MPM1D - Principles of Mathematics Unit 3 Lesson 11

Transcription

1 The Line Lesson

2 MPMD - Principles of Mathematics Unit Lesson Lesson Eleven Concepts Introduction to the line Standard form of an equation Y-intercept form of an equation Converting to and from standard to -intercept form Parallel lines Perpendicular lines Point of intersection of two lines x and intercepts Equation of a Line The equation of a line has basic forms. One is -intercept form and the other is called standard form. -intercept form takes the form = mx+ b Standard form looks like Ax +B + C=0 Y-intercept Form It is called -intercept form because we can use the -intercept in the equation to help us understand and graph the equation. = mx + b m value is the slope of the line. b s value is the spot on the axis where the line intercepts the axis. Example State the slope and -intercept for the following equations. a) = x+ 6 b) = x Copright 004, Durham Continuing Education Page of 5

3 MPMD - Principles of Mathematics Unit Lesson Solution a) = x+ 6 rise slope = m = = = -intercept = b = +6 run b) = x rise slope = m = = -intercept = b = - run Example Graph the following equations using the slope and -intercept. a) = x+ b) = x Solution rise a) = x+ m = - = = and b = + run First plot the -intercept. Starting at the -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 our line. = x+ Copright 004, Durham Continuing Education Page of 5

4 MPMD - Principles of Mathematics Unit Lesson b) = x = x Example Find the point of intersection of these two equations. (Solve the sstem of equations graphicall) = x+ = x+ Solution The point of intersection is (-, 5) which solves the sstem of equations. Copright 004, Durham Continuing Education Page 4 of 5

5 MPMD - Principles of Mathematics Unit Lesson (-, 5) is the onl ordered pair that will satisf both equations. = x+ = x + ( 5 = + 5 = 5 ) 5 = + 5 = 5 Support Questions. State the slope and -intercept of the equations below, then properl graph and label the equations using the slope and - intercept. a) = 4x+ b) = x 4 c) = x+ d) = x 5. Show b substitution which of the order pairs satisfies that equation. a) = x+ 4 (-,-5), (4,-4), (-,), (,-0) b) = x+ (9,5), (8,-5), (,-), (, -8) 4 c) = x (,-), (-4,6), (4,-6), (-,-). Solve for the sstem of equations b graphing. (Find the point of intersection) = x+ 4 a) b) = x+ 5 = x+ 6 = x+ 4 c) = x = 4x+ Copright 004, Durham Continuing Education Page 5 of 5

6 MPMD - Principles of Mathematics Unit Lesson Converting to and from Y-intercept to Standard Form Example Convert into standard form. a) = x+ Solution Needs to be in the form Ax + B + C = 0. Algebra is used to convert into standard form. = x+ 6 ( ) = x+ ( ) + x = x+ x+ 6 + x = 6 + x 6= 6 6 x+ 6= 0 Multipl each term b to eliminate the fraction. A=, B= and C=-6 Example Convert into -intercept form. a) x+ 4 + = 0 Solution - Convert into -intercept form. x+ 4 + = 0 x x+ 4 + = 0+ x 4 + = x 4 + = x 4 = x 4 x = 4 4 = x 4 4 Copright 004, Durham Continuing Education Page 6 of 5

7 MPMD - Principles of Mathematics Unit Lesson Support Questions 4. Convert the following linear equations from -intercept form to standard form. a) = x+ b) = x c) = 5x d) = x+ 5. Convert the following linear equations from standard form to -intercept form. a) x + 6=0 b) x+ 5 0= 0 c) 5x + =0 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 polarit. Copright 004, Durham Continuing Education Page of 5

8 MPMD - Principles of Mathematics Unit Lesson Example Which of the following equations are parallel to each other? = 5x = 5x+ = x = 5x+ Solution = 5x and = 5x+ slope of 5x. are parallel to each other because the have the same = 5x+ = 5x Copright 004, Durham Continuing Education Page 8 of 5

9 MPMD - Principles of Mathematics Unit Lesson Example Which of the following equations are perpendicular to each other. = x+ = x+ Solution = x+ 6 = x = x+ and = x+ 6 are perpendicular to each other because the have slope inverted of each other and opposite polarit. and Perpendicular means to cross at 90. = x+ 6 = x+ Support Questions 6. Identif then graph the pair of equations that are parallel. = x+ = x+ = x 5 = x 6 = x. Identif then graph the pair of equations that are perpendicular. = x+ = x+ = x 5 = x 6 = x+ Copright 004, Durham Continuing Education Page 9 of 5

10 MPMD - Principles of Mathematics Unit Lesson Finding the x intercept and the intercepts The x intercept is where a line intersects or hits the x axis and the intercept is where that same line intersects the axis. Example Find the x and intercepts for the equation x + 5 = 0. Solution To find the x intercept: = (0) = 0. Since this equals zero we can just ignore the part of the equation. Set = 0 Therefore we ignore the portion of the equation and solve for x. x 5 = 0 x 5+ 5 = 0+ 5 x = 5 x 5 = 5 x = This is the x intercept. Where the line x + -5=0 hit the x-axis. To find the intercept: Set x = 0 Therefore we ignore the x portion of the equation and solve for. 5 = = 0+ = 5 5 = 5 = 5 x = (0) = 0. Since this equals zero we can just ignore the x part of the equation. This is the intercept. Where the line x + -5=0 hit the -axis. Copright 004, Durham Continuing Education Page 0 of 5

11 MPMD - Principles of Mathematics Unit Lesson Support Questions 8. Find the x and intercepts for each of the following equations. a) x + 6=0 b) x+ 5 0= 0 c) 5x + =0 9. Find the x and intercepts for each of the following equations. a) = x+ b) = x Ke Question #. State the slope and -intercept of the equations below, then properl graph and label the equations using the slope and - intercept. (8 marks) a) = x b) = x+ 4 c) = x+ d) = x. Show b substitution which of the order pairs satisfies that equation. ( marks) a) = 5x (-,-5), (4,-4), (-,), (,-0) b) = x+ (9,5), (8,-5), (,-), (, 5) c) = x+ (,-), (-4,), (,-6), (-,-). Solve for the sstem of equations b graphing. (Find the point of intersection) (6 marks) = x+ 4 = x = x+ a) b) c) = x+ 5 = x 5 = x+ 4 Copright 004, Durham Continuing Education Page of 5

12 MPMD - Principles of Mathematics Unit Lesson Ke Question # (continued) 4. Convert the following linear equations from -intercept form to standard form. (4 marks) a) = x b) = x c) = x+ d) = x+ 5. Convert the following linear equations from standard form to - intercept form. ( marks) a) 5 x + =0 b) x+ 4= 0 c) 6x + 9=0 6. Identif then graph the pair of equations that are parallel. (4 marks) = x+ = x+ = x 5 = x 6 = x. Identif then graph the pair of equations that are perpendicular. (4 marks) = x+ = x+ = x 5 = x 6 = x+ 8. Find the x and intercepts for the following equations. (5 marks) a) 5 x + =0 b) x+ 4= 0 c) 6x + 9=0 d) = x e) = x Copright 004, Durham Continuing Education Page of 5

13 MPMD - Principles of Mathematics Unit Lesson Ke Question # (continued) 9. State the x-intercept, -intercept and slope for each line. (4 marks) a) b) 0. Is it easier to graph an equation in -intercept form or standard form? Explain. ( marks). An equation has an x-intercept of 5 and a -intercept of. Graph this equation. ( marks) Copright 004, Durham Continuing Education Page of 5

14 Direct and Partial Variation Lesson

15 MPMD - Principles of Mathematics Unit Lesson Lesson Twelve Concepts Introduction to direct and partial variation The origin on a Cartesian plane m in the equation =mx graphing equation of the form =mx Introduction to partial variation b in the equation =mx + b graphing equation of the form =mx + b Direct and Partial Variation Direct Variation Direct Variation is a relation that is of the form =mx. The graph of =mx is a straight line with the slope of m. The line =mx alwas passes through the order pair (0,0). (0,0) is called the origin. The relation =mx represents direct variation because there is a direct relationship. Example Graph each equation which models direct variation. a) = x b) Solution a) = x b) = x = x Slope is and passes through the origin. Slope is and passes through the origin. Copright 004, Durham Continuing Education Page 5 of 5

16 MPMD - Principles of Mathematics Unit Lesson Support Questions. State the value of m in each equation of the form =mx. a) = 4x b) = x c) = x d). Write an equation of the line through the origin with each slope. a) m = 5 b) m = c). Find the slope of each line, then write its equation. = 5 x m = d) m = 4 a) b) 4. Graph each line. a) = x b) 5 = x 5. Johnn earns $6 for ever hour worked. Write an equation for this statement, then create a table of values and graph. Copright 004, Durham Continuing Education Page 6 of 5

17 MPMD - Principles of Mathematics Unit Lesson Partial Variation Partial Variation is a relation that is of the form =mx+b. The graph of =mx+b is a straight line with the slope of m and a -intercept of b. The line =mx+b does not pass through the origin. The relation =mx +b represents partial variation because the value of varies partiall with the value of x. Example Graph each equation which models partial variation. a) = x b) Solution 4 = x+ 5 a) = x b) 4 = x+ 5 Slope is - and intersects the - axis at. Slope is 5 4 and intersects the -axis at +. Copright 004, Durham Continuing Education Page of 5

18 MPMD - Principles of Mathematics Unit Lesson Support Questions 6. Write an equation of the line with each slope and -intercept. a) m = 5, b = b) m =, b = -4 c) m =, b = Find the slope and -intercept of each line, and then write its equation. a) b) 8. Graph each line. a) = x+ b) = x 6 c) = x 4 9. Noah earns a $00 a week and $ for ever hour worked. Write an equation for this statement, then create a table of values and graph. Ke Question #. State the value of m in each equation of the form = mx. (4 marks) a) = x b) = x c) = x d) = 8 x Copright 004, Durham Continuing Education Page 8 of 5

19 MPMD - Principles of Mathematics Unit Lesson Ke Question # (continued). Write an equation of the line through the origin with each slope. (4 marks) a) m = b) m = c) m = d). Find the slope of each line, and then write its equation. (4 marks) m = 8 a) b) 4. Graph each line. (6 marks) a) = x b) = x c) = x 5 5. Brook spends $4.00 each da for lunch on work das. Write an equation for this statement, then create a table of values and graph. (4 marks) 6. Write an equation of the line with each slope and -intercept. ( marks) a) m =, b =0 b) m =, b = - c) m =, b = + 4. Find the slope and -intercept of each line, and then write its equation. (6 marks) a) b) Copright 004, Durham Continuing Education Page 9 of 5

20 MPMD - Principles of Mathematics Unit Lesson Ke Question # (continued) 8. Graph each line. (6 masks) a) = 4x b) = x+ c) = x The length of time to set up is 00 min. The time to 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 = x on a Cartesian plane. Then he checked with a classmate, he realized the graph was different. Is Stephen s graph correct? If so, explain how ou know. If not, explain what Stephen did wrong. (4 marks) Copright 004, Durham Continuing Education Page 0 of 5

21 Scatter Plots Lesson

22 MPMD - Principles of Mathematics Unit Lesson Lesson Thirteen Concepts Introduction to scatter plots Creating scatter plots Positive, negative and no correlation Determining the equation of best fit Extrapolation Interpolation Scatter Plots and Line of Best Fit Scatter plots A scatter plot is a graph of data that is a series of points. Example Stud for that Test Percent on Exam Here a set of data was plotted. Hours studing vs. Percent of Exam Hours of stud Data in a scatter plot can have a positive/negative or no correlation No Correlation Negative Correlation Copright 004, Durham Continuing Education Page of 5

23 MPMD - Principles of Mathematics Unit Lesson 80 Positive Correlation Example Make a scatter plot for the men s times. Plot the ear on the x-axes and the times on the -axes. Solution Year Time Year Time Year Time Winning Times for 00m Time (seconds) Year Copright 004, Durham Continuing Education Page of 5

24 MPMD - Principles of Mathematics Unit Lesson 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 -intercept. Winning Times for 00m Time (seconds) Year Example First pick two points that represent the general center of the points plotted. Then draw the line of best fit through those points generall dividing the plotted point even on both sides. What is the approximate equation for the line of best fit in the previous example? Solution Choose the coordinates of the two previousl chosen points used to draw the line of best fit. (985,.) and (989,.4) slope = m = = x x Copright 004, Durham Continuing Education Page 4 of 5

25 MPMD - Principles of Mathematics Unit Lesson 0. m = = intercept = b = + Therefore the equation of the line of best fit is = 0.05x+. Extrapolation and Interpolation Extrapolation is extending a graph to estimate the values that are beond the table of values. Interpolation is using a graph to estimate the values that are not in the table of values but are within the range of the lowest and highest values presented in the table of values. Example a) Using extrapolation what would be the approximate distance that the discus will be thrown during the 004 Summer Olmpics? b) Using Interpolation how far was the discus thrown in 95? Women's Olmpic Discus Records Distance (m) Year Copright 004, Durham Continuing Education Page 5 of 5

26 MPMD - Principles of Mathematics Unit Lesson Solution a) Using extrapolation, what would be the approximate distance that the discus will be thrown during the 004 Summer Olmpics? approximatel 8 meters. Women's Olmpic Discus Records Distance (m) Draw a vertical line from 004 until ou hit the line of best fit then run horizontall until ou hit the value on the axis Year b) Using Interpolation, how far was the discus thrown in 95? Approximatel 5 metres Women's Olmpic Discus Records Distance (m) Draw a vertical line from 95 until ou hit the line of best fit then run horizontall until ou hit the value on the axis Year Copright 004, Durham Continuing Education Page 6 of 5

27 MPMD - Principles of Mathematics Unit Lesson Support Questions. State whether the scatter plot has a positive, negative or no correlation. a) b) c). The table below shows the winning times for the 800-m race at the Olmpic Summer Games. 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?. What is the approximate winning time in the ear 00? 4. What approximate ear does the time drop below 04 seconds? Ke Question #. State whether the scatter plot has a positive, negative or no correlation. ( marks) a) b) c) Copright 004, Durham Continuing Education Page of 5

28 MPMD - Principles of Mathematics Unit Lesson Ke Question # (continued). The table below shows the winning heights in a men s high jump competition. (8 marks) Year Winning Countr Jump in Height (m) 9 Canada.9 9 United States England.99 9 United States.6 98 United States. 00 Australia.4 a) Create a properl 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?. The table below shows the percentage of high school girls who smoked more than one cigarette during the previous ear. (8 marks) Percent a) Graph the data in a scatter plot. b) Determine the equation of the line of best fit. c) Use our equation to predict the percentage of high school girls who smoke more than one cigarette in 000. d) Approximatel, what percentage smoked more than one cigarette in 98 and 994? Copright 004, Durham Continuing Education Page 8 of 5

29 Averages Lesson 4

30 MPMD - Principles of Mathematics Unit Lesson 4 Lesson Fourteen Concepts Introduction to averages (measures of central tendenc) Mean average Median average Mode average Measures of Central Tendenc There are three different tpes 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 b the number of entries in the data set. Example Find the mean of the following sets of numbers. a) {,,4,,,8,9, } b) { 4,,,5,,8,,9,4,,5,, } Solution a) {,,4,,,8,9, } mean = 8 50 mean = 8 mean = is the sum of the all the values in the numerator. Divide b 8 because there are 8 numbers in the set. b) { 4,,,5,,8,,9,4,,5,, } mean = 60 mean = mean 4.6 Copright 004, Durham Continuing Education Page 0 of 5

31 MPMD - Principles of Mathematics Unit Lesson 4 Support Questions. Calculate the mean average for each set of numbers. a) {,6,,,,5,8 } b) {,8,,5,8,,5,9, } c) { 5,4,5,69,84,88,94,9,5,4,45,6,6,5 }. Given the mean, and most of the set of data, find the missing value x in the set. a) { 4,,,,9,,,0,x }; mean = b) {,6,,5,9,,5,9,,x }; mean = 4.5 c) { 65,4,4,60,4,98,84,96,4,5,5,,6,58,x }; mean = 64. The salaries of the Toronto Maple Leafs is given below. What is the mean average for a plaer s salar? $,50,000 $950,000 $5,500 $,00,000 $95,000 $500,000 $,000,000 $900,000 $450,000 $,000,000 $850,000 $400,000 $,000,000 $00,000 $,600,000 $650,000 $,500,000 $585,640 $,400,000 $55,000 Copright 004, Durham Continuing Education Page of 5

32 MPMD - Principles 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) {,9,,,,8,,,4 } b) { 4,,,5,,8,,9,4,,5, } Solution a) {,9,,,,8,,,4 } Arrange in numerical order. {,,4,,,8,9,, } 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, therefore the median average is. Median = b) { 4,,,5,,8,,9,4,,5, } Arrange in numerical order. {,,,,4,4,5,5,,,8,9, } 4+ 5 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 Copright 004, Durham Continuing Education Page of 5

33 MPMD - Principles of Mathematics Unit Lesson 4 Support Questions 4. Calculate the median average for each set of numbers. a) {,6,,,,5,8 } b) {,8,,5,8,,5,9, } c) { 5,4,5,69,84,88,94,9,5,4,45,6,6,5 } 5. The salaries of the Toronto Maple Leafs is given below. What is the median average for a plaer s salar? Mode Average $4,50,000 $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 $00,000 $,600,000 $850,000 $,500,000 $85,640 $,400,000 $45,000 Mode average is the most common value in a set of numbers. Example Find the mode of the following sets of numbers. a) {,9,,,,8,,,4 } b) { 4,,,5,,8,,9,4,,5, } Solution a) {,9,,,,8,,,4 } Arrange in numerical order because it is easier to see the repeated numbers. {,,4,,,8,9,, } is the most common number in the set so therefore, the mode average =. Copright 004, Durham Continuing Education Page of 5

34 MPMD - Principles of Mathematics Unit Lesson 4 b) { 4,,,8,5,,8,,8,9,4,,8,5, } Arrange in numerical order because it is easier to se the repeated numbers. {,,,,4,4,5,5,,,8,8,8,8,9, } 8 is the most common number in the set so therefore, the mode average = 8. Support Questions 6. Calculate the mode average for each set of numbers. a) {,6,,,,5,8 } b) {,8,,5,8,,5,9,,8, } c) { 5,4,5,69,4,88,94,9,5,4,45,6,6,5,8,5,5 }. The salaries of the Toronto Maple Leafs is given below. What is the mode average for a plaer s salar? $4,50,000 $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 $85,640 $,400,000 $45, Find the mean, median and mode for the given set of numbers. { 6,4,,68,,4,0,65 } 9. Determine each measure of central tendenc based on the table given below. Annual Salar ($) Frequenc Copright 004, Durham Continuing Education Page 4 of 5

35 MPMD - Principles of Mathematics Unit Lesson 4 Ke Question #4. Find the mean, median and mode for each set of numbers. (9 marks) a) {4,4,,6,6,4,8,6,48} b) {,,6,4,,9,6,45,,6,8,6} c) { 8,6,,4,,6,,5,,,9,}. Two friends went golfing. Their score card is given below. (6 marks) Hole Total Steve Mar a) Calculate the mean score for each plaer. b) Calculate the mean score for the two plaers together. c) Calculate the median score for each plaer. d) Calculate the median score for the two plaers together. e) Determine the mode for each plaer. f) Determine the mode for the two plaers 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 5. Alberta 68.5 Saskatchewan 69. Manitoba. Ontario 5. Quebec 4.5 New Brunswick 4.6 Nova Scotia 6. Prince Edward Is. 5.4 Newfoundland.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? Copright 004, Durham Continuing Education Page 5 of 5

36 MPMD - Principles of Mathematics Unit Lesson 4 Ke Question #4 (continued) 4. Is each statement alwas true, sometimes true or sometimes false? Explain and provide an example to illustrate our 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. Given the mean, and most of the set of data, find the missing value x in the set. (4 marks) a) {,5,6,8,9,,,0,5,x }; mean = 4 b) { 6,,,9,4,x }; mean = 5 6. The April batting statistics of the 004 Toronto Bluejas 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)? Copright 004, Durham Continuing Education Page 6 of 5

37 MPMD - Principles of Mathematics Unit Lesson 4 Ke Question #4 (continued). Determine each measure of central tendenc based on the table given below. ( marks) Annual Salar ($) Frequenc Copright 004, Durham Continuing Education Page of 5

38 Perimeter Lesson 5

39 MPMD - Principles of Mathematics Unit Lesson 5 Lesson Fifteen Concepts Introduction to perimeter and circumference Radius and diameter Calculations using pi (π) Solving perimeter/circumference questions using formulas and substitution Perimeter 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 P = a+ b+ c+ d Copright 004, Durham Continuing Education Page 9 of 5

40 MPMD - Principles of Mathematics Unit Lesson 5 P = dπ π.4 d=r d: diameter r: radius Example Find the perimeter of each of the following shapes. a) b) 6cm 0 cm d = 0cm 8 cm 5 cm. c) d) cm. 8 c 8 cm. cm. Solution a) 6cm 0 cm 8 cm P = a+ b+ c P = P = 4cm Copright 004, Durham Continuing Education Page 40 of 5

41 MPMD - Principles of Mathematics Unit Lesson 5 b) d = 0 cm P = πd P =.4 0 ( )( P =.4cm ) c) 5 cm. 8 c 8 cm. P = ( l + w) P = (8 + 5) P = () P = 46cm d) cm cm Onl include sides instead of 4 sides of the rectangle since the 4 th side is ½ of a circle. πd P = l + l + w + P = P = P = 4.84cm (.4)( ) Circumference of circle but onl ½ of it since the perimeter does not include the inner portion. Copright 004, Durham Continuing Education Page 4 of 5

42 MPMD - Principles of Mathematics Unit Lesson 5 Example Find the perimeter. 5 m 5 m 0 m 8m 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 Copright 004, Durham Continuing Education Page 4 of 5

43 MPMD - Principles of Mathematics Unit Lesson 5 Support Questions. Calculate the perimeter for each of the following objects. a) b) c) cm 4cm 8.5 cm cm 5cm cm cm d) e) 5 cm f) cm 6 cm.5 cm g) h) 8 m 4 cm m 0 cm i) cm Copright 004, Durham Continuing Education Page 4 of 5

44 MPMD - Principles of Mathematics Unit Lesson 5 Ke Question #5. Calculate the perimeter for each of the following objects. ( marks) a) b) c) 8cm 5cm 0 cm 4 cm 6cm 5cm cm d) e) 4 cm f) 8cm cm.5 cm g) h) 0 m 5 m m 0 m 8 m 4 m 4 m i) 8 cm 9 m Copright 004, Durham Continuing Education Page 44 of 5

45 MPMD - Principles of Mathematics Unit Lesson 5 Ke Question #5 (continued. Explain how ou could find the circumference of a circle given its area. ( marks). A rectangular ard has an area of 4 m. What are four possible perimeters for this ard? (4 marks) 4. When a circle s radius doubles so does its circumference. True or False? Prove our answer with an example. (4 marks) 5. What is the total amount of edging that would be required to cover all edges of a rectangular prism measuring 0 cm b 5 cm b 0 cm? (4 marks) Copright 004, Durham Continuing Education Page 45 of 5

46 MPMD - Principles of Mathematics Unit Support Questions Answers Lesson. a) sl ope = 4, -int = b) slope =, -int = 4 c) slope =, -int = d) slope =, -int = - 5. a) (4, 4) b) (, -8) (8, -5) = x+ 4 ( 4) = (4) = = 4 = x + 4 ( 8) = () = 9+ 8 = 8 = x+ 4 5 = ( 8) = 6+ 5 = 5 c) (, -) (4, -6) = x = ( ) = = = x 6 = ( 4) 6 = 6. a) b) c) Copright 004, Durham Continuing Education Page 46 of 5

47 MPMD - Principles of Mathematics Unit Support Questions Answers 4. a) b) c) = x = x+ x+ = x x+ ( ) = ( ) x () x+ = + = x 4 x+ = x+ = 4 x+ = 0 x+ + 4 = 0 x + = 0 d) = x+ x + = x+ = 0 = 5x ( ) = (5 x) ( ) = 0x 0x+ = 0x+ + = 0 0x = 0 5. a) b) c) x + 6 = = x = x 6 x 6 = = x+ x+ 5 0 = = x 5 = x+ 0 5 x+ 0 = 5 5 = + 5 5x + = 0 + = 5x = 5x 5x = 5 = x+ 6. = x+ = x 5. = x+ = x 6 Copright 004, Durham Continuing Education Page 4 of 5

48 MPMD - Principles of Mathematics Unit Support Questions Answers 8. a) b) c) - intercept set x = = 0 = 6 = - intercept set x = = 0 5 = 0 = - intercept set x = 0 + = 0 = = x - intercept set = 0 x - intercept set = 0 set x - intercept = 0 x + 6 = 0 x = 6 x 0 = 0 x = 0 5x + = 0 5x = x = x = 5 x = 5 9. a) b) - intercept - intercept set x = 0 set x = 0 = = x - intercept set = 0 0 = x + = x x - intercept set = 0 0 = x x = ( ) x = ( ) x = 4 4 x = Lesson. a) 4 b) c) d) 5. a) = 5x b) = x c) = x d) = x 4 Copright 004, Durham Continuing Education Page 48 of 5

49 MPMD - Principles of Mathematics Unit Support Questions Answers. a) = x b) = 5 4 x 4. a) b) 5. E = 6h 6. a) = 5x+ b) = x 4 c) = x a) = x+ 5 b) 5 = x Copright 004, Durham Continuing Education Page 49 of 5

50 MPMD - Principles of Mathematics Unit Support Questions Answers 8. a) b) c) 9. E = h + 00 Lesson. a) no correlation b) positive correlation c) negative correlation Copright 004, Durham Continuing Education Page 50 of 5

51 MPMD - Principles of Mathematics Unit Support Questions Answers. a) 800 Metre Times Time (sec) Year Lesson 4 b) Equation of best fit Use the coordinates (964,05.) and (988,0.45) slope = = = = x x int = 0 = x+ 0 b) 0 sec c) 98. a) b) = 6 9 c) Copright 004, Durham Continuing Education Page 5 of 5

52 MPMD - Principles of Mathematics Unit Support Questions Answers. a) b) c) + x 0 + x = = x = x = x = 45 x = x = x = 960 x = / = $ a) {,,, 5,6,,8 } median = 5 b) {,5,,8,8,9,,,5 } median = 8 c) { 4,4,45,5,5,5,6,6,69,5,84,88,94,99} 6+ 6 = = 6.5 median = = = 9500 median = $ a) (occurs times) b) 8 or (occur three times) c) 4 (occurs times). $ mean = ( ) = median = 6,65,68,0,,4,4,, = { } mode = mean = $ median = = $4685 Mode = 5000 Copright 004, Durham Continuing Education Page 5 of 5

53 MPMD - Principles of Mathematics Unit Support Questions Answers Lesson 5. a) b) c) P = ( b+ c) P = P = 5 cm P = (4 + 5) P = (9) P = 8 cm P = ( l + w) P = (8.5 + ) P = (.5) P =.5 cm d) e) f) C = π r P = C = (.4)(5) P = 4.5 cm C =.4 cm P P P = 4( l) = 4() = 44 cm g) h) P = P = 60 m π r P = (.4)(5) P = 58 + P =. cm i) P P P P = ( π r) = ()(.4)() = = 80.5 cm Copright 004, Durham Continuing Education Page 5 of 5