Course 3 FINAL EXAM STUDY GUIDE. Solve each equation. Check your solution. Write the expression using exponents.

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1 Name: Class: Date: Course 3 FINAL EXAM STUDY GUIDE Write the expression using exponents. 1. d d d d d f f f f f Multiply. Express using exponents. 2. (4m 4 )( 7m 6 ) (3p 9 ) 2 Evaluate the expression Write the number in standard form Write the number in scientific notation. 7. 3,810 Find the square root. 8. Find the cube root. 9. Estimate to the nearest whole number Replace the with <, >, or = to make a true statement. 4 Solve the equation. Check your solution j = 43 Solve the problem by writing and solving an equation. 14. Josie bought a soda and 2 candy bars. The soda cost $1.10. Her total bill was $2.40. How much was each candy bar? Solve each equation. Check your solution (x + 7) = 7(x 7) 17. At Santa Maria High School the juniors and seniors are selling raffle tickets. So far, the juniors have solved 580 tickets and are averaging 29 tickets per day. The seniors have sold 490 tickets but vow to win the contest by selling an average of 35 tickets per day. If both grades continue collecting at these rates, after how many days will the number of tickets sold be equal? 18. The table shows the relationship between the wait time in minutes and the number of people in line. People in Line Number Wait Time (min.) What is the constant rate of change? Find the slope of the line that passes through the pair of points. 19. S(10, 16), T(19, 18) 20. The graph shows the cost of one pound of lemons at a grocery store. Find the slope of the line. The formula for the perimeter of a square is P = 4s, where s is the length of a side. Find the perimeter of the square. 12.

2 Graph the equation using the slope and the y-intercept. 21. y = x + 3 Solve the system of equations algebraically Allied Plumbing charges $45 per service call plus $30 per hour. Ajax Plumbing charges $60 per service call plus $25 per hour. How many hours would a service call have to last in order for the total cost of each company to be the same? 22. Use the x- and y-intercepts to graph the function. Determine whether the graph represents a linear or nonlinear function. 28. Write an equation of the line in slope-intercept form that passes through the pair of points. 23. ( 3, 4), ( 5, 12) Write an equation of the line in slope-intercept form that passes through the point with the given slope. 24. ( 2, 2), slope = 4 Solve the system of equations by graphing Determine whether the table represents a linear or nonlinear function x y Pete s Boat Rental charges an initial fee to rent a boat, plus an hourly fee. The table shows the cost to rent a canoe. Determine the initial fee that Pete s charges to rent a canoe. Assume that the relationship between the two quantities is linear. Number of Hours, Cost ($), x y a. $68 b. $54 c. $40 d. $14

3 Find the missing measure in the triangle If m 1 68, and 1 4, classify the relationship between 1 and 4. Then find m 2 and m 3. Explain your reasoning. 32. Write an equation you could use to find the length of the missing side of the right triangle. Then find the missing length. Round to the nearest tenth if necessary. 37. Triangle ABC has vertices, and. Graph the vertices of triangle after a translation of 5 units right and 4 units up. 33. Write an equation you could use to find the length of the missing side of the right triangle. Then find the missing length. Round to the nearest tenth if necessary. 34. Find the distance between the pair of points whose coordinates are given. Round to the nearest tenth if necessary. 38. Construct the reflection over the x-axis of the trapezoid given below: Classify each pair of angles as alternate interior, alternate exterior, or corresponding. 35. A and I: A and D: F and I: 39. Identify the coordinates for the triangle ABC, when it is rotated clockwise about the origin by.

4 40. Find the image of the figure after a dilation with the origin as the center by a scale factor of 2.5. Write a proportion to determine the missing measure. Round to the nearest tenth, if necessary. 45. A lighthouse casts a 72-yard shadow at the same time as a 32-foot tall billboard casts a 19-foot shadow. What is the height of the lighthouse? 46. For the pair of similar figures, find the area of the second figure. 41. Determine if the two figures are congruent by using transformations. Area = 48 Area =? Find the volume of the cylinder shown. If necessary, round to the nearest tenth Determine if the two figures are congruent by using transformations. Find the volume of the cone shown. If necessary, round to the nearest tenth. Write congruence statements comparing the corresponding parts in the congruent triangles shown Find the surface area of the cylinder shown. If necessary, round to the nearest tenth. The pair of polygons is similar. Write a proportion to find each missing measure. Then solve

5 50. Mrs. Lopez made decorative candles in different sizes for sale at her church. All of the candles are in cylindrical jars. The size of the largest candle was bigger than the smallest candle by a scale factor of two. If the height and radius of the smallest candle are 5 cm and 1.7 cm, respectively, calculate the volume of the biggest candle. Use 3.14 for. Round to the nearest hundredth. 51. What kind of relationship does the following scatter plot show? 54. What is the relative frequency of nurses who are between 30 and 49 years old to all nurses? Round to the nearest hundredth if necessary. Draw a box plot for the set of data , 44, 54, 31, 27, 52, 25, 37, 34, 34, 50 Find the mean, mode, and range of the set of data. Round to the nearest tenth if necessary , 14, 30, 11, 32, 33, 21, A behavioral study measured the number of positive responses received for a certain product during the 21 hours that it was sold. Fifteen pairs of data are represented in the scatter plot. The professor later studied the diagram to analyze if there was any correlation between the number of positive responses and time. 57. Construct a scatter plot of the number of people watching a movie and the number of veggie burgers sold. Draw the line of best fit. Write the equation of the best fit. Is there any relationship between the number of positive responses and the number of hours the product was sold? The two-way table shows the ages of doctors and nurses who work at a certain hospital. Doctors Nurses How many doctors and nurses work at the hospital?

6 Answer Key m p > y = 4x y = 4x = 16. Since length cannot be negative, each side of the square is 16, so 4(16) = 64 millimeters days Let x represent the number of days x = x 580 = x 90 = 6x x = 15 The number of tickets sold will be the same in 15 more days. 26. The solution set is minutes per person hours 28. nonlinear 29. linear

7 30. c cm cm none 36. Angles 1 and 4 are alternate interior angles; the measure of 2 is also 68.4 because angles 2 and 3 are vertical angles; the measure of 3 is or because 2 and 3 are supplementary b 42. d 43.,,,,, yd The scale factor of the two similar figures is, that is 2. The area of the first figure is 48. Area of smaller rectangle = = = 12 So, the area of the smaller rectangle is cm 51. positive relationship, linear 52. no relationship 53. d 54. a