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MATH 98: ELEMENTARY ALGEBRA Practice TEST: Inequalities and Graphing Directions: NAME_____________________ Complete all of the following. Show work neatly to receive partial credit. [-1, ∞) 1. Write the interval given in set-builder notation: 2. Sketch, in graphical notation, the set shown. { x | x < 5.5 } 3. Translate, using N as your variable, to an inequality: “Fifteen times the number of students is at least sixty.” (Do not solve.) 4. Solve and express your solution set in set-builder notation. (a) RANGE DEPENDENCE ON LAUNCH ANGLE Use the graph shown to answer the following questions. (a) What is the Range when the launch angle is 30 degrees? (b) What two launch angles give a Range of about 350 cm? 25 12 x 20 15x (b) 450 400 350 300 RANGE (cm) 5. 3 2 x 5 250 200 150 100 50 0 20 30 40 45 50 60 LAUNCH ANGLE (degrees) _____ 6. In which quadrant is the y-coordinate always positive and the x-coordinate always negative? A. I 7. B. II C. III D. IV Plot the points given on the graph provided; indicate each point on the graph using its given letter. A = (-4, 3.5) B = (4, 5) C = (-2.5, -1.5) D = ( 3, -3) 70 _____8. Which of the following coordinate pairs is not a solution to the equation below? 2x - y = 6 A. (-1,4) 9. B. (2,-2) C. (0, -6) Complete the table of values for the equation: x 0 3x 2 y 6 2 D. (3, 0) y 0 And graph the equation using these points. 10. What is the negative reciprocal of -4/5 ? ____________ _____ 11. (True/False) All graphs of linear equations have at least one intercept. 2 x 2 on the axes provided. 3 12. Graph the equation: y 13. Given the two line equations below. Are these lines parallel , perpendicular, or neither? Line #1: Line #2: 14. 3 y x3 2 3 y x3 2 Find the slope and y-intercept of the equation: 2 x 3 y 8 slope = _________ y-intercept = (___,___) 15. Write an equation for a vertical line that passes through (2, 3). 16. Fast Freddie drove to Spokane and back for a business trip on Monday. The total mileage for his trip was 324 miles and the total travel time was 6.25 hours. He used 18 gallons of gas and spent $85.00 in travel expenses. Determine the rates indicated below, rounding off to the nearest tenth. (a) What was his travel cost rate in dollars per mile? (b) What was his average speed in miles per hour? 17. Jan pledged a total of $500 to NPR for the next year. How much does this work out to per day? 18. Determine the slope of the line that passes through the points (-3,-1) and (5,5) 19. Write the equation for a line in slope-intercept form that has a slope m = 3/4 and passes through the point (-4, 3). 20. Determine the slope of the line: 3 -2y = 0 21. The equation of a line in slope-point form is given by: 1 y 3 ( x 2) : 2 Re-write the equation in slope-intercept form and graph. (reduce fractions…)