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Pre-Algebra Final review Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. Evaluate each expression. ____ 1. 6g – q if g = 10 and q = 10 a. 540 c. 70 b. 50 d. 590 Solve each equation mentally. ____ 2. a – 18 = 29 a. 47 c. 10 b. 11 d. 48 Name the property shown by each statement. ____ 3. 4 (3 + c) = 4 3 + 4 c a. Associative Property of Multiplication b. Commutative Property of Multiplication c. Distributive Property d. Identity Property of Multiplication The line plot shows the grades earned on Mr. Johnson’s science quiz. ____ 4. What is the range of the data? a. 25 c. 35 b. 30 d. 60 Find the mean for each set of data. Round to the nearest tenth if necessary. ____ 5. $100, $120, $94, $111, $156, $160, $138, $104, $99, $132 a. $121.40 c. $114.70 b. $135.25 d. $129.50 Find the mode for each set of data. If there is no mode, select or write none. ____ 6. 7, 3, 4, 6, 9, 10, 6, 4, 5, 3, 6, 8, 1, 8 a. 4 c. 8 b. 6 d. 3 Write an integer for each situation. ____ 7. a deposit of $245 a. –245 c. 245 b. 2450 d. 24.50 Subtract. ____ 8. 9 – 22 a. 13 c. –31 b. –13 d. 31 Write each sentence as an algebraic equation. ____ 9. A number less 12 equals . a. c. b. d. Solve each equation. Check your solution. ____ 10. a. 1 c. 50 2 b. 2 d. 5 Write each fraction as a percent. 2 ____ 11. 5 a. 40% c. 8% b. 160% d. 0.4% 1 ____ 12. 5 2 a. 55% c. 5.5% b. 550% d. 0.055% Add or subtract. Write in simplest form. 9 8 ____ 13. 1 13 1 13 a. 1 c. 1 1 13 21 b. 2 124 d. 3 4 169 13 Multiply. Write in simplest form. 4 6 ____ 14. 1 9 17 a. 54 c. 4 5 221 54 b. 26 d. 1 25 51 26 Find the perimeter of each figure. ____ 15. 16 ft 5 ft a. 21 ft c. 160 ft b. 42 ft d. 80 ft ____ 16. cm 5.3 cm 10.6 a. 31.8 cm c. 63.6 cm b. 56.18 cm2 d. 15.9 cm Find the area of each rectangle. ____ 17. yd 14.3 yd 6.7 a. 93.8 yd c. 98 yd2 b. 42 yd d. 95.81 yd2 Find the circumference of each circle. Use 3.14 or for . Round to the nearest tenth if necessary. ____ 18. 35 in. a. 55.0 in. c. 109.9 in. b. 108.5 in. d. 219.8 in. Find each unit rate. Round to the nearest tenth if necessary. ____ 19. $253 for 20 hours a. 1 hour/$15.50 c. $25.30/hour b. $12.65/hour d. 1 hour/$12.65 ____ 20. $316 for 4 VCRs a. 1 VCR/$79 c. $85/VCR b. $62.50/VCR d. $79/VCR Solve each problem. ____ 21. A map has a scale of 3.5 inches = 20 kilometers. If the distance between two cities on the map is 4.9 inches, what is the actual distance between the cities? a. 28 km c. 14.3 km b. 30.6 km d. 0.9 km Write each percent as a fraction in simplest form. 1 ____ 22. 61 2 % a. 123 c. 1 200 5 b. 61 d. 123 1000 20 Find each number. Round to the nearest tenth if necessary. ____ 23. 16.2% of 180 is what number? a. 18 c. 38.5 b. 29.2 d. 9 Find the percent of discount to the nearest percent. ____ 24. cereal: regular price, $4.50 sale price, $2.00 a. 44% c. 125% b. 56% d. 225% For each situation, make a tree diagram to show the sample space. Then give the total number of outcomes. ____ 25. picking a number from 1 to 4 and choosing the color red, green, or yellow a. 6 c. 12 b. 9 d. 24 A group of commuters from a large urban city was polled to study how people get to work each day. The results of the poll are shown in the circle graph. ____ 26. What is the least popular method of commuting to work among those polled? a. Other c. Drive Alone b. Public Transit d. Carpool Find the best name to classify each quadrilateral. ____ 27. a. rhombus c. trapezoid b. quadrilateral d. parallelogram Determine whether each pair of figures is similar. Justify your answer. ____ 28. 10 yd 5 yd 6 yd 14 yd a. similar b. not similar Determine which figures have line symmetry. If a figure has line symmetry, tell how many unique lines of symmetry there are. ____ 29. a. 1 line of symmetry c. 3 lines of symmetry b. 2 lines of symmetry d. no line symmetry ____ 30. a. 1 line of symmetry c. 3 lines of symmetry b. 2 lines of symmetry d. no line symmetry Short Answer Write an integer for each situation. 31. 60 seconds before liftoff Complete. 32. 196 oz = ____ lb Find the perimeter of each figure. 33. 15 ft 15 ft 18 ft Write an equation for each problem. Then solve. Round to the nearest tenth if necessary. 34. 84 is 28% of what number? Determine whether each statement is sometimes, always, or never true. 35. A rectangle is a square. Essay 36. Use the table of ordered pairs to answer the following questions. x y 4 2 –5 2 4 –4 a. Plot the ordered pairs in the table on a coordinate plane. b. In which quadrant is a point on the graph not represented? c. Connect the points on the graph. What special kind of triangle do they form? d. How would you double the size of the figure you drew in step c? e. Add four more columns to the table. Label the columns x + y, x – y, xy and x ÷ y. Complete the table. Record your answers on a sheet of paper. Show your work. 37. Emi delivers newspapers in her neighborhood. She receives a flat rate of $10 and an additional $0.25 for each newspaper she delivers. a. Write an equation to represent the total pay Emi receives. Use p for the total pay and n for each newspaper she delivers. b. If Emi delivers 15 newspapers, how much money does she receive? 38. Stephen is researching the value of his car. a. The value of his car decreased from $1,600 to $1,328. What is the percent of decrease? b. The current value of the car, $1,328, will increase by 8% if Stephen purchases new tires. What will be the value of the car with new tires? 39. 50 ft 40 ft A goat is tied to the corner of a square outbuilding with a 40 ft rope as pictured above. a. What is the measure of the partial circumference created as the goat walks at the full length of the rope? b. Since the goat is trimming the grass from part of the outbuilding, how much of the perimeter of the outbuilding will the building owner have to trim? 40. A deli offers sub sandwiches on wheat or rye bread, with a choice of ham, salami, or turkey. The deli also offers customers a choice of American, Provolone, or Cheddar cheese. Suppose a sandwich is chosen at random. a. Make a tree diagram that shows all of the possible outcomes. b. What is the probability that a randomly selected sandwich will be ham on rye with American cheese? c. What is the probability that a randomly selected sandwich will contain Provolone cheese or salami? Pre-Algebra Final review Answer Section MULTIPLE CHOICE 1. ANS: B You can evaluate an algebraic expression by replacing the variables with numbers and then finding the value of the numerical expression. DIF: Average OBJ: 1-4.1 Evaluate simple algebraic expressions. STO: MA.D.1.3.1-3, MA.D.1.3.1-4, MA.D.1.3.2-1, MA.D.1.3.2-2, MA.D.2.3.1-3 TOP: Evaluate simple algebraic expressions. KEY: Evaluating expressions, Algebraic expressions NOT: /A/ Do multiplication before addition. /B/ Correct! /C/ Watch addition and subtraction signs. /D/ Watch the order of operations. 2. ANS: A Some equations can be solved mentally by using basic facts or arithmetic skills you know. DIF: Basic OBJ: 1-5.1 Solve equations using mental math. STO: MA.A.3.3.3-1, MA.D.1.3.2-2, MA.D.2.3.1-3, MA.D.2.3.1-4 TOP: Solve equations using mental math. KEY: Mental math, Solving equations NOT: /A/ Correct! /B/ Use basic facts or arithmetic skills you know. /C/ Use basic facts or arithmetic skills you know./D/ Use basic facts or arithmetic skills you know. 3. ANS: C Distributive Property: a (b + c) = a b + a c DIF: Average OBJ: 1-6.2 Name properties of addition and multiplication shown in statements. STO: MA.A.3.3.1-3, MA.A.3.3.2-4, MA.D.2.3.2-2 TOP: Name properties of addition and multiplication shown in statements. KEY: Addition properties, Multiplication properties NOT: /a/ That is a x (b x c) = (a x b) x c. /b/ That is a x b = b x a. /c/ Correct! /d/ That is a x 1 = a. 4. ANS: C The range of the data is 95 – 60 = 35. DIF: Average OBJ: 2-3.2 Interpret line plots. STO: MA.E.1.3.1-2, MA.E.1.3.1-3 TOP: Interpret line plots. KEY: Line plots, Analyzing data NOT: /a/ The range is the difference between the greatest number and the least number. /b/ Remember, the range is the total spread of the data. It is the difference between the highest and lowest data points. /c/ Correct! /d/ Subtract the least number from the greatest number. 5. ANS: A Divide the sum of the numbers by the number of items in the set. DIF: Average OBJ: 2-4.1 Find the mean of a set of data. STO: MA.E.1.3.2-1, MA.E.1.3.2-2, MA.E.1.3.3-1 TOP: Find the mean of a set of data. KEY: Mean, Analyzing data NOT: /a/ Correct! /b/ Remember, the mean is the sum of the numbers in the data set divided by the number of items. /c/ Double check your work and try again. /d/ What is the sum of the numbers? Divide this by the number of items in the set. 6. ANS: B The mode is 6 because it occurs most often. DIF: Basic OBJ: 2-4.3 Find the mode of a set of data. STO: MA.E.1.3.2-1, MA.E.1.3.2-2, MA.E.1.3.3-1 TOP: Find the mode of a set of data. KEY: Mode, Analyzing data NOT: /a/ Is there a number that occurs more often than 4? /b/ Correct! /c/ Remember, the mode is the number that occurs most often in a set of data. /d/ Is there a number that occurs more often than 3? 7. ANS: C A deposit indicates a positive value, so 245 is the correct integer. DIF: Average OBJ: 3-1.1 Write integers. STO: MA.A.1.3.1-1, MA.A.1.3.2-1, MA.A.1.3.4-2, MA.A.1.3.4-3 TOP: Write integers. KEY: Integers, Numbers NOT: /a/ Does a deposit represent a negative or a positive amount? Think in terms of a bank deposit. /b/ What integer can be used to represent $245? /c/ Correct! /d/ 24.50 is not an integer. 8. ANS: B Sample: –22 – 15 Subtract the integer by adding its additive inverse. –22 + (–15) –37 DIF: Average OBJ: 3-5.1 Subtract positive integers. STO: MA.A.1.3.3-3, MA.A.3.3.1-1, MA.A.3.3.1-2, MA.A.3.3.1-4, MA.A.3.3.2-1 TOP: Subtract positive integers. KEY: Subtraction, Integers NOT: /A/ Be careful with your signs and try again. /B/ Correct! /C/ What is the additive inverse of the integer bring subtracted? Add this to the first integer./D/ To subtract an integer, add its additive inverse. 9. ANS: A Subtract the number from the variable. Then set the expression equal to the remaining number. DIF: Average OBJ: 4-1.2 Write verbal sentences as simple algebraic equations. STO: MA.D.1.3.2-2, MA.D.2.3.1-1 TOP: Write verbal sentences as simple algebraic equations. KEY: Verbal sentences, Algebraic equations NOT: /a/ Correct! /b/ Subtract the number from the variable. /c/ Check the sign of each number. /d/ Less means subtraction. 10. ANS: B Divide both sides by the coefficient of the variable. DIF: Basic OBJ: 4-3.1 Solve multiplication equations. STO: MA.A.3.3.1-3, MA.D.2.3.1-1, MA.D.2.3.1-4, MA.D.2.3.2-1 TOP: Solve multiplication equations. KEY: Multiplication, Solving equations NOT: /A/ Divide the right-hand side by the coefficient of the variable. /B/ Correct! /C/ Division undoes multiplication. /D/ Division undoes multiplication. 11. ANS: A Divide the numerator by the denominator. Then move the decimal two places to the right. DIF: Basic OBJ: 5-5.2 Write fractions as percents. STO: MA.A.1.3.1-1, MA.A.1.3.4-1, MA.A.1.3.4-2, MA.A.1.3.4-4 TOP: Write fractions as percents. KEY: Percent, Fractions NOT: /A/ Correct! /B/ Remember to divide not multiply by the denominator. /C/ Remember to divide by the denominator. /D/ Remember to move the decimal place. 12. ANS: B Sample: Write the mixed number as a decimal. Then multiply the number by 100 to write it as a percent. DIF: Average OBJ: 7-6.4 Write fractions as percents greater than 100% and percents less than 1%. STO: MA.A.1.3.4-1, MA.A.1.3.4-2, MA.A.1.3.4-4 TOP: Write fractions as percents greater than 100% and percents less than 1%. KEY: Fractions, Percent NOT: /A/ Remember the definition of a percent. What should you multiply the decimal by in order to write it as a percent? /B/ Correct! /C/ A percent is a ratio that compares a number to what other number? /D/ The number 1 represents 100%. Should your answer be greater than or less than 100%? 13. ANS: A To subtract mixed numbers with like denominators, subtract the whole numbers and subtract the fractions. Rewrite the first mixed number if necessary to subtract the fractions. Simplify. DIF: Average OBJ: 6-3.2 Subtract mixed numbers. STO: MA.A.3.3.1-1, MA.A.3.3.1-2, MA.A.3.3.1-3, MA.A.3.3.2-1, MA.A.3.3.2-2 TOP: Subtract mixed numbers. KEY: Subtraction, Mixed numbers NOT: /A/ Correct! /B/ Did you multiply? /C/ Did you divide?/D/ Did you add? 14. ANS: B To multiply mixed numbers, convert both factors to improper fractions. Then multiply the numerators and denominators. Simplify. DIF: Basic OBJ: 6-4.2 Multiply mixed numbers. STO: MA.A.3.3.1-1, MA.A.3.3.1-2, MA.A.3.3.1-3, MA.A.3.3.2-1, MA.A.4.3.1-1 TOP: Multiply mixed numbers. KEY: Multiplication, Mixed numbers NOT: /A/ Did you multiply the reciprocals after converting to improper fractions? /B/ Correct! /C/ Is that the product or the quotient? /D/ Did you multiply the second fraction by the reciprocal of the first? 15. ANS: B The perimeter of a rectangle is the sum of the measures of the sides. It can also be expressed as two times the length (l) plus two times the width (w). DIF: Basic OBJ: 6-8.1 Find the perimeters of figures. STO: MA.B.1.3.3-1, MA.B.1.3.3-2, MA.B.1.3.1-3, MA.B.1.3.3-3, MA.B.2.3.2-3 TOP: Find the perimeters of figures. KEY: Perimeter, Measurement NOT: /A/ Did you consider all four sides? /B/ Correct! /C/ Is your answer reasonable?/D/ How do you find the perimeter? 16. ANS: A The perimeter of a rectangle is the sum of the measures of the sides. It can also be expressed as two times the length (l) plus two times the width (w). DIF: Average OBJ: 6-8.1 Find the perimeters of figures. STO: MA.B.1.3.3-1, MA.B.1.3.3-2, MA.B.1.3.1-3, MA.B.1.3.3-3, MA.B.2.3.2-3 TOP: Find the perimeters of figures. KEY: Perimeter, Measurement NOT: /A/ Correct! /B/ Did you find the area? /C/ What is the formula for perimeter of a rectangle?/D/ Did you consider all four sides? 17. ANS: D The area of a rectangle equals the product of its length and width. DIF: Average OBJ: 6-8.2 Find the areas of figures. STO: MA.B.1.3.3-1, MA.B.1.3.3-2, MA.B.1.3.1-3, MA.B.1.3.3-3, MA.B.2.3.2-3 TOP: Find the areas of figures. KEY: Area, Measurement NOT: /A/ Be careful with multiplication and units./B/ That is the perimeter. /C/ How do you find the area of a rectangle? /D/ Correct! 18. ANS: C The circumference of a circle is equal to times its diameter or times twice the radius. DIF: Average OBJ: 6-9.1 Find the circumference of circles. STO: MA.B.1.3.1-3, MA.B.1.3.3-3, MA.C.1.3.1-6 TOP: Find the circumference of circles. KEY: Circumference, Circles NOT: /A/ Did you use the correct formula for circumference? /B/ What did you use for pi? /C/ Correct! /D/ Is 35 the radius or diameter? 19. ANS: B The unit rate is the amount earned for 1 hour. $253 ÷ 20 = $12.65/hour DIF: Average OBJ: 7-2.1 Determine unit rates. STO: MA.A.1.3.1-1, MA.A.1.3.4-2 TOP: Determine unit rates. KEY: Unit rate, Ratios NOT: /a/ Double check your computation to be sure you have the correct unit rate. Also, remember that the terms of the ratio should be written in the same order as the problem statement. /b/ Correct! /c/ Double check your computation to be sure you have the correct unit rate. /d/ The terms of the ratio should be written in the same order as the problem statement. 20. ANS: D The unit cost is the cost of 1 VCR. $316 ÷ 4 = $79/VCR DIF: Basic OBJ: 7-2.1 Determine unit rates. STO: MA.A.1.3.1-1, MA.A.1.3.4-2 TOP: Determine unit rates. KEY: Unit rate, Ratios NOT: /a/ The terms of the ratio should be written in the same order as the problem statement. /b/ Double check your computation to be sure you have the correct unit rate. /c/ Did you divide out the common factor from both terms? /d/ Correct! 21. ANS: A Set up a proportion and solve for the distance. DIF: Average OBJ: 7-4.1 Solve problems involving scale drawings. STO: MA.B.1.3.4-1, MA.B.1.3.4-2, MA.B.1.3.4-3, MA.B.2.3.1-3 TOP: Solve problems involving scale drawings. KEY: Scale drawings, Proportions NOT: /a/ Correct! /b/ Double check your computation and try again. /c/ Be careful when solving your proportion. What are the cross products of the proportion? /d/ Be careful when setting up your proportion. Be sure you order the terms correctly. 22. ANS: A Sample: % Write the percent over 100 and simplify. DIF: Average OBJ: 7-5.1 Write percents as fractions. STO: MA.A.1.3.4-1, MA.A.1.3.4-2, MA.A.1.3.4-4 TOP: Write percents as fractions. KEY: Percent, Fractions NOT: /A/ Correct! /B/ Be careful when writing the fraction in simplest terms. /C/ Double check your work and try again./D/ Should the fraction be greater than or less than 1? 23. ANS: B Set up a proportion to find the number. DIF: Average OBJ: 7-8.1 Solve problems using the percent proportion. STO: MA.A.3.3.2-3 TOP: Solve problems using the percent proportion. KEY: Percent proportion, Problem solving NOT: /a/ Write a proportion where one of the ratios is the percent over 100. Then solve for the number. /b/ Correct! /c/ Double check your work and try again. /d/ Be careful when setting up your proportion. The terms in the ratios must be consistent. 24. ANS: B Subtract the sale price from the regular price.Use the percent proportion to determine what percent the difference is of the regular price. DIF: Average OBJ: 8-5.2 Solve problems involving discounts. STO: MA.A.3.3.2-3 TOP: Solve problems involving discounts. KEY: Discounts, Problem solving NOT: /a/ Do not divide the sale price by the regular price. /b/ Correct! /c/ Do not divide the differenceby the sale price. /d/ Do not divide the regular price by the sale price. 25. ANS: C There are twelve possible outcomes: 1R, 1G, 1Y, 2R, 2G, 2Y, 3R, 3G, 3Y, 4R, 4G, and 4Y. DIF: Average OBJ: 9-2.1 Use tree diagrams to count outcomes and find probabilities. STO: MA.E.3.3.1-1, MA.E.3.3.1-2, MA.E.3.3.1-3 TOP: Use tree diagrams to count outcomes and find probabilities. KEY: Probability, Tree diagram NOT: /a/ List all of the possible outcomes for the number. Then branch off each number to list all of the possible outcomes for the color. /b/ Double check your work and try again. /c/ Correct! /d/ List all of the possible outcomes to make sure they are all unique. 26. ANS: D Carpool has the smallest section, so it is the least popular method. DIF: Basic OBJ: 10-2.2 Interpret circle graphs. STO: MA.E.1.3.1-3 TOP: Interpret circle graphs. KEY: Circle graph, Analyzing data NOT: /a/ Is there a section that is smaller than the Other section? /b/ Would the least popular method of travel have the smallest or the largest section of the circle graph? /c/ Which section of the circle graph is the smallest? /d/ Correct! 27. ANS: B The figure is simply a quadrilateral. DIF: Average OBJ: 10-5.1 Identify quadrilaterals. STO: MA.C.1.3.1-3, MA.C.1.3.1-4, MA.C.1.3.1-6 TOP: Identify quadrilaterals. KEY: Quadrilaterals, Identifying quadrilaterals NOT: /a/ A rhombus is a parallelogram with four congruent sides. /b/ Correct! /c/ Does the figure have a pair of opposite sides that are parallel? /d/ Are the pairs of opposite sides parallel to each other? 28. ANS: B Find the ratios of the corresponding sides to see if they are in proportion. The corresponding sides are not in proportion, so the figures are not similar. DIF: Average OBJ: 10-6.1 Determine whether figures are similar. STO: MA.A.3.3.2-5, MA.B.2.3.1-3 TOP: Determine whether figures are similar. KEY: Similarity, Similar figures NOT: /a/ Are the corresponding sides of the rectangles in proportion? /b/ Correct! 29. ANS: B Sketch all lines that will produce identical figures when reflected over the line. The figure has 2 lines of symmetry. DIF: Basic OBJ: 10-9.1 Identify figures with line symmetry. STO: MA.C.2.3.1-5, MA.C.2.3.2-3 TOP: Identify figures with line symmetry. KEY: Line symmetry, Symmetry NOT: /a/ Copy the figure onto your paper and sketch the line of symmetry. Are there any other lines that will produce identical figures when you fold along the line? /b/ Correct! /c/ Copy the figure onto your paper to verify that all three lines of symmetry will produce identical figures. /d/ Are there any lines that will produce identical figures when you fold along the line? 30. ANS: A Sketch all lines that will produce identical figures when reflected over the line. The figure has 1 line of symmetry. DIF: Average OBJ: 10-9.1 Identify figures with line symmetry. STO: MA.C.2.3.1-5, MA.C.2.3.2-3 TOP: Identify figures with line symmetry. KEY: Line symmetry, Symmetry NOT: /a/ Correct! /b/ Copy the figure onto your paper and verify that there are two lines that divide the figure into equal halves. /c/ Double check your answer by sketching the figure and any lines of symmetry on your paper. /d/ Are there any lines that will produce identical figures when you fold along the line? SHORT ANSWER 31. ANS: –60 Rationale: The time is given in relation to liftoff. Since it has not occurred yet, the value should be negative. –60 is the correct integer. DIF: Average OBJ: 3-1.1 Write integers. STO: MA.A.1.3.1-1, MA.A.1.3.2-1, MA.A.1.3.4-2, MA.A.1.3.4-3 TOP: Write integers. KEY: Integers, Numbers 32. ANS: When changing from a smaller unit to a larger unit, divide. Since there are 16 ounces in one pound, divide 196 by 16. DIF: Average OBJ: 6-7.1 Change units in the customary system. STO: MA.A.3.3.3-1, MA.B.2.3.1-1 TOP: Change units in the customary system. KEY: Measurement, Customary units 33. ANS: 48 ft The perimeter of a triangle is the sum of the measures of the sides. DIF: Average OBJ: 6-8.1 Find the perimeters of figures. STO: MA.B.1.3.3-1, MA.B.1.3.3-2, MA.B.1.3.1-3, MA.B.1.3.3-3, MA.B.2.3.2-3 TOP: Find the perimeters of figures. KEY: Perimeter, Measurement 34. ANS: base = 300 DIF: Average OBJ: 8-2.1 Solve problems by using the percent equation. STO: MA.A.3.3.2-3 TOP: Solve problems by using the percent equation. KEY: Percent equation, Problem solving 35. ANS: sometimes When a rectangle has four congruent sides, it is a square. DIF: Average OBJ: 10-5.2 Classify quadrilaterals. STO: MA.C.1.3.1-3, MA.C.1.3.1-4, MA.C.1.3.1-6 TOP: Classify quadrilaterals. KEY: Quadrilaterals, Classifying quadrilaterals ESSAY 36. ANS: a. y 5 4 3 2 1 –5 –4 –3 –2 –1 1 2 3 4 5 x –1 –2 –3 –4 –5 b. quadrant III c. y 5 4 3 2 1 –5 –4 –3 –2 –1 1 2 3 4 5 x –1 –2 –3 –4 –5 right triangle d. double the sides of the triangle. e. x y x+y x–y xy x÷y 4 2 6 2 8 2 –5 2 –3 –7 –10 –2.5 4 –4 0 8 –16 –1 Rationale: a. Plot the ordered pairs as directed. b. There are no points in the third quadrant. c. Connect the points as directed. They form a right triangle. d. The triangle’s size can be doubled by doubling the lengths of its sides. e. Perform the addition, subtraction, multiplication, and division using the properties of integers. DIF: Advanced OBJ: 3-8.1 Solve problems and show solutions. TOP: Solve problems and show solutions. KEY: Problem solving, Solutions 37. ANS: a. Emi will receive $10 regardless of the number of papers she delivers. For each paper delivered, Emi will receive an additional $0.25 per paper. In the equation, the variable p represents the total pay that Emi will receive, and n represents the number of newspapers delivered. b. $13.75 The equation from part a can be used to solve this equation. Since Emi delivers 15 newspapers, fifteen is substituted for the variable n. DIF: Advanced OBJ: 4-8.1 Solve problems and show solutions. TOP: Solve problems and show solutions. KEY: Problem solving, Solutions 38. ANS: a. 17% b. $1,434.24 DIF: Advanced OBJ: 8-7.1 Solve problems and show solutions. TOP: Solve problems and show solutions. KEY: Problem solving, Solutions 39. ANS: a. You need to find three fourths of the circumference of a circle with radius 40 feet. b. The perimeter of the building is 200 ft. The goat is trimming 40 ft of two of the sides leaving . DIF: Advanced OBJ: 6-10.1 Solve problems and show solutions. TOP: Solve problems and show solutions. KEY: Problem solving, Solutions 40. ANS: a. There are 18 possible outcomes: WHA, WHP, WHC, WSA, WSP, WSC, WTA, WTP, WTC, RHA, RHP, RHC, RSA, RSP, RSC, RTA, RTP, and RTC. b. There is only 1 favorable outcome (RHA) out of 18 possible outcomes. c. There are 10 outcomes that contain either Provolone cheese or salami (WHP, WSA, WSP, WSC, WTP, RHP, RSA, RSP, RSC, RTP). Write this over the total number of outcomes and simplify. DIF: Advanced OBJ: 9-8.1 Solve problems and show solutions. TOP: Solve problems and show solutions. KEY: Problem solving, Solutions

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