Algebra 1 EOC Study Guide General Notes This document is not state (OSPI) created or approved. This was developed using resources created by OSPI, the Seattle School District, the Bainbridge Island School district, and NSD. It has been designed to help students prepare for taking the Algebra 1 EOC. This is not an exhaustive sampling of EOC Exam test items. Rather it is intended to give students an idea of what their level understanding is for the Performance Expectations assessed on the state EOC. Information about the EOC Assessment The format of the exam questions will be: 29 multiple choice, 5 completion items, and 3 short answers. A graphing calculator can be used for all questions and will be cleared at the start of the exam. A formula sheet and graph paper will be provided in the test booklet. The formula sheet is provided on the next two pages of this document. There will be a total of 37 questions on the Year 1 Retake Exam. The following gives the strands to be assessed along with the estimated number of questions for each strand. End-of-Course Exam Items Number, Operations, Expression, and Variables Function Characteristics Linear Equations & Inequalities Data and Statistics Estimated Number of Questions (37 questions) 6-8 11 - 13 11 - 13 6-8 Organization of the Study Guide The study guide has been organized by using the strands given in the previous table. The number of test items for each strand is shown to help guide your study priorities. For each strand, you will find the specific state Performance Expectations that will be assessed for graduation. You will find the following information for each Performance Expectation: o The problem number(s) from the companion Practice Test that is aligned with this particular Performance Expectation o Sample Questions for each objective o Additional Practice Problems that can be found at www.interactmath.com Using the Interact Math Website: This website has practice problems that match our curriculum To use this site, you need to 1. Go to www.interactmath.com 2. Select Enter at the top of the page. 3. Select “Prentice Hall Algebra 1© 2011 from the drop down menu 4. Select Submit 5. You will then be able to select the chapter and exercises that match those listed on this guide. Northshore School District Jan. 3, 2011 Algebra 1 EOC Study Guide Northshore School District Jan. 3, 2011 Algebra 1 EOC Study Guide Northshore School District Jan. 3, 2011 Algebra 1 EOC Study Guide Number, Operations, Expression, and Variables Performance Expectation 1.2.A Compare and order real numbers with and without the number line Practice Exam Problem(s) #1 Sample Question(s) Which numbers are both less than 5 6? 6 5 O A. -2.1 and O B. O C. -0.65 and -1.2 O D. Additional Practice at www.interactmath.com Chapter 1 Section 3 Exercises: 40, 45 Chapter 7 Section 2 Exercises 7, 35 2 3 3 and 4 2 3 and -0.8 Answer: A Performance Expectation 1.2.B Determine all possible values of variables that satisfy prescribed conditions, and evaluate algebraic expressions that involve variables Practice Exam Problem(s) #2, 3 Sample Question(s) For what values of a is o o o o A. B. C. D. 1 𝑎 an integer? a = 1, 0 a≤1 a = 1, a ≠ 0 a>1 Answer: C Evaluate 2w + 6y2 for w = 4 and y = 3. o o o o A. B. C. D. 330 62 60 44 Answer: B Northshore School District Jan. 3, 2011 Additional Practice at www.interactmath.com Chapter 1 Section 2 Exercises: 47, 51 Chapter 7 Section 1 Exercises 37, 40 Algebra 1 EOC Study Guide Performance Expectation 1.2.C Interpret and use integer exponents and square and cube roots, and apply the laws and properties of exponents to simplify and evaluate exponential expressions. Practice Exam Problem(s) #4, 5, 6 Sample Question(s) Additional Practice at www.interactmath.com Chapter 7 Section 1 Exercises: 11, 12, 21, 22, 30, 33 Simplify: 2-2325 223-352 o A. 35 52 o B. 24325 o C. 35 245 o D. 32 245 Answer: C Chapter 7 Section 3 Exercises: 15, 24, 41 Chapter 7 Section 4 Exercises: 15, 19, 25, 29, 31, 54 Chapter 7 Section 5 Exercises: 15, 19, 23, 35, 37, 41, 67, 71 Simplify: (2x2y3)4 Chapter 10 Section 2 Exercises: 11, 17, 19, 22 o A. 8x6y7 o B. 8x8y12 o C. 16x6y7 o D. 16x8y12 Answer: D Simplify: √8 o A. √2 × √4 o B. 4 √2 o C. 2 √2 o D. 2 × 2 × 2 Answer: C Performance Expectation 1.7.D Solve an equation involving several variables by expressing one variable in terms of the others. Practice Exam Problem(s) #7 Sample Question(s) Solve A = p + prt for p 𝐴 1+𝑟𝑡 o A. o B. 𝑝 = o C. o D. =𝑝 𝐴 (𝑟𝑡) 1 𝐴 =𝑝 𝑟𝑡 𝑟𝑡 =𝑝 𝐴+1 Answer: A Northshore School District Jan. 3, 2011 Additional Practice at www.interactmath.com Chapter 2 Section 5 Exercises: 4, 19, 22, 23, 25, 39, 40 Algebra 1 EOC Study Guide Function Characteristics Performance Expectation 1.1.A Select and justify functions and equations to model and solve problems Practice Exam Problem(s) #8 Sample Question(s) Mrs. Morris gave her students this pattern of white tiles. She asked her students to write an equation to represent the number of white tiles, t, for any figure number, n. Additional Practice at www.interactmath.com This PE will show up in several lessons throughout an Algebra 1 textbook. Here are a few examples. Chapter 4 Section 2 Exercise: 7 Which equation represents the number of white tiles in the pattern? o A. t = n +2 o B. t = n + 4 o C. t = 4n + 4 o D. t = 4n + 8 Answer: C Chapter 7 Section 6 Exercises: 9, 11 Chapter 9 Section 7 Exercises: 3, 7, 12, 15, 25 Performance Expectation 1.1.E Solve problems that can be represented by exponential functions and equations. Practice Exam Problem(s) #9 Sample Question(s) E. coli bacteria reproduce by a simple process called binary fission—each cell increases in size and divides into two cells. In the laboratory, E. coli bacteria divide approximately every 15 minutes. A new E. coli culture is started with 1 cell. After what 15-minute interval will you have at least 500 bacteria? o A. 250 o B. 63 o C. 33 o D. 9 Answer: D Northshore School District Jan. 3, 2011 Additional Practice at www.interactmath.com Chapter 7 Section 7 Exercises: 5, 13, 14, 17, 20, 33, 41 Algebra 1 EOC Study Guide Performance Expectation 1.3.A Determine whether a relationship is a function and identify the domain, range, roots, and independent and dependent variables. Practice Exam Problem(s) #10, 11, 12 Sample Question(s) The ordered pairs in the sets below are of the form (x, y). In which set is y a function of x? a. {(1, -2), (1, 0), (1, 5), (1, 7)} b. {(1, 3), (2, 6), (3, 1), (6, 3)} c. {(0, 3), (1, 4), (2, 4), (2, 8)} d. {(1, 3), (3, 1), (3, 4), (4, 3)} Answer: B Below is the graph of 𝑓(𝑥) = −2|𝑥 − 1| + 5. Determine the domain and range of this function. o A. Domain: 𝑥 ≥ 0 Range: 𝑓(𝑥) ≥ 0 o B. Domain: 𝑥 ≤ 5 Range: 𝑓(𝑥) ≤ 5 o C. Domain: x can be all real numbers Range: 𝑓(𝑥) ≤ 5 o D. Domain: x can be all real numbers Range: f(x) can be all real numbers Answer: C Tammy wanted to be a professional basketball player. Ever since she was a child she would keep track of what was the average salary for a female basketball player since the year 1995. If Tammy were to write a function relating salary, s, and years, y, what would be the dependent variable? o A. salary, s o B. years, y o C. salary per year, s/y o D. year per salary, y/s Answer: A Northshore School District Jan. 3, 2011 Additional Practice at www.interactmath.com Chapter 4 Section 6 Exercises: 9, 13, 18, 22, 29 Algebra 1 EOC Study Guide Performance Expectation 1.3.B Represent a function with a symbolic expression, as a graph, in a table, and using words, and make connections among these representations. Practice Exam Problem(s) #13 Sample Question(s) A population of bacteria doubled every hour, starting with 4 bacteria. The table below represents the total population, p, at a given hour, t. hour Number of bacteria 0 4 1 8 2 16 3 32 Additional Practice at www.interactmath.com Chapter 4 Section 2 Exercises: 9, 15 Chapter 4 Section 3 Exercises: 7, 9 , 12 Chapter 5 Section 3 Exercise: 50 Which equation best represents the total population (P) of bacteria at a given hour, t. o A. P(t) = 2t o B. P(t) = 2t + 4 o C. P(t) = 4t o D. P(t) = 4(2t) Chapter 7 Section 6 Exercise: 29 Chapter 10 Section 5 Exercises: 17, 23 Chapter 11 Section 6 Exercises: 15, 21, 25 Answer: D Performance Expectation 1.3.C Evaluate f(x) at a and solve for x in the equation f(x) = b. Practice Exam Sample Question(s) Problem(s) #14, 15 For the function 𝑓(𝑥) = √𝑥 + 3, find 𝑓(6) 1 o A. 2 o B. 6 o C. 3 o D. 9 Answer: C For the function 𝑓(𝑥) = 2𝑥 − 9, find x when 𝑓(𝑥) = 3 o A. -9 o B. -3 o C. 3 o D. 6 Answer: D Northshore School District Jan. 3, 2011 Additional Practice at www.interactmath.com Chapter 4 Section 6 Exercises: 3, 16 Algebra 1 EOC Study Guide Performance Expectation 1.4.E Describe how changes in the parameters of linear functions and functions containing an absolute value of a linear expression affect their graphs and the relationships they represent. Practice Exam Problem(s) #16, 17 Sample Question(s) Use the following situation for the next two questions: A gas station’s 10,000-gallon underground storage tank contains 1,000 gallons of gasoline. Tanker trucks pump gasoline into the tank at a rate of 400 gallons per minute. How long will it take to fill the tank? Find a function that represents this situation. o A. f(x) = 400x + 10, 000 o B. f(x) = 400x + 1000 o C. f(x) = -400x + 10000 o D. f(x) = -400x + 9000 Answer: B If the flow rate increases from 400 to 500 gallons per minute, how will the graph of the function change? o A. o B. o C. o D. The y-intercept will increase The y-intercept will decrease The slope will decrease The slope will increase Answer: D Describe how the graph of y = |x| has been transformed to produce the graph of y = |x| - 5. Answer: The graph of y = |x| has been translated down 2 units. Northshore School District Jan. 3, 2011 Additional Practice at www.interactmath.com Chapter 4 Section 6 Exercises: 3, 16 Algebra 1 EOC Study Guide Performance Expectation 1.7.A For an exponential function of the form y = ab where n is an integer, describe the effects that changes in the parameters a and b have on the graph, and answer questions that arise i n situations modeled by exponential functions. Practice Exam Problem(s) #18 Sample Question(s) Which equation below describes a function that increases most quickly as x increases? o A. y 4(5) x Additional Practice at www.interactmath.com Chapter 7 Section 6 Exercises: 20, 22, 29, 31, 41 o B. y 5(4) x o C. y 4(0.2) x o D. y 5(0.25) x Answer: A Performance Expectation 1.7.B Find and approximate solutions to exponential equations. Practice Exam Problem(s) #19 Sample Question(s) For 𝑦 = −3(2)𝑥 , find the approximate value of x when y is approximately -0.09. o A. x = -1.3 o B. x = -5.1 o C. x = -5.5 o D. x = 66.7 Answer: A Additional Practice at www.interactmath.com Chapter 7 Section 7 Exercises: 5, 14, 15, 33, 41 Performance Expectation 1.7.C Express arithmetic and geometric sequences in both explicit and recursive forms, translate between the two forms, explain how rate of change is represented in each form, and use the forms to find specific terms in the sequence. Practice Exam Problem(s) #20 Sample Question(s) What is the fifth term in the geometric sequence with a first term of 3 and a second term of 6? O A. 15 O B. 18 O C. 32 O D. 48 Answer: D Northshore School District Jan. 3, 2011 Additional Practice at www.interactmath.com Chapter 4 Section 7 Exercises: 9, 18, 30, 33, 37, 49 Algebra 1 EOC Study Guide Linear Functions and Inequalities Performance Expectation 1.1.B Solve problems represented by linear functions, equations and inequalities Practice Exam Problem(s) #21, 22 Sample Question(s) A taxi ride costs $29.40. The driver charged $3 plus $0.40 per 0.2 mile traveled. How far did the taxi travel on this trip? o o o o A. B. C. D. 9.8 miles 13.2 miles 66 miles 73.5 miles Answer: B A health plan offers two plans. Plan A has $100 membership and charges $3 per visit. Plan B has a $160 membership fee and offers unlimited visits. For how many visits is the cost of Plan B less than the cost of Plan A? o More than 20 visits o More than 33 visits o More than 40 visits o More than 53 visits Answer: A Additional Practice at www.interactmath.com Chapter 2 Section 3 Exercises: 55, 61, 65 Chapter 2 Section 4 Exercises: 44, 46 Chapter 3 Section 2 Exercises: 42, 69, 75 Chapter 3 Section 3 Exercise: 31 Chapter 3 Section 4 Exercises: 5, 44 Performance Expectation 1.1.C Solve problems that can be represented by a system of two linear equations or inequalities. Practice Exam Problem(s) #23 Sample Question(s) Only chocolate and vanilla ice cream cones are sold at an ice cream store. In one day, the number of chocolate cones sold was 1 more than 4 times the number of vanilla cones sold. A total of 121 cones were sold that day. Let c = the number of chocolate cones sold Let v = the number of vanilla cones sold Write equations to determine the number of chocolate cones sold that day. Use the equations to determine the number of chocolate cones sold that day. Answer: 97 Northshore School District Jan. 3, 2011 Additional Practice at www.interactmath.com Chapter 6 Section 1 Exercises: 21, 34 Chapter 6 Section 2 Exercises: 23, 25, 32 Chapter 6 Section 3 Exercises: 13, 39 Chapter 6 Section 4 Exercises: 7, 9, 11 Chapter 6 Section 6 Exercises: 3, 31 Algebra 1 EOC Study Guide Performance Expectation 1.4.A Solve linear equations and inequalities in one variable Practice Exam Problem(s) #24, 25, 26 Sample Question(s) Solve for x: 2(x – 3) + 4x = 14 + 2x o A. 2 o B. 5 o C. 4 o D. 6 Answer: B The equation 2|x - 1| - 10 = -4 has two real solutions. Determine the negative solution to the equation. o -1 o -2 o -3 o -4 Answer: B Determine whether the student made an error when solving the following inequality. If an error was made, then completely describe the error. Problem 9 – 5(2x + 1) ≥ -28 Step 1 9 – 10x – 5 ≥ -28 Step 2 4 – 10x ≥ -28 Step 3 4 – 10x ≥ -28 -4 -4 -10x ≥ -32 Step 4 -10x ≥ -32 -10 -10 Step 5 x ≥ 3.2 Answer: In Step 4 the student did not reverse the inequality symbol when dividing by a negative number. Northshore School District Jan. 3, 2011 Additional Practice at www.interactmath.com Chapter 2 Section 3 Exercises: 1, 4, 13, 22, 29, 49 Chapter 2 Section 4 Exercises: 15, 17, 21, 26, 27, 30 Chapter 3: Section 4 Exercises: 2, 11, 13, 17, 19, 23, 33, 37 Chapter 3 Section 7 Exercises: 1, 3, 11, 15, 17, 23, 26, 27, 33, 35, 41 Algebra 1 EOC Study Guide Performance Expectation 1.4.B Write and graph an equation for a line given the slope and the y-intercept, the slope and a point on the line, or two points on the line, and translate between forms of linear equations. Practice Exam Problem(s) #27, 28 Sample Question(s) Which equation represents the line that passes through the points (2, 2) and (4, 1)? O A. 𝑦 = −2𝑥 + 6 1 2 O B. 𝑦 =− 𝑥+3 O C. 𝑦 = 2𝑥 + 1 O D. 𝑦 = 2𝑥 − 2 1 Additional Practice at www.interactmath.com Chapter 5 Section 3 Exercises: 11, 13, 21, 23, 29, 38, 44, 47 Chapter 5 Section 4 Exercises: 8, 13, 17, 21, 31 Chapter 5 Section 5 Exercises: 16, 19, 27, 28, 35, 36, 37 Answer: B Use the equation 𝑦 − 7 = 2(𝑥 − 2)(without sketching the graph) to describe the graph. o A. the graph has a negative slope and y-intercept of -2 o B. the graph has a negative slope and y-intercept of 3 o C. the graph has a positive slope and y-intercept of -2 o D. the graph has a positive slope and y-intercept of 3 Answer: D Performance Expectation 1.4.C Identify and interpret the slope and intercepts of a linear function, including equations for parallel and perpendicular lines. Practice Exam Problem(s) #29, 30 Sample Question(s) Mary is going to deposit an equal amount of money into a checking account each month until she has saved $500. The amount of money, y, in the account after x months can be modeled by the equation 𝑦 = 25𝑥 + 100. What does the slope of the graph of the equation represent? O A. The amount of money deposited monthly O B. The amount of money originally in the account O C. The number of months it would take to earn $100 O D. The number of months it would take to reach $500 Answer: A What is the slope of a line that is parallel to the line 3x + 5y = 10? 𝟑 Answer: − 𝟓 Northshore School District Jan. 3, 2011 Additional Practice at www.interactmath.com Chapter 5 Section 4 Exercise: 23 Chapter 5 Section 6 Exercises: 7, 11, 12, 13, 17, 18, 19, 20 Algebra 1 EOC Study Guide Performance Expectation 1.4.D Solve systems of two linear equations and inequalities in two variables. Practice Exam Problem(s) #23, 31 Sample Question(s) See the example for Performance Expectation for 1.1.C Two lines divide the coordinate plane into the four lettered regions shown. Additional Practice at www.interactmath.com Chapter 6 Section 1 Exercises: 3, 10, 14, 17, 18, 24 Chapter 6 Section 2 Exercises: 1, 11, 15, 17, 21, 27 Chapter 6 Section 3 Exercises: 1, 7, 8, 10, 15, 19, 21, 36 Chapter 6 Section 6 Exercises: 11, 15, 17, 19, 24 One region represents the solution set to the system of inequalities given. 𝑦 ≥ 2𝑥 + 1 1 { 𝑦 ≤− 𝑥−3 3 Which region represents the solution set for the system of inequalities given? O A. Region M O B. Region N O C. Region P O D. Region Q Answer: C Data and Statistics Performance Expectation 1.6.A Use and evaluate the accuracy of summary statistics to describe and compare data sets. Practice Exam Problem(s) #32 Sample Question(s) There are 17 employees at a company. The employees earn these hourly wages. 8 employees earn $9 per hour. 7 employees earn $12 per hour. 2 employees earns $33 per hour. Determine and explain mathematically which measure of center best represents the hourly wages of employees at the company. Answer: Median Northshore School District Jan. 3, 2011 Additional Practice at www.interactmath.com Chapter 12 Section 3 Exercises: 1, 7, 13, 16, 19 Chapter 12 Section 4 Exercises: 6, 9, 13, 16, 17 Algebra 1 EOC Study Guide Performance Expectation 1.6.B Make valid inferences and draw conclusions based on data. Practice Exam Problem(s) #33 Sample Question(s) Dr. Wilson noticed that as her patients ate more broccoli, their cholesterol levels dropped. She concluded that eating broccoli causes lower cholesterol levels in the blood. Additional Practice at www.interactmath.com Chapter 5 Section 7 Exercise: 13 Explain any flaws in Dr. Wilson’s conclusion: Answer: Correlation does not imply causation. For example, patients who are eating broccoli may be doing other things that contribute to lowering cholesterol levels, like exercise. Thus, it might not be the act of eating broccoli that is causing the lower cholesterol, but another factor which is making the variable move (like exercise). Performance Expectation 1.6.C Describe how linear transformations affect the center and spread of univariate data. Practice Exam Problem(s) #34 Sample Question(s) At a particular company, every employee receives a 4% cost-ofliving increase to their salary. What impact does this cost-of-living increase have on the mean and on the range of employee salaries at this company? o o o o A. The mean increases but the range does not change. B. The mean does not change but the range increases. C. The mean and range both increase. D. The mean and range do not change. Answer: C Northshore School District Jan. 3, 2011 Additional Practice at www.interactmath.com Chapter 12 Section 3 Exercises: 3, 21 Algebra 1 EOC Study Guide Performance Expectations 1.6.D and 1.6.E Find the equation of a linear function that best fits bivariate data that are linearly related, interpret the slope and y-intercept of the line, and use the equation to make predictions. Describe the correlation of data in scatterplots in terms of strong or weak and positive or negative. Practice Exam Problem(s) #35, 36 Sample Question(s) Use the given scatterplot to answer the following questions. Which statement describes the correlation of the data graphed in the scatterplot? o A. Strong negative o B. Strong positive o C. Weak negative o D. Weak positive Answer: B Which equation represents a line that fits the data? o A. 𝑦 = 29𝑛 + 180 o B. 𝑦 = 60𝑛 + 180 2 o C. 𝑦 = 3 𝑛 + 180 o D. 𝑦 = Answer: A 200 𝑛 3 Northshore School District Jan. 3, 2011 + 180 Additional Practice at www.interactmath.com Chapter 5 Section 7 Exercises: 1, 7, 9