p times 10 b. p subtracted from 10 p less than 10 c. the quotient of 10 and p 10 divided by p d. the quotient of p and 10 p divided by 10

Transcription

1 Math Olympics Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Give two ways to write the algebraic expression p 1 in words. a. the product of p and 1 p times 1 b. p subtracted from 1 p less than 1 c. the quotient of 1 and p 1 divided by p d. the quotient of p and 1 p divided by 1 2. Julia wrote 14 letters to friends each month for y months in a row. Write an expression to show how many total letters Julia wrote. a. 14 y b. 14y c y d. 3. Salvador s class has collected 88 cans in a food drive. They plan to sort the cans into x bags, with an equal number of cans in each bag. Write an expression to show how many cans there will be in each bag. a. 88x b x c. d. 88 x 4. Evaluate the expression m + o for m = 9 and o = 7. a. 15 b. 16 c. 2 d Evaluate the expression q v for q = 5 and v = 1. a. 3 b. 4 c. 5 d Evaluate the expression xy for x = 6 and y = 3. a. 21 b. 24 c. 9 d Evaluate the expression a b for a = 24 and b = 8. a. 192 b. 16 c. 3 d Mike scored 4 points in the first half of the basketball game, and he scored y points in the second half of the game. Write an expression to determine the number of points he scored in all Then, find the number of points he scored in all if he scored 2 points in the second half of the game. a. 4y; 42 points b. 4 y; 38 points c. ; 38 points d. 4 + y; 42 points 9. aron has saved 72 sand dollars and wants to give them away equally to y friends. Write an expression to show how many sand dollars each of aron s friends will receive. Then, find the total number of sand dollars each of aron s friends will get if aron gives them to 12 friends. a. 72 y; 6 sand dollars b y; 6 sand dollars c. ; 6 sand dollars d. 72y; 6 sand dollars 1. Salvador reads 12 books from the library each month for n months in a row. Write an expression to show how many books Salvador read in all. Then, find the number of books Salvador read if he read for 7 months.

2 a. 12 n; 19 books b. ; 84 books c n; 19 books d. 12n; 84 books 12. Subtract using a number line. 5 ( 3) 11. Evaluate the expression for and. a. 23 b. 25 c. 32 d. 18 ( 3) a. 3 b. 2 c. 5 d. 13. dd (1) a. 55 b. 13 c. 55 d Evaluate x + ( 9) for x = 35. a. 4 b. 6 c. 26 d Subtract. 5 ( 8) a. 13 b. 13 c. 3 d Evaluate x ( 1) for x = 12. a. 2 b. 2 c. 22 d. 17. The highest temperature recorded in the town of Westgate this summer was 11ºF. Last winter, the lowest temperature recorded was 9ºF. Find the difference between these extremes. a. 92ºF b. 92ºF c. 11ºF d. 11ºF 18. The temperature on the ground during a plane s takeoff was 4ºF. t 38, feet in the air, the temperature outside the plane was 38ºF. Find the difference between these two temperatures. a. 34ºF b. 42ºF c. 34ºF d. 2ºF 19. The elevator in the a downtown skyscraper goes from the top floor down to the lowest level of the underground parking garage. If the building is 47 feet tall and the elevator descends 53 feet from top to bottom, how far underground does the parking garage go? a. 99 feet b. 6 feet c. 1, feet d. 5 feet 2. Multiply. 8 9 a. 1 b. 72 c. 17 d Evaluate 5u for u =. a. 9 b. 25 c. d ivide. 8 8 a. 384 b. 6 c. 56 d. 23. Evaluate k ( 11) for k = 33. a. 363 b. 3 c. 2 d ivide.

3 a b c d ivide a b c. undefined d. 26. arina hiked at Yosemite National Park for 1.75 hours. Her average speed was 3.5 mi/h. How many miles did she hike? a. 2 mi b. 2 mi c mi d mi 27. Write the power represented by the geometric model. a. 3 5 b. 5 2 c. 5 3 d Simplify. a. 27 b. 93 c. 729 d Write 9 as a power of the base 3. a. b. c. d. 33. Suppose you have developed a scale that indicates the brightness of sunlight. Each category in the table is 6 times brighter than the next lower category. For example, a day that is dazzling is 6 times brighter than a day that is radiant. How many times brighter is a dazzling day than an illuminated day? Sunlight Intensity ategory rightness im 2 Illuminated 3 Radiant 4 azzling 5 a. 36 times brighter b. 2 times brighter c. 6 times brighter d. 216 times brighter 34. If the population of an ant hill doubles every 1 days and there are currently 4 ants living in the ant hill, what will the ant hill population be in 2 days? a. 32 ants b. 16 ants c. 1,6 ants d. 8 ants 29. Simplify. a. 81 b. 81 c. 1 d Simplify. a. b. 16 c. 8 d Simplify. a. b c d

4 35. The design shows the layout of a vegetable garden and the surrounding path. The path is 1.5 feet wide. First, find the total area of the vegetable garden and path. Then, find the area of the vegetable garden and the area of the path. If one bag of gravel covers 1 square feet, how many bags of gravel are needed to cover the path? 12 ft To cover the path, 7 bags of gravel are needed. b. The total area is 144 sq ft. The area of the vegetable garden is sq ft, and the area of the path is sq ft. To cover the path, 4 bags of gravel are needed. c. The total area is 144 sq ft. The area of the vegetable garden is 81 sq ft, and the area of the path is 63 sq ft. To cover the path, 7 bags of gravel are needed. d. The total area is 144 sq ft. The area of the vegetable garden is 72 sq ft, and the area of the path is 72 sq ft. To cover the path, 8 bags of gravel are needed. 36. Find the square root. a. 14 b. 98 c d ft 37. The area of a square garden is 22 square feet. Estimate the side length of the garden. a. The total area is 81 sq ft. The area a. 16 ft b. 12 ft of the vegetable garden is 144 sq ft, and the area of the path is 63 sq ft. c. 17 ft d. 14 ft 38. Write all classifications that apply to the real number. a. rational number, terminating decimal b. rational number, repeating decimal c. irrational number d. rational number 39. Write all classifications that apply to the real number. a. irrational number, integer b. irrational number c. rational number, terminating decimal, integer, whole number, natural number d. rational number, terminating decimal 4. set of numbers is said to be closed under a certain operation if, when you perform the operation on any two numbers in the set, the result is also a number in the set. Is the set of irrational numbers closed under addition? Explain.

5 a. Yes, the set of irrational numbers is closed under addition. For example, the sum of and is which is an irrational number. b. Yes, the set of irrational numbers is closed under addition. The result of adding any two irrational numbers is an irrational number. c. No, the set of irrational numbers is not 42. Simplify. a. 21 b. 75 c. 39 d Evaluate for x = 9. a. 8 b. 58 c. 5 d. 72 closed under addition. For example, the sum of and is not an irrational number. d. No, the set of irrational numbers is not closed under addition. The result of adding any two irrational numbers is an irrational number. 41. Simplify. a. 1 b. 2 c. 22 d Evaluate 1 + x 2 6 for x = 4. a. 12 b. 97 c. 94 d Simplify the expression. a. 14 b. 23 c. 4 d Translate the word phrase, the product of 8.5 and the difference of and 8, into a numerical expression. a. b. c. d. 47. Tatia has coins in pennies, nickels, dimes, and quarters. The total amount of money she has in dollars can be found using the expression (P + 5N Q) 1. Use the table to find how much money Tatia has. P N Q a. $14.5 b. $33.3 c. $.42 d. $ Use the numbers 2, 3, 5, and 8 to write an expression that has a value of. You may use any operations, and you must use each of the numbers at least once. a. b. c. d. 49. Simplify the expression. a b. 1 c d Write using the istributive Property. Then simplify. a ; 649 b. (11 + 5)(11 + 9); 1,22 c ; 748 d ; Write using the istributive Property. Then simplify.

6 a. ; 13 b. ; 114 c. ; 6 d. ; 168 a. b. c. d. 52. Simplify by combining like terms. 53. The table shows, step-by-step, how to simplify the algebraic expression. Justify Step 4. Step Procedure Justification istributive Property a. Multiply b. ssociative Property c. ombine like terms d. ommutative Property 54. Fill in the missing justifications. Procedure Justification efinition of subtraction??? Simplify efinition of subtraction a. istributive Property; ssociative Property; ommutative Property b. ssociative Property; ommutative Property; istributive Property c. ommutative Property; istributive Property; ssociative Property d. ommutative Property; ssociative Property; istributive Property 55. Graph the point (1, 4).

7 a. 5 y 56. Name the quadrant where the point ( 3, 2) is located. y x b. 5 5 y 5 5 x 5 c. 5 5 x 5 5 y a. Quadrant III b. Quadrant I c. Quadrant IV d. Quadrant II 57. Name the quadrant where the point (3, ) is located. 5 y 5 5 x 5 5 x 5 d. 5 y x a. Quadrant III b. No quadrant (y-axis) c. No quadrant (x-axis) d. Quadrant I 5

8 58. phone company advertises a new plan in which the customer pays a fixed amount of $25 per month for unlimited calls in the country, and $.1 per minute for international calls. Find a rule for the monthly payment a customer pays according to the new plan. Write ordered pairs for the monthly payment when the customer uses 9, 12, 145, and 15 international minutes in a month. a. ; (34, 9), (37, 12), (39.5, 145), (4, 15) b. ; (9, 34), (12, 37), (145, 39.5), (15, 4) c. ; (34, 9), (37, 12), (145, 39.5), (15, 4) d. ; (34, 9), (37, 12), (145, 39.5), (15, 4) 59. reate a table of ordered pairs for the function using the values x =, 1,, 1, and 2. Graph the ordered pairs and describe the shape of the graph. a. b. c. The points form an S shape. The points form a straight line.

9 d. The points form a V shape. The points form a U shape. 6. The coordinates of three vertices of a rectangle are,, and. Find the coordinates of the fourth vertex. Then, find the area of the rectangle. a. ; rea = 8 square units b. ; rea = 72 square units c. ; rea = 8 square units d. ; rea = 72 square units 61. Give two ways to write the algebraic expression 6p in words. a. the quotient of 6 and p 6 divided by p b. p subtracted from 6 p less than 6 c. 6 times p 6 groups of p d. p more than 6 p added to dd using a number line a. b. 6 c. d Solve. a. p = 22 b. p = 2 c. p = 1 d. p = Solve. a. s = 52 b. s = 42 c. s = 43 d. s = Solve 14 + s = 32.

10 a. s = 46 b. s = 18 c. s = 6 d. s = toy company's total payment for salaries for the first two months of 25 is $21,894. Write and solve an equation to find the salaries for the second month if the first month s salaries are $1,25. a. The salaries for the second month are $11,689. b. The salaries for the second month are $21,894. c. The salaries for the second month are $1,947. d. The salaries for the second month are $32, The range of a set of scores is 23, and the lowest score is 33. Write and solve an equation to find the highest score. (Hint: In a data set, the range is the difference between the highest and the lowest values.) a. The highest score is 1. b. The highest score is 56. c. The highest score is The time between a flash of lightning and the sound of its thunder can be used to estimate the distance from a lightning strike. The distance from the strike is the number of seconds between seeing the flash and hearing the thunder divided by 5. Suppose you are 17 miles from a lightning strike. Write and solve an equation to find how many seconds there would be between the flash and thunder. d. The highest score is 79. a., so t is about 85 seconds. 68. Solve. a. q = 46 b. q = 25 c. q = 36 d. q = b., so t is about 3.4 seconds. c., so t is about 22 seconds. d., so t is about.3 seconds. 69. Solve 3n = 42. a. n = 39 b. n = 15 c. n = 45 d. n = Solve. a. b. c. d. 72. If, find the value of. a. 3 b. 5 c. 5 d Solve. a. a = 9 b. a = 29 c. a = 15 d. a = Solve.

11 a. b. c. d. 75. Solve. a. b. c. d. 76. Sara needs to take a taxi to get to the movies. The taxi charges $4. for the first mile, and then $2.75 for each mile after that. If the total charge is $2.5, then how far was Sara s taxi ride to the movie? a. 6 miles b. 7 miles c. 5.1 miles d. 7.5 miles 8. Solve. 77. If 8y 8 = 24, find the value of 2y. a. 8 b. 11 c. 2 d The formula gives the profit p when a number of items n are each sold at a cost c and expenses e are subtracted. If,, and, what is the value of c? a..8 b c d Solve. a. b. c. d. a. n = b. n = c. n = d. n = Solve. Tell whether the equation has infinitely many solutions or no solutions. a. Two solutions b. No solutions c. Infinitely many solutions d. Only one solution 82. video store charges a monthly membership fee of $7.5, but the charge to rent each movie is only $1. per movie. nother store has no membership fee, but it costs $2.5 to rent each movie. How many movies need to be rented each month for the total fees to be the same from either company? a. 3 movies b. 5 movies c. 7 movies d. 9 movies 83. Find three consecutive integers such that twice the greatest integer is 2 less than 3 times the least integer. a. 2, 3, 4 b. 4, 5, 6 c. 6, 7, 8 d. 8, 9, professional cyclist is training for the Tour de France. What was his average speed in kilometers per hour if he rode the 194 kilometers from Laval to lois in 4.7 hours? Use the formula, and round your answer to the nearest tenth. a kph b kph c kph d kph 85. The formula for the resistance of a conductor with voltage V and current I is. Solve for V. a. I = Vr b. c. V = Ir d. 86. Solve for x.

12 a. b. c. d. 87. Solve for y. a. b. c. d. 88. The fuel for a chain saw is a mix of oil and gasoline. The ratio of ounces of oil to gallons of gasoline is 7:19. There are 38 gallons of gasoline. How many ounces of oil are there? a ounces b. 2 ounces c. 14 ounces d. 3.5 ounces 89. Ramon drives his car 15 miles in 3 hours. Find the unit rate. a. Ramon drives 5 miles per hour. b. Ramon drives 1 mile per 5 hours. c. Ramon drives 3 miles per hour. d. Ramon drives 15 miles per 3 hours. 9. The local school sponsored a mini-marathon and supplied 84 gallons of water per hour for the runners. What is the amount of water in quarts per hour? a. 672 qt/h b. 336 qt/h c. 168 qt/h d. 21 qt/h 91. Solve the proportion. a. x = 36 b. x = 26 c. x =.3 d. x = n architect built a scale model of a shopping mall. On the model, a circular fountain is 2 inches tall and 22.5 inches in diameter. If the actual fountain is to be 8 feet tall, what is its diameter? a. 7 ft b. 7.1 ft c. 9 ft d. 1.5 ft 93. omplementary angles are two angles whose measures add to 9. The ratio of the measures of two complementary angles is 4:11. What are the measures of the angles? a. 51.4, 38.6 b. 26, 64 c. 24, 66 d. 24, Find the value of MN if cm, cm, and cm. LMNO a cm b cm c cm d cm 95. On a sunny day, a 5-foot red kangaroo casts a shadow that is 7 feet long. The shadow of a nearby eucalyptus tree is 35 feet long. Write and solve a proportion to find the height of the tree.

13 a. ; 25 feet b. ; 49 feet c. ; 245 feet d. ; 175 feet 96. right triangle has legs 15 inches and 12 inches. Every dimension is multiplied by to form a new right triangle with legs 5 inches and 4 inches. How is the ratio of the areas related to the ratio of corresponding sides? a. The ratio of the areas is the square of the ratio of the corresponding sides. b. The ratio of the areas is equal to the ratio of the corresponding sides. c. The ratio of the areas is the cube of the ratio of the corresponding sides. d. None of the above 97. Triangles and are similar. The area of triangle is The base of triangle is 6.72 in. Each dimension of is the corresponding dimension of. What is the height of? a. 2.4 in b. 17 in c. 5.6 in d in 98. Find 55% of 125. a b c d What percent of 74 is 481? If necessary, round your answer to the nearest tenth of a percent. a. 6.5% b. 65% c. 55% d % is 56% of what number? If necessary, round your answer to the nearest hundredth. a..85 b c d compound is made up of various elements totaling 8 ounces. If the total amount of lead in the compound weighs 15 ounces, what percent of the compound is made up of lead? If necessary, round your answer to the nearest hundredth of a percent. a % b % c. 5.33% d..19%

14 12. ccording to the United States ensus ureau, the United States population was projected to be 293,655,44 people on July 1, 24. The two most populous states were alifornia, with a population of 35,893,799, and Texas, with a population of 22,49,22. bout what percent of the United States population lived in alifornia or Texas? Round your answer to the nearest percent. a. 8% b. 12% c. 2% d. 37% 13. aron works part time as a salesperson for an electronics store. He earns $6.75 per hour plus a percent commission on all of his sales. Last week aron worked 17 hours and earned a gross income of $ Find aron s percent commission if his total sales for the week were $3,35. If necessary, round your answer to the nearest hundredth of a percent. a. 1.3% b..5% c. 5.25% d. 6% 14. fter 6 months the simple interest earned annually on an investment of $8 was $975. Find the interest rate to the nearest tenth of a percent. a..2 % b. 22.4% c..244% d. 24.4% 15. Hidemi is a waiter. He waits on a table of 4 whose bill comes to $ If Hidemi receives a 2% tip, approximately how much will he receive? a. $14. b. $84. c. $13.55 d. $ Hannah had dinner at her favorite restaurant. If the sales tax rate is 4% and the sales tax on the meal came to $1.25, what was the total cost of the meal, including sales tax and a 2% tip? a. $52.5 b. $45.63 c. $31.25 d. $ Find the percent change from 52 to 39. Tell whether it is a percent increase or decrease. If necessary, round your answer to the nearest percent. a. 65% decrease b. 87% decrease c. 65% increase d. 87% increase 18. Find the result when 28 is decreased by 25%. a. 21 b. 35 c. 7 d The price of a train ticket from tlanta to Oklahoma ity is normally $117.. However, children under the age of 16 receive a 7% discount. Find the sale price for someone under the age of 16. a. $35.1 b. $198.9 c. $81.9 d. $ bookstore buys lgebra 1 books at a wholesale price of $16 each. It then marks up the price by 83%, and sells the lgebra 1 books. What is the amount of the markup? What is the selling price?

15 a. The amount of the markup is $29.28, and the selling price is $ b. The amount of the markup is $13.28, and the selling price is $ c. The amount of the markup is $13.28, and the selling price is $2.72. d. The amount of the markup is $83, and the selling price is $ Solve Mr. hang sells holiday greeting cards in his gift shop. efore the holidays, he sells the cards at a 225% markup on the price he paid his supplier. fter the holidays, he discounts the cards 6%. What is the post-holiday price of two cards he originally bought from his supplier for $1.5 and $2., respectively? a. $2.3; $2.7 b. $1.35; $1.8 c. $2.93; $3.9 d. $1.95; $ Solve. a. x = or x = 14 b. x = 7 c. x = d. x = 7 or x = 1 a. x = 1 b. x = 11 6 c. No solution d. x = escribe the solutions of in words. a. The value of y is a number less than or equal to 3. b. The value of y is a number greater than 4. c. The value of y is a number equal to 3 d. The value of y is a number less than 4. a. b Graph the inequality m < c d Write the inequality shown by the graph m a. m 3 b. m > 3 c. m 3 d. m < To join the school swim team, swimmers must be able to swim at least 5 yards without stopping. Let n represent the number of yards a swimmer can swim without stopping. Write an inequality describing which values of n will result in a swimmer making the team. Graph the solution. a n

16 b. c n d n n 118. Sam earned $45 during winter vacation. He needs to save $18 for a camping trip over spring break. He can spend the remainder of the money on music. Write an inequality to show how much he can spend on music. Then, graph the inequality. a. ; s b. ; s c. ; s d. ; s Solve the inequality n + 6 < 1.5 and graph the solutions. a. n < b. n < arlotta subscribes to the Hoturn music service. She can download no more than 11 song files per week. arlotta has already downloaded 8 song files this week. Write, solve, and graph an inequality to show how many more songs arlotta can download. a. s > c. n < 7.5 b. s d. n < 4.5 c. s d. s < 3

17 enise has $365 in her saving account. She wants to save at least $635. Write and solve an inequality to determine how much more money enise must save to reach her goal. Let d represent the amount of money in dollars enise must save to reach her goal. a. ; b. ; c. ; d. ; 122. Solve the inequality and graph the solution. b c d a Solve the inequality > 3 and graph the solutions. a. x > 24 b. x > c. x > 3 8 d. x > Solve the inequality 2m 18 and graph the solutions. a. m 9 1 b. m c. m d. m

18 Solve the inequality 2 and graph the solutions. a. z Solve the inequality n 4 < 3 and graph the solutions. a. n < 7 1 b. z b. n > c. z c. n > d. z d. n < Solve the inequality 2f 8 and graph the solutions. a. f 13. Solve the inequality z z and graph the solutions. a. z 3 1 b. f b. z c. f c. z d. f d. z Marco s rama class is performing a play. He wants to buy as many tickets as he can afford. If tickets cost $2.5 each and he has $14.75 to spend, how many tickets can he buy? a. tickets b. 5 tickets c. 6 tickets d. 4 tickets 128. What is the greatest possible integer solution of the inequality? a b. 4 c. 6 d Solve and graph family travels to ryce anyon for three days. On the first day, they drove 15 miles. On the second day, they drove 19 miles. What is the least number of miles they drove on the third day if their average number of miles per day was at least 18? a. 54 mi b. 18 mi c. 21 mi d. 2 mi

19 a. x > b. x < c. x > d. x < Mrs. Williams is deciding between two field trips for her class. The Science enter charges $135 plus $3 per student. The ino iscovery Museum simply charges $6 per student. For how many students will the Science enter charge less than the ino iscovery Museum? a. 132 or more students b. 132 or fewer students c. More than 45 students d. Fewer than 45 students 134. Solve the inequality and graph the solution. a b c d Solve the inequality. a. z 2 9 b. z c. all real numbers d. no solutions Solve. a. b. c. d Fly with Us owns a..1 airplane that has seats for 24 people. The company flies this airplane only if there are at least 1 people on the plane. Write a compound inequality to show the possible number of people in a flight on a..1 with Fly with Us. Let n represent the possible number of people in the flight. Graph the solutions. a b.

20 c d Solve and graph the solutions of the compound inequality. a. N b. N c. N d. N Solve and graph the compound inequality. OR a. OR s b. OR s c. OR s d. OR s 14. Write the compound inequality shown by the graph x a. N b. N c. OR d. OR 141. Which of the following is a solution of N? a. 2 b. 14 c. 12 d.

21 142. Solve the inequality a. and graph the solutions. Then write the solutions as a compound inequality b c d Solve and graph the solutions of. Write the solutions as a compound inequality. a. 9 < x < b. x < 15 OR x > c. x > d. x < 9 OR x > Numeric Response 144. n architect charges $18 for a first draft of a three-bedroom house. If the work takes longer than 8 hours, the architect charges $15 for each additional hour. What would be the total cost for a first draft that took 14 hours to complete? 145. The maximum speed of a greyhound is 153 miles per hour less than 3 times the maximum speed of a cheetah. If a greyhound s maximum speed is 42 miles per hour, what is the maximum speed of a greyhound? heck to make sure your answer is reasonable.

22 146. car rental company increases daily rental fees 15% in the summer to cover increased fuel costs. They then have a 25% off promotion for the fall. If a car rented for $36. per day before the summer, what would the per-day rental cost be during the fall promotion? Matching 147. What is the least possible integer solution of the inequality? 148. volleyball team scored 14 more points in its first game than in its third game. In the second game, the team scored 28 points. The total number of points scored was less than 8. What is the greatest number of points the team could have scored in its first game? Match each vocabulary term with its definition. a. algebraic expression b. numerical expression c. like terms d. absolute value e. evaluate f. variable g. constant 149. a symbol used to represent a quantity that can change 15. a value that does not change 151. an expression that contains at least one variable Match each vocabulary term with its definition. a. real numbers b. additive inverse c. opposites d. multiplicative inverse e. natural numbers f. reciprocal g. absolute value 154. numbers that are the same distance from zero on opposite sides of the number line 155. the opposite of a number Match each vocabulary term with its definition. a. coefficient b. variable 152. a mathematical phrase that contains operations and numbers 153. to find the value of an algebraic expression by substituting a number for each variable and simplifying by using the order of operations 156. for any real number 157. the distance from zero on a number line 158. the reciprocal of the number

23 c. power d. perfect square e. square root f. exponent g. base 159. the number in a power that is used as a factor 16. a number that is multiplied to itself to form a product 161. a number whose positive square root is a whole number Match each vocabulary term with its definition. a. real numbers b. positive numbers c. negative numbers d. integers e. irrational numbers f. rational numbers g. natural numbers h. whole numbers 164. the set of numbers that can be written in the form, where a and b are integers and 165. the set of counting numbers 166. the set of natural numbers and zero Match each vocabulary term with its definition. a. repeating decimal b. terminating decimal c. reciprocal d. absolute value e. term f. coefficient g. like terms h. order of operations 17. a rational number in decimal form that has a block of one or more digits that repeats continuously 171. a number multiplied by a variable 162. an expression written with a base and an exponent or the value of such an expression 163. the number that indicates how many times the base in a power is used as a factor 167. the set of rational and irrational numbers 168. the set of whole numbers and their opposites 169. the set of real numbers that cannot be written as a ratio of integers 172. a part of an expression to be added or subtracted 173. terms with the same variables raised to the same exponents

24 174. rule for evaluating expressions: First, perform operations in parentheses or other grouping symbols. Second, evaluate powers and roots. Third, perform all multiplication and division from left to right. Match each vocabulary term with its definition. a. coordinate plane b. ordered pair c. origin d. quadrant e. y-axis f. x-axis g. axes 176. the intersection of the x- and y-axes in a coordinate plane 177. the vertical axis in a coordinate plane 178. the horizontal axis in a coordinate plane Match each vocabulary term with its definition. a. x-axis b. x-coordinate c. y-coordinate d. input e. output f. y-axis g. quadrant h. coordinate plane 181. the second number in an ordered pair, which indicates the vertical distance of a point from the origin on the coordinate plane 182. the first number in an ordered pair, which indicates the horizontal distance of a point from the origin on the coordinate plane Fourth, perform all addition and subtraction from left to right a rational number in decimal form that has a finite number of digits after the decimal point 179. the two perpendicular number lines, also known as the x-axis and the y-axis, used to define the location of a point in a coordinate plane 18. a pair of numbers that can be used to locate a point on a coordinate plane 183. the result of substituting a value for a variable in a function 184. a value that is substituted for the independent variable in a relation or function 185. one of the four regions into which the x- and y-axis divide the coordinate plane

25 186. a plane that is divided into four regions by a horizontal line called Match each vocabulary term with its definition. a. expression b. solution of an equation c. contradiction d. identity e. formula f. inequality g. equation h. literal equation 187. a mathematical sentence that shows that two expressions are equivalent 188. an equation that contains two or more variables 189. an equation that is true for all values of the variables Match each vocabulary term with its definition. a. proportion b. formula c. ratio d. unit rate e. identity f. conversion factor g. rate 193. a rate in which the second quantity in the comparison is one unit 194. the ratio of two equal quantities, each measured in different units 195. a ratio that compares two quantities measured in different units Match each vocabulary term with its definition. a. conversion factor b. scale c. scale drawing d. scale factor e. scale model f. proportion g. similar the x-axis and a vertical line called the y-axis 19. a value or values that make the equation or inequality true 191. a literal equation that states a rule for a relationship among quantities 192. an equation that is not true for any value of the variable 196. an equation that states that two ratios are equal 197. a comparison of two numbers by division

26 198. a drawing that uses a scale to represent an object as smaller or larger than the original object 199. the ratio of any length in a drawing to the corresponding actual length 2. in a dilation, the ratio of a linear measurement of the image to the corresponding measurement of the preimage Match each vocabulary term with its definition. a. proportion b. corresponding sides c. indirect measurement d. like terms e. cross products f. similar g. corresponding angles 23. the product of the means bc and the product of the extremes ad in the statement 24. sides in the same relative position in two different polygons that have the same number of sides 25. two figures that have the same shape, but not necessarily the same size Match each vocabulary term with its definition. a. commission b. interest c. rate d. sales tax e. markup f. principal g. tip 28. an amount of money added to a bill for service 21. a three-dimensional model that uses a scale to represent an object as smaller or larger than the actual object 22. the ratio of two equal quantities, each measured in different units 26. angles in the same relative position in two different polygons that have the same number of angles 27. a method of measuring an object by using formulas, similar figures, and/or proportions 29. the amount of money charged for borrowing money or the amount of money earned when saving or investing money

27 21. money paid to a person or company for making a sale 211. a percent of the cost of an item that is charged by governments to raise money Match each vocabulary term with its definition. a. rate b. markup c. percent change d. percent decrease e. ratio f. percent g. percent increase h. discount 213. a decrease given as a percent of the original amount 214. an increase given as a percent of the original amount 215. an amount by which an original price is reduced Match each vocabulary term with its definition. a. compound inequality b. inequality c. intersection d. solution of an inequality e. union f. Venn diagram g. equation 219. the set of all elements that are common to both sets, denoted by 22. the set of all elements that are in either set, denoted by 221. a statement that compares two expressions by using one of the following signs: <, >,,, or 222. a value or values that make the inequality true 223. two inequalities that are combined into one statement by the word and or or 212. an amount of money borrowed or invested 216. an increase or decrease given as a percent of the original amount 217. a ratio that compares a number to the amount by which a wholesale cost is increased

28 Math Olympics nswer Section MULTIPLE HOIE 1. NS: The operation means divided by or quotient. p 1: the quotient of p and 1 p divided by 1 heck the operation in the algebraic expression. heck the operation in the algebraic expression. heck the order of the variable and constant. TOP: 1-1 Variables and Expressions 2. NS: y represents the number of letters Julia wrote. Think: y groups of 14 letters. 14y Think: how many groups of letters are there? Think: how many groups of letters are there? To translate words into an algebraic expression, look for words that indicate the action. TOP: 1-1 Variables and Expressions 3. NS: x represents the number of bags. Think: How many groups of 88 are in x? Think: how many groups of cans are in the number of bags? Think: how many groups of cans are in the number of bags?

29 To translate words into an algebraic expression, look for words that indicate the action. TOP: 1-1 Variables and Expressions 4. NS: m + o Substitute 9 for m and 7 for o. 16 Simplify. heck your addition. This expression involves addition, not subtraction. This expression involves addition, not multiplication. TOP: 1-1 Variables and Expressions 5. NS: Substitute the values for q and v into the expression, and then subtract. heck your subtraction. This expression involves subtraction, not division. This expression involves subtraction, not addition. TOP: 1-1 Variables and Expressions 6. NS: Substitute the values for x and y into the expression, and then multiply. heck your multiplication. heck your multiplication. This expression involves multiplication, not addition. TOP: 1-1 Variables and Expressions 7. NS: Substitute the values for a and b into the expression, and then divide.

30 This expression involves division, not multiplication. This expression involves division, not subtraction. heck your division. TOP: 1-1 Variables and Expressions 8. NS: The expression 4 + y models the number of points Mike scored in all Evaluate 4 + y for y = = 42 If Mike scored 2 points in the second half of the game, then he scored 42 points in all. Use a different operation. Use a different operation. Use a different operation instead of division. TOP: 1-1 Variables and Expressions 9. NS: The expression models the number of sand dollars each of aron s friends will receive. Evaluate for y = 12. = 6 If aron gives 72 sand dollars to 12 friends, each friend will get 6 sand dollars. Use a different operation. Use a different operation. Use a different operation instead of multiplication. TOP: 1-1 Variables and Expressions 1. NS: The expression 12n models the number books Salvador read in all. Evaluate 12n for n = 7.

31 12(7) = 84 If Salvador read for 7 months, then that means Salvador read 84 books. Use a different operation. Use a different operation. Use a different operation. TOP: 1-1 Variables and Expressions 11. NS: Substitute 7 for m and 9 for n. Simplify. Remember: means 2 times m. You switched the values of the variables. First, substitute the given values. Then, simplify the expression. When there is no operation sign between a number and a variable, it means it is multiplication. TOP: 1-1 Variables and Expressions 12. NS: The lower vector shows the minuend and the upper vector shows the subtrahend. The number at which the upper vector stops is the difference of the two integers. Move left on a number line to subtract a positive integer; move right to subtract a negative integer. Move left on a number line to subtract a positive integer; move right to subtract a negative integer. Move left on a number line to subtract a positive integer; move right to subtract a negative integer. TOP: 1-2 dding and Subtracting Real Numbers

32 13. NS: To add two integers with the same sign, find the sum of their absolute values and use the sign of the two integers. To add two integers with different signs, find the difference of their absolute values and use the sign of the integer with the greater absolute value. When adding two integers with the same sign, find the sum of their absolute values. When adding two integers with different signs, find the difference of their absolute values. When adding two integers with the same sign, find the sum of their absolute values. When adding two integers with different signs, find the difference of their absolute values. heck the sign of your answer. TOP: 1-2 dding and Subtracting Real Numbers 14. NS: Substitute 35 for x, and then add the integers. To add two integers with the same sign, find the sum of their absolute values and use the sign of the two integers. To add two integers with different signs, find the difference of their absolute values and use the sign of the integer with the greater absolute value. Substitute for x, and then add the integers. heck the sign of your answer. When adding two integers with the same sign, find the sum of their absolute values. When adding two integers with different signs, find the difference of their absolute values. TOP: 1-2 dding and Subtracting Real Numbers 15. NS: hange the subtraction sign to an addition sign, and change the sign of the second number. hange the subtraction sign to an addition sign, and change the sign of the second number. hange the subtraction sign to an addition sign, and change

33 the sign of the second number. Pay attention to the sign. TOP: 1-2 dding and Subtracting Real Numbers 16. NS: Substitute 12 for x, and then subtract the integers. To subtract, change the subtraction sign to an addition sign, and change the sign of the second number. Pay attention to the sign. hange the subtraction sign to an addition sign, and change the sign of the second number. hange the subtraction sign to an addition sign, and change the sign of the second number. TOP: 1-2 dding and Subtracting Real Numbers 17. NS: Subtract the negative temperature from the positive temperature to calculate the difference in the two readings. heck the signs. heck the signs. Subtract the lower temperature from the higher one. TOP: 1-2 dding and Subtracting Real Numbers 18. NS: Subtract the lower temperature from the higher temperature to calculate the difference in the two readings. Subtract the lower temperature from the higher temperature. Subtract the lower temperature from the higher temperature. heck the signs. TOP: 1-2 dding and Subtracting Real Numbers 19. NS:

34 Subtract the height of the building from the height of the elevator. The difference represents how far underground the parking garage goes. heck your subtraction. Subtract the numbers instead of adding them. heck your subtraction. TOP: 1-2 dding and Subtracting Real Numbers 2. NS: Multiply the two integers. If the signs are the same, the product is positive; if the signs are different, the product is negative. Multiply the integers, not add. e sure to multiply the integers. If the signs of the two integers are the same, the product will be positive. If the signs are different, the product will be negative. TOP: 1-3 Multiplying and ividing Real Numbers 21. NS: Substitute for u. Then multiply. Substitute the value in the variable, and then multiply. heck your multiplication. If the signs of the two integers are the same, the product will be positive; if they are different, the product will be negative. TOP: 1-3 Multiplying and ividing Real Numbers 22. NS: ivide the two integers. If the signs are the same, the quotient is positive; if the signs are different, the quotient is negative. This expression involves division, not multiplication. If the signs of the two integers are the same, the quotient will be positive. If the signs are different, the quotient will be

35 negative. This expression involves division, not subtraction. TOP: 1-3 Multiplying and ividing Real Numbers 23. NS: Substitute 33 for k in the expression. Then divide the integers. If the signs are the same, the quotient is positive; if the signs are different, the quotient is negative. This expression involves division, not multiplication. This expression involves division, not subtraction. If the signs of the two integers are the same, the product will be positive. If the signs are different, the product will be negative. TOP: 1-3 Multiplying and ividing Real Numbers 24. NS: Write as an improper fraction. To divide by multiply by. Multiply. 8 8 Simplify. 21 First convert the mixed number to an improper fraction. Multiply by the reciprocal. First convert the mixed number to an improper fraction. Then multiply by the reciprocal. TOP: 1-3 Multiplying and ividing Real Numbers 25. NS: The quotient of and any nonzero number is.

36 Multiply or divide by. Multiply or divide by. Only division by is undefined. TOP: 1-3 Multiplying and ividing Real Numbers 26. NS: istance = rate time istance = Substitute 3.5 for rate and 1.75 for time. Multiply to find the distance. To find distance, multiply rate by time. To find distance, multiply rate by time. Then estimate to check if your answer is reasonable. The decimal point is not in the correct place. Use estimation to check if your answer is reasonable. TOP: 1-3 Multiplying and ividing Real Numbers 27. NS: The figure is 5 cubes tall, 5 cubes wide, and 5 cubes long. The factor 5 is used 3 times. The length, width, and height of the figure is 5. Is the figure 2-dimensional or 3-dimensional? The length, width, and height of the figure is 5. TOP: 1-4 Powers and Exponents 28. NS: The exponent tells the number of times to multiply the base number by itself. Multiply 9 by itself 3 times. Multiply the base number by itself as many times as the exponent tells you. Multiply using the base. The exponent just tells how many

37 times to multiply the base by itself. Multiply the number by itself rather than adding two different numbers. TOP: 1-4 Powers and Exponents 29. NS: The exponent tells the number of times to multiply the base number by itself. The negative sign in front of the expression multiplies the expression by 1. Multiply 3 by itself 4 times, and then multiply your answer by 1. Think of the negative sign in front as multiplying the expression by -1. Multiply the base number by itself rather than adding. Multiply the base number by itself. The exponent tells how many times to multiply the base by itself. TOP: 1-4 Powers and Exponents 3. NS: The exponent tells the number of times to multiply the base number by itself. Multiply by itself 2 times. Multiply the base number by itself rather than adding. This is the product of the base and the exponent. The exponent tells how many times to multiply the base by itself. heck the sign of your answer. The product of an even number of negative factors is positive; the product of an odd number of negative factors is negative. TOP: 1-4 Powers and Exponents 31. NS: The exponent tells how many times to multiply the fraction by itself. Multiply by itself 2 times. The exponent tells how many times to multiply the fraction by itself.

38 Raise both the numerator and denominator to the exponent. Raise both the numerator and denominator to the exponent. TOP: 1-4 Powers and Exponents 32. NS: The number given as a base should be multiplied by itself a certain number of times in order to represent the value of the whole number given. The product of two 3 s is 9. n exponent is written as a small number raised slightly above the base number. The exponent tells how many times to multiply the base by itself. The number given as a base should be multiplied by itself a certain number of times in order to represent the value of the whole number given. TOP: 1-4 Powers and Exponents 33. NS: If each category represents sunlight that is 6 times brighter than the category before, then a dazzling day would be 36 times brighter than an illuminated day because: a dazzling day is 6 times brighter than a radiant day, a radiant day is 6 times brighter than an illuminated day, and an illuminated day is 6 times brighter than a dim day. The brightness number is just for identifying the category. You need to use the number of times brighter as a factor. You need to use the number of times brighter as a factor one more time. heck to see whether you used the number of times brighter as a factor too many times. TOP: 1-4 Powers and Exponents 34. NS:

39 If the population of the ant hill is 4 ants and it doubles every 1 days, then to find its population in 2 days, make a chart to see what the population is after a certain number of days. In 1 days, the population is 4 ants. In 2 1 days, the population is 4 2 ants. In 3 1 days, the population is 4 3 ants. In 4 1 days, the population is 4 4 ants. Make a chart to see what the population is after a certain number of days. Make a chart to see what the population is after a certain number of days. Make sure that the ant population doubles. TOP: 1-4 Powers and Exponents 35. NS: Step 1 Find the total area of the vegetable garden and path. Step 2 Find the area of the vegetable garden and the area of the path. Find the side length of the vegetable garden. Find the area of the vegetable garden. To find the area of the path, subtract the area of the vegetable garden from the total area. Step 3 Find the number of gravel bags needed to cover the path. So, 7 bags of gravel are needed to cover the path. You switched the area of the vegetable garden and the area of the path. To find the area of the path, subtract the area of the vegetable garden from the total area. To find the area of the path, subtract the area of the vegetable garden from the total area.

40 TOP: 1-4 Powers and Exponents 36. NS: 196 = What number squared equals 196? = 14 The sign to the left of the radical determines whether the square root is positive or negative. This is half of the number. The square root of a number, multiplied by itself, equals that number. Find the square root of the number under the radical sign, not the square of that number. The + or - sign to the left of the radical is the sign of the square root. TOP: 1-5 Square Roots and Real Numbers 37. NS: 22 is between 196 and 225. Since 22 is closer to 196, the best estimate for the side length is 14 ft. Find the two perfect squares that the area is between. Find the two perfect squares that the area is between. Of the two perfect squares that the area is between, which is closer to the area? TOP: 1-5 Square Roots and Real Numbers 38. NS: ny number that can be written as a fraction is a rational number. Rational numbers include terminating decimals and repeating decimals. If a rational number simplifies to a whole number or its opposite, it is also an integer. If a rational number simplifies to a nonzero whole number, it is also a natural number.

41 To check whether the number is a terminating or repeating decimal, divide the numerator by the denominator. Since this number can be written as a fraction, it is not an irrational number. There are more ways to classify the number. heck to see whether it is a terminating or repeating decimal. TOP: 1-5 Square Roots and Real Numbers 39. NS: rational number can be written as a fraction. Rational numbers include integers, fractions, terminating decimals, and repeating decimals. n irrational number cannot be expressed as either a terminating decimal or repeating decimal. rational number will either terminate or repeat, but an irrational number will not. If the fraction simplifies to a nonzero whole number, the number is also an integer and a natural number. rational number will either terminate or repeat, but an irrational number will not. If the fraction simplifies to a nonzero whole number, the number is also an integer and a natural number. rational number will either terminate or repeat, but an irrational number will not. If the fraction simplifies to a nonzero whole number, the number is also an integer and a natural number. TOP: 1-5 Square Roots and Real Numbers 4. NS: If there is an example of two irrational numbers whose sum is not an irrational number, then the set of irrational numbers is not closed under addition. dd the following irrational numbers: The result is which is equal to, and is a rational number. nother example is and. The sum is which is a rational number.

42 Find an example of two irrational numbers whose sum is not an irrational number. If there is an example of two irrational numbers whose sum is not an irrational number, then the set of irrational numbers is not closed under addition. The set of irrational numbers being closed under addition means that when you add any two irrational numbers, the sum is also an irrational number. TOP: 1-5 Square Roots and Real Numbers 41. NS: Use the order of operations: 1. Perform operations in parentheses. 2. Evaluate powers. 2. Multiply or divide from left to right. 3. dd or subtract from left to right. The exponent tells how many times to use the base as a factor with itself. The order of operations is correct, but check your signs. fter evaluating the exponents and evaluating within parentheses, multiplication must be performed before addition or subtraction. TOP: 1-6 Order of Operations 42. NS: Use the order of operations: 1. Perform operations in parentheses. 2. Evaluate powers. 3. Multiply or divide from left to right. 4. dd or subtract from left to right. Use the order of operations. Perform operations in parentheses first. ivide before you add.

43 TOP: 1-6 Order of Operations 43. NS: Substitute 9 for x in the expression. Then use the order of operations to evaluate the expression. 1. Perform operations in parentheses. 2. Evaluate powers. 3. Multiply or divide from left to right. 4. dd or subtract from left to right. Use the order of operations. Multiply before adding or subtracting. Use the order of operations. Multiply before adding or subtracting. Use the order of operations. Multiply before adding or subtracting. TOP: 1-6 Order of Operations 44. NS: Substitute 4 for x in the expression. Then use the order of operations to evaluate the expression. 1. Perform operations in parentheses. 2. Evaluate powers. 3. Multiply or divide from left to right. 4. dd or subtract from left to right. Use the order of operations. Evaluate powers before multiplying or adding. Use the order of operations. Evaluate powers before multiplying or adding. Use the order of operations. Evaluate powers before multiplying or adding. TOP: 1-6 Order of Operations 45. NS:

44 First, simplify the numerator of the fraction, and then divide the numerator by the denominator. Next, subtract the terms in the absolute value, and then find the absolute value. = Finally, add the two terms. = 14 Only square the value that has an exponent, not both numbers in the numerator. Subtract within the absolute value bars before taking the absolute value. Simplify the numerator before dividing by the denominator. TOP: 1-6 Order of Operations 46. NS: Use parentheses so that the difference is evaluated first. Product means multiplication. "Product" indicates multiplication. Use parentheses so the difference is evaluated first. When finding a difference, subtract the second number from the first. TOP: 1-6 Order of Operations 47. NS: Use the formula (P + 5N Q) 1. Substitute the values from the table. Total Tatia has $1.9.

45 First perform operations inside parentheses, and then divide. Multiply before you add. Multiply the number of coins of each type by its coin value before performing the addition. TOP: 1-6 Order of Operations 48. NS: You must use each of the numbers at least once, and you may use any operations. Pay attention to the order of operations. Evaluate powers before performing subtraction. Perform multiplication before subtraction. The number 8 must be used also. TOP: 1-6 Order of Operations 49. NS: Use the ommutative Property. Use the ssociative Property to make groups of compatible numbers. Simplify. The sum of two mixed numbers is the sum of the whole parts plus the sum of the fractional parts. To add two fractions, first find a common denominator and then add the numerators. The sum of the fractional parts is greater than 1. TOP: 1-7 Simplifying Expressions 5. NS: Rewrite 59 as Then multiply each term by 11 and add the products.

46 Multiply the first number by each digit in the second number, then add the two products. Multiply the first number by each digit in the second number, then add the two products. Multiply the first number by each digit in the second number, then add the two products. TOP: 1-7 Simplifying Expressions 51. NS: Notice that 19 is very close to 2. Rewrite 19 as 2 +. Then use the istributive Property. You've reversed multiplication and addition. Look at the istributive Property again. Use mental math. Notice that the two-digit factor is close to a multiple of 1. Use mental math. Notice that the two-digit factor is close to a multiple of 1. TOP: 1-7 Simplifying Expressions 52. NS: Group like terms. dd or subtract the coefficients. ombine only like terms. heck the signs of all the coefficients. First, group like terms. Then, add or subtract the coefficients. TOP: 1-7 Simplifying Expressions 53. NS: The ommutative Property allows for you to add or subtract terms in any order.

47 Multiplication is used in Step 3. The ssociative Property is used in Step 5. Like terms are combined in Step 6. TOP: 1-7 Simplifying Expressions 54. NS: Procedure Justification efinition of subtraction ommutative Property ssociative Property istributive Property Simplify efinition of subtraction What is the difference between the ommutative Property and the istributive Property? The ssociative Property involves grouping of numbers. What does the ommutative Property state? What is the difference between the ssociative Property and the istributive Property? TOP: 1-7 Simplifying Expressions 55. NS: The x-coordinate of the ordered pair tells how many units to move left or right from the origin. The y-coordinate of the ordered pair tells how many units to move up or down from the origin. The first number in the ordered pair tells whether to move left or right from (, ). The second number tells whether to move up or down. The first number in the ordered pair tells whether to move left or right from (, ). The second number tells whether to move

48 up or down. The first number in the ordered pair tells whether to move left or right from (, ). The second number tells whether to move up or down. TOP: 1-8 Introduction to Functions 56. NS: If both x and y are positive, the point is in Quadrant I. If x is negative and y is positive, the point is in Quadrant II. If both x and y are negative, the point is in Quadrant III. If x is positive and y is negative, the point is in Quadrant IV. 5 y Quadrant II Quadrant I 5 5 x Quadrant III Quadrant IV 5 The coordinate plane is divided by the x-axis and the y-axis into four quadrants. The signs of x and y determine which quadrant the point is in. The coordinate plane is divided by the x-axis and the y-axis into four quadrants. The signs of x and y determine which quadrant the point is in. The coordinate plane is divided by the x-axis and the y-axis into four quadrants. The signs of x and y determine which quadrant the point is in. TOP: 1-8 Introduction to Functions 57. NS: If x =, the point is on the y-axis.

49 If y =, the point is on the x-axis. The coordinate plane is divided by the x-axis and the y-axis into four quadrants. If x =, the point is on the y-axis. If y =, the point is on the x-axis. The coordinate plane is divided by the x-axis and the y-axis into four quadrants. If x =, the point is on the y-axis. If y =, the point is on the x-axis. The coordinate plane is divided by the x-axis and the y-axis into four quadrants. If x =, the point is on the y-axis. If y =, the point is on the x-axis. TOP: 1-8 Introduction to Functions 58. NS: Let y represent the monthly payment and x represent the number of minutes of international calls. monthly payment is $25 plus $.1 for each international minute y = x Number of international minutes Rule Monthly payment Ordered pair x (input) y (output) (x, y) 9 $34. (9, 34) 12 $37. (12, 37) 145 $39.5 (145, 39.5) 15 $4. (15, 4) The monthly payment is determined by the number of international minutes, so the number of international minutes is the input and the monthly payment is the output. The monthly payment is determined by the number of international minutes, so the number of international minutes is

50 the input and the monthly payment is the output. The monthly payment is $25 plus $.1 for each international minute. TOP: 1-8 Introduction to Functions 59. NS: Make a table to find values of (x, y) for. x y (x, y) (, 6) 1 ( 1, ) (, ) 1 (1, ) 2 (2, 6) The points form a U shape. This is a cubic function. Use the given values for x to get the values for y. This is a linear function. Use the given values for x to get the values for y. This is an absolute value function. Use the given values for x to get the values for y. TOP: 1-8 Introduction to Functions 6. NS: Step 1 Plot the points.