Chapter Three Review
- 1. Chapter Three Review Linear Equations Recursive Sequences Time/Distance Relationships Intercept Form Rate of Change Solving Equations Problem Solving
- 2. Recursive Sequences Write a recursive routine that generates each sequence; then use your routine to figure out the 10 th term in each pattern 7.8, 3.6, -0.6, -4.8, . . . -9.2, -6.5, -3.8, -1.1, . . . 1, 3, 9, 27, . . . 36, 12, 4, 1.3, . . .
- 3. Recursive Sequences Write a recursive routine that generates each sequence; then use your routine to figure out the 10 th term in each pattern 7.8, 3.6, -0.6, -4.8, . . . -9.2, -6.5, -3.8, -1.1, . .. 1, 3, 9, 27, . . . 36, 12, 4, 1.3, . . . 7.8, 3.6, -0.6, -4.8, . . . Start at 7.8, subtract 4.2 (-30) -9.2, -6.5, -3.8, -1.1, . . Start at –9.2, add 2.7 (15.1) 1, 3, 9, 27, . . . Start at 1, multiply by 3 (19,683) 36, 12, 4, 1.3, . . . Start at 36, divide by 3 (.00176)
- 4. Time/Distance Relationships Mr. Bress’s two nephews are having a race. Because he is older, Joseph gives Ari a 5m head start. Joseph runs at a speed of 7.7 mps, and Ari runs at a speed of 6.5 mps. The race is 50 meters. Write an equation to find out how long it will take Joseph to finish the race. Write an equation to find out how long it will take Ari to finish the race. Determine who will win the race, and determine how far ahead the winner was when he crossed the finish line.
- 5. Time/Distance Relationships Mr. Bress’s two nephews are having a race. Because he is older, Joseph give Ari a 5m head start. Joseph runs at a speed of 7.7 mps, and Ari runs at a speed of 6.5 mps. The race is 50 meters. Write an equation to find out how long it will take Joseph to finish the race. Write an equation to find out how long it will take Ari to finish the race. Determine who will win the race, and determine how far ahead the winner was when he crossed the finish line. Write an equation to find out how long it will take Joseph to finish the race. y = 7.7x (when y = 50) Write an equation to find out how long it will take Ari to finish the race. y = 5 + 6.5x (when y = 50) Determine who will win the race, and determine how far ahead the winner was when he crossed the finish line. Joseph wins by 0.4 seconds (6.5 to 6.9) and is 2.6 meters ahead at the finish line
- 6. Intercept Form For each table of values, determine the rate of change and the starting value, then write an equation in intercept form 5 4 3 y 2 1 0 x .03 .02 .01 y 3 2 1 x 11 5 1 y 3 0 -2 x 2 -3 5 y 2 12 -4 x
- 7. Intercept Form For each table of values, determine the rate of change and the starting value, then write an equation in intercept form 1; 3; y = 3 + 1x .01; 0, y = 0 + .01x 2; 5; y = 5 + 2x -0.5; 3, y = 3 – 0.5x 5 4 3 y 2 1 0 x .03 .02 .01 y 3 2 1 x 11 5 1 y 3 0 -2 x 2 -3 5 y 2 12 -4 x
- 8. Rate of Change The equation d = 1032 – 210t represents the distance in miles and time in hours from a specific destination Find the distance from the destination after 4.8 hours Find the time traveled if the destination is 770 miles away Determine the RATE OF CHANGE for each table below 15 6 13 5 11 4 9 3 7 2 Output Input Output Input -26 7 -14 4 -2 1 10 -2 22 -5 Output Input -16 12 -11 7 -6 2 -1 -3 4 -8
- 9. Rate of Change The equation d = 1032 – 210t represents the distance in miles and time in hours from a specific destination Find the distance from the destination after 4.8 hours d = 1032-210(4.8); 1032-1008=24 miles Find the time traveled if the destination is 770 miles away 770=1032-210x; -262/-210=1.25 hrs. Determine the RATE OF CHANGE for each table below 2/1 = 2 -12/3 = -4 -5/5 = -1 15 6 13 5 11 4 9 3 7 2 Output Input Output Input -26 7 -14 4 -2 1 10 -2 22 -5 Output Input -16 12 -11 7 -6 2 -1 -3 4 -8
- 10. Solving Equations 14x = 63 9n – 6 = 15 2 4.2 = -2x – 42.6 14 + 2(x – 8) = 10 7
- 11. Solving Equations 14x = 63 x = 63/14 x = 4.5 9n – 6 = 15 2 9n – 6 = 30 9n = 36 n = 36/9 n = 4 4.2 = -2x – 42.6 46.8 = -2x 46.8/-2 = x -23.4 = x 14 + 2(x – 8) = 10 7 2(x – 8) = -4 7 2(x – 8) = -28 x - 8 = -28/2 x - 8 = -14 x = -6
- 12. Problem Solving Mr. Bress’s son Michael is running in the Philadelphia Marathon in November, and Mr. Bress is trying to figure out where to park his car. There are three lots that are convenient to the start/finish line: Landmark Parking charges $5 for the first hour and $2 for each additional hour Franklin Park and Lock charges $3 per hour Safe and Sound Garage charges $15 for the entire day Complete the table, and determine the cost for parking for up to 8 hours at each lot Michael assumes that it will take about 3.25 hours to run the race, and he needs about 1.5 hours before the race for check in and warm up. He’ll need about 45 minutes after the race to warm down. Based on the information in the chart, which lot should he choose?
- 13. Problem Solving Mr. Bress’s son Michael is running in the Philadelphia Marathon in November, and Mr. Bress is trying to figure out where to park his car. There are three lots that are convenient to the start/finish line: Landmark Parking charges $5 for the first hour and $2 for each additional hour Franklin Park and Lock charges $3 per hour Safe and Sound Garage charges $15 for the entire day Complete the table, and determine the cost for parking for up to 8 hours at each lot Michael assumes that it will take about 3.25 hours to run the race, and he needs about 1.5 hours before the race for check in and warm up. He’ll need about 45 minutes after the race to warm down. Based on the information in the chart, which lot should he choose? 3.25 + 1.5 + .75 = 5.5 hours, or 6 hours of parking At 6 hours, either LANDMARK or SAFE and SOUND costs the same ($15)
- 14. Problem Solving 8 7 6 5 4 3 2 1 Safe/Sound Franklin Landmark Hours
- 15. Problem Solving 15 24 19 8 15 21 17 7 15 18 15 6 15 15 13 5 15 12 11 4 15 9 9 3 15 6 7 2 15 3 5 1 Safe/Sound Franklin Landmark Hours