Name Class Date. Understanding Functions

Size: px
Start display at page:

Download "Name Class Date. Understanding Functions"

Transcription

1 Name Class Date 3-2 Relations and Functions Going Deeper Essential question: How do you represent functions? F-IF.. ENGAGE Understanding Functions A set is a collection of items called elements. A function pairs each element in one set, called the domain, with exactly one element in a second set, called the range. For example, the function below pairs each element in the domain with its square. Domain Range A function can be described using function notation. The function f assigns the output value f (x) in the range to the corresponding input value x from the domain. The notation f (x) is read as f of x. (It does not indicate the product f times x. ) For the function shown above, f (3) = 9. REFLECT a. The domain of the function can be written using set notation as {0,, 2, 3, 4}. Write the range of the function using set notation. b. Tell how to read the statement f (4) = 6. Then interpret what it means in terms of input and output values. c. Suppose the 3 were paired with the 4 instead of the 9. Would the pairing of the two sets still be a function? Why or why not? d. Suppose the 3 were paired with the 4 and the 9. Would the pairing of the two sets still be a function? Why or why not? e. If you pair each month with all the possible numbers of days in the month, will you get a function? Why or why not? Chapter 3 2 Lesson 2

2 Functions are often used to describe a relationship between two variables. The independent variable represents an input value of the function and the dependent variable represents an output value. An algebraic expression that defines a function is a function rule. For example, x 2 is the function rule for the squaring function f (x) = x 2. If you know a value for the independent variable, you can use a function rule to find the corresponding value for the dependent variable. 2 F-IF..2 EXAMPLE Representing Discrete Linear Functions The cost of sending m text messages at $0.25 per message can be represented by the function C(m) = 0.25m. A Complete the table for the given domain values. Write the results as ordered pairs in the form (independent variable, dependent variable). Independent variable, m Dependent variable, C(m) = 0.25m (m, C(m)) (0) = 0 (0, 0) B Choose a beginning, an end, and a scale for the vertical axis. C Graph the function by plotting the ordered pairs. The independent variable goes on the horizontal axis and the dependent variable on the vertical axis. Use scales that will make it easy to read points. Label the graph. C(m) m Chapter 3 22 Lesson 2

3 REFLECT 2a. Use function notation to represent the cost of sending 5 text messages. Evaluate the function for that value. Include units. 2b. Suppose that the domain of the function is not limited as in the Example. Describe a reasonable domain of the function. 2c. Suppose that the domain of the function is not limited as in the Example. Describe a reasonable range of the function. 2d. Is the independent variable represented by the horizontal axis or the vertical axis? Why does this make sense? 2e. Would it make sense to connect the points on the graph with a line? Why or why not? 2f. The figure below shows a representation of the function rule. Explain what is being shown in the context of the situation. Input Rule: C(m) = 0.25m Output g. Suppose the cost per text message were $0.20 instead of $0.25. Then the cost of sending m text messages could be represented by the function C(m) = 0.2m. Describe a reasonable domain and range for this function. Chapter 3 23 Lesson 2

4 3 F-IF.2.5 EXAMPLE Representing Discrete Nonlinear Functions Ben wants to tile part of a floor with 36 square tiles. The tiles come in whole-number side lengths from 2 to 6 inches. If s is the side length of a tile, the area that he can cover is A(s) = 36 s 2. A Identify the domain of the function. B Make a table of values for this domain. Write the results as ordered pairs in the form (independent variable, dependent variable). Independent variable, s Dependent variable, A(s) = 36 s 2 (s, A(s)) C Choose a beginning, an end, and a scale for the vertical axis. D Graph the function by plotting the ordered pairs. A(s) s Chapter 3 24 Lesson 2

5 REFLECT 3a. Identify the range of the function. 3b. What does A(3) = 324 mean in this context? 3c. Describe another reasonable beginning, end, and scale for the vertical axis. Include units. 3d. Do the points appear to lie in a straight line? PRACTICE Tell whether each pairing of numbers describes a function. If so, identify the domain and the range. If not, explain why not.. Each whole number from 0 to 9 is paired with its opposite. 2. Each odd number from 3 to 9 is paired with the next greater whole number. 3. The whole numbers from 0 to 2 are paired with their factors. 4. Each even number from 2 to 0 is paired with half the number. 5. {(36, 6), (49, 7), (64, 8), (8, 9), (36, -6), (49, -7), (64, -8), (8, -9)} 6. {(-64, -4), (-27, -3), (-8, -2), (-, -), (0, 0), (, ), (8, 2), (27, 3), (64, 4)} Chapter 3 25 Lesson 2

6 7. Whitley has a $5 gift card for music downloads. Each song costs $ to download. The amount of money left on the card can be represented by the function M(d) = 5 - d, where d is the number of songs she has downloaded. a. Make a table and graph the function. d M(d) (d, M(d)) M(d) d b. Identify the domain and range of the function and the units of the independent and dependent variables. 8. Ben wants to cover a table that has an area of 864 square inches. The function T(s) = gives the number of tiles he needs with side length s. The tiles come in s side lengths of in., 4 in., 6 in., and 2 in. a. Make a table and graph the function. s T(s) (s, T(s)) T(s) s b. Identify the domain and range of the function and the units of the independent and dependent variables. Chapter 3 26 Lesson 2

7 Name Class Date 3-2 Additional Practice Express each relation as a table, as a graph, and as a mapping diagram.. {( 5, 3), ( 2, ), (, ), (4, 3)} x y 2. {(4, 0) (4, ), (4, 2), (4, 3), (4, 4), (4, 5)} x y Give the domain and range of each relation. Tell whether the relation is a function. Explain x y D: D: D: R: R: R: Function? Function? Function? Explain: Explain: Explain: Chapter 3 27 Lesson 2

8 Problem Solving Give the domain and range of each relation and tell whether it is a function.. The mapping diagram shows the ages 2. and grade level of four children. Age Shoe Size The list represents the number of cars sold and the bonus received by the salespeople of a car dealership. {(, 50), (2, 50), (3, 00), (4, 50)} 4. A 2-inch-tall plant grows at a rate of 2.5 inches every week for 5 weeks. Let represent the number of weeks and represent the height of the plant. Use the graph below to answer questions 5 6. A conservation group has been working to increase the population of a herd of Asian elephants. The graph shows the results of their efforts. Select the correct answer. 5. Which relation represents the information in the graph? A {(, 4.5), (2, 6), (3, 0), (4, 4.5)} B {(, 5), (2, 6), (3, 0), (4, 5)} C {(4.5, ), (6, 2), (0, 3), (4.5, 4)} D {(5, ), (6, 2), (0, 3), (5, 4)} 6. What is the range of the relation shown in the graph? F {0,, 2, 3, 4, 5} G {, 2, 3, 4} H {4.5, 6, 0, 4.5} J {5, 6, 0, 5} Chapter 3 28 Lesson 2

Unit Essential Questions: Does it matter which form of a linear equation that you use?

Unit Essential Questions: Does it matter which form of a linear equation that you use? Unit Essential Questions: Does it matter which form of a linear equation that you use? How do you use transformations to help graph absolute value functions? How can you model data with linear equations?

More information

Essential Questions. Key Terms. Algebra. Arithmetic Sequence

Essential Questions. Key Terms. Algebra. Arithmetic Sequence Linear Equations and Inequalities Introduction Average Rate of Change Coefficient Constant Rate of Change Continuous Discrete Domain End Behaviors Equation Explicit Formula Expression Factor Inequality

More information

Jakarta International School 8 th Grade AG1

Jakarta International School 8 th Grade AG1 Jakarta International School 8 th Grade AG Practice Test - Green Unit : Graphing Name: Date: Score: 85 Goal 4: Students convert graphical, symbolic, and numerical representations of data. The points (-,)

More information

Processing, representing and interpreting data

Processing, representing and interpreting data Processing, representing and interpreting data 21 CHAPTER 2.1 A head CHAPTER 17 21.1 polygons A diagram can be drawn from grouped discrete data. A diagram looks the same as a bar chart except that the

More information

Lesson 1.1 Exercises, pages 8 12

Lesson 1.1 Exercises, pages 8 12 Lesson 11 Exercises, pages 8 12 A 4 Circle each sequence that could be arithmetic Determine its common difference, d a) 6,10,14,18, b) 9,7,5,, d is: 10 6 4 d is: 7 9 2 c) -11, -4,,10, d) 2, -4, 8, -16,

More information

About Finish Line Mathematics 5

About Finish Line Mathematics 5 Table of COntents About Finish Line Mathematics 5 Unit 1: Big Ideas from Grade 1 7 Lesson 1 1.NBT.2.a c Understanding Tens and Ones [connects to 2.NBT.1.a, b] 8 Lesson 2 1.OA.6 Strategies to Add and Subtract

More information

Advanced Algebra I Simplifying Expressions

Advanced Algebra I Simplifying Expressions Page - 1 - Name: Advanced Algebra I Simplifying Expressions Objectives The students will be able to solve problems using order of operations. The students will identify expressions and write variable expressions.

More information

Unit 0: Extending Algebra 1 Concepts

Unit 0: Extending Algebra 1 Concepts 1 What is a Function? Unit 0: Extending Algebra 1 Concepts Definition: ---Function Notation--- Example: f(x) = x 2 1 Mapping Diagram Use the Vertical Line Test Interval Notation A convenient and compact

More information

Name Class Date. Using Graphs to Relate Two Quantities

Name Class Date. Using Graphs to Relate Two Quantities 4-1 Reteaching Using Graphs to Relate Two Quantities An important life skill is to be able to a read graph. When looking at a graph, you should check the title, the labels on the axes, and the general

More information

Create a bar graph that displays the data from the frequency table in Example 1. See the examples on p Does our graph look different?

Create a bar graph that displays the data from the frequency table in Example 1. See the examples on p Does our graph look different? A frequency table is a table with two columns, one for the categories and another for the number of times each category occurs. See Example 1 on p. 247. Create a bar graph that displays the data from the

More information

Designing Rectangular Boxes

Designing Rectangular Boxes Designing Rectangular Boxes Finding the right box for a product requires thought and planning. A company must consider how much the box can hold as well as the amount and the cost of the material needed

More information

Simplifying Expressions

Simplifying Expressions Unit 1 Beaumont Middle School 8th Grade, 2017-2018 Math8; Intro to Algebra Name: Simplifying Expressions I can identify expressions and write variable expressions. I can solve problems using order of operations.

More information

Advanced Algebra Chapter 3 - Note Taking Guidelines

Advanced Algebra Chapter 3 - Note Taking Guidelines Advanced Algebra Chapter 3 - Note Taking Guidelines 3.1 Constant-Increase or Constant-Decrease Situations 1. What type of function can always be used to model a Constant-Increase or Constant-Decrease Situations

More information

MEP Scheme of Work: YEAR 7A

MEP Scheme of Work: YEAR 7A 1 1. LOGIC 1.1 Logic Puzzels Deductive reasoning, given clues Rana, Toni and Millie are sisters. Deduce which sister is 9, 12 and 14 years old if 1. Toni's age is not in the 4-times table. 2. Millie's

More information

STANDARDS OF LEARNING CONTENT REVIEW NOTES ALGEBRA I. 4 th Nine Weeks,

STANDARDS OF LEARNING CONTENT REVIEW NOTES ALGEBRA I. 4 th Nine Weeks, STANDARDS OF LEARNING CONTENT REVIEW NOTES ALGEBRA I 4 th Nine Weeks, 2016-2017 1 OVERVIEW Algebra I Content Review Notes are designed by the High School Mathematics Steering Committee as a resource for

More information

The y-intercept in this problem represents: represents:

The y-intercept in this problem represents: represents: Go to butenhoffmath.com and check out the algebra notes video: A 7-1 AStd2a: I can model a linear function given a situation, table and rule. AStd2b: I can determine the equation of a line given a point

More information

3.1 Start Thinking. 3.1 Warm Up. 3.1 Cumulative Review Warm Up. Consider the equation y x.

3.1 Start Thinking. 3.1 Warm Up. 3.1 Cumulative Review Warm Up. Consider the equation y x. 3.1 Start Thinking Consider the equation y x. Are there any values of x that you cannot substitute into the equation? If so, what are they? Are there any values of y that you cannot obtain as an answer?

More information

Objectives. Vocabulary. 1-1 Exploring Transformations

Objectives. Vocabulary. 1-1 Exploring Transformations Warm Up Plot each point. D Warm Up Lesson Presentation Lesson Quiz 1. A(0,0) 2. B(5,0) 3. C( 5,0) 4. D(0,5) C A B 5. E(0, 5) 6. F( 5, 5) F E Algebra 2 Objectives Apply transformations to points and sets

More information

Making Science Graphs and Interpreting Data

Making Science Graphs and Interpreting Data 6 th In Class Worksheet Name Graph Practice Teacher Due Making Science Graphs and Interpreting Data Scientific Graphs: Most scientific graphs are made as line graphs. There may be times when other types

More information

Unit 3, Activity 1, Vocabulary Self-Awareness Chart

Unit 3, Activity 1, Vocabulary Self-Awareness Chart Unit 3, Activity, Vocabulary Self-Awareness Chart Vocabulary Self-Awareness Chart Word + - Example Definition Relation Function Domain Range Graph Vertical line test F(x) input output independent dependent

More information

Density Curve (p52) Density curve is a curve that - is always on or above the horizontal axis.

Density Curve (p52) Density curve is a curve that - is always on or above the horizontal axis. 1.3 Density curves p50 Some times the overall pattern of a large number of observations is so regular that we can describe it by a smooth curve. It is easier to work with a smooth curve, because the histogram

More information

Lesson 5: Identifying Proportional and Non-Proportional Relationships in Graphs

Lesson 5: Identifying Proportional and Non-Proportional Relationships in Graphs Lesson 5: Identifying Proportional and Non-Proportional Relationships in Graphs Student Outcomes Students decide whether two quantities are proportional to each other by graphing on a coordinate plane

More information

Fractions, Decimals, Ratio and Percentages (FDRP) Measures (MEA)

Fractions, Decimals, Ratio and Percentages (FDRP) Measures (MEA) Termly assessment Number and Place Value (NPV) Addition and Subtraction (AS) Multiplication and Division (MD) Fractions, Decimals, Ratio and Percentages (FDRP) Measures (MEA) Geometry (GEO) Statistics

More information

Lesson #6: Basic Transformations with the Absolute Value Function

Lesson #6: Basic Transformations with the Absolute Value Function Lesson #6: Basic Transformations with the Absolute Value Function Recall: Piecewise Functions Graph:,, What parent function did this piecewise function create? The Absolute Value Function Algebra II with

More information

Essentials. Week by. Week. All About Data. Algebra Alley

Essentials. Week by. Week. All About Data. Algebra Alley > Week by Week MATHEMATICS Essentials Algebra Alley Jack has 0 nickels and some quarters. If the value of the coins is $.00, how many quarters does he have? (.0) What s The Problem? Pebble Pebble! A pebble

More information

EXPLORING PATTERNS THAT INVOLVE SPACE AND MEASUREMENT: SOME EXAMPLE OF NON LINEAR PATTERNS OR GROWTH PATTERNS

EXPLORING PATTERNS THAT INVOLVE SPACE AND MEASUREMENT: SOME EXAMPLE OF NON LINEAR PATTERNS OR GROWTH PATTERNS EXPLORING PATTERNS THAT INVOLVE SPACE AND MEASUREMENT: SOME EXAMPLE OF NON LINEAR PATTERNS OR GROWTH PATTERNS KARSAN HUTCHINSON You need to work in a group of four for this learning experience. Two of

More information

HIGLEY UNIFIED SCHOOL DISTRICT 2016/2017 INSTRUCTIONAL ALIGNMENT

HIGLEY UNIFIED SCHOOL DISTRICT 2016/2017 INSTRUCTIONAL ALIGNMENT HIGLEY UNIFIED SCHOOL DISTRICT 2016/2017 INSTRUCTIONAL ALIGNMENT Third Grade Quarter 4 Unit 10: Geometry and Measurement Word Problems Approximately 40 Days Begin around March 27 th This 40-day final unit

More information

Archdiocese of Washington Catholic Schools Academic Standards Mathematics

Archdiocese of Washington Catholic Schools Academic Standards Mathematics 5 th GRADE Archdiocese of Washington Catholic Schools Standard 1 - Number Sense Students compute with whole numbers*, decimals, and fractions and understand the relationship among decimals, fractions,

More information

5th Grade Mathematics Essential Standards

5th Grade Mathematics Essential Standards Standard 1 Number Sense (10-20% of ISTEP/Acuity) Students compute with whole numbers*, decimals, and fractions and understand the relationship among decimals, fractions, and percents. They understand the

More information

March 13, Bellwork. Due Today!

March 13, Bellwork. Due Today! Bellwork Due Today! Bellwork March 13, 2014 Bellwork Kayla has taken three tests worth 100 points each. Her scores are 85, 93, and 88. She has one test left to take. What score must she get on her last

More information

Math 111: Midterm 1 Review

Math 111: Midterm 1 Review Math 111: Midterm 1 Review Prerequisite material (see review section for additional problems) 1. Simplify the following: 20a 2 b 4a 2 b 1 ( 2x 3 y 2 ) 2 8 2 3 + ( 1 4 ) 1 2 2. Factor the following: a)

More information

Student Outcomes. Lesson Notes. Classwork. Discussion (4 minutes)

Student Outcomes. Lesson Notes. Classwork. Discussion (4 minutes) Student Outcomes Students write mathematical statements using symbols to represent numbers. Students know that written statements can be written as more than one correct mathematical sentence. Lesson Notes

More information

Answers Investigation 3

Answers Investigation 3 Answers Applications 1. a. 25 shirts would cost $70. You could use a table by trying to find the cost C for every value of n. Thus, the table would reflect values for n = 1, 2, 3,..., 25. You could use

More information

Name Period Date MATHLINKS GRADE 8 STUDENT PACKET 3 PATTERNS AND LINEAR FUNCTIONS 1

Name Period Date MATHLINKS GRADE 8 STUDENT PACKET 3 PATTERNS AND LINEAR FUNCTIONS 1 Name Period Date 8-3 STUDENT PACKET MATHLINKS GRADE 8 STUDENT PACKET 3 PATTERNS AND LINEAR FUNCTIONS 1 3.1 Geometric Patterns Describe sequences generated by geometric patterns using tables, graphs, and

More information

TEACHER GUIDE INCLUDES. Tier 1 Tier 2 Tier 3 Correlations. Diagnostic Interviews for Every Common Core Cluster

TEACHER GUIDE INCLUDES. Tier 1 Tier 2 Tier 3 Correlations. Diagnostic Interviews for Every Common Core Cluster TEACHER GUIDE FOR THE COMMON CORE STATE STANDARDS FOR MATHEMATICS 3 INCLUDES Tier Tier Tier 3 Correlations Diagnostic Interviews for Every Common Core Cluster Tier Lessons, Tier Prerequisite Skills, and

More information

STANDARDS OF LEARNING CONTENT REVIEW NOTES. ALGEBRA I Part II. 3 rd Nine Weeks,

STANDARDS OF LEARNING CONTENT REVIEW NOTES. ALGEBRA I Part II. 3 rd Nine Weeks, STANDARDS OF LEARNING CONTENT REVIEW NOTES ALGEBRA I Part II 3 rd Nine Weeks, 2016-2017 1 OVERVIEW Algebra I Content Review Notes are designed by the High School Mathematics Steering Committee as a resource

More information

Math 1201 Unit 5: Relations & Functions. Ch. 5 Notes

Math 1201 Unit 5: Relations & Functions. Ch. 5 Notes Math 1201 Unit 5: Relations & Functions Read Building On, Big Ideas, and New Vocabulary, p. 254 text. 5.1 Representing Relations (0.5 class) Read Lesson Focus p. 256 text. Outcomes Ch. 5 Notes 1. Define

More information

End of Year Test B. Whole Numbers, Decimals, and Integers. Fractions. Name Date END OF YEAR TEST B. Answers. 5x 2 3y 3x 2y 5 8, 5 2 3, 1

End of Year Test B. Whole Numbers, Decimals, and Integers. Fractions. Name Date END OF YEAR TEST B. Answers. 5x 2 3y 3x 2y 5 8, 5 2 3, 1 Whole Numbers Decimals and Integers 1. Which list orders the integers from greatest to least? A. 15 8 1 0 B. 0 1 5 C. 18 12 7 D. 10 5 0 5 2. The coldest U.S. temperature on record occurred at Prospect

More information

Lesson 10 ~ Three-Dimensional Figures

Lesson 10 ~ Three-Dimensional Figures Lesson 10 ~ Three-Dimensional Figures Name a solid that fits each description. 1. a can of beans 2. a shoe box 3. a pyramid with five lateral faces 4. a solid with six vertices 5. a prism with bases shaped

More information

Unit 6: Formulas and Patterns

Unit 6: Formulas and Patterns Section 6.1: Connect the Dots? Section 6.2: Equations and Graphs Section 6.3: Graphing Equations by Plotting Points Section 6.4: Intercepts Section 6.5: Horizontal and Vertical Lines Section 6.6: Looking

More information

Organizing and Summarizing Data

Organizing and Summarizing Data 1 Organizing and Summarizing Data Key Definitions Frequency Distribution: This lists each category of data and how often they occur. : The percent of observations within the one of the categories. This

More information

CLEP Pre-Calculus. Section 1: Time 30 Minutes 50 Questions. 1. According to the tables for f(x) and g(x) below, what is the value of [f + g]( 1)?

CLEP Pre-Calculus. Section 1: Time 30 Minutes 50 Questions. 1. According to the tables for f(x) and g(x) below, what is the value of [f + g]( 1)? CLEP Pre-Calculus Section : Time 0 Minutes 50 Questions For each question below, choose the best answer from the choices given. An online graphing calculator (non-cas) is allowed to be used for this section..

More information

UNIT 4 DESCRIPTIVE STATISTICS Lesson 2: Working with Two Categorical and Quantitative Variables Instruction

UNIT 4 DESCRIPTIVE STATISTICS Lesson 2: Working with Two Categorical and Quantitative Variables Instruction Prerequisite Skills This lesson requires the use of the following skills: plotting points on the coordinate plane, given data in a table plotting the graph of a linear function, given an equation plotting

More information

Algebra Area of Parallelograms

Algebra Area of Parallelograms Lesson 10.1 Reteach Algebra Area of Parallelograms The formula for the area of a parallelogram is the product of the base and height. The formula for the area of a square is the square of one of its sides.

More information

Objective: Find the total volume of solid figures composed of two nonoverlapping

Objective: Find the total volume of solid figures composed of two nonoverlapping Lesson 6 Objective: Find the total volume of solid figures composed of two nonoverlapping Suggested Lesson Structure Fluency Practice Application Problem Concept Development Student Debrief Total Time

More information

Number. Measure. Geometry. Key:

Number. Measure. Geometry. Key: Year R Maths - Key Performance Indicator Can count reliably with numbers from one to 0. Can find one more or one less than a given number. Using quantities or objects, can add or subtract two single digit

More information

Test Booklet. Subject: MA, Grade: HS ACE Geometry End-of-Instruction Student name:

Test Booklet. Subject: MA, Grade: HS ACE Geometry End-of-Instruction Student name: Test Booklet Subject: MA, Grade: HS Student name: Author: Oklahoma District: Oklahoma Released Tests Printed: Sunday September 02, 2012 1 Which sequence of statements is an example of deductive reasoning?

More information

End Behavior and Symmetry

End Behavior and Symmetry Algebra 2 Interval Notation Name: Date: Block: X Characteristics of Polynomial Functions Lesson Opener: Graph the function using transformations then identify key characteristics listed below. 1. y x 2

More information

Name: Beaumont Middle School 8th Grade, Advanced Algebra I Topic 3a

Name: Beaumont Middle School 8th Grade, Advanced Algebra I Topic 3a Beaumont Middle School 8th Grade, 2018-2019 Advanced Algebra I Topic 3a Name: I can model a life situation with a graph. I can distinguish between a function and a relation. I can represent ordered pairs

More information

Accelerated Algebra I Final Review Linear and Exponential Functions 1. If f (x) = 3x 5 and the domain of f is {2, 4, 6}, what is the range of f (x)?

Accelerated Algebra I Final Review Linear and Exponential Functions 1. If f (x) = 3x 5 and the domain of f is {2, 4, 6}, what is the range of f (x)? Accelerated Algebra I Final Review Linear and Exponential Functions 1. If f (x) = 3x 5 and the domain of f is {2, 4, 6}, what is the range of f (x)? 2. Given the graph of f (x) below, what is f (2)? 3.

More information

Math-3 Lesson 1-7 Analyzing the Graphs of Functions

Math-3 Lesson 1-7 Analyzing the Graphs of Functions Math- Lesson -7 Analyzing the Graphs o Functions Which unctions are symmetric about the y-axis? cosx sin x x We call unctions that are symmetric about the y -axis, even unctions. Which transormation is

More information

Pre-Algebra HS Semester 2 Practice Exam B

Pre-Algebra HS Semester 2 Practice Exam B 1. A right triangle is shown below. 5 What is the value of x? 1 17 4 169 12 x Figure is not drawn to scale. 4. Which of the following measurements represent a right triangle? I., 4, 5 II. 5, 12, 1 III.

More information

Proportional Relationships: Connections

Proportional Relationships: Connections Proportional Relationships: Connections Henri Picciotto A set of activities using multiple mathematical tools (and some real world applications) to help middle school students make connections between

More information

Correlation of Ontario Mathematics 2005 Curriculum to. Addison Wesley Mathematics Makes Sense

Correlation of Ontario Mathematics 2005 Curriculum to. Addison Wesley Mathematics Makes Sense Correlation of Ontario Mathematics 2005 Curriculum to Addison Wesley Math Makes Sense 2 Number Sense and Numeration Overall Expectations By the end of Grade 2, students will: read, represent, compare,

More information

Stamford Green Primary School Mathematics Expectations

Stamford Green Primary School Mathematics Expectations This document is for use in planning for the teaching of mathematics. These are the basic expectations of what all children in the class will be able to do in mathematics by the end of each school year.

More information

Chapter 6 Normal Probability Distributions

Chapter 6 Normal Probability Distributions Chapter 6 Normal Probability Distributions 6-1 Review and Preview 6-2 The Standard Normal Distribution 6-3 Applications of Normal Distributions 6-4 Sampling Distributions and Estimators 6-5 The Central

More information

Math A Regents Exam 0103 Page 1

Math A Regents Exam 0103 Page 1 Math A Regents Exam 0103 Page 1 1. 010301a, P.I. A.S.6 The accompanying diagram shows a box-andwhisker plot of student test scores on last year's Mathematics A midterm examination. 4. 010304a, P.I. 7.N.3

More information

10.4 Measures of Central Tendency and Variation

10.4 Measures of Central Tendency and Variation 10.4 Measures of Central Tendency and Variation Mode-->The number that occurs most frequently; there can be more than one mode ; if each number appears equally often, then there is no mode at all. (mode

More information

10.4 Measures of Central Tendency and Variation

10.4 Measures of Central Tendency and Variation 10.4 Measures of Central Tendency and Variation Mode-->The number that occurs most frequently; there can be more than one mode ; if each number appears equally often, then there is no mode at all. (mode

More information

Measures of Dispersion

Measures of Dispersion Lesson 7.6 Objectives Find the variance of a set of data. Calculate standard deviation for a set of data. Read data from a normal curve. Estimate the area under a curve. Variance Measures of Dispersion

More information

Section 2C Formulas with Dividing Decimals

Section 2C Formulas with Dividing Decimals Section 2C Formulas with Dividing Decimals x Look at the following z-score formula again from statistics. z. Suppose we want to calculate the z-score if x 17.6 pounds, 1.8 pounds, and 2.5 pounds. Not only

More information

Complete Assignment #1 listed below on WK #1 in packet. Textbook required!!!

Complete Assignment #1 listed below on WK #1 in packet. Textbook required!!! 400Algebra 2H ASSIGNMENT SHEETrev14 CHAPTER 3: Linear Functions with Review of Chapter 1 and 2 (3-1 to 3-4 Highlights on reverse side) Directions: 1. Review classwork and read each section in textbook

More information

Integrated Algebra A Packet 1

Integrated Algebra A Packet 1 Name Date Integrated Algebra A Packet 1 Lesson/Notes Homework Coordinate Plane HW #1 Connecting Points To Make Figures HW #2 Intro to Transformations/Translations HW #3 Reflections HW #4 Symmetry HW #5

More information

STRAIGHT LINE GRAPHS THE COORDINATES OF A POINT. The coordinates of any point are written as an ordered pair (x, y)

STRAIGHT LINE GRAPHS THE COORDINATES OF A POINT. The coordinates of any point are written as an ordered pair (x, y) THE COORDINATES OF A POINT STRAIGHT LINE GRAPHS The coordinates of any point are written as an ordered pair (x, y) Point P in the diagram has coordinates (2, 3). Its horizontal distance along the x axis

More information

Eighth Grade Mathematics 2017 Released Items Analysis

Eighth Grade Mathematics 2017 Released Items Analysis Step Up to the by GF Educators, Inc. Eighth Grade Mathematics 2017 Released s Teacher: Copyright 2017 Edition I www.stepup.com 8th Grade Mathematics Released s Name: Teacher: Date: Step Up to the by GF

More information

Gift Card Representations

Gift Card Representations Name Gift Card Representations Charmaine received a gift card for $ worth of media downloads. The cost of each download is $.5. Complete each representation for this scenario below. The remaining balance

More information

1-8 Exploring Transformations

1-8 Exploring Transformations 1-8 Exploring Transformations Warm Up Lesson Presentation Lesson Quiz 2 Warm Up Plot each point. D 1. A(0,0) 2. B(5,0) 3. C( 5,0) 4. D(0,5) 5. E(0, 5) 6. F( 5, 5) C A F E B Objectives Apply transformations

More information

6th Grade Math. Parent Handbook

6th Grade Math. Parent Handbook 6th Grade Math Benchmark 3 Parent Handbook This handbook will help your child review material learned this quarter, and will help them prepare for their third Benchmark Test. Please allow your child to

More information

Grade 5. Massachusetts Curriculum Framework for Mathematics 48

Grade 5. Massachusetts Curriculum Framework for Mathematics 48 Grade 5 Introduction In grade 5, instructional time should focus on four critical areas: (1) developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication

More information

MOUNTAIN VIEW SCHOOL DISTRICT

MOUNTAIN VIEW SCHOOL DISTRICT MOUNTAIN VIEW SCHOOL DISTRICT THIRD GRADE MATH 3.OA.1 Represent and solve problems involving multiplication and division. Interpret products of whole numbers, e.g., interpret 5 7 as the total number of

More information

UNIT 1A EXPLORING UNIVARIATE DATA

UNIT 1A EXPLORING UNIVARIATE DATA A.P. STATISTICS E. Villarreal Lincoln HS Math Department UNIT 1A EXPLORING UNIVARIATE DATA LESSON 1: TYPES OF DATA Here is a list of important terms that we must understand as we begin our study of statistics

More information

MINI LESSON. Lesson 1a Introduction to Functions

MINI LESSON. Lesson 1a Introduction to Functions MINI LESSON Lesson 1a Introduction to Functions Lesson Objectives: 1. Define FUNCTION 2. Determine if data sets, graphs, statements, or sets of ordered pairs define functions 3. Use proper function notation

More information

Lesson 8: Graphs and Graphing Linear Equations

Lesson 8: Graphs and Graphing Linear Equations A critical skill required for the study of algebra is the ability to construct and interpret graphs. In this lesson we will learn how the Cartesian plane is used for constructing graphs and plotting data.

More information

Chapter 5: The standard deviation as a ruler and the normal model p131

Chapter 5: The standard deviation as a ruler and the normal model p131 Chapter 5: The standard deviation as a ruler and the normal model p131 Which is the better exam score? 67 on an exam with mean 50 and SD 10 62 on an exam with mean 40 and SD 12? Is it fair to say: 67 is

More information

Percentage and Ratio. Properties of Number. Perimeter and Area. Position and Direction MATHS LADDER CONTENTS LEARNING LADDERS

Percentage and Ratio. Properties of Number. Perimeter and Area. Position and Direction MATHS LADDER CONTENTS LEARNING LADDERS MATHS NAME CLASS CONTENTS Page 4 Page 6 Page 8 Page 10 Page 12 Page 14 Page 18 Page 20 Page 22 Page 26 Page 28 Page 32 Page 34 Page 36 Page 40 Page 44 Page 46 Times Tables Addition Subtraction Multiplication

More information

Page 1 of 11 02/13/15

Page 1 of 11 02/13/15 1 How many centimeters are in 3 meters? Multiply or Divide Using Equivalents 1 How many meters are in 500 centimeters? Use at least two different methods to solve. To convert from one unit of measurement

More information

Math 112 Spring 2016 Midterm 2 Review Problems Page 1

Math 112 Spring 2016 Midterm 2 Review Problems Page 1 Math Spring Midterm Review Problems Page. Solve the inequality. The solution is: x x,,,,,, (E) None of these. Which one of these equations represents y as a function of x? x y xy x y x y (E) y x 7 Math

More information

Pre-Algebra Notes Unit 8: Graphs and Functions

Pre-Algebra Notes Unit 8: Graphs and Functions Pre-Algebra Notes Unit 8: Graphs and Functions The Coordinate Plane A coordinate plane is formed b the intersection of a horizontal number line called the -ais and a vertical number line called the -ais.

More information

2nd Grade Iowa Core - I Cans...

2nd Grade Iowa Core - I Cans... Operations and Algebraic Thinking 2.OA Operations and Algebraic Thinking 2.OA Represent and solve problems involving addition Represent and solve problems involving addition and subtraction. and subtraction.

More information

Unit 2A: Systems of Equations and Inequalities

Unit 2A: Systems of Equations and Inequalities Unit A: Systems of Equations and Inequalities In this unit, you will learn how to do the following: Learning Target #1: Creating and Solving Systems of Equations Identify the solution to a system from

More information

Section 1.1 Patterns in Division

Section 1.1 Patterns in Division Section 1.1 Patterns in Division Divisibility refers to whether or not a number is divisible by another number. If a number divides evenly into another number (no remainder), then it is divisible by that

More information

Mississippi College and Career Readiness Standards for Mathematics Scaffolding Document. Grade 2

Mississippi College and Career Readiness Standards for Mathematics Scaffolding Document. Grade 2 Mississippi College and Career Readiness Standards for Mathematics Scaffolding Document Grade 2 Operations and Algebraic Thinking Represent and solve problems involving addition and subtraction 2.OA.1

More information

RETEACHING: Graphing Skill #1: What Type of Graph is it?

RETEACHING: Graphing Skill #1: What Type of Graph is it? RETEACHING: Graphing Skill #1: What Type of Graph is it? There are several types of graphs that scientists often use to display data. They include: Pie Graphs Bar Graphs Histograms Line Graphs Scatter

More information

X & Y COORDINATES. Teachers Guide

X & Y COORDINATES. Teachers Guide Teachers Guide Background: One piece of information that is essential to us on a daily basis is our location. We may not realize how often we use this type of information, but a little reflection on your

More information

Number and Place Value. Calculations

Number and Place Value. Calculations Maths Targets Number and Place Value I can count to and across 100, forwards and backwards, beginning from 0 or 1, or from any given number I can count in multiples of twos, five and tens I can count,

More information

Larkrise Maths Curriculum Pitch & Expectations Shape, Space & Measure

Larkrise Maths Curriculum Pitch & Expectations Shape, Space & Measure Larkrise Maths Curriculum Pitch & Expectations Shape, Space & Measure Measurement Compare, describe and solve practical problems for lengths and heights, mass/weight, capacity and volume time Measure and

More information

4.5 Notes Domain and Range

4.5 Notes Domain and Range Algebra 1 4.5 Notes Domain and Range Name: Date: Class #: A relation is. The entire set of numbers that are put into a relation or function is called the After putting the numbers in the domain into the

More information

Age Related Maths Expectations

Age Related Maths Expectations Step 1 Times Tables Addition Subtraction Multiplication Division Fractions Decimals Percentage & I can count in 2 s, 5 s and 10 s from 0 to 100 I can add in 1 s using practical resources I can add in 1

More information

Selby Abbey C.E. (VC) Primary School Mathematics Curriculum

Selby Abbey C.E. (VC) Primary School Mathematics Curriculum Selby Abbey C.E. (VC) Primary School Mathematics Curriculum 2018-2019 Essential Characteristics of Mathematicians An understanding of the important concepts and an ability to make connections within mathematics.

More information

3 RD GRADE MATH-COMMON CORE PACING GUIDE 1ST 9 WEEKS Standard I Can Statements Date

3 RD GRADE MATH-COMMON CORE PACING GUIDE 1ST 9 WEEKS Standard I Can Statements Date 3 RD GRADE MATH-COMMON CORE PACING GUIDE 1ST 9 WEEKS 2013-2014 Standard I Can Statements Date Taught Operations and Algebraic Thinking (OA) 3.OA.1. Interpret products of whole numbers, e.g., interpret

More information

8 th Grade Math STAAR Review

8 th Grade Math STAAR Review 8 th Grade Math STAAR Review 1. Five students are each trying to raise the same amount of money for a fundraiser. The table below shows how much of each student s goal has been met. Write the numbers in

More information

Course 1 Unit 5 Practice

Course 1 Unit 5 Practice Course Unit Practice Lesson -. Attend to precision. Use the Triangle Inequality Property to determine whether a triangle can be formed with the given side lengths in inches. If a triangle can be formed,

More information

Practice A. Solving Right Triangles. sin. cos A 5. tan 2

Practice A. Solving Right Triangles. sin. cos A 5. tan 2 Name Date Class Solving Right Triangles In Exercises 1 3, fill in the blanks to complete the description of the inverse trigonometric ratios. 1. If sin A = x, then sin 1 x =. 2. If cos A =, then cos 1

More information

Casey County Schools- 3 rd Grade Math Map

Casey County Schools- 3 rd Grade Math Map Week(s) Standard I can statement(s) Critical Vocabulary 3.MD.1 (Teach throughout the year) Resources Used throughout the year (math minutes, automaticity) Formative Assessment(s) (this will be left blank

More information

Revision Booklet. Grade 6

Revision Booklet. Grade 6 Kingdom of Bahrain Ministry of Education Private Educational Directorate Ahlia school MATHEMATICS DEPARTMENT 2017-2018 Revision Booklet For the 2 nd semester Final Exam Grade 6 NAME : DATE : Prepared by

More information

12/11/2018 Algebra II - Semester 1 Review

12/11/2018 Algebra II - Semester 1 Review Name: Semester Review - Study Guide Score: 72 / 73 points (99%) Algebra II - Semester 1 Review Multiple Choice Identify the choice that best completes the statement or answers the question. Name the property

More information

FSA Algebra I End-of-Course Review Packet. Functions and Modeling

FSA Algebra I End-of-Course Review Packet. Functions and Modeling FSA Algebra I End-of-Course Review Packet Functions and Modeling Table of Contents MAFS.912.F-BF.2.3 EOC Practice... 3 MAFS.912.F-IF.1.2 EOC Practice... 5 MAFS.912.F-IF.1.1 EOC Practice... 7 MAFS.912.F-IF.2.5

More information

Number Sense Third Grade Fourth Grade Fifth Grade MA.4.NS.1.a.1: Read, demonstrate, and write whole numbers up to 500.

Number Sense Third Grade Fourth Grade Fifth Grade MA.4.NS.1.a.1: Read, demonstrate, and write whole numbers up to 500. Number Sense MA.4.NS.1.a.1: Read, demonstrate, and write whole numbers up to 500. MA.3.NS.1.a.1: Read, demonstrate, and write whole numbers up to 200, in standard and word form. MA.3.NS.2.a.1: Compare

More information

8.5 Graph and Write Equations of Hyperbolas p.518 What are the parts of a hyperbola? What are the standard form equations of a hyperbola?

8.5 Graph and Write Equations of Hyperbolas p.518 What are the parts of a hyperbola? What are the standard form equations of a hyperbola? 8.5 Graph and Write Equations of Hyperbolas p.518 What are the parts of a hyperbola? What are the standard form equations of a hyperbola? How do you know which way it opens? Given a & b, how do you find

More information

Sec 4.1 Coordinates and Scatter Plots. Coordinate Plane: Formed by two real number lines that intersect at a right angle.

Sec 4.1 Coordinates and Scatter Plots. Coordinate Plane: Formed by two real number lines that intersect at a right angle. Algebra I Chapter 4 Notes Name Sec 4.1 Coordinates and Scatter Plots Coordinate Plane: Formed by two real number lines that intersect at a right angle. X-axis: The horizontal axis Y-axis: The vertical

More information