes the amount of money in a bank account?

4. Name the property

a. (2

3) (

3

2) = 1 b. (3∙4) ∙ 5 = (4∙3) ∙ 5 c. x + (y + z) = (x + y) + z

Practice 1-2: Complete your assignment on a separate sheet of paper. Show all work.

Graph the numbers on a number line.

1. 1

52

, −4, 2.25, 1

63

, 8

Name the property of real numbers illustrated by each equation.

2. 6(2 + x) = 6 · 2 + 6 · x 3. 2 · 20 = 20 · 2 4. 8 + (−8) = 0

5. 2(0.5 · 4) = (2 · 0.5) · 4 6. −11 + 5 = 5 + (−11)

7. Estimate the numbers graphed at the labeled points.

Property Addition Multiplication

Closure a + b is a real number ab is a real number

Commutative a + b = b + a ab = ba

Associative (a + b) + c = a + (b + c) (ab)c = a(bc)

Identity 0 is the additive identity

1 is the multiplicative

identity

a + 0 = a a•1 = a

Inverse a + -a = 0 a • (1/a) =1, a ≠ 0

Distributive a( b + c) = ab + ac

1-3 Algebraic Expressions

Objective

A2. F.BF.A.1 Write a function that describes a relationship between two quantities.

Key Concepts

__________________ - an expression that is a number, a variable, or the product of a

number and one or more variables

______________________- the numerical factor of a term

______________________________- a term with no variable

_____________________- the same variables raised to the same power

Examples

1. Write the algebraic expression for the phrases.

a. Seven fewer than t __________

b. Two times the sum of a and 5 __________

c. Four more than three times the difference of x and 12 __________

2. Model the situation using an algebraic expression.

a. A job pays $12.50 per hour and 20% commission. __________

b. Your allowance is $150 per month and you spend $3 a day. __________

3. You are hosting a party and decide to buy pizza, chips and drinks. Each pizza costs $5,

each bag of chips costs $3.50 and each 2-Liter drink costs $1.25. Write an algebraic

expression that models the situation and determine the total cost to purchase 3 pizzas, 2

bags of chips and 4 drinks.

4. Simplify by combining like terms.

a. 4𝑥2 + 5𝑥 − 12𝑥2 − 3 + 𝑥 ______________________________

b. −1 + 3𝑥 − 4𝑥 + 𝑥2 − 2 ______________________________

c. 3(𝑎 + 4) − 𝑥 + 2(𝑥 − 4) ______________________________

5. Evaluate the expression 6c + 5d - 4c - 3d + 3c - 6d; for the given values of the variables

c = 4 and d = -2

Practice 1-3: Complete your assignment on a separate sheet of paper. Show all work.

Write an algebraic expression that models each word phrase.

1. six less than the number r 2. five times the sum of 3 and the number m

Write an algebraic expression that models each situation.

3. Alexis has $250 in her savings account and deposits $20 each week for w weeks.

4. You have 30 gallons of gas and you use 5 gallons per day for d days.

Evaluate each expression for the given values of the variables.

5. −2a + 5b + 6a − 2b + a; a = −3 and b = 2

6. y(3 − x) + x2; x = 2 and y = 12

7. 3(4e − 2f) + 2(e + 8f); e = −3 and f = 10

Write an algebraic expression to model the total score in each situation. Then

evaluate the expression to find the total score.

8. In the first half, there were fifteen two-point shots, ten three-point shots and 5

one-point free throws.

1-4 Solving Equations

Objectives

A2. F.BF.A.1 Write a function that describes a relationship between two quantities.

A2.A.CED.A.2 Rearrange formulas to highlight a quantity of interest.

Key Concepts

Property Definition

Reflexive

Symmetric

Transitive

Substitution

Addition/

Subtraction

Multiplication/

Division

___________________- an equation that is true for every value of the variable.

________________________________- an equation that uses at least 2 letters as variables. You

can solve for any variable “in terms of” the other variables.

Examples

1. Solve the one-step equations.

a. 𝑤 − 2 = 10 b. 𝑦

4= −3

2. Solve the two-step equations.

a. −4𝑧 + 1 = 26 b. 2

3𝑥 − 2 = 10

3. Solve the multi-step equations.

a. 3(2𝑥 − 1) = 11𝑥 b. −6𝑦 + 27 = 3(𝑦 − 3)

4. Determine whether the equations are always true, sometimes true or never true.

a. 11 + 3 − 7 = 6𝑥 + 5 − 3𝑥 b. 6𝑥 + 5 − 2𝑥 = 4 + 4𝑥 − 1

5. Solve the literal equations.

a. 𝑑 = 𝑟𝑡 for 𝑟 b. 𝐶 =5

9(𝐹 − 32) for 𝐹

6. The cost to rent a moving truck is $75 plus $58 per hour. If Keisha paid $336 to rent the

truck, how many hours did she rent the truck?

7. Avery charges $10 to babysit one child and $3.50 for each additional child. If Avery

earned $38.00, how many children did she babysit?

Practice 1-4: Complete your assignment on a separate sheet of paper. Show all work.

Solve each equation. Check your answer.

1. 5x + 4 = 2x + 10 2. 4(d − 3) = 2d 3. 5w + 8 − 12w = 16 − 15w

Write an equation to solve each problem.

4. Lisa and Beth have babysitting jobs. Lisa earns $30 per week and Beth earns $25

per week. How many weeks will it take for them to earn a total of $275?

1-5 Solving Inequalities

Objective

A2. F.BF.A.1 Write a function that describes a relationship between two quantities.

Key Concepts Writing and graphing inequalities

__________________________ - two inequalities joined with the word and or the word or

AND means that a solution makes BOTH inequalities true.

OR means that a solution makes EITHER inequality true.

x > 4 x is greater than 4

x ≥ 4 x is greater than or equal to 4

x < 4 x is less than 4

x ≤ 4 x is less than or equal to 4

Examples

1. Write an inequality that represents the sentence.

a. Two fewer than a number is at most ten. __________________________

b. The quotient of a number and 5 is no more than 14. _________________

c. A person must be at least 48 inches to ride. ________________________

2. Graph the inequalities

a. 𝑛 ≤ 5

b. 𝑥 > −2

c. 4 ≤ 𝑎

3. Solve the inequality and graph the solution.

a. 2𝑥 + 6 > 13 b. −3(2𝑥 − 5) + 1 ≤ 4

4. A music download service has two subscription plans. The first plan has a $9

membership fee and then charges $1 per download. The second plan charges a $25

membership fee and $.50 per download. How many songs must you download for the

second plan to cost less than the first plan?

5. Is the inequality, always, sometimes or never true?

a. −2(3𝑥 + 1) > −6𝑥 + 7 b. 5(2𝑥 − 3) − 7𝑥 ≤ 3𝑥 + 8

6. Solve the compound inequality and graph 7 < 2𝑥 + 1 and 3𝑥 ≤ 18.

7. Solve the compound inequality and graph 7 + 𝑘 ≥ 6 or 8 + 𝑘 < 3.

8. Solve the compound inequality and graph −6 ≤ 2𝑥 − 4 ≤ 12

9. Write the solution set as a graph and as an interval.

a. 𝑛 ≤ −3 ______________

b. −1 ≤ 𝑛 ≤ 5 ______________

c. 𝑥 > 2 ______________

d. 𝑥 > 0 𝑎𝑛𝑑 𝑥 ≤ 6 ______________

e. 𝑥 ≤ −3 𝑜𝑟 𝑥 ≥ −2 _____________

Practice 1-5: Complete your assignment on a separate sheet of paper. Show all work.

Write the inequality that represents the sentence.

1. Five less than a number is at least −28.

2. The product of a number and four is at most −10.

3. Six more than a quotient of a number and three is greater than 14.

Solve each inequality. Graph the solution.

4. 5a − 10 5 5. 25 − 2y ≥ 33

6. −2(n + 2) + 6 ≤ 16 7. 2(7a + 1) 2a − 10

Solve the following problem by writing an inequality.

8. The width of a rectangle is 4 cm less than the length. The perimeter is at

most 48 cm. What are the restrictions on the dimensions of the rectangle?

Is the inequality always, sometimes, or never true?

9. 5(x − 2) ≥ 2x + 1 10. 2x + 8 ≤ 2(x + 1)

11. 6x + 1 3(2x − 4) 12. 2(3x + 3) 2(3x + 1)

Solve each compound inequality. Graph the solution.

13. 2x −4 and 4x 12

14. 3x ≥ −12 and 5x ≤ 5

Write an inequality to represent each sentence.

15. The average of Shondra’s test scores in Physics is between 88 and 93.

1-6 Absolute Value Equations and Inequalities

Objective

A2. F.BF.A.1 Write a function that describes a relationship between two quantities.

Key Concepts

______________________________ - the distance from zero on the number line.

Written |x|

__________________________________- a solution derived from an original equation

that is NOT a solution to the original equation.

Steps to solve an absolute value equation

1.

2.

3.

4.

Examples

1. Solve and check the absolute value equation.

a. |2𝑥 − 1| = 5 b. 3|𝑥 + 2| − 1 = 8

2. Solve and check for extraneous solutions.

a. |3𝑥 + 2| = 4𝑥 + 5

3. Solve and graph the inequality.

a. |2𝑥 − 1| + 1 < 5 b. |2𝑥 + 4| ≥ 6

4. Solve and graph the inequality.

a. |𝑥−3

2| + 2 < 6 b.

2

3|6𝑥 − 2| ≥ 4

Practice 1-6: Complete your assignment on a separate sheet of paper. Show all work.

Solve each equation. Check your answers. Graph the solution.

1. 2 = 12x 2. 7 = 1t

3. 4 + 1 = 24z 4. 2 1 5w

5. 5 2 3 8y 6. 2 5 3 10t t

7. 2 4 1 4 10y y 8. 1 5 2w w

Write an absolute value equation to describe each graph.

9. 10.