Algebra 1 Semester Exam

Transcription

1 Algebra 1 Semester Exam questions Topics: Expressions, Equations, and Inequalities Functions inear Function Systems of Equations and Inequalities Reporting Category 1: (50% of the Semester Exam) Algebra and odeling Reporting Category : (50% of the Semester Exam) Functions and odeling This Study Guide includes sample problems from the textbook that students can use to help prepare for the exam. They are NOT the test items. This is geared towards the DISTRICT semester exam. There will not be a study guide that is geared towards any state assessment (End of Year EOC). Answers will not be provided by District Office for the Study Guide.

2 BENCHARK DOK Skill/Concepts Example problem or problems to support studying AFS.91.A-CED.1.1 AFS.91.F-IF.1.1 Create an inequality that represents context and use to solve a problem domain would not make a function (given a range) a. A full year membership to a gym costs $35 upfront with no monthly charge. A monthly membership costs $100 upfront and $30 per month. For what numbers of months is it less expensive to have a monthly membership? b. arcus has accepted a job selling cell phones. He will be paid $1500 plus 15% of his sales each month. He needs to earn at least $430 to pay his bills. For what amount of sales will arcus be able to pay his bills? Give the domain and range of each relation. Tell whether the relation is a function. Explain. a. b. Find the equation for each of the lines below. AFS.91.A-REI.4.10 equation of a line on a graph AFS.91.F-E.1.1 AFS.91.A-CED.1.4 AFS.91.F-IF.1. AFS.91.F-IF..6 Justify why a linear function is a function Solve for a specific variable in a surface area formula Evaluate the function for two given values and find the difference between them average rate of change of a function a. Ronda wants to justify that f(x) = 4x 9 is a linear function. If she evaluated f(x) for consecutive integer values, write a statement that justifies the claim that f(x) is a linear function. b. Cassie wants to justify that f(x) = 1 x 4 is a linear function. If she evaluated f(x) for consecutive integer values, write a statement that justifies the claim that f(x) is a linear function. a. Solve for Fahrenheit. C = 5 (F 3) 9 b. Solve for k. E = 1 kx c. Solve for w. SA = (lw + hw + hl) a. The function f(h) can be used to find the height, h, in feet, of a tree, y, years after it was planted. f(h) = 3y + What is the difference in height, h, of the tree between years 4 and 9? b. The function f(h) can be used to find the height, h, in feet, of a tree, y, years after it was planted. f(h) = 5y 8 What is the difference in height, h, of the tree between years 3 and 11? Each day a dolphin trainer receives 150 pounds of fish to divide equally among x dolphins. This function relates the number of pounds, f, of fish each dolphin gets. f = 150 The number of dolphins has increased from 11 to 15. What is the average rate of change in the number of pounds of fish per dolphin? x

3 AFS.91.F-E.1.1 Algebra 1 Semester Exam Study Guide interval shows a constant rate of change a. The table shows the volume of gasoline in a gas tank at different times. Find the rate of change for each time interval. During which time interval did the volume decrease at the greatest rate? b. The table shows the length of a baby at different ages. Find the rate of change for each time interval. Round your answers to the nearest tenth. During which interval did the baby have the greatest growth rate? AFS.91.A-SSE.1.1 Interpret parts of a function within a context a. The function f(x) = 100x + 75 represents what the daycare center charges during a time period. If x represents the number of weeks, what does the 100 represent? What does the 75 represent? b. The function f(x) = x represents the amount of water within a family swimming pool. If x represents the number of days, what does the 60m 3 represent? What does the represent? AFS.91.F-IF.1. Find the value of x given f(x) a. Given the function f(x) = x + 3, what is the value of x 3 when f(x) = 4? b. Given the function f(x) = 3 x 8, what is the value of x 5 when f(x) = 13? a. A person s body mass index (BI) is calculated by dividing the person s mass in kilograms by the person s height in meters. The table shows the median BI for U.S. males from age to age 1. For which intervals is the average rate of change in the BI positive? AFS.91.F-IF..6 effect of rate of changes on a graph b. Eleanor is conducting an experiment. She starts with 5 samples of lemonade at different temperatures. Then, she recorded how long it took each sample to freeze solid. The graph shows her results. What conclusions can you make from the graph with regards to rate of change?

4 AFS.91.F-IF.3.7a AFS.91.A-SSE.1.1 AFS.91.F-IF..4 AFS.91.F-IF.3.9 AFS.91.A-CED.1.3 AFS.91.A-REI.1.1 AFS.91.F-IF..5 Algebra 1 Semester Exam Study Guide graph has the same slope as a given line Determine what x represents in an expression Interpret the key features of a table (relative maximum/ minimum) Determine what the y-intercept is of a function with the greater rate of change (equation/ two points) solution is plausible in a systems of linear inequalities step is valid in solving an equation for x Determine a reasonable domain for a function within a given context a. Determine a line that has the same slope as 4y 8 = x. Graph it on a coordinate plane. b. Determine a line that has the same slope as x + 3y = 1. Graph it on a coordinate plane. a. This expression describes the cost, in dollars, for Beth to buy some new clothes. (0 + 18x) 1.1 If x represents the number of skirts, what would the 18 represent? What would the 0 represent? What would the 1.1 represent? b. This expression describes the cost, in dollars, for Bob to buy some new clothes. (50 + 1x) 1.16 If x represents the number of pants, what would the 1 represent? What would the 50 represent? What would the 1.16 represent? a. The profit produced by an apple orchard increases as more trees are planted. aryann graphs this continuous relationship with the domain of 0 x 40 on a coordinate plane. Apples Profit What is true about the maximum and minimum for the graph? a. Given the function f(x) = 5x + 4 and the points for function g(x) (-1, -6) and (, 3). Which function has the greater y-intercept? Which function has the greater rate of change? b. Given the function f(x) = 3x + 8 and the points for function g(x) (-, -4) and (5, 3). Which function has the greater y-intercept? Which function has the greater rate of change? a. Charlene makes $10 per hour babysitting and $5 per hour gardening. She wants to make at least $80 a week, but can work no more than 1 hours a week. Write a system of linear equations. Graph the solutions of the system. Describe all possible combination of hours that Charlene could work at each job if only whole numbers are allowed. What is the greatest amount Charlene can earn? b. Zoe plans to knit a scarf. She wants the scarf to be more than 1 but less than 1.5 feet wide, and more than 6 but less than 8 feet long. Graph all possible dimensions of Zoe s scarf. ist two possible combinations. Solve the following equations. Justify each step. 1 x + 4x 7 = 4x n = 3n + 4 a. Jerry earns $1 per hour for his after-school job. He never works more than 14 hours in a week, and he never works a fraction of an hour. The equation that models this situation is A=1h where A represents the amount Jerry earns and h represents the number of hours Jerry works in a week. What

5 is the reasonable domain of the function A in the given context? b. Joanie earns $16 per hour for his after-school job. She never works more than 15 hours in a week, and she never works a fraction of an hour. The equation that models this situation is A=16h where A represents the amount Joanie earns and h represents the number of hours Joanie works in a week. What is the reasonable domain of the function A in the given context? AFS.91.A-REI.3.6 relationship between two equations (parallel or perpendicular) AFS.91.A-CED.1. AFS.91.A-REI..3 AFS.91.A-REI.1.1 AFS.91.F-E..5 H Real world situation with systems of linear equations ( variables) Create equations and solve Solve an equation for x (variables are included) reason in an algebraic proof increase of rate of change in two equations a. ast month Stephanie spent $57 on 4 allergy shots and 1 office visit. This month she spent $9 after 1 office visit and a refund for allergy shots from her insurance company. How much does an office visit cost? an allergy shot? b. The ees spent $31 on movie tickets for adults and 3 children. The acias spent $6 on movie tickets for adults and children. What are the prices for adult and child movie tickets? a. ook at this equation. 1 (x + b) = 5 Which expression 3 represents the value of x for the equation? b. ook at this equation. 3 (6x + b) = 15 Which expression 4 represents the value of x for the equation? a. What two properties are used in the following solution to 4b 3 = 17? b. What two properties are used in the following solution to 7 b = 3n + 4? a. The function A(d) = 0.45d models the amount A, in dollars, that Terry s company pays him based on the roundtrip distance d, in miles, that Terry travels to a job site. The company is modifying its pay structure so that Terry will get paid a total of $350 for traveling 165 miles round trip and $450 for traveling? By how much will the price per mile increase for the roundtrip distance?

6 a. What does the c intercept mean in the graph below? AFS.91.F-IF..4 Interpret the meaning of the intercept within context AFS.91.A-REI.4.11 AFS.91.A-CED.1. AFS.91.F-BF.1.1 AFS.91.A-CED.1.1 solution of the equation f(x) = g(x) equation represents the context equation represents the context Create the equation to represent the situation a. Some values for two different linear functions, f(x) and g(x), are shown in this table. x f(x) g(x) What is the solution of the equation f(x) = g(x)? b. Some values for two different linear functions, f(x) and g(x), are shown in this table. x f(x) g(x) What is the solution of the equation f(x) = g(x)? a. Binh brought $3 with her to the county fair. She purchased a $5 T-shirt and now wants to buy some locally grown plants for $.50 each. What are the numbers of plants that she can purchase with her remaining money? Write an equation to represent this situation. b. A 15-foot-tall cedar tree is growing at a rate of feet per year beneath power lines that are 58 feet above the ground. The power company will have to prune or remove the tree before it reaches the lines. How many years can the power company wait before taking action? Write an equation to represent this situation. a. A small swimming pool initially contains 400 gallons of water, and water is being added at a rate of 10 gallons per minute. Write an expression that represents the volume of the pool after t minutes. b. iguel has $50 dollars saved, and he adds $5 to his savings every week. Write a function that describes the amount A, in dollars, that iguel has saved after t weeks. a. A landscaper is planting a row of 10 shrubs along the walkway shown below. There must be one shrub at the very beginning and one shrub at the very end, and the shrubs in between will be equally spaced along the length of the walkway. Write an equation can the landscaper use to find the distance d in feet to leave between the shrubs?

7 a. The amount of money that Theresa earns in a week is a function of h, the number of hours she works, as shown in the table below. Write a function that represents this situation. AFS.91.F-IF.1. correct function for the table h f(h) b. Write a function that represents this situation. h f(h) a. Claire purchased just enough fencing to border either a rectangular or tirangular garden, as shown, whose perimeters are the same. How many feet of fencing did she buy? b. The table shows the membership fees of three different gyms. AFS.91.A-CED.1.1 Solve an equation to find the total amount within the context of the problem