Patterns & Graphs FPMath 70 Unit 3 Worksheet

Transcription

1 1. The image below shows a pattern of sections from a fence made from boards. a. Sketch the net two sections of the fence: b. Complete the following chart: Fence # (variable) # of boards c. How man boards are added for each new section?. d. If the same number of boards has been added to each fence section, how man boards would fence zero theoreticall have? This number will be the constant. e. If "" is used to represent the fence #, the equation can be represented b: 2. a. Complete the table on the right for the pattern shown above b. Ever time the figure number increases b one the number of heagons increases b c. How man heagons would be in the zero figure?. d. Write the epression that represents the relationship between the figure number and the number of heagons. Figure # (variable) # of heagons Page 1 of 15

2 3. Draw the net two figures in this toothpick pattern: Figure Number of toothpicks Write an epression for the relationship between the figure number and the number of toothpicks: 4. Write an epression for the relationship between the figure and the number of squares: 5. Complete the pattern in this table: Which epression represents this pattern? a. + 4 = b = c. 4 = d. = + 1 Page 2 of 15

3 6. Complete the pattern in this table: Circle the epression represents this pattern? 2 = = 2 2 = + 5 = 7. Create an epression from the following table of values: Term Number a. How much does the number increase for each term (variable)? b. What would the number be at the 0 term (constant)? c. What epression would represent the pattern? 8. Create an epression from the following table of values: 1. What equation would represent the pattern? Term Number Verif the equation b substituting values from the table Page 3 of 15

4 9. Discover the relationship between and in each table below b completing the table then write the relationship between and as an equation. The first one has been done for ou Equation: = 10 Number of Tickets Cost Hours worked Salar ($) Distance (k) Time (hr) Boes Sold Profit Equation: Page 4 of 15

5 10. The pizza Brenda is buing costs $8.50 plus $2.50 for each topping. She wants to figure out the cost for a pizza with different amounts of toppings. She started to make a chart: Toppings Cost of Toppings $ Pizza $ Total $ Then she realized it might be easier to work out a formula or epression for the total cost. a. Which price doesn t change? (This number will be the CONSTANT.) b. The number of toppings changes each time. This is the VARIABLE and can be represented b t. How is the variable related to the cost of the toppings? What is the coefficient? c. What epression or formula could she use to figure out the cost for a pizza? 11. Brent paid $4.00 to enter the carnival and $1.25 for each ride. The variable is the number of rides. a. Write an epression to represent the total cost of going to the carnival. b. If Brent started with $30 how man rides could he take? 12. Mar made $30 in tips and worked a number of hours at $10 an hour. a. Write an epression for how much she earned that da. b. If she worked 6 hours how much did she make in total? Page 5 of 15

6 13. For each table of values, sketch them on the grid and determine a rule (or equation) that epresses the relationship between and Equation: Equation: Equation: Page 6 of 15

7 14. Make a table of values for each equation below with at least 4 points in each table, then graph each equation on the grid provided. Remember, MANY different values can be entered in the table. 3 = = 2 5 = = -5 Page 7 of 15

8 15. From the following graphs, make a table of values. Then determine the linear relation (equation) that describes the graph. Page 8 of 15

9 16. From the following graphs, make a table of values. Then determine the linear relation (equation) that describes the graph. Page 9 of 15

10 17. You will now tr an easier wa to determine the equation for graphs. Identif the slope triangle and the -intercept on the graph, as well. -intercept -intercept equation equation -intercept -intercept equation equation Page 10 of 15

11 18. You will now tr an easier wa to determine the equation for graphs. Identif the slope triangle and the -intercept on the graph, as well. -intercept -intercept equation equation -intercept = none -intercept (trick one) equation equation Page 11 of 15

12 19. You will now tr an easier wa to determine the equation for graphs. Identif the slope in a fraction form prior to drawing the equation. Equation: = Equation: = -3-1 a parallel line: a parallel line: Equation: = (2/3) + 2 Equation: = 5 a parallel line: a parallel line: Page 12 of 15

13 20. You will now tr an easier wa to determine the equation for graphs. Identif the slope triangle and the -intercept on the graph, as well. Equation: = 2 Equation: = (-2/5) - 1 a perpendicular line: a perpendicular line: Equation: = + 6 Equation: = a perpendicular line: a perpendicular line: Page 13 of 15

14 21. The cost to print digital photos at an online store is shown in the graph below. a. Etrapolate to estimate the cost of printing 60 photos b. Etrapolate to estimate the number of photos ou could print for $1.00 c. Interpolate to estimate the cost of printing 45 photos d. Interpolate to estimate the number of photos ou could print for $ The following graph shows the cost to rent the gm for 2, 4 or 6 hours at $30.00 per hour. a. Etrapolate to find the cost to rent the gm for 8 hours. b. Etrapolate to find how long ou could rent the gm for $ c. Interpolate to find cost to rent the gm for 2.5 hours d. Interpolate to find how long ou could rent the gm for $ Page 14 of 15

15 23. Determine the equations of the following equations in =m+b form. a. Slope is 2 and passes through the point (2,3). b. -intercept is 5 and passes through the point (-4,1). c. Slope is 2 and -intercept is (4,0). d. Passes through points (1,2) and (5,10). e. Slope is -2 and passes through the point (2,-3). Page 15 of 15