Algebra 1 Semester 1 Final Exam Study Guide PDF

Name:_________________________________________________ Period:_________ Algebra 1 Semester 1 Final Study Guide You may use a scientific calculator or the Desmos test mode (scientific) app (NO GRAPHING) 1. Select all the equations that are e...

Name:_________________________________________________ Period:_________ Algebra 1 Semester 1 Final Study Guide You may use a scientific calculator or the Desmos test mode (scientific) app (NO GRAPHING) 1. Select all the equations that are equivalent to: 2𝑥 + 8 = 15 a. −30 = −4𝑥 − 16 b. 2𝑥 + 8 − 8 = 15 − 8 c. 0.5(8𝑥 − 4) = 15 d. 4𝑥 + 8 = 30 ! e. 15 = " (4𝑥 + 16) + 2 f. −2(−𝑥 − 4) = 5 − 3𝑥 + 8 + 3𝑥 + 2 2. Suppose that the water level of a river is 34 feet and that it is receding at a rate of 0.5 foot per day. Write an equation for the water level, y, after x days. a. 𝑦 = 34𝑥 +.050 b. 𝑦 = 0.5𝑥 + 34 c. 𝑦 = 0.5𝑥 − 34 d. 𝑦 = −0.5𝑥 + 34 3. Using your equation from question 2, In what will the water level be after 16 days? 4. Hailey has saved up $225, but is spending $15 a month on a gym membership. After how many months will she have $165 left? a. 3 months b. 4 months c. 5 months d. 10 months 5. Identify the slope of each of the following lines. a. −2𝑥 + 3𝑦 = −10 b. 5𝑥 + 2𝑦 = 3 c. 3𝑥 − 3𝑦 = 6  Use the graph to answer questions #6-8 6. What is the vertical intercept (y-intercept)? a. 150 b. 140 c. 70 d. 80 7. What is the slope of the graph? a. −20 b. −2 ! c. − " ! d. − "# 8. Select all the statements that are true: a. As the number of adult tickets increases, the number of children tickets increases. b. As the number of adult tickets decreases, the number of children tickets also decreases. c. As the number of adult tickets increases, the number of children tickets decreases. d. The number of children tickets decreases at a rate of 2. e. When no children tickets are purchased, 140 adult tickets were purchased. f. When the number of children tickets decrease by 20, number of adult tickets decreased by 10. 9. Write the equation of the line that passes through the points (−2, 5) and (3, −1). $ & a. 𝑦 = − % 𝑥 + " % !& b. 𝑦 = − $ 𝑥 + $ % "& c. 𝑦 = $ 𝑥 − $ $ ' d. 𝑦 = % 𝑥 − " 10. Write the equation of the line that passes through the points (1, −3) and (4, −3). a. 𝑦 = −3 b. 𝑦 = 3 c. 𝑥 = −3 d. 𝑥 = 3 11. Write the equation of the line that passes through the points (−2, −3) and (−2, 4). 12. Write the equation of the line that passes through (0, −1) and is perpendicular to the line shown? 13. Consider the equation −𝑥 + 2𝑦 = −8. For each question, explain or show your reasoning. a. If we graph the equation, what is the slope of the graph? b. Where does the graph intersect the y-axis? c. Where does it intersect the x-axis? 14. Solve the equations: a. −3(2𝑛 − 3) = 25 − 8𝑛 b. −3𝑥 −3(−4𝑥 + 2) = 2𝑥 − 27 15. Which linear system has exactly one solution? " 𝑦 =− 𝑥+7 3𝑥 − 2𝑦 = 4 𝑦 = −2𝑥 + 6 3𝑥 + 5𝑦 = 2 & a. 5 b. " c. " d. # ( 𝑦 =− 𝑥+7 6𝑥 − 4𝑦 = 8 𝑦 = −2𝑥 − 5 −6𝑥 − 10𝑦 = 4 & 𝑦 = −2𝑥 + 10 16. Solve the system of equations: 6 3𝑥 − 4𝑦 = 15 2𝑥 + 3𝑦 = 10 17. Solve the system of equations: 6 4𝑥 + 6𝑦 = 15 3𝑥 − 2𝑦 = 6 18. Solve the system of equations: 6 6𝑥 − 4𝑦 = 12 19. Solve the inequalities: !) &*+!" , &,-$ a. 84 < 4(1 + 4𝑥) b. − " ≥ ( c. ( −2≤ !" 20. Select all values that make the inequality true. −2(−4 − 𝑥) < 3𝑥 + 6 a. 𝑥 = 10 b. 𝑥 = 4 c. 𝑥 = 2 d. 𝑥 = −1 e. 𝑥 = 5 21. Select the inequality that matches the graph ) a. 𝑦 ≤ − $ 𝑥 + 5 ) b. 𝑦 < − 𝑥 + 5 $ ) c. 𝑦 ≥ − $ 𝑥 + 5 ) d. 𝑦 > − $ 𝑥 + 5 22. Select all the points that are solutions to the graph. a. (2, 0) b. (0, 0) c. (0, −1) d. (0, −4) e. (−1, 3) f. (−4, −5) 𝑦