Algebra 1 Semester 1 Final Exam Review (Chapters 2, 3, 4, & 5)

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1 Name: Date Block: Algebra 1 Semester 1 Final Exam Review (Chapters 2, 3, 4, & 5) Chapter 2: Solving Equations 1. Solve each equation. Show your work! 5 1 3n y a) f = 8 b) h + = c) 2p = 54 d) - 15 =- e) - 8 = f) -3(b + 9) = -6 g) -5m m = 2m + 11 h) 5(r 1) = 2(r 4) 6 2. Lola spends one-third of her allowance on movies. She spends $8 per week at the movies. Write and solve an equation to determine Lola s weekly allowance. 3. Brian has job offers at two companies. One company offers a starting yearly salary of $28,000 with a raise of $3000 each year. The other company offers yearly a starting salary of $36,000 with a raise of $2000 each year. a) After how many years would Brian s salary be b) What would that salary be? the same with both companies? 4. Solve each equation for the variable indicated. Show your work! m + 3 a) Solve for x: 3x 7y = z b) Solve for n: = p n

2 5. Write an equation for the story problem, solve the equation, and write your answer as a complete sentence. a) Tanya made $15.50 while babysitting. She b) One phone company charges $60 plus now has a total of $ How much money $1.50 per text. Another charges $15 plus did she have before she babysat?. $2 per text. After how many texts will the two phone plans cost the same? Chapter 3: Solving Inequalaties 6. Graph each inequality. a) k > -12 b) b Write the inequality shown by each graph. a) b) 8. Solve each inequality and graph the solutions. a) -4 > t 12 b) 0.42d < d 9. Solve each inequality and graph the solutions. a) -1 < 4(x + 5) b) 3a 5-2

3 10. Write an inequality for the story problem, solve the inequality, and write your answer as a complete sentence. a) Jesse has $25. If comic books cost #5.50, b) Star Painter charges $120 plus $15 per how many can he buy? hour. Prolific Painter charges a flat fee of. $500. After how many hours of painting will the cost of Prolific Painter be less than Star Painter? Chapter 4: Functions 11. Choose the graph that best represents each situation. a) x + 9 b) z 7 a) Mark leaves home, drives through town, then on the highway, and finally stops at a rest area. b) Julie leaves home, drives to the other end of town and buys groceries, then returns home. c) Lora walks to a friend s house where she stays overnight. 12. Write a possible situation for each graph. a)

4 b) 13. Express the relation as a table, as a graph, and as a mapping diagram. {(-2, 0), (-2, 1), (-2, 2), (-2, 3), (-2, 4), (-2, 5)} a) b) c) d) Is this a function? 14. Give the domain and range of each relation. Tell whether the relation is a function. Explain. a) b) c) D: D: D: R: R: R: Function? Function? Function? Explain: Explain: Explain: 15. Identify the independent and dependent variables in each situation (ONLY WORDS, NO NUMBERS) a) Ice cream sales increase when the temperature rises. I.V.: D.V.:

5 b) Food for the catered party costs $12.75 per person. I.V.: D.V.: c) More program money is given out to cities with larger populations. I.V.: D.V.: d) Sales tax in the state of Maryland is 5% of the purchase price. I.V.: D.V.: 16. Write an equation to show the relationship between the x- and y-values. a) b) {(-1, -4), (0, -2), (2, 2), (5, 8)} 17. Evaluate each function for the given input values. Show your work! a) f(x) = 3x + 2 when x = 4 and when x = -1. f(4): f(-1): b) g(x) = -6x when x = -5 and when x = 3. f(-5): f(3): _

6 18. A fitness class is being offered twice a week for four weeks. The registration fee is $8.50 and the cost for each class attended is $4.75. Write a function rule to describe the total cost of the class. function rule: 19. Graph the function y = x 2 3 with D: All Real Numbers. x y = x 2 3 (x, y) 20. Determine whether each scatter plot has a positive correlation, negative correlation, or no correlation. a) b) c) 21. Identify the correlation you would expect to see between the pair of data sets. Explain. a) The number of pets a person has and the number of times they go to a pet store. b) The number of chicken pox vaccines given and the number of chicken pox cases reported. c) The number of vacation days given to employees and their level of job satisfaction.

7 22. Neal kept track of the number of minutes it took him to assemble sandwiches at his restaurant. The information is in the table below. Number of sandwiches Minutes a) Graph a scatter plot of the data. b) Draw a trend line. c) Describe the correlation. d) Based on the trend line you drew, predict the amount of time it will take Neal to assemble 12 sandwiches. Chapter 5: Linear Functions 23. For each relation, determine whether it represents a function and whether it is linear. Explain how you know. a) Is the relation a function? Is the relation linear? b) Is the relation a function? Is the relation linear? c) y = 2x 2 3x + 1 Is the relation a function? Is the relation linear?

8 24. Find the x- and y-intercepts and the slope of the graphed lines. a) b) x-intercept: y-intercept: Slope: x-intercept: y-intercept: Slope: 25. The change in water level of one portion of the Mississippi River is about -0.3 ft per day. The water level starts at 17 feet and falls for x days, which is represented the function f(x) = x, graphed at right. Find the intercepts. What does each intercept represent? The x-intercept is approximately It means the water level is after days. The y-intercept is It means the water level is after days. 26. Tell whether the slope of each line is positive, negative, zero, or undefined. a) b) c) d) 27. Find the slope of the line that contains each pair of points. Show your work! a) (6, 2) and (9, 1) b) (-2, -5) and (-4, 3)

9 28. Find the slope, x-intercept, and y-intercept of the line described by each equation. a) y + 3 = 2x b) -2x 8y = 24 Slope: x-int: y-int: Slope: x-int: y-int: 29. Write the equation that describes each line in slope-intercept form. 3 a) slope = -, y-intercept = 1 b) slope = -3 and point (-3, 4) c) (-3, 6) and (2,1) Write the equation that describes each line in point-slope form. 1 a) slope = -, (-2, 3). b) slope = -4, (2, -1) d) (0, -5) and (6, -3) Identify which lines are parallel to y = 6x - 7 a) -2y = -12x + 16 b) y =!" x + 4 c) y + 6x = -1 # d) y 9 = -6(x + 2) e). y = 6x + 10 d) y + 3 = 6(x - 5) 32. Identify which lines are perpendicular to y =!" ' x + 3 a) -2y = -4x + 16 b) y =!" x + 4 c) y - 2x = -1 ' d) y 11 = 2(x + 5) e). y = -2x + 3 d) y + 8 = " (x - 1) '