Ron Paul Curriculum 7th Grade Mathematics Problem Set #41. There is no problem set for Lesson #41.

Transcription

1 Problem Set #41 There is no problem set for Lesson #41.

2 Problem Set #42 Convert the following units. Be sure to write out the conversion factors you use meter to inches miles to kilometers (use 1 mile 1.6 kilometers) 3. 6 ft. to cm 4. 2 in. to mm cm to in km to mi mm to in mi. to yd yd. to cm in. to cm.

3 Problem Set #43 Convert the following units. Be sure to write out the conversion factors you use liters to ml 2. ½ gal. to fl. oz c. to T. 4. 1/10 m 3 to liters 5. 1 qt. to t pt. to fl. oz gal. to t cc to liters 9. 5 pt. to T gal. to qt.

4 Problem Set #44 Convert the following units. Be sure to write out the conversion factors you use pounds to oz oz. to gr kg. to lbs. (use 1 kg. 2.2 lbs.) 4. 1/10 ton to oz tonne to tons mg to gr oz. to g gr. to oz. 9. 1,000,000 g to tonnes 10. 1,000,000 oz. to tons

5 Problem Set #45 There is no problem set for Lesson #45.

6 Problem Set #46 Convert the following units. Be sure to write out the conversion factors you use decades to months 2. 1 week to minutes months to days 4. 1 hour to seconds 5. 1,000,000 seconds to days Convert the following temperatures: F to Celsius C to Fahrenheit F to Celsius C to Fahrenheit F to Celsius

7 Problem Set #47 In Ray s New Higher Arithmetic, read pp Add 6.19 yd.; 2 yd. 2 ft. 9¾ in.; 1 ft in.; 10 yd ft.; ¾ yd.; ft.; ⅞ in. 2. Add 15 sq. yd. 5 sq. ft. 87 sq. in.; 16½ sq. yd.; 10 sq. yd sq. ft.; 4 11 sq. ft sq. in.; 32 sq. yd. 3. Add 23 cu. yd. 14 cu. ft cu. in.; 41 cu. yd. 6 cu. ft cu. 7 in.; 9 cu. yd cu. ft.; 15cu. yd. 4. Add ½ wk.; ½ day; ½ hr.; ½ min.; ½ sec. In Ray s New Higher Arithmetic, read pp From 1 gal. 3 qt. 2 pt. subtract 2 qt. 1 pt. 1 c. 6. What is the difference between 10 lbs. 14 oz gr. and 4 lbs. 15 oz gr.? 7. From 12 days subtract 3 days, 16 hours and 27 minutes. 8. What is the difference between 5 miles and 5 kilometers?

8 Problem Set #48 In Ray s New Higher Arithmetic, read bottom of p Multiply 4 gal. 1 qt. 1 c. by Multiply 1 day 15 hrs. 27 min. 12 sec. by Multiply 1 mile 1 yard 1 foot by Multiply 150 lbs. 12 oz. by 20. In Ray s New Higher Arithmetic, read bottom of p Divide 4 gal. 1 qt. 1 c. by Divide 1 day 15 hrs. 27 min. 12 sec. by Divide 1 mile 1 yard 1 foot by Divide 150 lbs. 12 oz. by 20.

9 Problem Set #49 1. An apartment building has 175 apartments on 25 floors. How many apartments per floor? 2. Bill read 8 books of 300 pages each in 120 days. How many pages per day? 3. John earned $64 in an eight-hour day. How much does he earn per hour? 4. Katy bought 32 ounces of soda for $2.00. How much did she pay per ounce? 5. Tim drove 312 miles in 8 hours. What was his average rate of speed? 6. If strawberries are $3/pound, how much will 15 pounds cost? 7. If Greg can average 400 miles per day driving, how far will he go in 1 week? 8. If I eat 3500 calories per day, how many calories do I eat in 1 month? 9. If Bob earns $1500 per month, how much does he earn in 1 year? 10. If Laura gets 24 miles per gallon in her car, how much fuel will she use on a 3600 mile trip? At $3.50/gallon for gas, how much will her trip cost?

10 Problem Set #50 1. Convert 1 month to hours 2. Convert 1,000,000 hours to years 3. Convert 1 decade to minutes 4. Convert 70 C to Fahrenheit 5. Convert 150 F to Celsius 6. Convert 25 F to Celsius 7. Convert 40 C to Fahrenheit 8. Add 3 years 7 months 12 days 11 hours; 9 months 15 days 8 hours 42 minutes; 1 year 1 month 1 day 1 hour 1 minute; 3 hours 57 minutes. 9. Add 15 lbs. 11 oz gr.; 7 lbs. 15 oz gr.; 43 lbs. 3 oz gr.; 17 lbs. 9 oz gr. 10. Add 12 sq. yds. 7 sq. ft. 131 sq. in.; 5 sq. yds.; 3 sq. ft. 97 sq. in.; 13 sq. yds. 2 sq. ft. 115 sq. in.; 3 sq. yds. 8 sq. ft. 58 sq. in. 11. What is the difference between 12 sq. yds. 7 sq. ft. 58 sq. in. and 5 sq. yds. 4 sq. ft. 111 sq. in.? 12. From 3 years 7 months 12 days 11 hours subtract 9 months 15 days 8 hours 42 minutes. 13. Multiply 9 months 15 days 8 hours 42 minutes by Multiply 12 sq. yds. 7 sq. ft. 58 sq. in. by Divide 9 months 15 days 8 hours 42 minutes by Divide 15 lbs. 12 oz gr. by Roland can buy a 12 ounce can of orange juice for 50 cents or a 1 gallon jug of orange juice for $5.50. Which is the better deal in dollars per ounce?

11 18. Gilbert drove miles in 3 weeks in his truck between filling the tank. Then he filled the gas tank with 14.3 gallons of fuel for $ a) How many miles per gallon did he get? b) How many miles per dollar did he get? c) How much does it cost to drive 1 mile? d) How many gallons of fuel are needed to drive 1 mile? e) What is the price of the fuel? f) How many miles did he drive on average each week? Each day? g) How much did he spend on fuel each week? Each day? h) If he wants to take a 2000 mile trip, how much will it cost? i) What does the answer to (h) assume? j) How much fuel will he use on the 2000 mile trip?

12 Problem Set #51 Enter the information in the table below into your spreadsheet program. 1. Make the column labels at the top of the columns bold. 2. Format the Date column, Units Sold column, Price, and Total Sales columns appropriately. 3. Center the column label cells, the Units Sold column, and Date column. 4. Left-justify the Description column. Right-justify the Price and Total Sales columns. 5. Adjust the column widths to fit the data. 6. Sort all the data by date. 7. Make sure that Price and Total Sales columns have two decimal places. 8. Change the name of the worksheet to April 2009 sales - by date. 9. Create a new worksheet called April 2009 sales - by total. 10. Copy the data from your first worksheet into the new worksheet, and sort all the data by total sales. 11. SAVE THIS SPREADSHEET! You will need it again for Problem Set #52. Date Description Price Units Sold Total Sales 4/15/2009 Fishing rod $ $ /11/2009 Tackle box $ $ /17/ lb. monofilament spool $5 4 $20 4/8/2009 Spinning reel $ $ /26/2009 Salt water reel $ $ /21/2009 Minnow lure $ $ /2/2009 Super Glowing Rattle Lure $ $ /7/2009 Casting reel $ $ /17/ lb. monofilament spool $6 21 $126 4/5/2009 Herring lure $2 9 $18 4/30/ lb. braided line spool $9 5 $45

13 Problem Set #52 Use the spreadsheet workbook that you created for the Lesson #51 problem set. 1. At the top of the worksheet, add a cell with an appropriate label for sales tax with the value 7.25%. You will probably need to make space for this information. 2. Insert a column between the Price and Units Sold column, and label it Sales Tax. Fill in this column with the amount of the sales tax for each item. 3. Insert two columns after Units Sold labeled Original Inventory and Units Remaining. 4. In the Original Inventory column, put the values 25, 9, 32, 11, 3, 20, 17, 6, 30, 18 and 28 for the 11 items in the list. 5. In the Units Remaining column, subtract the Units Sold from the Original Inventory. 6. Add a column after Total Sales labeled Total Tax, and calculate the total sales tax for all the units sold. 7. Add a column after Total Tax labeled Net Sales and calculate the total sales minus the sales tax for each item.

14 Problem Set #53 Make a budget spreadsheet with two worksheets, labeled Budget and Savings. In the Budget worksheet, make a list labeled Expense with the following items: Housing (rent or mortgage) Utilities Phones Food Clothing Miscellaneous expenses Fuel Insurance Entertainment Charitable giving Savings Label the next column Amount and fill in what you think is a realistic amount to budget for one month for your family. Format this column as currency. Ask the adult responsible for the finances in your family to look at your budget and tell you if your numbers are realisitc. NOTE: I am not asking you to find out what your family budget is if an adult does not want to share this with you. But they can comment on whether your budget is realistic for what a family the size of yours might actually spend on each item.

15 Problem Set #54 1. Make a spreadsheet with three columns, labeled n, Fn and Fn+1/Fn. These will be the Fibonacci number index, the Fibonacci number, and the ratio of two consecutive numbers. 2. In the n column, enter numbers 0 through In the Fn column, enter 0, then 1. Then use the spreadsheet to caclulate the Fibonacci numbers through n = In the Fn+1/Fn column, use the spreadsheet to calculate each Fibonacci number divided by the Fibonacci number immediately preceding it. What happens if you do this for n = 1? 5. Increase the number of digits showing in the second two columns until you can see all of the information. 6. Now make two more columns and label them Gn and Gn+1/Gn. 7. Repeat steps 3-5, only this time for the first two numbers in the Gn column, use 112 and 41. What do you notice?

16 Problem Set #55 There is no problem set for Lesson #55.

17 Problem Set #56 Answer the questions below using the information about the planets in the following table. 1. What is the ratio of the heaviest (most massive) planet to the lightest? 2. What is the ratio of the diameter of the earth to the diameter of Jupiter? What percent of the diameter of Jupiter is the diameter of the earth? 3. What is the ratio of the length of a day on earth to the length of a day on Saturn? What percent of a day on earth is a day on Saturn? 4. What is the ratio of the solar distance of Mercury to the solar distance of Neptune? 5. Jimmy has a coin collection. He has 124 coins from the United States and 86 coins from other countries. (a) What is the ratio of U. S. coins to total coins in Jimmy s collection? (b) What is the ratio of foreign coins to total coins in Jimmy s collection? (c) What is the ratio of U. S. to foreign coins in Jimmy s collection?

18 (d) What is the ratio of foreign to U. S. coins in Jimmy s collection? (e) What percent of Jimmy s coin collection is U. S. coins? (f) What percent of Jimmy s coin collection is foreign coins? (g) What is the difference between the number of U. S. coins and the number of foreign coins in Jimmy s collection? 6. In October, Lauren spent 6 hours watching TV and 28 hours reading. Tim spent 10 hours watching TV and 36 hours reading. Who had a higher ratio of reading to watching TV?

19 Problem Set #57 Solve the following proportion problems: 1. 1 = 3 9 h 18 t 2. = = a x = = y 36 Use a proportion to solve the following problems. Assume all the relationships are proportional. 6. If a person sleeps 8 hours per day, how many hours will they sleep in one year? 7. If a person watches 16 hours of TV in two weeks, how many hours of TV will they watch in one year? 8. Doug stacked 24 rows of firewood in 4 hours. How long will it take him to stack 42 rows of firewood? 9. Ben must prepare 60 lessons in 4 weeks. How many lessons must he prepare in 36 weeks? 10. A company spends $60 for every 4 employees that attend the Christmas party. How much will the company spend if 72 employees attend the Christmas party?

20 Problem Set #58 Write out the first 12 rows of Pascal s triangle neatly in your study notebook. Make a list in your study notebook of the special properties of Pascal s triangle that we discussed in the lesson.

21 Problem Set #59 1. Write your full name in the Pascal triangle code. 2. Write the following message in the Pascal triangle code, counting to the right: THE PIG WILL FLY AT MIDNIGHT 3. Write the following message in the Pascal triangle code, counting to the left: FOUR BEAGLES KNOW TOO MUCH

22 Problem Set #62 Evaluate the following algebraic expressions for the given value of the variables: 2x x for x = d + 3d 1 for d = 3 x z x x for x = 4 for z = 10 for x = y y 2 3 for y = 2 x y x + y for x = 1, y = 1 8. b b 2 4ac 2a for a = 2, b = 4, c = a 2 + 2a 6 for a = r + 2+ s r s 2 for r = 5, s = 4

23 Problem Set #63 Solve the following algebraic equations. Show your transformation step. 1. x + 4 = y 8 = d = 32 t = 5. 6x = p 12 = s = y = z = 30 r 10. = 3 12

24 Problem Set #64 Solve the following algebraic equations. Show your transformation steps. 1. 3x + 4 = y 8 = 19 d 3. 6= = 3 t x = p 12 = s 9= y = z + 20 = r = 3

25 Problem Set #65 Evaluate the following algebraic expressions for the given value of the variables: 1. x 3 + x 2 + x + 1 for x = x 100 for x = 3 3. y+ 10 y 89 for y = 100 x x for x = 3 5. x x for x = p 2 + 2p 10 for p = 2 Solve the following algebraic equations. Show your transformation steps: 1 7. x + 3= y + 4 = z 13 = d = x = x + 5 = x + 12= y = 1

26 Problem Set #66 In the graph below, label the following: a) x and y axes b) Quadrants I - IV c) origin d) coordinates of points A-F e) location of points ( 7, 4); (4, 7); (7, 4); (8, 2); (12, 6); (0, 10)

27 Problem Set #67 Use graph paper to draw a Cartesian coordinate system and graph the following equations. Use a different graph for each equation y = x 2 2. x = 4 3. y = x 4. y = 1/x (Hint: find points for values of x equals positive and negative 1/5, 1/2, 1, 2, and 5 for x) 5. y = x 3 6. y = x 2 x 7. y = x 2 /4 8. y = 0 9. y = 2x y = x 2

28 Problem Set #68 Use your spreadsheet program to make graphs of the equations from Problem Set #67. Experiment with changing the scale of the axes; changing the style and color of the lines/points; graphing two or three equations in one chart; adding titles and axis labels.

29 Problem Set #69 Use an online equation graphing program to graph the following equations. Some possibilities for websites are: Notice that we can more easily graph complex equations than when we are drawing the graphs with paper and pencil. Experiment with the features of the program you are using, such as graphing multiple equations and adjusting the scale of the axes. 1. y = x 2 4x y = x 3 3. y = x 3 4. y = 1/x 5. y = 2 x 6. y = 2 x 7. y = 2 x + 2 x 8. y = 10 x^2 The following equations use mathematical operations you have not encountered in this class. Don t worry about them yet, but see what their graphs look like. 9. y = sin(x) 10. y = cos(x) 11. y = cos(10*x) 12. y = 10*sin(50*x)*e^( x) 13. y = abs(10*sin(50*x)*e^( x^2))

30 Problem Set #70 Graph the following equations on graph paper, in your spreadsheet program, and online: 1. y = 2x y = x 3 3. y = x 2 4. y = 3x y = x 3 3x 2

31 Problem Set #71 Graph the following linear equations. You may graph more than one equation per set of axes as long as the graph is not confusing. For each equation, identify the slope and the y-intercept. 1. y = 3x 4 2. y = 2x y = x 4. y = y = x y = x+ 3 2

32 Problem Set #72 Write down the equation for the lines in the following graphs

33 Problem Set #73 Here are the three forms of linear equations you have learned: Slope-intercept form: y = mx + b Point-slope form: y y 1 = m(x x 1 ) y2 y1 Two-point form: y y1 = ( x x1 ) x2 x 1 Write the correct linear equation and graph the following: 1. A line through the points (1, 0) and (4, 3) 2. A line with slope 2 through point ( 3, 3) 3. A line with slope ¾ and y-intercept 1 4. A line through the points ( 2, 1) and (0, 0) 5. A line through point (5, 6) with slope A line with slope 9 and y-intercept 100

34 Problem Set #74 1. Use what you learned about solving algebraic equations to fill out the following table for six different hikes that Tom took on six different days. Write the correct number or algebraic expression in the blanks. 2. Sandy plans to travel around the world, a distance of 24,900 miles, in 80 days. a) Write a distance-rate-time equation for the trip. b) Solve the equation for the rate to find what Sandy s average rate of speed will be in miles per day. c) On Tuesday, Sandy is already 560 miles from home. Write a distance-rate-time equation to show how far Sandy has gone from home as she travels on Tuesday at her average rate. 3. Jeff leaves work on his bicycle at 5:30 PM and starts toward his home 7 miles away. It takes Jeff one hour to get home on his bicycle. Write a distance-rate-time equation to show how far Jeff is from home during his bicycle ride.

35 Problem Set #75 Graph the following linear equations: 1. y = x y = 3x y = x+ 3 2 Write down the equation for the lines in the following graph: Refer to the equations in Problem Set #73 to write the correct equation for the following: 7. A line with slope 5 through point (0, 3). 8. A line through the points ( 4, 2) and (3, 3). 9. A line with slope ½ and y-intercept Todd runs at a rate of 8 miles per hour. At this pace, how long will it take Todd to run a marathon (assume 26 miles)? Write a distance-rate-time equation and solve it to find the answer.

36 Problem Set #76 Name each of the following polynomials by degree and number of terms, or state why it is not a polynomial. 1. 4y x x t 7 7t 6 + t 4 2t t 2 8t t 2 + 3t 4 6. x + 6x 9+ 2 x 7. 8d y 4 + y x 2 + 3x x 3 + 4x 2 2x + 1

37 Problem Set #77 Find the solutions using distribution. Show your steps as in this example: 0. 3(4 + 5) = = (5 3) = 2. 7(9 + 6) = 3. 4(x + 1) = 4. 9(1 x) = 5. x(2 + 4) = 6. x(x + 7) = 7. x(y + z) = 8. x 2 (4 + 6) = 9. y 2 (y + 1) = 10. y 2 (x + y) =

38 Problem Set #78 Find the following products of polynomials: 1. (2 + 6)(5 3) = 2. (x + 1)(x + 6) = 3. (4x 3)(2x + 1) = 4. (x + 1)(1 x) = 5. (3y + 7)(3y + 4) = 6. (x + 7)(x 2 + 2x + 1) = 7. (2z + 8)(z 3)(3z + 4) = 8. (3x 4)(x 2 + 4x + 6) = 9. (4y 1)(y + 3)(y 5) = 10. (2x 5)(x 2 6x + 5) =

39 Problem Set #79 Find the linear binomial factors of the following quadratic trinomials. Check your answers by finding the products. 1. x 2 + 6x + 8 = 2. y 2 6y + 8 = 3. z 2 + 8z + 12 = 4. a 2 + 7a + 12 = 5. b 2 9b + 20 = 6. c 2 2c + 1 = 7. d 2 5d + 4 = 8. x 2 + 7x + 6 = 9. y 2 + 7y + 10 = 10. x 2 6x + 5 =

40 Problem Set #80 Name the following polynomials by degree and number of terms: 1. 3x y z 2 3z d Use the distributive rule for the following: 5. a(b + 2) = 6. x 2 (y 2 + z 2 ) = 7. 4(2 + c) = 8. 2x(2y + z) = Find the following products of polynomials: 9. (x + 2)(x + 1) = 10. (2a + 3)(a 7) = 11. (4y 1)(y 2 2y + 1) = 12. (3z + 3)(3z 2 + 3z + 3) = Find the linear binomial factors of the following polynomials: 13. a 2 + 3a + 2 = 14. b 2 4b + 3 = 15. x x + 25 = 16. m 2 9m + 14 =

41 Problem Set #81 Solve the following simultaneous equations by adding or subtracting. 1. 3x + 4y = 2 3x 4y = x + y = 24 3x + 5y = x 9y = 55 9y + x = x 4y = 7 x + 6y = 3 5. y x = 7 x + 3y = x + 9y = 15 5x + 9y = x + 4y = 16 4x y = y 3x = 20 3x 4y = 4

42 Problem Set #82 Solve the following simultaneous equations by graphing them y= x 2 x + y = x y = 0 x + y = y = x y = x x + 4y = y = x x + y = 8 2x y = 4 5

43 Problem Set #83 Solve the following simultaneous equations by substitution. Check your answers. 1. x + 4y = 4 x y = 5 2. y = x 4 y = x x + y = 6 5x y = x 6y = 15 x + 2y = x y = 4 y + 10 = 10x 6. 3x + y = 10 y = x + 2

44 Problem Set #84 Determine whether the following equations are inconsistent, equivalent, or have solutions. If the equations have solutions, find the solutions. 1. 4x 3y = 5 6y 10 = 8x 2. 2x + 3y = 0 2x + 3y = 6 3. y = 3x + 2 y = 3x 4 4. x + 2y = 7 x y = x y = x = 3y 6. 3x + y = 10 y = 3x + 1

45 Problem Set #85 Solve the following simultaneous equations by the method of your choice. If they are inconsistent or equivalent, say so. 1. x + y = 6 y = 2x 2. x + 4y = 13 3x 2y = x 3y = 44 5x + 12y = x + 2y = 7 6x + 21 = 6y 5. y = 3x + 8 y + x = x + 5y = 10 y = 2x x + y = 4 2y 2 = 10x 8. 3x y = 0 x + y = 4 9. x + 2y = 4 y = x x + y = 3 x + y = 7

46 Problem Set #86 1. Loretta is 6 years older than Charlie. Six years ago she was twice as old as him. How old is each now? 2. A 25-foot-long board is to be cut into two parts. The longer part is to be 1 foot more than twice the shorter part. How long is each part? 3. Mr. Sanborn wished to invest a sum of money so that the interest each year would pay for his son s college expenses. If the money was invested at 8% and the college expenses were $10,000 each year, how much should Mr. Sanborn invest?

47 Problem Set #87 1. Matt has some coins in his pocket consisting of dimes, nickels and pennies. He has two more nickels than dimes, and three times as many pennies as nickels. How many of each kind of coin does he have if the total value is 52 cents? x: number of dimes x + 2: number of nickels 3(x + 2): number of pennies 2. In a 3-digit number, the hundreds digit is four more than the units (ones) digit, and the tens digit is twice the hundreds digit. If the sum of the three digits is 12, find the three digits. Write the number. (Hint: Don t worry about the fact that it is a three digit number. Just find the three numbers.) 3. A rectangle has a length which is 4 feet less than three times the width. The perimeter is 224 feet. What are the dimensions of the rectangle? (Perimeter is the length of the edges of the rectangle, that is, the sum of the four sides.)

48 Problem Set #88 1. Sandra works Saturdays in a nut shop. She is supposed to add some Spanish peanuts worth 84 cents a pound to 40 pounds of Virginia peanuts worth 71 cents a pound to make a mixture worth 79 cents a pound. Find out how many pounds of Spanish peanuts she should add by doing each of the following: a) Letting x represent the number of pounds of Spanish peanuts added and y the number of pounds of peanuts in the mixture, write an equation relating x, y, and 40. b) In terms of x, how much are the Spanish peanuts worth? c) In terms of y, how much is the mixture worth? d) Write an equation relating the worth of the two kinds of peanuts used to the worth of the mixture. e) Solve the simultaneous equations that you have written for x and y. f) How many pounds of Spanish peanuts should Sandra use? 2. On a fishing trip, Huck caught 31 fish, some of which were bullheads averaging 1.5 pounds each the rest of which were catfish averaging 5 pounds each. The entire catch weighed 92 pounds. Find out how many fish of each kind Huck caught by doing each of the following: a) Letting x and y represent the numbers of bullheads and catfish, respectively, write a pair of equations, one relating the numbers of fish and the other relating their weights. b) Solve the equations. c) How many fish of each kind did he catch?