Unit 7: Algebra 1A Semester Review Unit 1 Key Concepts 1. A car rents for $23 per day, with a $32 fee for insurance. Write an expression to determine the total cost in terms of the number of days the car is rented, d. 2. Evaluate the expression for p = 2 and q = 4. 3. Order the numbers from least to greatest: -7/8, 7/4, -15/2, and -13/16 Simplify. 4. 2(3y – 4) 5. 5 – 3x + y + 6 6. 2x + 3(x – 5) + 9 7. -20 – (-5) * ( -5)2 8. Write an algebraic expression for the phrase the quotient of a and 6. Unit 2 Key Concepts Solve the following equations. 9. p + 3/8 = 5/4 10. 2a + 5 = 9a – 16 12. (5/8)t – 7 = - 22 13. Solve for x: m – 3x = 2x + p Unit 3 Key Concepts Solve each inequality. Graph the solution on the number line. 14. y – 4 + 2 ≥ 10 15. -3/4 < -3/8m 16. -3(j + 3) + 9j < -15 17. -2 ≤ d + 0.5 ≤ 4.5 11. 12.2 = 5.3x – 3.7 Show your work. 18. To enter a competition, students must score a total of at least 450 points on five qualifying tests. Each test is worth 100 points. On the first four tests, your scores were 94, 88, 79 and 95. What are three possible scores you can earn on the last test to enter the competition? 19. A sales associate in a shoe store earns $325 per week, plus a commission equal to 4% of her sales. This week her goal is to earn at least $475. At least how many dollars’ worth of shoes must she sell in order to reach her goal? 20. Suppose U = {1,2,3,4,5} is the universal set and A = {2,3}. What is A’? 21. Solve: |y + 8| ≥ 3 22. A ski shop owner surveys 200 people who ski or snowboard. If 196 people ski and 154 people do both activities, how many people snowboard? Unit 4 Key Concepts 23. The ordered pairs (0,-3), (1,2), (2,7), (3,12) represent a function. What is a rule that represents this function? 24. The size of a bee’s nest increases as time passes. Your friend says that time is the dependent variable because size depends on time. Is your friend correct? 25. A helicopter hovers 40 ft above the ground. Then the helicopter climbs at a rate of 21 ft/s. Write a rule that represents the helicopter’s height, h, above the ground as a function of time, t. what is the helicopter’s height after 45 s? 26. Is the following relation a function? (4,2), (1,1), (0,0), (1, -1), (4, -2). Give the domain and range. 27. Is the sequence arithmetic? 15, 14.5, 14, 13.5, 13,……If so, give the common difference. 28. What is the vertical line test? Unit 5 Key Concepts 29. Graph y = |x – 3| (Graph provided at the end of this document). 30. For the data in the table, does y vary directly with x? If it does, write an equation for the direct variation. X 4 8 10 Y 6 12 15 31. Graph 2x – 3y = 15 by putting it into slope-intercept form. (Graph provided at the end of this document). 32. Find the slope of the line that contains the points (-2, 5) and (-1, 7). 33. Find the slope of the line graphed at the right. 34. Write an equation in point-slope form of the line that has a slope of ½ and passes through the point (5, -2). Graph the line. (Graph provided at the end of this document). 35. Write an equation in slope-intercept form of the line that contains the points in the table. X Y 1 9 4 10 7 11 13 13 36. Write y = ½x – 5 in standard form. 37. Tell if the following pair of lines is parallel, perpendicular or neither. 3x – 2y = 16 y = -2/3x + 4 Parallel lines have _____________ slopes. Perpendicular lines have ___________________ slopes. 38. Write an equation of a line that is parallel to y = 3x – 5 and goes through the point (3, 1). Unit 6 Key Concepts 39. Describe the number of solutions for each system of equations graphed below. 40. Solve this system and list the method that you chose (graphing, substitution or elimination). y = 2x – 12 y = -x + 3 41. The Badys and their maid, Alice, took a trip to Hawaii for their summer vacation. The travel agent told Ike that the trip would cost $210 for each child plus another $315 per adult. According to Ike Bady’s credit card receipt, the trip cost a total of $2205 for all 9 of them. Find the number of adults and children on the trip by writing a system of equations. 42. Graph y > -1/3x + 2 and give two possible solutions. When graphing linear inequalities, the line is “dashed” when you have ______ or ______. The line is “solid” when you have ______ or ______. You shade _______ the line when you have > or >. You shade _______ the line when you have < or <. The solutions of linear inequality are _____________________. 43. Graph the system of linear inequalities and give two possible solutions. y > ¼x – 3 y + 2x < 1 Graphs