Unit 1 Study Guide [MGSE9-12.N.Q.1-3, MGSE9-12.A.CED.1]

Transcription

1 Name: Class: Date: Unit 1 Study Guide [MGSE9-12.N.Q.1-3, MGSE9-12.A.CED.1] Matching a. algebraic expression f. variable b. numerical expression g. constant c. like terms h. solution of an equation d. absolute value i. equation e. evaluate 1. a value that does not change 2. to find the value of an algebraic expression by substituting a number for each variable and simplifying by using the order of operations 3. an expression that contains at least one variable 4. a symbol used to represent a quantity that can change 5. a mathematical phrase that contains operations and numbers 6. a value or values that make the equation true 7. a mathematical sentence that shows that two expressions are equivalent a. proportion e. identity b. formula f. conversion factor c. ratio g. rate d. unit rate h. scale 8. the ratio of two equal quantities, each measured in different units 9. a rate in which the second quantity in the comparison is one unit 10. an equation that states that two ratios are equal 11. a ratio that compares two quantities measured in different units 12. a comparison of two numbers by division 13. the ratio of any length in a drawing to the corresponding actual length a. conversion factor e. scale model b. corresponding sides f. cross products c. scale drawing g. dimensional analysis d. scale factor h. corresponding angles 14. a three-dimensional model that uses a scale to represent an object as smaller or larger than the actual object 15. a drawing that uses a scale to represent an object as smaller or larger than the original object 1

2 Name: 16. the product of the means bc and the product of the extremes ad in the statement a b = c d 17. a process that uses rates to convert measurements from one unit to another 18. angles in the same relative position in two different polygons that have the same number of angles 19. sides in the same relative position in two different polygons that have the same number of sides a. proportion e. tolerance b. precision f. similar c. indirect measurement g. accuracy d. scale factor h. dimensional analysis 20. a method of measuring an object by using formulas, similar figures, and/or proportions 21. in a dilation, the ratio of a linear measurement of the image to the corresponding measurement of the preimage 22. two figures that have the same shape, but not necessarily the same size 23. the level of detail of a measurement, determined by the unit of measure 24. the closeness of a given measurement or value to the actual measurement or value 25. the amount by which a measurement is permitted to vary from a specified value a. expression d. identity b. solution of an equation e. formula c. literal equation 26. an equation that is true for all values of the variables 27. a literal equation that states a rule for a relationship among quantities 28. an equation that contains two or more variables Numeric Response 1. 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? Check to make sure your answer is reasonable. Short Answer 1. Solve 44 = 14 2a. 2. Solve f 2 =

3 Name: 3. Solve 43a a = Devon pays $24.95 for her roller skates. After that she pays $3.95 for each visit to the roller rink. What is the greatest number of visits she can afford if the total amount she spends cannot be more than $76.30? 5. If 8y 8 = 24, find the value of 2y. 6. The formula p = nc e gives the profit p when a number of items n are each sold at a cost c and expenses e are subtracted. If p = 3750, n = 3000, and e = 900, what is the value of c? 7. Solve 50q 43 = 52q Solve n 8 + n = 1 4n. 9. Solve 6m 6 + 8m = 5 + 2m 1. Tell whether the equation has infinitely many solutions or no solutions. 10. A video store charges a monthly membership fee of $7.50, but the charge to rent each movie is only $1.00 per movie. Another store has no membership fee, but it costs $2.50 to rent each movie. How many movies need to be rented each month for the total fees to be the same from either company? 11. Find three consecutive integers such that twice the greatest integer is 2 less than 3 times the least integer. 12. A professional cyclist is training for the Tour de France. What was his average speed in miles per hour if he rode the 120 miles from Laval to Blois in 4.7 hours? Use the formula d = rt, and round your answer to the nearest tenth. 13. The formula for the resistance of a conductor with voltage V and current I is r = V. Solve for V. I 14. Solve 4x z = y for x. 15. Solve 3.8y + 4 x + 2 = 0 for y 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? 17. Ramon drives his car 150 miles in 3 hours. Find the unit rate. 18. A pipe is leaking at the rate of 8 fluid ounces per minute. Use dimensional analysis to find out how many gallons the pipe is leaking per hour. 19. Solve the proportion 5 6 = x An architect built a scale model of a shopping mall. On the model, a circular fountain is 20 inches tall and 22.5 inches in diameter. If the actual fountain is to be 8 feet tall, what is its diameter? 3

4 Name: 21. Complementary angles are two angles whose measures add to 90. The ratio of the measures of two complementary angles is 4:11. What are the measures of the angles? 22. Find the value of MN if AB = 21 cm, BC = 16.8 cm, and LM = 28 cm. ABCD LMNO 23. 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. 24. A right triangle has legs 15 inches and 12 inches. Every dimension is multiplied by 1 to form a new right 3 triangle with legs 5 inches and 4 inches. How is the ratio of the areas related to the ratio of corresponding sides? 25. Triangles C and D are similar. The area of triangle C is 47.6 in 2. The base of triangle D is 6.72 in. Each dimension of D is 6 5 the corresponding dimension of C. What is the height of D? 26. Choose the most precise measurement: 23 in., 4 ft, in., or ft. 27. A weight that measures exactly ounces is placed on three different balance scales. Scale 1 shows a weight of 3.03 ounces, scale 2 shows a weight of 2.99 ounces, and scale 3 shows a weight of ounces. Which scale is the most precise? Which is the most accurate? 28. A company sells furniture for home assembly. Their largest bookcase has shelves that should be 115 cm, with a tolerance of 0.6 cm (115 cm ± 0.6 cm). A set of six shelves had lengths of cm, cm, cm, cm, cm, and cm. Which, if any, of the shelves are not within the specified tolerance? 29. Write the possible range of the measurement to the nearest hundredth. 25 km ± 5% 30. Write the possible range of the measurement to the nearest hundredth. 40 km ± 1% 31. Round the measurement and underline the last significant digit meters to the nearest ten meters. 4

5 Name: 32. Round the measurement and underline the last significant digit liters to the nearest liter. 33. Give two ways to write the algebraic expression p 10 in words. 34. Give two ways to write the expression 7t in words. 35. 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. 36. 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. 37. Evaluate the expression m + o for m = 9 and o = Evaluate the expression q v for q = 5 and v = Evaluate the expression xy for x = 6 and y = Evaluate the expression a b for a = 24 and b = Juan scored 26 points in the first half of the basketball game, and he scored n 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 18 points in the second half of the game. 42. Salvador has saved 130 sand dollars and wants to give them away equally to n friends. Write an expression to show how many sand dollars each of Salvador s friends will receive. Then, find the total number of sand dollars each of Salvador s friends will get if Salvador gives them to 10 friends. 43. Isabel reads 15 books from the library each month for y months in a row. Write an expression to show how many books Isabel read in all. Then, find the number of books Isabel read if she read for 12 months. 44. Evaluate the expression 2m + n for m = 7 and n = Solve p 6 = 16. Check your answer. 46. Solve s + 6 = 48. Check your answer. 47. Solve 14 + s = A toy company's total payment for salaries for the first two months of 2005 is $21,894. Write and solve an equation to find the salaries for the second month if the first month s salaries are $10, 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.) 5

6 Name: 50. Solve q 5 = 41. Check your answer. 51. Solve 3n = 42. Check your answer. 52. Solve 2 10 b = 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. 54. If 4x = 32, find the value of 35 5x. 55. Denise has $365 in her saving account. She wants to save at least $635. Write and solve an inequality to determine how much more money Denise must save to reach her goal. Let d represent the amount of money in dollars Denise must save to reach her goal. 56. Marco s Drama class is performing a play. He wants to buy as many tickets as he can afford. If tickets cost $2.50 each and he has $14.75 to spend, how many tickets can he buy? 6