Evaluate algebraic expressions and use exponents. Translate verbal phrases into expressions.

Transcription

1 Algebra 1 Notes Section 1.1: Evaluate Expressions Section 1.3: Write Expressions Name: Hour: Objectives: Section 1.1: (The "NOW" green box) Section 1.3: Evaluate algebraic expressions and use exponents. Translate verbal phrases into expressions. Vocabulary: Section 1.1: I. Variable: A variable is a letter used to represent one or more numbers. numbers variables II. Algebraic Expression An algebraic expression consists of,, (variable expression): and operations. To evaluate an algebraic expression, substitute a number for the variable, perform the operation(s), and simplify the result if necessary. expression III. Power: A power is an that represents repeated multiplication of the same factor number expression IV. Base (base of a power): The or that is (see the glossary) used as a factor in a repeated multiplication number variable represents V. Exponent: The or that the number of times the base of a power is used Section 1.3: VI. Translating Verbal Phrases: as a factor Operation Key words/phrases Verbal Phrase Expression ADDITION SUBTRACTION MULTIPLICATION DIVISION sum, plus, total, more than, increased by difference, less than, minus, decreased by times, product, multiplied by, of quotient, divided by, divided into The sum of and a number x + x A number n plus 7 n + 7 The difference of a number n and 6 n 6 A number y minus 5 y 5 1 times a number y 1y ⅓ of a number x The quotient of a number k and ⅓ x k

2 real-world VII. Verbal Model: A situation using words as labels Notes 1.1 & 1.3 page and using math symbols to relate the words fraction two VIII. Rate: A that compares quantities measured in different units. denominator fraction 1 IX. Unit Rate: A rate in which the of the is Examples: 1. Consider 5. What is the base? What is the power? What is the exponent?. Write the power in words and as a product: 3 3. Evaluate the expression. a. n 5 when n = 3 b. d when d = 5 9. Translate the verbal phrase into an expression. a. 8 times the quantity plus a number n. b. 1 decreased by a number x. c. The quotient of the square of a number w and 5. d. The difference of and the square of a number m. e. The quotient when the quantity ten plus a f. Seventeen less than two times a number x. number x is divided by two. 5. A 16-ounce box of cereal costs $.99. Find the unit rate to the nearest cent. 6. Your basic monthly charge for cell phone service is $60 which includes unlimited talk time and 300 text messages. You pay a fee for each extra text message that you send or read if you go over the 300 included text messages. One month you paid $.35 for 15 extra text messages. Find your total bill if you used 5 extra text messages.

3 Algebra 1 Notes Section 1.: Apply Order of Operations Objective: You will use the order of operations to evaluate expressions. Vocabulary: I. Order of Operations: Rules for evaluating an expression involving more than one operation. Step 1: Evaluate expressions inside grouping symbols. Step : Evaluate powers. Step 3: Multiply and divide from left to right. Step : Add and subtract from left to right. ( ) { } II. Grouping Symbols: Parentheses: Brackets: Fraction Bar: Examples: 1. Evaluate the expression. Show your work. Circle your answer. a x b. ( 1) c. 8 (6 + 5 ) d. 3[3 ( + 6)] e f. 5 + (7 5)

4 Notes 1. page. Evaluate the expression 10x ( x ) when x = John had copies of a science report made to give to his lab partners. In each copied report there were 0 black-and-white pages and 5 color pages. He paid a copy center to make and bind the copies. His cost in dollars is given by the expression (5c + 0b), where c is the cost of a color page and b is the cost of a black-and-white page. What is the total cost if a color page costs $ and a black-and-white page costs $0.05?. Insert grouping symbols in the expression so that the value of the expression is equal to

5 Algebra 1 Notes Section 1.: Write Equations and Inequalities Objective: You will translate verbal sentences into equations or inequalities. Vocabulary: mathematical statement I. Open Sentence: A that contains two algebraic expressions and a symbol that compares them. open sentence = II. Equation: An that contains the symbol. open sentence III. Inequality: An that contains one of <,, >, or the symbols. IV. Symbols and their meanings: Symbol Meaning Associated Words = is equal to the same as < is less than fewer than is less than or equal to at most, no more than > is greater than more than is greater than or equal to at least, no less than Combining Inequalities: Sometimes two inequalities are combined. For example, x > and x < 9 can be combined to form the inequality < x < 9 However, x > or x < 9 cannot be combined to form an inequality. V. Solution of an Equation: A that produces a (see the glossary) when number true statement substituted for the variable in an equation. number VI. Solution of an Inequality: A that produces a true statement when substituted for the variable in an inequality.

6 Examples: Notes 1. page 1. Write an equation or an inequality. a. The sum of twice a number r and three is eleven. b. The quotient of a number n and two is at most sixteen. c. A number q is at least five and is less than 17.. Write an expression or an equation. a. Three less than twice a number x. b. Three is less than twice a number x. 3. Check whether 5 is a solution of the equation or inequality. a. 3d = 9 b. w 7 3 c. + 3p > 19. Solve the equation using mental math. h a. y + 8 = 13 b. a 6 = 3 c. 8c = 3 d Sarah enrolled in a guitar class. The enrollment fee was $5. She paid a total of $70 for the enrollment fee and 3 lessons. What is the cost of 3 lessons? How much did each lesson cost? 6. Tyler would like to make no less than $610 selling coffee mugs online. If he sells 8 mugs for $ each, will he achieve his goal?

7 Algebra 1 Notes Section 1.6: Represent Functions as Rules and Tables Section 1.7: Represent Functions as Graphs Objectives: Section 1.6: Section 1.7: You will represent functions as rules and as tables. You will represent functions as graphs. Vocabulary: I. Function: A rule that consists of: domain A set called the containing numbers called and range inputs outputs a set called the containing numbers called. Definition of function: A pairing of inputs with outputs such that each input is paired with exactly one output.. * A function may be represented by a mapping diagram. * A function cannot have one input mapped to two (or more) different outputs. II. Independent Variable: The variable. input III. Dependent Variable: The variable. output IV. Function Rules: Verbal Rule Equation Table The output is 3 more than the input. y = x + 3 Input, x 0 1 3, y V. Ordered Pair of a Function: The point, ( input, output ) from a table.

8 Examples: 1. The input-output table shows the amount of money Miguel earns at his job for several numbers of hours. List the domain and the range of the function. Input (hours) (dollars) Notes 1.6 & 1.7 page. Tell whether the pairing is a function. Use the definition of a function to tell why or why not (if it is not a function, give the specific example(s) from the problem shown that do not fit the definition). Input Input a. b. c. 0 0 Input d. e. Input 1 1 Input The domain of the function y = x + is 0,, 3, 6, and 9. Complete the table for this function. Then write the entries of the table as ordered pairs for the function. Input Ordered pairs:

9 Notes 1.6 & 1.7 page 3. Write a rule for the function: Input p 5. The table shows the profit p (in thousands of dollars) at a small toy store each year from 000 to 00 as a function of the time t in years since 000. Graph the function. 3 t p Profit (in thousands) Time (years since 000) t y 6. Write a rule (equation) for the function represented by the graph. Identify the domain and the range of the function. 6 5 Rule: 3 Domain: 1 Range: x