MFM1P Foundations of Mathematics Unit 3 Lesson 11

Transcription

1 The Line Lesson

2 MFMP Foundations of Mathematics Unit Lesson Lesson Eleven Concepts Overall Expectations Apply data-management techniques to investigate relationships between two variables; Determine the characteristics of linear relations; Demonstrate an understanding of the constant rate of change and its connection to linear relations; Connect various representations of a linear relation, and solve problems using the representations. Specific Expectations Construct tables of values and graphs, using a variety of tools; Construct tables of values, scatter plots, and lines or curves of best fit as appropriate using a variety of tools; Identify through investigation, some properties of linear relations; Determine values of a linear relation by using a table of values, by using the equation of the relation, and by interpolating or extrapolating from the graph of the relation; Express a linear relation as an equation in two variables, using the rate of change and the initial value. Equation of a Line The equation of a line has basic forms. One being the y-intercept form and the other is called standard form. y - intercept form takes the form y = mx + b Y-intercept Form It is called y-intercept form because we can use the y-intercept in the equation to help us understand and graph the equation. y = mx + b m value is the slope of the line. b s value is the spot on the y axis where the line intercepts the y axis. Copyright 005, Durham Continuing Education Page of 5

3 MFMP Foundations of Mathematics Unit Lesson Example State the slope and y-intercept for the following equations. a) y = x + 6 b) y = x Solution a) y = x + 6 rise slope = m = = = y - intercept = b = +6 run b) y = x rise slope = m = = y - intercept = b = - run Example Graph the following equations using the slope and y-intercept. a) y = x + b) y = x Copyright 005, Durham Continuing Education Page of 5

4 MFMP Foundations of Mathematics Unit Lesson Solution First plot the y-intercept. rise a) y = x + m = - = run = and b = + Starting at the y-intercept go down and right then down again and right one again and so on Then draw a line through the points plotted to create your line. y = x + Copyright 005, Durham Continuing Education Page 4 of 5

5 MFMP Foundations of Mathematics Unit Lesson b) y = x y = x Example Find the point of intersection of these two equations. (Solve the system of equations graphically) Solution y = x + y = x + 7 Copyright 005, Durham Continuing Education Page 5 of 5

6 MFMP Foundations of Mathematics Unit Lesson The point of intersection is (-, 5) which solves the system of equations. (-, 5) is the only two ordered pairs that will satisfy both equations. y = x + y = x = ( ) + 5 = = 5 5 = 5 Support Questions. State the slope and y-intercept of the equations below, then properly graph and label the equations using the slope and y - intercept. a) y = 4x + b) y = x 4 c) y = x + 7 d) y = x 5. Show by substitution which of the order pairs satisfies that equation. a) y = x + 4 (-, -5), (4, -4), (-, 7), (, -0) b) y = x + 4 c) y = x (9, 5), (8, -5), (, -7), (, -8) (, -), (-4, 6), (4, -6), (-, -). Solve for the system of equations by graphing. (Find the point of intersection) y = x + 4 a) b) y = x + 5 y = x + 6 y = x + 4 c) y = x y = 4x + Copyright 005, Durham Continuing Education Page 6 of 5

7 MFMP Foundations of Mathematics Unit Lesson Parallel and Perpendicular Lines Lines that are parallel to each other have the same slope. Lines that are perpendicular to each other will have inverted slopes with opposite polarity. Example Which of the following equations are parallel to each other? y = 5x y = 5x + y = x y = 5x + Solution y = 5x and y = 5x + are parallel to each other because they have the same slope of 5x. y = 5x + y = 5x Example Which of the following equations are perpendicular to each other. y = x + y = x + y = x + 6 y = x Copyright 005, Durham Continuing Education Page 7 of 5

8 MFMP Foundations of Mathematics Unit Lesson Solution y = x + and y = x + 6 are perpendicular to each other because they have slope inverted of each other and opposite polarity. and Perpendicular means to cross at 90. y = x+ 6 y = x + Support Questions 4. Circle then graph the pair of equations that are parallel. y = x + y = x + y = x 5 y = x 6 y = x 7 5. Circle then graph the pair of equations that are perpendicular. y = x + y = x + 7 y = x 5 y = x 6 y = x + Copyright 005, Durham Continuing Education Page 8 of 5

9 MFMP Foundations of Mathematics Unit Lesson Key Question #. State the slope and y-intercept of the equations below, then properly graph and label the equations using the slope and y - intercept. (8 marks) a) y = x b) y = x + 4 c) y = x + d) y = x. Show by substitution which of the order pairs satisfies that equation. ( marks) a) y = 5x (-, -5), (4, -4), (-, ), (, -0) b) y = x + (9, 5), (8, -5), (, -7), (, 5) c) y = x + 7 (, -), (-4, ), (, -6), (-, -). Solve for the system of equations by graphing. (Find the point of intersection) ( marks) y = x + 4 a) b) y = x + 5 y = x y = x + 4 c) y = x + y = x 5 4. Circle then graph the two pairs of equations that are parallel. (4 marks) y = x + y = x + y = x 5 y = x 6 y = x 7 5. Circle then graph the pairs of equations that are perpendicular. (4 marks) y = x + y = x + 7 y = x 5 y = x 6 y = x + Copyright 005, Durham Continuing Education Page 9 of 5

10 MFMP Foundations of Mathematics Unit Lesson Key Question # 6. State the x - intercept, y - intercept and slope for each line. (4 marks) a) b) 7. Explain the steps needed to graph a line using an equation in y - intercept form and without using a table of values. (4 marks) Copyright 005, Durham Continuing Education Page 0 of 5

11 Direct and Partial Variation Lesson

12 MFMP Foundations of Mathematics Unit Lesson Lesson Twelve Concepts Overall Expectations Apply data-management techniques to investigate relationships between two variables; Determine the characteristics of linear relations; Demonstrate an understanding of the constant rate of change and its connection to linear relations; Connect various representations of a linear relation, and solve problems using the representations. Specific Expectations Construct tables of values and graphs, using a variety of tools; Construct tables of values, scatter plots, and lines or curves of best fit as appropriate using a variety of tools; Identify through investigation, some properties of linear relations; Determine other representations of a linear relation arising from a realistic situation, given one representation; Determine values of a linear relation by using a table of values, by using the equation of the relation, and by interpolating or extrapolating from the graph of the relation; Express a linear relation as an equation in two variables, using the rate of change and the initial value; Describe the effects on a linear graph and make the corresponding changes to the linear equation when the conditions of the situation they represent are varied; Determine graphically the point of intersection of two linear relations, and interpret the intersection point in the context of an application. Direct and Partial Variation Direct Variation Direct Variation is a relation that is of the form y = mx. The graph of y = mx is a straight line with the slope of m. The line y = mx always passes through the order pair (0, 0). (0, 0) is called the origin. The relation y = mx represents direct variation because there is a direct relationship. Copyright 005, Durham Continuing Education Page of 5

13 MFMP Foundations of Mathematics Unit Lesson Example Graph each equation which models direct variation. a) y = x b) y = x Solution a) y = x b) y = x Slope is and passes through the origin. Slope is and passes through the origin. Support Questions. State the value of m in each equation of the form y = mx. a) y = 4x b) y = x c) y = x d) y = x 5. Write an equation of the line through the origin with each slope. a) m = 5 b) m = c) 7 m = d) m = 4 Copyright 005, Durham Continuing Education Page of 5

14 MFMP Foundations of Mathematics Unit Lesson. Find the slope of each line, and then write its equation. a) b) 4. Graph each line. a) y = x b) y = x 5 5. Johnny earns $6 for every hour worked. Write an equation for this statement, then create a table of values and graph. Partial Variation Partial Variation is a relation that is of the form y = mx+b. The graph of y = mx+b is a straight line with the slope of m and a y-intercept of b. The line y = mx+b does not pass through the origin. The relation y = mx +b represents partial variation because the value of y varies partially with the value of x. Example Graph each equation which models partial variation. Copyright 005, Durham Continuing Education Page 4 of 5

15 MFMP Foundations of Mathematics Unit Lesson 4 a) y = x b) y = x + 5 Copyright 005, Durham Continuing Education Page 5 of 5

16 MFMP Foundations of Mathematics Unit Lesson Solution 4 a) y = x b) y = x + 5 Slope is - and intersects the y- axis at. Slope is 5 4 and intersects the y-axis at +. Support Questions 6. Write an equation of the line with each slope and y-intercept. a) m = 5, b = b) m =, b = -4 c) 7 m =, b = Find the slope and y-intercept of each line, and then write its equation. a) b) Copyright 005, Durham Continuing Education Page 6 of 5

17 MFMP Foundations of Mathematics Unit Lesson 8. Graph each line. a) y = x + b) y = x 6 c) y = x 4 9. Noah earns a $00 a week and $ for every hour worked. Write an equation for this statement, then create a table of values and graph. Key Question #. State the value of m in each equation of the form y = mx. ( marks) a) y = 7x b) y = x c) y = x d) y = x 7 8. Write an equation of the line through the origin with each slope. ( marks) a) m = 7 b) m = c) m = d) m = 8. Find the slope of each line, and then write its equation. ( marks) a) b) 4. Graph each line. ( marks) a) y = x b) y = x c) y = x 5 5. Brook spends $4.00 each day for lunch on work days. Write an equation for this statement, then create a table of values and graph. ( marks) 6. Write an equation of the line with each slope and y-intercept. ( marks) a) m =, b =0 b) m =, b = - c) m =, b = +7 4 Copyright 005, Durham Continuing Education Page 7 of 5

18 MFMP Foundations of Mathematics Unit Lesson Key Question # 7. Find the slope and y-intercept of each line, and then write its equation. (4 marks) a) b) 8. Graph each line. ( marks) a) y = 4x b) y = x + c) y = x The length of time to set up is 00 min. The time to make paint each sign is 5 min. Write an equation for this statement, then create a table of values and graph. ( marks) 0. Stephen graphed the equation y = x on a Cartesian plane. When he checked with a classmate, he realized the graph was different. Is Stephen s graph correct? If so, explain how you know. If not, explain what Stephen did wrong. (4 marks) Copyright 005, Durham Continuing Education Page 8 of 5

19 Scatter Plots Lesson

20 MFMP Foundations of Mathematics Unit Lesson Lesson Thirteen Concepts Overall Expectations Apply data-management techniques to investigate relationships between two variables; Determine the characteristics of linear relations; Demonstrate an understanding of the constant rate of change and its connection to linear relations; Connect various representations of a linear relation, and solve problems using the representations. Specific Expectations Construct tables of values and graphs, using a variety of tools; Construct tables of values, scatter plots, and lines or curves of best fit as appropriate using a variety of tools; Identify through investigation, some properties of linear relations; Determine other representations of a linear relation arising from a realistic situation, given one representation; Determine values of a linear relation by using a table of values, by using the equation of the relation, and by interpolating or extrapolating from the graph of the relation; Scatter Plots and Line of Best Fit Scatter plots A scatter plot is a graph of data that is a series of points. Example Study for that Test Percent on Exam Here a set of data was plotted. Hours studying vs. Percent of Exam Hours of study Copyright 005, Durham Continuing Education Page 0 of 5

21 MFMP Foundations of Mathematics Unit Lesson Data in a scatter plot can have a positive/negative or no correlation No Correlation Negative Correlation Positive Correlation Example Make a scatter plot for the men s times. Plot the year on the x-axes and the times on the y-axes. Year Time Year Time Year Time Copyright 005, Durham Continuing Education Page of 5

22 MFMP Foundations of Mathematics Unit Lesson Solution Winning Times for 00m Time (seconds) Year Line of Best Fit Line of best fit is a line that passes as close as possible to a set of plotted points. Example Find the line of best fit for the data in the previous example. Solution This is the y-intercept. Winning Times for 00m Time (seconds) Year First pick two points that represent the general center of the points plotted. Copyright 005, Durham Continuing Education Page of 5

23 MFMP Foundations of Mathematics Unit Lesson Then draw the line of best fit through those points generally dividing the plotted points evenly on both sides. Example What is the approximate equation for the line of best fit in the previous example? Solution Choose the coordinates of the two previously chosen points used to draw the line of best fit. (985,.7) and (989,.4) slope = m = y x y x.4.7 = m = 0. 4 = y intercept = b = + Therefore the equation of the line of best fit is y = x +. Extrapolation and Interpolation Extrapolation is extending a graph to estimate the values that are beyond the table of values. Interpolation is using a graph to estimate the value that are not in the table of values but are within the range of the lowest and largest values presented in the table of values. Example a) Using extrapolation what would be the approximate distance for the discus will be thrown during the 004 Summer Olympics? b) Using Interpolation how far was the discus thrown in 95? Copyright 005, Durham Continuing Education Page of 5

24 MFMP Foundations of Mathematics Unit Lesson Women's Olympic Discus Records Distance (m) Year Solution a) Using extrapolation, what would be the approximate distance for the discus will be thrown during the 004 Summer Olympics? approximately 78 metres Women's Olympic Discus Records Distance (m) Draw a vertical line from 004 until you hit the line of best fit then run horizontally until you hit the value on the y axis Year Copyright 005, Durham Continuing Education Page 4 of 5

25 MFMP Foundations of Mathematics Unit Lesson b) Using Interpolation, how far was the discus thrown in 95? Approximately 5 metres Women's Olympic Discus Records Distance (m) Draw a vertical line from 95 until you hit the line of best fit then run horizontally until you hit the value on the y axis Year Support Questions. State whether the scatter plot has a positive, negative or no correlation. a) b) c). The table following shows the winning times for the 800-m race at the Olympic Summer Games. Copyright 005, Durham Continuing Education Page 5 of 5

26 MFMP Foundations of Mathematics Unit Lesson Year Men s Time a) Construct a scatter plot and line of best fit for the data. b) What is the equation of the line of best fit? c) What is the approximate winning time in the year 00? d) What approximate year does the time drop below 04 seconds? Key Question #. State whether the scatter plot has a positive, negative or no correlation. ( marks) a) b) c). The table below shows the winning heights in a men s high jump competition. (8 marks) Year Winning Country Jump in Height (m) 9 Canada.9 9 United States England United States.6 98 United States. 00 Australia.4 a) Create a properly labelled Scatter Plot using the data given in the table. b) Draw a line of best fit. c) What is the approximate slope of the line of best fit? d) Using extrapolation, what would the approximate winning height be in 0? Copyright 005, Durham Continuing Education Page 6 of 5

27 MFMP Foundations of Mathematics Unit Lesson Key Questions #. The table below shows the percentage of high school girls who smoked more than one cigarette during the previous year. (8 marks) Year Percent a) Graph the data in a scatter plot. b) Determine the equation of the line of best fit. c) Use your equation to predict the percent of high school girls who smoke more than one cigarette in 000. d) Approximately, what percent of girls smoked more than one cigarette in 98 and 994? Copyright 005, Durham Continuing Education Page 7 of 5

28 Averages Lesson 4

29 MFMP Foundations of Mathematics Unit Lesson 4 Lesson Fourteen Concepts Overall Expectations Apply data-management techniques to investigate relationships between two variables; Specific Expectations Pose problems, identify variables, and formulate hypotheses associated with relationships between two variables; Describe trends and relationships observed in data, make inference from data, compare the inferences with hypotheses about the data, and explain any differences between the inferences and the hypotheses. Measures of Central Tendency There are three different types of averages: Mean, Median and Mode. Mean Average Mean is a single number that is used to represent a set of numbers. To find the mean average, all the numbers in the data set are added together and the sum is divided by the number of entries in the data set. Example Find the mean of the following sets of numbers. a) {,, 4, 7, 7, 8, 9, } b) {4, 7,, 5,, 8,, 9, 4, 7, 5, } Solution a) {,, 4, 7, 7, 8, 9, } mean = 8 50 mean = 8 mean = is the sum of the all the values in the numerator. Divide by 8 because there are 8 numbers in the set. Copyright 005, Durham Continuing Education Page 9 of 5

30 MFMP Foundations of Mathematics Unit Lesson 4 b) {4, 7,, 5,, 8,, 9, 4, 7, 5, } mean = 60 mean = mean 4. 6 Support Questions. Calculate the mean average for each set of numbers. a) {, 6,, 7,, 5, 8} b) {, 8,, 5, 8,, 5, 9, } c) {75, 4, 57, 69, 84, 88, 94, 97, 5, 4, 45, 6, 6, 57}. The salaries of the Toronto Maple Leafs is given below. What is the mean average for a player s salary? $,750,000 $950,000 $5,500 $,00,000 $95,000 $500,000 $,000,000 $900,000 $450,000 $,000,000 $850,000 $400,000 $,000,000 $700,000 $,600,000 $650,000 $,500,000 $585,640 $,400,000 $575,000 Copyright 005, Durham Continuing Education Page 0 of 5

31 MFMP Foundations of Mathematics Unit Lesson 4 Median Average Median average is the middle number of a set of numbers arranged in numerical order. If there are an even number of values in the set of data then the there will be two middle numbers and the mean of those two numbers is the median average. Example Find the median of the following sets of numbers. a) {7, 9,,, 7,,, 4} b) {4, 7,, 5, 8,, 9, 4, 7, 5, } Solution a) {7, 9,,, 7,,, 4} Arrange in numerical order. {,, 4, 7, 7, 9,, } There are an equal number of values on both sides of the median. In this example there are 4 on both sides. The middle value of this set of data is 7, therefore the median average is 7. Median = 7 b) {4, 7,, 5, 8,, 9, 4, 7, 5, } Arrange in numerical order. {,,, 4, 4, 5, 5, 7, 7, 8, 9} mean = 9 mean = mean = 4.5 This time there are two middle numbers so the median is the mean of 4 and 5. Therefore the median of the set of data is 4.5. Median average = 4.5 Copyright 005, Durham Continuing Education Page of 5

32 MFMP Foundations of Mathematics Unit Lesson 4 Support Questions. Calculate the median average for each set of numbers. a) {, 6,, 7,, 5, 8} b) {, 8,, 5, 8,, 5, 9, } c) {75, 4, 57, 69, 84, 88, 94, 97, 5, 4, 45, 6, 6, 57} 4. The salaries of the Toronto Maple Leafs is given below. What is the median average for a player s salary? $4,750,000 $950,000 $5,500 $4,00,000 $95,000 $500,000 $,000,000 $900,000 $450,000 $,500,000 $850,000 $400,000 $,000,000 $700,000 $,600,000 $850,000 $,500,000 $785,640 $,400,000 $475,000 Copyright 005, Durham Continuing Education Page of 5

33 MFMP Foundations of Mathematics Unit Lesson 4 Mode Average Mode average is the most common value in a set of numbers. Example Find the mode of the following sets of numbers. a) {7, 9,,, 7, 8,,, 4} b) {4, 7,, 5,, 8,, 8, 4, 7, 5,, 8, 8, 9} Solution a) {7, 9,,, 7, 8,,, 4} Arrange in numerical order because it is easier to se the repeated numbers. {,, 4, 7, 7, 8, 9,, } 7 is the most common number in the set so therefore, the mode average = 7. b) {4, 7,, 5,, 8,, 8, 4, 7, 5,, 8, 8, 9} Arrange in numerical order because it is easier to se the repeated numbers. {,,,, 4, 4, 5, 5, 7, 7, 8, 8, 8, 8, 9} 8 is the most common number in the set so therefore, the mode average = 8. Copyright 005, Durham Continuing Education Page of 5

34 MFMP Foundations of Mathematics Unit Lesson 4 Support Questions 5. Calculate the mode average for each set of numbers. a) {, 6,, 7,, 5, 8} b) {, 8,, 5, 8,, 5, 9,, 8} c) {75, 4, 57, 69, 84, 88, 94, 97, 5, 4, 45, 6, 6, 57, 8, 4, 5} 6. The salaries of the Toronto Maple Leafs is given below. What is the mode average for a player s salary? $4,750,000 $950,000 $5,500 $4,00,000 $95,000 $55,000 $,000,000 $900,000 $400,000 $,500,000 $850,000 $400,000 $,000,000 $850,000 $,600,000 $850,000 $,500,000 $785,640 $,400,000 $475, Find the mean, median and mode for the given set of numbers. {6, 74, 77, 68, 7, 74, 70, 65} 8. Determine each measure of central tendency (mean, median and mode) based on the table given below. Annual Salary ($) Frequency Copyright 005, Durham Continuing Education Page 4 of 5

35 MFMP Foundations of Mathematics Unit Lesson 4 Key Question #4. Find the mean, median and mode for each set of numbers. ( marks) a) {4, 47,, 6, 6, 4, 8, 6, 48} b) {,, 6, 4,, 9, 6, 45,, 6, 8, 6} c) {8, 6,, 4, 7, 6,, 5,, 7, 9, 7}. Two friends went golfing. Their score card is given below. (6 marks) Hole Total Steve Mary a) Calculate the mean score for each player. b) Calculate the mean score for the two players together. c) Calculate the median score for each player. d) Calculate the median score for the two players together. e) Determine the mode for each player. f) Determine the mode for the two players together.. The average price of gas in cents per litre is given for each province. ( marks) Province Cost of Gas per Litre (cents) British Columbia 75. Alberta 68.5 Saskatchewan 69. Manitoba 7. Ontario 75. Quebec 74.5 New Brunswick 74.6 Nova Scotia 76. Prince Edward Is Newfoundland 77.9 a) What is the mean price of gas for all the Canadian Provinces? b) What is the median price of gas for all the Canadian Provinces? Copyright 005, Durham Continuing Education Page 5 of 5

36 MFMP Foundations of Mathematics Unit Lesson 4 Key Question #4 4. Is each statement always true, sometimes true or sometimes false? Explain and provide an example to illustrate your understanding. (8 marks) a) If a list of numbers has a mode, it is one of the numbers in the list? b) The median of a list of whole numbers is a whole number. c) The mean of a list of numbers is one of the numbers in the list? d) The mean, median, and mode of a list of numbers are not equal. 5. The April batting statistics of the 004 Toronto Blue Jays is given below. (6 marks) a) What is the team s mean batting average (AVG)? b) What is the team s mode for doubles(b)? c) What is the team s mean at bats (AB)? d) What is the team s median for strikeouts (S0)? e) What is the team s mean slugging percents (SLG)? f) What is the team s mean, median and mode for home runs (HR)? 6. Determine each measure of central tendency based on the table given below. (6 marks) Annual Frequency Salary ($) Copyright 005, Durham Continuing Education Page 6 of 5

37 Perimeter Lesson 5

38 MFMP Foundations of Mathematics Unit Lesson 5 Lesson Fifteen Concepts Overall Expectations Determine, through investigation, the optimal values of various measurements of rectangles; Solve problems involving the measurements of two-dimensional shapes and volumes of three-dimensional figures. Specific Expectations Determine the minimum perimeter of a rectangle with a given area by constructing a variety of rectangles, using a variety of tools; Solve problems that require maximizing the area of a rectangle for a fixed perimeter of minimizing the perimeter of a rectangle for a fixed area Perimeter Perimeter is the distance around an object. If that object is a circle then the perimeter is called circumference. Formulas to be used to calculate perimeter. P = l + w or P = ( l + w) or P = l + w + l + w P = b + c or P = ( b + c) or P = b + c + b + c P = a + b + c Copyright 005, Durham Continuing Education Page 8 of 5

39 MFMP Foundations of Mathematics Unit Lesson 5 P = a + b + c + d P = dπ π.4 d=r d: diameter r: radius or P = π r Example Copyright 005, Durham Continuing Education Page 9 of 5

40 MFMP Foundations of Mathematics Unit Lesson 5 Solution a) 6cm 0 cm 8 cm P = a + b + c P = P = 4 cm d = 0 cm b) P = πd P = (.4)( 0 P =.4 cm ) c) 5 cm. 8 c 8 cm. P = (l + w) P = (8 + 5) P = () P = 46cm Copyright 005, Durham Continuing Education Page 40 of 5

41 MFMP Foundations of Mathematics Unit Lesson 5 d) cm cm Only include sides instead of 4 sides of the rectangle since the 4 th side is ½ of the circle πd P = l + w + l + P = P = P = 74.84cm (.4)( ) Circumference of circle but only ½ of it since the perimeter does not include the inner portion Example Find the perimeter. 5 m 5 m 0 m 8m Copyright 005, Durham Continuing Education Page 4 of 5

42 MFMP Foundations of Mathematics Unit Lesson 5 Solution It is important to recognize the lengths of all side of the object. 5 m These two lengths together make the part of the length of the opposite side = m 5 m 5m 0 m 8m All sides that have this single tick mark are considered the same length. All sides that have this double tick mark are considered the same length. 5m 5m m 0 m These two lengths together make the length of the opposite side = 0 m So the Perimeter is P = = 96 m or P = 4(5) + (0) = 96 m Copyright 005, Durham Continuing Education Page 4 of 5

43 MFMP Foundations of Mathematics Unit Lesson 5 Support Questions. Calculate the perimeter for each of the following objects. a) b) c) 7cm 4cm 8.5 cm cm 5cm cm cm d) e) 5 cm f) cm 6 cm.5 cm Copyright 005, Durham Continuing Education Page 4 of 5

44 MFMP Foundations of Mathematics Unit Lesson 5 Key Question #5. Calculate the perimeter for each of the following objects. (9 marks) a) b) c) 8cm 5cm 0 cm 4 cm 6cm 5cm cm d) e) 4 cm f) 8cm 7 cm.5 cm g) h) 0 m 4 m 7 m 6 m 5 m m 7 m i) 8 cm m Copyright 005, Durham Continuing Education Page 44 of 5

45 MFMP Foundations of Mathematics Unit Lesson 5 Key Question #5. Explain how you could find the circumference of a circle given its area. ( marks). A rectangular yard has an area of 4 m. What are four possible perimeter s for this yard? (4 marks) 4. When a circle s radius doubles so does its circumference. True or False? Prove your answer with an example. (4 marks) 5. What is the total amount of edging that would be required to cover all edges of a cube measuring 0 cm on all edges? (4 marks) Copyright 005, Durham Continuing Education Page 45 of 5

46 MFMP Foundations of Mathematics Support Question Answers Support Question Answers Lesson. a. slope = 4, y-int = b. slope =, y-int = 4 c. slope =, y-int = 7 d. slope =, y-int = 5. a. (4, -4) b. (, -8) c. (-, -) y = x + 4 y = x + 4 y = x ( 4) = (4) + 4 = ( ) ( 8) = () + 4 = = 4 = 4 8 = 9 + = 8 = 8 Note: (4, -6) also works. a. b. c. Copyright 005, Durham Continuing Education Page 46 of 5

47 MFMP Foundations of Mathematics Support Question Answers 4. y = x + y = x 5 5. y = x + 7 y = x 6 Lesson. a. 4 b. c. d. 5. a. y = 5x b. y = x c. y = x d. y = x a. y = x b. y = x 4 4. a. b. Copyright 005, Durham Continuing Education Page 47 of 5

48 MFMP Foundations of Mathematics Support Question Answers 5. E = 6h 6. a. y = 5x + b. y = x 4 c. y = x a. y = x + 5 b. y = 5 8. a. b. c. 9. E = h + 00 Copyright 005, Durham Continuing Education Page 48 of 5

49 MFMP Foundations of Mathematics Support Question Answers Lesson. a. no correlation b. positive correlation c. negative correlation. a. 800 Metre Times Time (sec) Year. b. Equation of best fit Use the coordinates y slope = x y int = 07 y x y = x + 07 c. 0 sec d. 98 = (964,05.) and (988,0.45) = 4 = Copyright 005, Durham Continuing Education Page 49 of 5

50 MFMP Foundations of Mathematics Support Question Answers Lesson a b. = c / = $ a. {,,, 5,6,7, 8} median = 5 b. {,5,,8, 8,9,,,5} median = 8 c. { 4,4,45,5,57,57, 6,6, 69,75,84,88,94,99} = = 6.5 median = = = 9500 median = $ a. (occurs times) b. 8 (occurs three times) c. 4 (occurs times) 6. $ mean = ( ) = median = 6,65,70, 7,74,74,77, = 7 { } mode = mean = median = = $46875 mode = 5000 $ Copyright 005, Durham Continuing Education Page 50 of 5

51 MFMP Foundations of Mathematics Support Question Answers Lesson 5. a. b. c. d. P = P = (b + c) P = (l + w) P = P = 5 cm P = (4 + 5) P = (8.5 + ) P = 4.5 cm P = (9) P = (.5) P = 8 P =.5 e. f. g. C = πr P = 4(l) P = C = (.4)(5) C =.4 cm P = 4() P = 44 cm P = 60 m h. i. πr P = P = ( πr) (.4)(5) P = 58 + P = ()(.4)() P = 7.7 cm P = P = 80.5 cm Copyright 005, Durham Continuing Education Page 5 of 5