Accelerated Intermediate 2 Summer Math Packet

Transcription

1 Chapter 1: Expressions, Equations, and Functions For Questions 1-2, write an algebraic expression for each verbal expression. 1. the sum of the square of a number and the product of 5 and twice a number 3. Write a verbal expression for 4n! Evaluate 2! Evaluate 3w + 8 v t if w = 4, v = 5, and t = 2. For Questions 6-7, name the property used in each equation. Then find the value of n = n = 7 + n 8. Evaluate Name the property used in each step.

2 9. Rewrite using the Distributive Property. Then simplify. Simplify each expression w 6w + 14w! y y For Questions 12-13, evaluate each expression !! 4 9!! 14. Find the solution of 5b 13 = 22 if the replacement set is 5, 6, 7, 8, Solve!!!! (!)! 1 = y

3 For Questions 16-17, use the graph that shows temperature as a function of time. 16. Identify the independent and dependent variables. 17. Name the ordered pair at point C and explain what it represents. For Questions 18-20, use the table that shows airmail letter rates to Greenland. 18. Write the data as a set of ordered pairs. 19. Draw a graph that shows the relationship between the weight of a letter sent airmail and the total cost. 20. Interpret the end behavior of the function.

4 Chapter 2: Linear Equations 1. Translate the following sentence into an equation: A number x subtracted from 36 is three times the sum of four and x. 2. Translate the following equation into a verbal sentence: 3 x + y = 2y x Solve each equation. Check your solution r = = p b = 35 6.! w = 9! 7.!!" =!!"#

5 8. 3a + 4 = 14 For Questions 9-10, write an equation for each problem. Then solve the equation. Check your solution. 9. What number decreased by 3.5 equals 12.7? 10. Twelve is added to the product of a number and 5. The result is -3. Find the number. 11. Julie cashed a paycheck and repaid her brother $10 that she had borrowed from him. She then spent $30 on fuel for her car and half of the remaining money on a new tent for camping. She bought a pair of running shoes for $29.95 and had $17.75 left. How much did Julie receive when she cashed her paycheck? 12. Evaluate 4t + n if t = 2 and n = 5.

6 For Questions 13-14, solve each equation. Then graph the solution set t 1 = a + 1 = Use cross products to determine whether the pair of ratios!! Write yes or no.!" and form a proportion.!" 16. Solve the proportion!"!" =!"!. For Questions 17-19, solve each equation. Check your solution. 17. x + 4 = x n + 7 = 7 n + 1 2n

7 19. 4 p = 2 p 1 7p Solve! x c = 0 for x.! 21. State whether the percent of change is a percent of increase or a percent of decrease. Then find the percent of change. Original: 55 New: A shirt costs $ If the sales tax is 7%, find the total cost.

8 23. How many liters of a 90% acid solution must be added to 6 liters of a 15% acid solution to obtain a 40% acid solution? 24. A freight train leaves a station travelling 60 miles per hour. Thirty minutes later a passenger train leaves the station in the same direction on a parallel track at a speed of 72 miles per hour. How long will it take the passenger train to catch the freight train? 25. A container company wants to make a cylindrical can with a volume of 1188 cubic inches. The formula V = πr! h represents the volume of a cylinder. In this formula, V represents the volume, r represents the radius of the cylinder s base, and h represents the height of the cylinder. Solve for h. What height should the company make the can if the radius of the base must be 6 inches?

9 Chapter 3: Linear Functions 1. Tickets for a spaghetti dinner cost $4 for children and $6 for adults. The equation 4x + 6y = 36 represents the number of children x and adults y who can eat at the dinner for $36. If no children are eating at the dinner, how many adults can eat for $36? 2. If a, 9 is a solution to the equation 4a = b 21, what is a? 3. Find the x-intercept of x 2y = Graph the equation y =! x 2.! 5. Find the x-intercept and the y-intercept of 3x 2y = 18.

10 For Questions 6-8, find the slope of the line passing through each pair of points. If the slope is undefined, write undefined. 6. (2, 5) and (3, 6) 7. (6, 4) and ( 3, 7) 8. ( 1, 3) and (6, 3) 9. In 1972, federal vehicle emission standards allowed 3.4 hydrocarbons released per mile. By 2007, the standards allowed only 0.8 hydrocarbons per mile driven. What was the rate of change from 1972 to 2007? 10. If a shark can swim 27 miles in 9 hours, how many miles will it swim in 12 hours?

11 For Questions 11-12, determine whether each equation is a linear equation. If so, write the equation in standard form. 11. xy = x + 3y + 7 = Graph the equation x 4y = Graph y =! x + 3.!

12 15. Graph the equation 4x 2y = Determine whether the sequence 10, 7, 4, 1, is an arithmetic sequence. Write yes or no. If so, state the common difference. 17. Find the next three terms of the arithmetic sequence 8, 15, 22, 29, 18. Write an equation for the nth term of the sequence 12, 5, 2, 9,

13 For Questions 19-20, use the table below that shows the amount of gasoline a car consumes for different distances driven. 19. Write an equation in function notation for the relationship between distance and gasoline used. 20. How many gallons will the car consume after driving for 150 miles?

14 Chapter 4: Equations of Linear Functions 1. Write a linear equation in slope-intercept form to model the situation: A telephone company charges $28.75 per month plus $0.10 per minute for long-distance calls. 2. Write an equation in standard form of the line that passes through (7, 3) and has a y-intercept of Write the slope-intercept form of an equation for the line graphed below. 4. Graph the line with a y-intercept of 3 and slope!!.

15 5. Write an equation in slope-intercept form for the line that passes through ( 1, 2) and (3, 4). 6. Write an equation in standard form for the line that has an undefined slope and passes through ( 6, 4). 7. Write an equation in point-slope form for the line that has slope! and passes through! 2, Write the standard form of the equation y + 4 =!"! x Write the slope-intercept form of the equation y 2 = 3 x Write the slope-intercept form of the equation of the line parallel to the graph of 2x + y = 5 that passes through (0, 1).

16 11. Write the slope-intercept form of the equation of the line perpendicular to the graph of y =! x 7 that passes through (3, 2).! 12. A scatter plot of data showing the percentage of total internet users who visited an online store on a given day in December includes the points 2008, 2.0 and 2010, 4.5. Write the equation in slope-intercept form of an equation for the line of fit. 13. In a certain lake a 1-year-old bluegill fish is 3 inches long, while a 4-year-old bluegill fish is 6.6 inches long. Assuming the growth rate can be approximated by a linear equation, write an equation in slope-intercept form for the length l of a bluegill fish in inches after t years. Then use the equation to determine the age of a 9-inch bluegill.

17 For Questions 14-16, use the data in the table. 14. Make a scatter plot relating time spent studying to the score received. 15. Write the slope-intercept form of the equation for a line of fit for the data. Use your equation to predict a student s score if the student spent 35 minutes studying. 16. Is it reasonable to use the equation to estimate the score received for any length of time spent studying? 17. Graph the inverse of the function graphed at the right.

18 18. If f x =!!!!!", find f!! (x). 19. Write the inverse of 6x + 8y = 13 in f!! (x) notation. 20. Find the inverse of f x = x.