Chapter 1. Expressions, Equations, and Functions
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1 Chapter 1 Expressions, Equations, and Functions
2 1.1 Evaluate Expressions I can evaluate algebraic expressions and use exponents. CC.9-12.N.Q.1
3 Vocabulary: Variable a letter used to represent one or more numbers Algebraic expression expression that includes at least one variable
4 Evaluate an Algebraic Expression Substitute a number for each variable and simplify, if needed Example: Evaluate the expression when c = 4 a)4c b)8/c c)15 + c
5 Powers: Note: anything to the zero power = 1
6 Examples: Write the power in words and as a product. a)5 2 b) 1 2 3
7 Example: Evaluate the expression. A) n 5 when n = 3 B) d 2 when d = 9 5
8 HOMEWORK: p. 5 #1, 2, 4 48 even
9 1.2 Apply Order of Operations I can use order of operations to evaluate expressions. CC.9-12.A.SSE.1
10 In most languages, the meaning of words depend on the order: Ex. Sign the check Is not the same as Check the sign
11 Mathematics is a type of language with its own syntax and grammar. Ex X 2 What do we do first? Add or multiply? If we add first: X 2 If we multiply first: X 2 8 X Uh Oh! Which one is the correct answer?
12
13 What is PEMDAS? In order to make sure every person gets the same answer to a math problem, mathematicians came up with a rule called the order of operations Parenthesis ( ) [ ] Exponents 2 3 Multiplication X Division Addition + Subtraction - In order from left to right! In order from left to right!
14 Example: Evaluate (1 (-3)) 3 14
15 Example: Evaluate -4x 2 + 6x 5 when x = -3 15
16 HOMEWORK: p. 10 #1, 2, 4-34 even
17 1.3 Write Expressions I can translate verbal phrases into expressions. CC.9-12.A.SSE.1
18 Translate Verbal Expressions
19 Example: Translate the verbal phrase into an expression. a)8 times the quantity 4 plus a number n b)12 decreased by a number x c)the quotient of the square of a number w and 5
20 Vocabulary: Verbal model: describes real-world situations using words and math symbols Rate: fraction that compares two quantities measured in different units Unit rate: rate where the denominator is 1 unit
21 Example: A runner travel 730 yards in 5 minutes. Find the unit rate in feet per second. * Check your unit analysis!
22 HOMEWORK: p. 18 #1, 2, 4 28 even, 31, 32
23 1.4 Write Equations and Inequalities I can translate verbal sentences into equations or inequalities. CC.9-12.A.CED.1
24 Vocabulary: Equation: Inequality: Open sentence:
25 Symbol Meaning Words = < > Equal to Less than Less than or equal to Greater than Greater than or equal to The same as Fewer than At most, no more than More than At least, no less than
26 Example: Write an equation or inequality. a) The sum of twice a number r and 3 is 11. b) The quotient of a number n and 2 is at most 16. c) A number q is at least 5 and less than 17.
27 Solution of the equation or inequality: a number that makes the equation/inequality true. Example: check whether 5 is a solution of the equation or inequality a) 24 3d = 9 b) 4 + 3p > 19
28 HOMEWORK: p. 24 #1, 2, 4 36 even, pick 3 from #39-43
29 1.5 Use a Problem Solving Plan I can use a problem solving plan to solve problems. CC.9-12.A.CED.1
30 Vocabulary: Formula equation that relates two or more quantities. Examples:
31 4 Step Plan: 1)Understand 2)Plan 3)Solve 4)Check
32 A builder lays sod on the lawns of new homes. The installed cost for sod is $.38 per square foot. What is the cost of installing sod on a rectangular lawn that is 32 feet long and 18 feet wide?
33 Activity
34 HOMEWORK: p. 31 #1 10, 14-19
35 1.6 Use Precision and Measurement I can compare measurements for precision. CC.9-12.N.Q.3
36 Vocabulary: Precision level of detail that an instrument can measure Significant digits digits in a measurement that carry meaning that contributes to precision of measurement
37 Precision: Choose the more precise measurement a) 7 cm or 7.3 cm b) 0.2 gal or 6 qt c) 7 in or 2.02 ft
38 Significant Digits (figures): numbers that are important to precision of measurement All non zero digits (5 sig figs) Zeros to the right of the last nonzero digit and the decimal point (2 sig figs) Zeros between significant digits (4 sig figs)
39
40 Example: Determine the number of significant digits in each measurement. a) 250 b) c) 30.04
41 Rules for Sig Figs in Calculations: Addition/Subtraction: Round the answer to same place as last digit of the least precise measurement. Multiplication/Division: answer must have the same number of digits as the least precise measurement.
42 HOMEWORK: p. 38 #1-28
43 1.7 Represent Functions as Rules and Tables I can represent functions as rules and as tables. CC.9-12.A.CED.2
44 Vocabulary: Function: pairing of inputs with outputs so that each input is paired with exactly one output. Domain: set of all inputs Range: set of all outputs
45 Input Output Example: Look at the input value and determine what rule applies to get the output value
46 Example: Tell whether the pairing is a function.. a) Input output b) Input output
47 Function Rules: Independent variable input variable Dependent variable value depends on value of input; output
48 Example: The domain of the function is y = x + 4 is 0, 2, 3, 6, and 7. Make a table for the function. Identify the domain and range.
49 HOMEWORK: p. 44 #1 10, 14-21
50 1.8 Represent Functions as Graphs I can represent functions as graphs. CC.9-12.F.IF.4
51 perimeter Model: Let n = # of triangles Let p = the perimeter of each figure Table: Graph: Equation: n p Dependent p n # of triangles Dependent p = n + 2
52 This chart shows the price of sliced fruit platters. Platter Weight Price 1 lb. $ lb. $ lb. $ lb. $ lb. $8.10 3) How much would a 10 lb. platter cost? 1) How much would a 6 lb. platter cost? 2) Write an equation for the cost of a platter that weighs w lbs. Let p = price of platter p = 1.50 w Change Start Value
53 A taxi cab charges a flat rate of $2.50 and 15 cents per mile. Write a linear equation for the charge in terms of the number of miles driven. Then graph the function. Let C = charge in dollars Let m = # of miles driven
54 A car s fuel tank is filled at a rate of 1.6 gal/min. The tank held 5 gallons of gas before refueling. Let m = # of minutes Let V = Volume of gas in tank Equation: Table: m V Graph:
55 HOMEWORK: p. 52 #1 13, 15-17
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