b) systematic-survey every 10 th person that enters the store.

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1 MPM1D1 Exam Review Chapter -Relations 1. Define and give example(s): primary data, secondary data, sample, population, census, random sample, simple random sampling, systematic random sampling, stratified random sampling, non-random sampling, bias dependent variable, independent variable, interpolate, extrapolate. Primary data-original data that a researcher gathers specifically for a particular experiment or survey. Secondary data-data that someone else has already gathered for some other purpose. Sample-Any group of people or items selected from a population. Population-The whole group of people or items being studied. Census-A survey of all members of a population. Random Sample-A sample in which all members of a population have an equal chance of being chosen. Simple Random Sampling-Choosing a specific number of members randomly from the entire sample. Systematic Random Sampling-Choosing members of a population at fixed intervals from a randomly selected member. Stratified Random Sampling-Dividing a population into distinct groups and then choosing the same fraction of members from each group. Non-Random Sampling-Using a method that is not random to choose a sample from a population. Bias-Error resulting from choosing a sample that does not represent the whole population. Dependent Variable-A variable that is affected by some other variable (often y, vertical axis). Independent Variable-A variable that affects the value of another variable (often x, horizontal axis). Interpolate-Estimate a value between two measurements in a set of data. Extrapolate-Estimate a value beyond the range of a set of data.. No Frills would like to survey a representative sample of its shoppers about the fruit they purchase. Describe a suitable sample for each type of sampling. a) simple random-survey 100 people that enter the store. b) systematic-survey every 10 th person that enters the store. c) stratified-survey 10% of the shoppers in each department of the store (produce, meat, dairy, etc.). d) non-random-survey the first 0 shoppers that enter the store.. A movie theatre owner will continue to show a movie as long as it will attract a minimum of 50 viewers per week. This data shows the number of people who have attended the current movie over a ten-week period. Week Viewers a) Create a scatter plot and draw a line of best fit. b) Predict when the owner should bring in a new movie:

2 After 11 weeks c) What method did you use in (b) to determine answer? extrapolation 4. The manager of a movie theatre gathers data regarding the number of movie tickets sold and the number of buckets of popcorn sold. The data table is below. Movie Tickets Buckets of Popcorn a) The independent variable is Movie Tickets The dependent variable is Buckets of Popcorn b) Create a scatter plot of the number of movie tickets sold versus the number of buckets of popcorn sold. Draw a line of best fit. c) Use the line of best fit to estimate the number of buckets of popcorn sold when 100 movie tickets were sold 60. Did you use interpolation or extrapolation to get this answer? interpolation d) Use the line of best fit to estimate the number of buckets of popcorn sold when 00 movie tickets were sold 185. Did you use interpolation or extrapolation to get this answer? extrapolation 600 D E 5. The graph at right shows the trip of one skier to the top of Blue Mountain in a chairlift and then skiing down the mountain. a) Did the chairlift stop before the skier reached the top of the mountain? Explain. Yes. Chairlift stopped at BC where the slope is 0 and distance stays the same. b) During what period of time is the chairlift moving the fastest? Justify your answer A G F B C H Time Elapsed in Minutes

3 Chairlift is moving the fastest during CD where the graph is the steepest. c) Describe the skier s trip down the hill. Include information about distance, time, and speed. After 7 minutes on the chairlift, the skier starts to come down the hill. Skier starts at 50 m/min for min, takes a break for 1 min, then continues at 150 m/min for the remaining min. Total time to get down hill is 7 min. Chapter -Polynomials 1. Simplify. a) (-) 4 =81 b) - 4 = -16 c) (-y )(y )(y)= -6y 6 d) 15x e) 5x g) ( 9x 4 6 x = -x 4 f) (x y ) = 9x 6 y 4 )(x ) 6x y = -x h) 8 7 x 4 xy = x y. Expand and simplify. a) (x - x + 1)+(4x x) b) (x + 5) -(x + 1) c) x(x - 5x + 1) - x(4 - x) 6x 6x + 7 -x + 1 x 8x x. A rectangular window has a length of (5x - ) and a width of (x). Determine its perimeter and its area. Simplify your answer. Perimeter=(5x + x)=(8x )= 16x 4 Area=x(5x )= 15x 6x Chapter 4-Equations 1. Solve. a) x + 14 = b) x 7 = 11 x=-11 x=9 c) x + 6 = 5x 6 d) (x ) = 5 (8 x) x=4 x=- e) x 5 f) x 7 1 x x x=6. Jane works at a clothing store in a shopping mall. She earns $9 per hour, plus % commission. a) Write an equation to represent Jane s earnings. Clearly define your variables. Let E represent her earnings, s represent her sales, and n represent number hour worked.

4 E=9n+0.0s b) Find the amount Jane makes in 40 hours with $1 000 in sales. E=9(40)+0.0(1000)=$70 c) How much does Jane have to have in sales to earn $0 in a 0-hour work week? 0=9(0)+0.0s s=$5000. Daryl earns $100 more per week than his roommate Barry and $150 less than Connor, his other roommate. Together the three friends earn $000 per week. a) Write an equation to represent the situation. Define the variable. Let x represent Barry s earnings. Therefore, Daryl s earnings are x+100 and Connor s earnings are x+50. b) Solve your equation and find out how much each boy earns per week? x+x+100+x+50=000 x+50=000 x=550 Barry earns $550, Daryl earns $650, and Connor earns $800. Chapter 5 Modelling With Graphs & 6 Analyse Linear Relations 1. Find the equation of each of the lines being described: a) slope - and y-intercept of 7 y= -x + 7 b) slope 4 and the same y-intercept as y = 5x y=4x - c) same slope as y = -6x + and same y-intercept as y = -x 5 y=-6x - 5 d) parallel to x= and passes through point (-, -4) x=- e) perpendicular to x=- and passes through the point (1,-5) y=-5 f) perpendicular to y = x 7 with the same y-intercept as y = -x + 1 y x g) parallel to y = -x 1 and passes through the point (0,-) y=-x -. Find the slope of the line joining the points given: a) (4,5) and B(8,9) b) P(-,-) and Q(-5,9) m=1 m=-4. Write the equation of the line that a) passes through the points (-5,-4) and (-7,) y= -x b) is perpendicular to the line y x 1 and passes through the point (-,4). y= x Do the following lines intersect? Yes or No? Explain. a) y = 0.75x + and y x 5 4 b) x = - and y = c) y = -x + 4 and y = x 1 d) y = -x + and y x x y

5 b, c & d intersect because they are not parallel lines with the same slope. 5. Write an equation in the form y=mx + b for the data in the table. y= -x Determine the x and y-intercept for x 5y =15. x-intercept (5, 0) y-intercept (0, -) 7. Find the point of intersection between the following pairs of lines by graphing. a) y = x 1 and y = x b) y x 1 and y = -x 8. Video City has a yearly membership fee of $10 and rents videos to its members for $ per video. Movies to Go has no membership fee, but charges its customers $4 per video. a) Write an equation to represent the cost of renting from each store. Let C represent total cost and n represent the number of videos. VC: C=n+10 MTG: C=4n b) Graph both equations on the same axis. Find the point of intersection.

6 P.O.I. (5, 0) c) What advice would you give to your cousin who is trying to decide which store to rent videos from? If you will rent less than 5 videos, go with MTG. If you will rent more than 5 videos, go with VC. If you will rent exactly 5 videos, both places cost the same so it doesn t matter which on you go with. d) If Video City decreased its yearly membership fee to $8, what would happen to its graph? Graph would shift down units with a lower y-intercept and same slope. e) If Video City increased its video rental for members to $4, what would happen to its graph? Graph would start at the same y-intercept, but be steeper. 9. The NCIVS Graduating Class wants to have a class trip. Wild Water Works: $00 to rent a bus and $15 per student for admission to the park Canada s Wonderland: $800 to rent a bus and $1 per student for admission to the park Let n stand for the number of students who go on the trip and C stand for the Total Cost of the trip. a) Write an equation for the total cost of each possible trip: Wild Water Works: C= n Canada s Wonderland: C= n b) Given the number of students, complete the table of values for each possible trip: Number of Wild Water Works Canada s Students Wonderland

7 c) Graph both sets of data on the same axis. Find the point of intersection. (00, 00) d) What should the graduating class do for their class trip? Explain. If less than 00 students, go to WWW. If more than 00 students, go to CW. If exactly 00 students, the price is the same Chapter 7-Geometric Relationships 1. Find the values of the variables in each of the following, and place your answer in the space provided. The diagrams are not drawn to scale. c = 70 o h= 55 o k= 108 o d = 70 o i = 55 o e = 40 o j = 15 o. Write an equation and solve for x. a) b) c)

8 x =60 x-4+x+19=180 0x+40=540 x=88 x=9 x=5 Chapter 8-Measurement Relationships 1. Determine the value of the unknown in each of the following diagrams. a) b) =x y +11 =18 x=6 cm y=14. m. Find the area of the given shape. A=61.5x x.5x51.0x7.= =64.9 mm. Calculate the surface area and volume of the shape shown, to nearest hundredth. SA 4 (4 ) (4)(14.4) 56.97mm V 4 (4 ) (4 )(14.4) mm 4. The volume of the rectangular prism is 1070 cm. Find the height of the prism. 1070=(15)(1)(x) x=5.9 cm Chapter 9-Optimizing Measurements Rectangle: A=s P=4s Square Based Prism: SA = 6s V= s Cylinder: SA = 6πr V= πr 1. Jill wants a rectangle with perimeter of 6 m and the largest possible area. a) What are the dimensions of the rectangle that satisfies her conditions? b) What is the area of this rectangle? a) 4s=6 s=9 m Dimensions of rectangle are 9m by 9m (a square).

9 b) A=9 =81 m. Bob wants a square-based prism with volume of 00 m and the smallest possible surface area. a) What are the dimensions of the square-based prism that satisfies his conditions to nearest hundredth of a metre? b) What is the surface area of this square-based prism to nearest square metre? a) 00=s s=5.85 m Dimensions square-based prism are 5.85 m by 5.85 m by 5.85 m (a cube). b) SA=6(5.85) =05 m. Jane wants a cylinder with surface area of 60 cm and the largest possible volume. (4 marks) a) What are the dimensions of the cylinder that satisfies her conditions to nearest hundredth of a centimetre? b) What is the volume of this cylinder to nearest cubic centimetre? a) 60 6 r r=1.78 cm Radius is 1.78 cm. b) V (1.78) 5cm