Practice Exam for Algebra II Module 1 1. Frank swam 50 laps at the pool at a constant speed of 300 feet per minute. Which of the following describes a varying quantity in this situation? a. The speed Frank swam in feet per minute b. The amount of time elapsed in minutes since Frank began swimming c. The length of one lap in feet d. The amount of time it took Frank to swim one lap 2. A sprinter gradually sped up during the first 100 meters of a 200-meter race. He reached his top speed at the 50-meter point after 6 seconds since he began the race. He continued running at that same speed another 7 seconds until he reached the 100 meter mark. He gradually slowed down until he finished the race 28.8 seconds after he started running. a. Label the axes with the appropriate quantities, then construct a rough sketch of the runner s distance from the starting line (in meters) in terms of the number of seconds since he began the race. Runner s Distance from Start in meters Time Elapsed since Runner Began in seconds 3. Mary lives 2000 feet north of her school. Let x represent the distance in feet Mary has walked from her house toward her school. a. What values can the variable x take on in the context of this problem? 0 x 2000 b. Write an expression to represent how far Mary is away from her school.
c. Danielle leaves the school and starts riding her bike toward Mary s house at the same time that Mary starts walking toward the school. Danielle is biking four times as fast as Mary is walking. When Mary has walked a distance of x feet toward the school, how many feet has Danielle rode her bike from the school toward Mary s house? Explain your reasoning. Since Danielle is biking 4 times as fast as Mary is walking she will have traveled 4 times the distance that Mary has traveled. d. What does the expression 2000 5x represent in the context of this problem? 2000 5x represents the distance between Mary and Danielle. 4. If 2x - 12 = 7, then 2x + 1 = 5. Solve the following equations for x. a. 2x 8 = 7 3( x 2) b. 3.2 5.8 x = 4.7 5.12 5 3 x = x + d. 6( x 2(3 ) 4) x = 6 5 c. 1 8 3( 2)
6. Lola bought hair extensions at a 35% discount and paid $90.00. What was the regular price of the hair extensions? The regular price of hair extensions is $138.46. 7. A bakery has a sale for 18% off the original price, p. The store than charges 7% sales tax on the discounted purchase. Which of the following best describes the amount you would pay for the purchase as a percentage of its original price, p? a. Exactly 89% of the original price b. A little less than 89% of the original price c. A little more than 89% of the original price. 8. Tim has made 19 out of 30 free throws this basketball season. There are three games remaining in the season. If Tim shoots 15 free throws in the remaining three games, set up an equation to determine, x, the number of free throws Tim must make in the final three games to end the season having made 85% of his free throws? 9. A go-cart ride at an amusement park allows children that are taller than 48 inches and shorter than 62 inches to ride. a. Represent, using algebraic symbols, the heights, x, of children that are allowed on the ride. b. Represent the heights, x, of children that are allowed on the roller ride on a number line.
10. Given the two inequalities below, write three numbers for x that make each inequality true: a. 2x > 4.4 b. x > 3.5 11. Illustrate on a number line the set of values that make each of the inequalities true. a. 2x > 4.4 b. x > 3.5 12. Solve the following inequalities for x. a. 7x 2 > 13 b. 9 0.5x 6x + 4 c. 1< 2x 4 < 9 d. 5 1 7 < 3x < 4 4 12 13. The maximum weight that can be safely carried on a elevator is 2500 lbs. After the first stop 5 people weighing 114 lbs., 138 lbs., 115 lbs., 145 lbs and 250 lbs. have boarded the elevator. What amount of weight x can be safely added to the elevator at the next stop? (Hint: Set up an inequality and solve for x.) The amount of weight that can be safely added to the elevator at the next stop must be less than or equal to 1738 pounds.
14. Given the inequality, x 1 < 6 a. What values of x make the above inequality true. b. Illustrate the solution to the inequality (the values of x that make it true) on a number line. 15. Use BOTH absolute value notation and a number line to represent the values of x described below. a. All numbers, x, whose distance from 3 is less than 2.5. b. All numbers, x, whose distance from -5 is greater than 2. 16. a. Use absolute value notation to represent all measurements, x, of a candy bar that are greater than 0.05 inches away from 9 inches. b. Use a number line to represent all measurements, x, of a candy bar that are greater than.05 inches away from 9 inches.
17. José extends his arm straight out, holding a 1.5-foot string with a ball on the end. He twirls the ball around in a circle with his hand at the center, so that the plane in which it is twirling is perpendicular to the ground. Answer the following questions assuming the ball twirls counter-clockwise starting at the 3 o clock position. a. Construct a graph that relates the ball s vertical distance above José s hand in terms of the fractional part of the circular path that the ball has rotated from the 3 o clock position, as the ball travels counter-clockwise in a circle around José s hand. (Hint: Mark off ¼ rotation, ½ rotation, ¾ rotation, 1 full rotation on the horizontal axes.) Let x = the fractional part of a circle that the ball has rotated from the 3 o clock position. Define the output variable, y, you will use to model this situation. y = Label the axes and construct your graph here. b. As the ball travels from the 3 o clock position to ¼ of a counter-clockwise rotation, how does the vertical distance of the ball above José s hand change?