Grade 8, Term 1 Revision Sheets

Transcription

1 Grade 8, Term 1 Revision Sheets Chapter 1: Real Numbers Lesson 1: Rational Numbers Write each fraction or mixed number as a decimal. 1.! " 2. " # 3. $ %& 4.!' "& 5. )) )* 6. $!% 7. 3 ) " 8. 4! # 9. "!! 10. ' $ )) )# ))!& Write each decimal as a fraction or mixed number in simplest form

2 16. Refer to the table at the right. a. Express the fraction for Asian as a decimal. b. Find the decimal equivalent for the fraction of the population that is African American. Asian Population of Florida by Race Race African American Hispanic Fraction of Total Population ) "& + %" ) " c. Write the fraction for Hispanic as a decimal. 17. Use the figure at the right. a. Write the width of the jellybean as a fraction. b. Write the width of the jellybean as a decimal. 18. Nuclear power provided 78% of the energy used in France in Write 0.78 as a fraction in simplest form. 2

3 Lesson 2: Powers and Exponents Write each expression using exponents ! #! #! # 5. c ) + c ) + ) + 6. s 6 s s 6 6 s 7. 8 x x 8 8. a ( 4) b a b ( 4) ( 4) 9. ) n 4 n ) n x w x y w 9 y!! Evaluate each expression ! " 13. ( 8) 3 Evaluate each expression if g = 2 and h = (g + h)! 15. h + (h g)! 16. Florida has about 2 % 3 % 5! islands (over 10 acres). About how many islands is this? 3

4 17. The volume of a cube can be found by raising the side length to the third power. What is the volume of the cube below? 18. A scientist estimates that after a certain amount of time, there would be 2 " 3! 10 " bacteria in a Petri dish. About how many bacteria is this? Lesson 3: Multiply and Divide Monomials Carry out the following operations: 1. 5 $ 5! 2. 3 # 3 3. c c * 4. m " m % 5. 3x 4x + 6. (2h ' )(7h) 7. = A? 8. (6k " )( k + ) 9. +D " F " A ' G. 4

5 10. 7z + ( 3z # ) 11.!IJ (K*) G! L (K*) A 12. 3a+ 6a % 13. 3m! n % (8mn! ) 14. 7t " ( 6t " ) 15. (3ab % )(a % c " ) 16. A company has set aside 10 ' dollars for annual employee bonuses. If the company has 10 + employees and the money is divided equally among them, how much will each employee receive? 17. After making a down payment, Mr. Nadir will make 6 % monthly payments of 6! dollars each to pay for his new car. What is the total of the monthly payments? 18. The area of the rectangle in the figure is 24a % b! square units. Find the width of the rectangle. 5

6 Lesson 4: Powers of Monomials Simplify. 1. (7 % )! 2. (3 % ) * 3. (8! ) % 4. (9 + ) % 5. (d ' ) * 6. (m " ) " 7. (h * )! 8. (z ' )! 9. [(4! ) % ] ( 5a % b ' ) ' 11. (2m " g )) ) * Express the area of each square below as a monomial

7 Express the volume of each cube below as a monomial In the Metric System, you would need to have (10 + ) % grams to equal 1 metric ton. Simplify this measurement by multiplying the exponents, then simplify by finding the actual number of grams needed to equal 1 metric ton. 17. A video-game designer is using the expression 6n! in a program to determine points earned, where n is the game level. Simplify the expression for the n % level. 18. Majed loves beads and wants to know which amount would be more, a thousand beads or (6 % )! beads? 7

8 Lesson 5: Negative Exponents Write each expression using a positive exponent K" 2. 5 K' 3. m K$ 4. s K* 5. f K! 6. ( 2) K* Evaluate each expression. 7. ( 5) K" 8. 3 K% 9. 8 K! 10. ( 9) K+ Write each fraction as an expression using a negative exponent. 11. ) )% F 12. ) #) 13. ) 8

9 Simplify. Express using positive exponents K* 2! 15. Z D Z [> 16. A state highway that is 4 + miles long runs parallel to a smaller country road that is 4 % miles long. How many times longer than the country road is the state highway? Write the answer as a number with a positive exponent. 17. The hospital spent 9 " dollars on new medical equipment this year. Last year, they spent 9 ' dollars. How many times more money did they spend last year than this year? milligram is equal to 10 K! grams. Write this number using a positive exponent. 9

10 Lesson 6: Scientific Notation Write each number in standard form ) ! % " ' K) K* Write each number in scientific notation , , ,733, ,204,000,

11 16. The table lists the populations of five countries. List the countries from least to greatest population. Country Population Australia 2 10 ' Brazil # Egypt ' Luxembourg " Singapore * 17. Pluto is $ miles from the Sun. Write this number in standard form. 18. One centimeter is equal to about mile. Write this number in scientific notation. 11

12 Lesson 7: Compute with Scientific Notation Evaluate each expression. Express the result in scientific notation. 1. ( " )( % ) 2. ( * )( ) %.$"% )&@ %.&"% )&L 3. 4.!.* )& F ".+ )& > 5. ( ' ) + ( " ) 6.( ) + ( ! ) 7. ( ' ) ( * ) 8. ( " ) ( ! ) *.%"* )&D %.### )&G *.# )& > '.%% )& A 11. ( ! )( * ) 12. ( ' )( % ) 13. ( ) ( %!.&%+ )&@ ) # )& A 15. ( # ) + ( * ) 12

13 16. The diameter of Mars is about ! kilometers. The diameter of Earth is about kilometers. About how much greater is Earth s diameter than the diameter of Mars? 17. A factory builds a new warehouse that is approximately " square feet. Later, they add on ! more square feet for offices. Use scientific notation to write the total size of the new building. 18. Humpback whales are known to weigh as much as pounds. The tiny krill they eat weigh only K! pounds. How many times greater than krill are humpback whales? Find each square root or cube root. Lesson 8: Roots F ,744 F 5. 1,331 F

14 Solve each equation. Check your solution(s). 9. s % = t % = x % = = z % = y % = h % 15. c % = +$ *+ 16. Hessa has 196 pepper plants that she wants to plant in square formation. How many pepper plants should she plant in each row? 17. A new restaurant has ordered 64 tables for its outdoor patio. If the manager arranges the tables in a square formation, how many will be in each row? 14

15 18. The formula for the perimeter of a square is P = 4s, where s is the length of a side. Find the perimeter of each square. Estimate to the nearest integer. Lesson 9: Estimate Roots F F F c290! ' 15

16 16. The radius of a cylinder with volume V and height 10 centimeters is approximately c d!& If a can that is 10 centimeters tall has a volume of 900 cubic centimeters, estimate its radius. 17. The formula s = 18d can be used to find the speed s of a car in miles per hour when the car needs d feet to come to a complete stop after slamming on the brakes. If it took a car 12 feet to come to a complete stop after slamming on the brakes, estimate the speed of the car. 18. The formula for the area of a square is A = s2, where s is the length of a side. Estimate the length of a side for each square. 16

17 Lesson 10: Compare Real Numbers Name all sets of numbers to which each real number belongs ) % # ' $ Replace each with <, >, or = to make a true statement ) % % " ) * 38 Order each set of numbers from least to greatest. Verify your answer by graphing on a number line , 5, ", 2.3, 3 % , 2.95, 2.9, 3.1, The geometric mean of two numbers a and b is ab. Find the geometric mean of 32 and

18 17. The area of a square painting is 600 square inches. To the nearest hundredth inch, what is the perimeter of the painting? 18. If the area of a square is 33 square inches, which is greater: the length of a side of the square to the nearest tenth of an inch or 40? Chapter 2: Equations in One Variable Lesson 1: Solve Equations with Rational Coefficients Solve each equation. Check your work. 1. ) x = 5 2. % w = 24 # $ 3.! )% k = '!" 4. # )% p = $ )# v = c = )* y = ))!! 8. )&!& n = )!!$ 18

19 = 0.36m f = h = ) # n = % ' 13. )* %& y = )$!# 14. )%!* n = %& = 1.26m Define a variable. Then write and solve an equation for each situation. 16. Omar peeled 14 potatoes in ) hour. At this rate, how many potatoes can Omar peel in " one hour? 17. In the eighth grade, 322 students voted for the new mascot to be a tiger. This was ' )& of the total number of students in the eighth grade. How many students are in the eighth grade? 19

20 18. Rashid budgeted $76.50 for school clothes. This is 0.45 of his total budget. How much does Rashid have in his total budget? Lesson 2: Solve Two-Step Equations Solve each equation. Check your solution. 1. 3n + 4 = = 2s c 6 = = 2t f 12 = = 4v d 6 = k + 12 = = 3m = 8z a 2 = s = 16 20

21 13. 1 = 4 5x = 9 2x 15. 2x + 12 = Ms. Noura shops at a store that has an annual membership fee of AED 30. Today she paid her annual membership and bought several fruit baskets costing AED 15 each as gifts for her coworkers. Her total was AED 105. Solve the equation 15b + 30 = 105 to find the number of fruit baskets Ms. Noura purchased. 17. A card game has 50 cards. After dealing 7 cards to each player, Hamdan has 15 cards left over. Solve the equation 50 7p = 15 to find the number of players. 18. Janna bought 5 reams of paper at the store for a total of AED 21. The tax on her purchase was AED 1. Solve 5x + 1 = 21 to find the price for each ream of paper. 21

22 Lesson 3: Write Two-Step Equations Translate each sentence into an equation. 1. Four more than twice a number is Three more than four times a number is Five less than twice a number is One less than four times a number is Seven more than the quotient of a number and 2 is Six less than six times a number is Five less than the quotient of a number and 3 is Seven more than twice a number is 1. Define a variable. Then write and solve an equation to find each number. 9. The difference between 5 times a number and 3 is Nine more than three times a number is Nine more than the quotient of a number and 4 is Four less than the quotient of a number and 3 is Nine less than six times a number is Three less than the quotient of a number and 6 is Eight more than the quotient of a number and 5 is 3. 22

23 16. The world s two highest dams are both in Tajikistan. The Rogun dam is 35 meters taller than the Nurek dam. Together they are 635 meters tall. Find the height of the Nurek dam. 17. Khalid bought a canvas and 8 tubes of paint for AED If the canvas cost AED 6.95, how much did each tube of paint cost? 18. Three consecutive integers can be represented by n, n + 1, and n + 2. If the sum of three consecutive integers is 57, what are the integers? 23

24 Lesson 4: Solve Equations with Variables on Each Side Solve each equation. Check your solution. 1. 3w + 6 = 4w 2. a + 18 = 7a 3. 8c = 5c d + 10 = 6d 5. 2e = 4e v = 2v n 6 = 10n 8. 2y + 27 = 5y 9. 8h = 6h g = 4g 11. 4x 9 = 6x c 15 = 2c t + 10 = 7t z + 6 = 7z

25 Write and solve an equation to solve each exercise. 16. For an annual membership fee of AED 500, Mr. Adel can join a country club that would allow him to play a round of golf for AED 35. Without the membership, the country club charges AED 55 for each round of golf. How many rounds of golf would Mr. Adel have to play for the cost to be the same with and without a membership? 17. Jassim has 45 CDs in his collection, and Majed has 61. If Jassim buys 4 new CDs each month and Majed buys 2 new CDs each month, after how many months will Jassim and Majed have the same number of CDs? 18. The Star Shipping Company charges AED 14 plus AED 2 a pound to ship an overnight package. Discount Shipping Company charges AED 20 plus AED 1.50 a pound to ship an overnight package. For what weight is the charge the same for the two companies? 25

26 Lesson 5: Solve Multi-Step Equations Solve each equation. Check your solution. 1. 4(2 + 3c) = = 3(1 2n) = 5(2a 1) + 2a 4. g + 2(3 + g) = 4(g + 1) 5. 7p (3p + 4) = 2(2p 1) (t + 5) + (4t + 2) = 8 7. ) ( 4 + 6x) = ) x + % (x + 9) 8. 8 n = 3(2n 4) %!! 9. 2i ) q + 1k = 3(2q 1) + 4(2q + 1) 10. 4(2 y) + 3y = 3(y 4) % 26

27 11. Currently, 96 members participate in the morning workout, and this number has been increasing by 2 people per week. Currently, 80 members participate in the afternoon workout, and this number has been decreasing by 3 people per week. In how many weeks will the number of people working out in the morning be double the number of people working out in the afternoon? 12. Two cyclists leave town at the same time on the same road going in the same direction. Cyclist A is going 6 miles per hour faster than cyclist B. After 8 hours, cyclist A has traveled three times the distance as cyclist B. Use the equation 24x = 8(x + 6) to find how fast cyclist B is traveling. 13. Huda mows lawns during the summer. She charges AED 15 if she cuts the grass but charges AED 5 more if she also trims the grass. Last week she trimmed 5 more yards than she cut. If she made AED 415 last week, how many yards did she trim? 27

28 Chapter 3: Equations in Two Variables Lesson 1: Constant Rate of Change Determine whether the relationship between the two quantities described in each table is linear. If so, find the constant rate of change. If not, explain your reasoning. 1. Money 2. Hours Spent Earned Babysitting (AED) Time (min) Temperature ( F) Number of Number of 4. Students Magazines Sold Number of Trees Number of Apples Determine whether a proportional relationship exists between the two quantities shown in each graph. Explain your reasoning

29 For Exercises 7 and 8, refer to the graphs below. 7. a. Find the constant rate of change and interpret its meaning b. Determine whether a proportional linear relationship exists between the two quantities shown in the graph. Explain your reasoning 8. a. Find the constant rate of change and interpret its meaning. b. Determine whether a proportional linear relationship exists between the two quantities shown in the graph. Explain your reasoning. 29

30 Lesson 2: Slope Find the slope of the line that passes through each pair of points. 1. A( 2, 4), B(2, 4) 2. C(0, 2), D( 2, 0) 3. E(3, 4), F(4, 2) 4. G( 3, 1), H( 2, 2) 5. I(0, 6), J( 1, 1) 6. K(0, 2), L(2, 4) 7. O(1, 3), P(2, 5) 8. Q(1, 0), R(3, 0) 9. S(0, 4), T(1, 0) Find the slope of each line

31 The points given in each table lie on a line. Find the slope of the line. Then graph the line. 4. x x y y x y Use the graph at the right. It shows the depth in feet of snow after each two-hour period during a snowstorm. a. Find the slope of the line. b. Does the graph show a constant rate of change? Explain. c. If the graph is extended to the right, could you expect the slope to remain constant? Explain 31

32 Lesson 3: Equations in y = mx Form For Exercises 1 3, determine whether each linear function is a direct variation. If so, state the constant of variation. 1. Price, x AED 5 AED 10 AED 15 AED 20 Tax, y AED 0.41 AED 0.82 AED 1.23 AED Hours, x Distance, y (miles) Age, x Grade, y If y varies directly with x, write an equation for the direct variation. Then find each value. 4. If y = 5 when x = 2, find y when x = Find y when x = 1, if y = 3 when x = 2. 32

33 6. The number of vehicles a dealership sells varies directly with the money spent on advertising. How many vehicles does the dealership sell for each $1,000 spent on advertising? 7. Mohamed rents snowmobiles to tourists. He charges AED 135 for 4 hours and AED for 6 hours. What is the hourly rate Mohamed charges to rent a snowmobile? 8. The power absorbed by a solar panel varies directly with its area. If an 8 square meter panel absorbs 8,160 watts of power, how much power does a 12 square meter solar panel absorb? 9. Mr. Mustafa used 40 pounds of insecticide to cover 1,760 square feet of lawn and 60 pounds to cover an additional 2,640 square feet. How many pounds of insecticide would Mr. Mustafa need to cover his whole lawn of 4,480 square feet? 33

34 Lesson 4: Slope-Intercept Form State the slope and the y-intercept for the graph of each equation. 1. y = x y = 2x 2 3. y = 3x 1 4. y = x y = ) % x 5 6. y = )! x Graph a line with a 8. Graph a line with a 9. Graph a line with a slope of 1 and a slope of 2 and a slope of )! and a y-intercept of 4. y-intercept of 3. y-intercept of 1. Graph each equation using the slope and the y-intercept. 10. y = 3x y = x y = ) % x The entrance fee to the national park is AED 15. A 34

35 campsite fee is AED15 per night. The total cost y for a camping trip for x nights can be represented by the equation y = 15x a. Graph the equation. b. Use the graph to find the total cost for 4 nights. c. Interpret the slope and the y-intercept. 14. The equation y = 0.2x can be used to find the amount of accumulated snow y in inches x hours after 5 PM on a certain day. Identify the slope and y- intercept of the graph of the equation and explain what each represents. 15. Sara s weekly salary can be represented by the equation y = x, where x is the dirham total of her sales for the week. Identify the slope and y-intercept of the graph of the equation and explain what each represents. 35

36 Lesson 5: Graph a Line Using Intercepts State the x- and y-intercepts of each function. Then graph the function. 1. 3x 5y = ) x + 3y = 3 % 3. 4x 6y = x + 3y = % x ) y = 2 6. x + y = 2!! 36

37 State the x- and y-intercepts of each function. 7. 6x + 8y = 24 8.! x 6y = ) x ) y = x 10y = 20 +! 11. x + y = x y = ) % 13. Mr. Jamal raises cows and chickens on his farm. Altogether, his cows and chickens have 140 legs. This can be represented by the function 4x + 2y = 140. Graph the function. Then interpret the x- and y-intercepts. 14. Monty has a total of AED 290 in ten dirham and five dirham bills. This can be represented by the function 10x + 5y = 290. Interpret the x- and y-intercepts. 37

38 Lesson 6: Write Linear Equations Write an equation in point-slope form and slope-intercept form for each line. 1. passes through (4, 7), slope = 2 2. passes through ( 2, 1), slope = 4 3. passes through (8, 4), slope = ) % 4. passes through (1, 3), slope = 1 5. passes through ( 4, 5), slope =! + 6. passes through (3, 8), slope = 3 7. passes through (2, 7), slope = 3 8. passes through ( 1, 6), slope = 4 38

39 Write the point-slope form of an equation for each line graphed The table shows the temperature at certain hours. Assuming the temperature change is linear, write an equation in point-slope form to represent the temperature y at x hour. Temperature Hour ( F) After 2 hours, a car travels 70 miles. After 2.25 hours in the same trip, the car travels miles. Write an equation in point-slope form to represent the distance y of the car after x hours. 39

40 Lesson 7: Solve Systems of Equations by Graphing Solve each system of equations by graphing. 1. y = x y = 5x 1 y = 2x 2 y = 5x y = x 1 4. y = 6x 3 y x = 1 y = 3 40

41 5. There are thirty-three students in the Chess Club. There are five more boys than girls in the club. Write and solve a system of equations to find the number of boys and girls in the Chess Club. Write and solve a system of equations that represents each situation. Interpret the solution. 6. Yassin and Rashid scored a total of 54 points in the basketball game. Rashid scored four more points than Yassin. 7. Nasser is 15 years younger than Mr. Ahmed. Their combined age is

42 Lesson 8: Solve Systems of Equations Algebraically Solve each system of equations algebraically. 1. y = x 8 2. y = x 4 3. y = x + 11 y = 5x y = 3x y = 12x 4. y = x y = x y = x + 15 y = 6x y = 2x y = 4x 7. y = x y = x y = x + 18 y = 4x y = 7x y = 8x 42

43 Write and solve a system of equations that represents each situation. Interpret the solution. 10. Marawan watched 6 times as many hours of television over the weekend as Zafer. Together they watched a total of 14 hours of television. How many hours of television did each person watch over the weekend? 11. Najla is a cross-country ski racer. On Saturday, she skied twice as many miles as she did on Sunday. Over the weekend she skied a total of 63 miles. How far did she ski on each day? 12. Rawdah and Layla played a game of darts, and Layla scored 4 more points than Rawdah. The total of their scores was 180. How many points did each of them score? 13. Eissa drove a total of 248 miles on Monday. He drove 70 fewer miles in the morning than he did in the afternoon. How many miles did he drive in the afternoon? 43

44 Chapter 4: Functions Lesson 1: Representing Relationships 1. A fitness instructor exercises about 15 hours per week. a. Write an equation to find the total number of hours h the instructor exercises in any number of weeks w. b. Use the equation to determine the total number of hours the instructor will exercise in 9 weeks. Weeks, w Total Hours, h A real estate company sells 8 houses per month. a. Write an equation to find the total number of houses h sold in any number of months m. b. Use the equation to determine how many houses are sold in 15 months. Months, m Total Houses, h The graph shows the amount of money Majed s family spends on movies each month. a. Write an equation to find the total amount of money c spent on movies in any number of months m. b. Use the equation to determine how much they will spend on movies in one year. 44

45 4. The graph shows the total cost of hats that are on sale at Hats Shop. a. Write an equation to find the total cost c of any number of hats h. b. Use the equation to find the cost of 30 hats. 5. A manufacturer produces 950 light bulbs per day. a. Write an equation to find the number of bulbs b the manufacturer makes in any number of days d. b. Use the equation to determine how many bulbs the manufacturer will make in 25 days. Days, d Bulbs, b , , , The workers at a plant drink 38 gallons of water per day. a. Write an equation to find the number of gallons g the workers drink in any number of days d. Days, d Gallons, g b. Use the equation to determine how many gallons of water the workers will drink in 30 days. 45

46 Name the ordered pair for each point. 1. A 2. B Lesson 2: Relations 3. C 4. D Graph each ordered pair on a coordinate plane. 5. (3, 3) 6. (1, 1) 7. ( 4, 2) 8. ( 4, 3) Express each relation as a table and a graph. Then state the domain and range. 9. {(4, 2), ( 1, 1), (2, 3), (3, 0)} x y 46

47 10. {(3, 4), (1, 2), (4, 1), (2, 2)} x y 11. Rashid pays AED 48 per month for satellite television service. a. Make a table of ordered pairs in which the x-coordinate represents the number of months and the y-coordinate represents the total cost for 1, 2, 3, or 4 months. b. Graph the ordered pairs. x y 47

48 Lesson 3: Functions Find each function value. 1. f(2) if f(x) = x f(9) if f(x) = x 8 3. f(3) if f(x) = 2x f(6) if f(x) = 2x 5 5. f( 7) if f(x) = 3x f(8) if f(x) = 3x 10 Choose four values for x to make a function table for each function. Then state the domain and range of the function. 7. f(x) = x f(x) = x f(x) = 2x + 8 x x +7 f(x) x x 13 f(x) x 2x + 8 f(x) 48

49 10. f(x) = 2x f(x) = 3x f(x) = 7 3x x 2x 3 f(x) x 3x + 4 f(x) x 7 3x f(x) 13. The school baseball team wants to have each player s name imprinted on the player s jacket. The cost is AED 75 plus AED 8.50 for each name. Write a function to represent the cost c(n) for n names. What is the cost to have names imprinted on 25 jackets? 14. Khalid sold 10 glasses of lemonade while setting up his lemonade stand. After opening, he sold an average of 20 glasses each hour. Write a function to represent the approximate number of glasses g(h) sold after h hours. About when did he sell the 100th glass of lemonade? 49

50 Lesson 4: Linear Functions Complete the function table. Then graph the function. 1. y = x + 4 x x + 4 y (x, y) y = 2x 1 x 2x 1 y (x, y) Graph each function. 3. y = x 6 4. y = 2x 3 5. y = 1 x 6. y = 2x 7. y = -4x 8. y = x 4 50

51 9. Mr. Hossam can assemble a chair in 1 day and a table in 4 days. Graph the function y = 5 ) x to determine + how many of each type of furniture Mr. Hossam can assemble in 20 days. Is the function continuous or discrete? Explain. 10. A fitness center has set a goal to have 500 members. The fitness center already has 150 members and adds an average of 25 members per month. The function f(x) = x represents the membership after x months. Graph the function to determine the number of months it will take for the fitness center to reach its membership goal. Is the function continuous or discrete? Explain. 51

52 Lesson 5: Compare Properties of Functions 1. The number of gallons y a pool drains in x minutes is represented by the function y = 20x. The table shows the time it takes to fill up a pool. Compare the functions for each process by comparing the times. Number of Minutes Number of Gallons Chinook winds are warm dry winds that blow down the side of the mountain that causes drastic temperature changes. The graph shows the outside temperature change caused from chinook winds after a number of hours. In another location, the temperature y after x hours can be represented by the function y = 68x. Compare the functions by comparing the temperatures. 3. The speeds of a coyote and giraffe are shown in the graph and table below. a. Compare the functions by comparing the rates of change. b. How much farther does a coyote run than a giraffe after 3 hours? Land Speed of a Giraffe Number of Hours Distance Ran (mi)

53 4. Rawdah kept track of the number of steps she took in a day using a pedometer. The average number of steps she took y per hour x can be represented by the function y = 700x. The table below shows the number of steps per hour that Noura walked. Compare the functions for each person by comparing the number of steps. Number of Number of Hours Steps , , A new car gets 33 miles per gallon of gas. The graph shows the number of miles y that an older car gets per gallon x of gas. Compare the miles per gallon for each car. 53

54 Lesson 6: Construct Functions 1. When Noura planted her tomato plant, it grew 3 inches in one week. After 5 weeks, the tomato plant was 23 inches tall. Assume the relationship is linear. Find and interpret the rate of change and the initial value. 2. The total cost of renting a vacation home includes a deposit and a daily rental fee of AED 125. A family rents a vacation home for 5 days and pays AED 700. Assume the relationship is linear. Find and interpret the rate of change and the initial value. 3. In order to enter the state fair, there is an admission cost. Each game is AED 3. Jassim went to the state fair, played 4 games and spent a total of AED 20 on admission and games. Assume the relationship is linear. Find and interpret the rate of change and the initial value. 4. After writing part of his novel, Hamdan is now writing 16 ages per week. After 4 weeks, he has written 85 pages. Assume the relationship is linear. Find and interpret the rate of change and the initial value. 5. A photographer charges AED 20 for an 8 10 photo plus a sitting fee. Ismail spent AED 55 on two 8 10 photographs and the sitting fee. Assume the relationship is linear. Find and interpret the rate of change and the initial value. 6. To perform car maintenance, a mechanic charges for parts and AED 45 an hour for labor. The total cost that Eissa spent for 2 hour of car maintenance is AED 125. Assume the relationship is linear. Find and interpret the rate of change and the initial value. 54

55 1. The Pep Club rented a shaved ice machine to sell shaved ice as a fundraiser. They paid an initial fee and then an hourly charge. The table shows the cost per hour. Find and interpret the rate of change and initial value. Assume the relationship between the two quantities is linear. Number of Hours, x Cost (AED), y Fawaz planted a tomato plant and measured its height weekly. The total height at 2, 3, 4, and 5 weeks respectively were 13, 16, 19, and 22 inches tall. How tall was the tomato plant when Fawaz planted it? Assume the relationship is linear. 4. The cost of having photos taken includes a sitting fee and AED 12 for each portrait. The cost of 3, 6, and 9 photos respectively is AED 51, AED 87, and AED 123. What is the sitting fee? 55

56 Lesson 7: Linear and Nonlinear Functions Determine whether each table represents a linear or a nonlinear function. Explain x x y y x y x y x y x y x y x y The East Tool Company uses the equation p = 150t to calculate the gross profit p the company makes, in dirham, when it sells t tools. Is the gross profit a linear or nonlinear function of the number of tools sold? Explain. 56

57 10. The table shows the cost of a speeding ticket as a function of the speed of the car. Is the cost a linear or nonlinear function of the car s speed? Explain. Speed (mph) Cost (AED) The table shows the charge for a long-distance call as a function of the number of minutes the call lasts. Is the charge a linear or nonlinear function of the number of minutes? Explain. Minutes Cost (AED)

58 Graph each function. Lesson 8: Quadratic Functions 1. y = 4x % 2. y = 6x % 3. y = x % y = x % 5 5. y = x % y = x % 1 7. y = 2x % 3 8. y = 2x % y = 2x % 2 58

59 10. y = 3x % y = 3x % y = 5x % The quadratic equation K = 500s % models the kinetic energy in joules of a 1,000- kilogram car moving at a speed of s meters per second. Graph this function. Then use your graph to estimate the kinetic energy at a speed of 8 meters per second. 14. The quadratic equation p = r % models the gross profit made by a factory that produces r ovens. Graph this function. Then use your graph to estimate the profit for 5 ovens. 59

60 Lesson 9: Qualitative Graphs Solve. 1. The graph below shows the speed of a roller coaster during the first 30 seconds. Describe the change in speed over time. 3. The graph below shows the altitude of a hiker during a hike. Describe the change in altitude over time. 2. The graph below shows the amount of money in the Soccer Club s account. Describe the change in balance over time. 4. The graph below shows the tempo of a song as it is played. Describe the change in tempo over time. 5. Yasser monitored his heart rate while exercising. During the warm up, his heart rate increased slowly. While exercising, his heart rate increased rapidly and then steadied. During cool down, his heart rate lowered quickly. Sketch a qualitative graph to represent the situation. 60

61 6. The graph below displays the attendance at the state fair over time. Describe the change in attendance over time. 7. The graph below displays the amount of gasoline in a vehicle over time. Describe the change in the amount of gasoline over time. 8. Omar received a loan and is paying it off in monthly installments. Sketch a qualitative graph to represent the balance of the amount owed over time. 9. A hot air balloon begins on the ground and rises. It floats along and then returns to the ground steadily. Sketch a qualitative graph to represent the height over time. 61