TasThe 100 m Olympic Records

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Marilynn Lucas
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1 TasThe 100 m Olympic Records E43 Einstein High School and Newton High School compete in High School Olympic events in different cities every two years. Some students wondered if there was a relationship between the year of the event and the winning times for the 100 m race. They also wanted to compare the winning times of the two schools. The following scatter plots represent the winning times for each school. Time (in seconds) Time (in seconds) Einstein High School (Times for the 100 m Race) Year Newton High School (Times for the 100 m Race) Year Grade 9 ssessment of Mathematics 1

2 a) From the graph, determine the year Einstein High School ran 100 m with a time of 13.4 s. b) raw a line of best fit on both scatter plots. c) escribe how you decided where to draw your lines of best fit for the relationships. d) i) Which line of best fit is steeper? ii) escribe what this steeper slope tells you about how the Einstein High School times are changing compared to the Newton High School times. 2 Grade 9 ssessment of Mathematics

3 e) There were no High School Olympics in y using the graph, Sajan predicted that if there had been Olympics in 1982, the time for Newton High School would have been approximately 14.3 s. Pat says that he thinks the time would have been closer to 14.0 s. Write the prediction that is more reliable. Give reasons for your answer. f) local newspaper had a news story that claimed Newton High School will never run as fast as Einstein High School. o your scatter plots support this claim? Give reasons for your answer. Grade 9 ssessment of Mathematics 3

4 Tasabysitting Service 6254 P5Y anielle has a babysitting service. The amount she charges consists of a flat fee of $10.00 for transportation plus $5.00 per hour. a) omplete the table of values. KU N01 Number of hours, n mount charged, ($) Grade 9 ssessment of Mathematics

5 b) reate a scatter plot and join the points to show the relationship between the amount charged,, in dollars, and the number of hours, n. KU R12 mount harged vs. Number of Hours mount charged ($) n Number of hours c) Write an equation for the relationship between the amount charged,, and the number of hours that anielle babysits, n. P R15 Grade 9 ssessment of Mathematics 5

6 d) Jolina also has a babysitting service. She charges $7.50 per hour. KU R12 omplete the amount charged column in the table of values below. Number of hours, n mount charged, ($) Finite differences e) omplete the finite differences column in the table of values above. f) Is the relationship between the amount charged and the number of hours linear or non-linear? ircle one: linear or non-linear KU-R21 Give reasons for your answer. 6 Grade 9 ssessment of Mathematics

7 g) The Smiths need a babysitter for New Year s Eve. PS N31 They will leave at 4 p.m. and expect to return home at 3 a.m. Jolina charges twice her hourly rate after midnight. Should the Smiths hire anielle or Jolina? Show your work. Hint: anielle charges a flat fee of $10.00 for transportation plus $5.00 per hour. Jolina charges $7.50 per hour and double after midnight. Grade 9 ssessment of Mathematics 7

8 TasGumball Machine 905 M1N The upper part of a gumball machine is a cylinder. company needs to estimate how often it must refill the machine. a) Each gumball has a diameter of 1 cm. alculate the volume of one gumball. Show your work. KUM14FPE Zoom one gumball 1 cm Hint: V = πr3 8 Grade 9 ssessment of Mathematics

9 b) Sunreeta and Jodi are trying to figure out how many gumballs are in the machine. Sunreeta claims that the following calculation will give the correct number of gumballs. Number of gumballs in the machine = volume of the cylinder volume of one gumball Jodi disagrees, stating, It s not that simple. Which of the two girls do you agree with? Give reasons for your answer. P N8FE/M20 c) top view of the gumball machine is shown below. Estimate the diameter of the machine by counting the gumballs. KUN1/N2FEP Top of Gumball Machine Zoom one gumball d 1 cm Grade 9 ssessment of Mathematics 9

10 d) The height of the cylinder, h, is the same as its diameter, d. Therefore, h = d. Use your estimate for the diameter from question c) to calculate the volume of the cylinder. Show your work. P M20 d Hint: h V = πr 2 h e) Make your own estimate of the number of gumballs in the machine. escribe how you got your estimate. PS N1/N2FEP f) The gumball machine must never be less than 20% full. pproximately 50 gumballs are purchased each day from the machine. Use your estimate from question e) to calculate how often the company must refill the dispenser. Show your work. PS N5/N6P 10 Grade 9 ssessment of Mathematics

11 TasMatch Me 6709 P3X aniel walks in front of a motion sensor. The graph below represents the relationship between time, t, in seconds, and distance from the motion sensor,, in metres. 9 8 istance vs. Time istance (m) Time (s) t a) escribe aniel s walk. Include as many mathematical details as possible. KU R20 Hint: Include information about distance time speed direction Grade 9 ssessment of Mathematics 11

12 b) Junaid walks in front of the motion sensor, trying to recreate aniel s graph. His graph does not look exactly the same. istance vs. Time 9 8 istance (m) aniel s walk Junaid s walk t Time (s) Use the table below to compare Junaid s walk with aniel s walk. P R22 Similarities ifferences 12 Grade 9 ssessment of Mathematics

13 c) Micheline tries to recreate aniel s walk. She starts 1 m away from the motion sensor then walks 1 m away from it every 2 s. i) omplete the table below. P-R12 Time (s) (start) 0 istance from motion detector (m) ii) Graph Micheline s walk below. KU-R12 9 istance vs. Time istance (m) aniel s walk t Time (s) d) Explain how Micheline should change her walk to make her graph look exactly like aniel s graph. PS R22 Grade 9 ssessment of Mathematics 13

14 TasParallelograms 965 6N Three students each construct a different parallelogram using dynamic geometry software. In each parallelogram,,, and are bisected and the lines are extended to intersect the opposite sides. The three results are shown below. R Q P S Q R P S Q R P S a) Look at the shaded shape, PQRS, in each diagram above. Make a hypothesis about the shape of PQRS. PS M23 14 Grade 9 ssessment of Mathematics

15 b) is a parallelogram where = 60. Find the measures of, and and write them on the diagram below. Show your work. KU M22 60º c) Four line segments are drawn to bisect each of the interior angles of the parallelogram in question b). Write the measures of a, b, c and d on the diagram below. Show your work. KU M22 b b c c a a d d Grade 9 ssessment of Mathematics 15

16 d) For each shaded triangle, use the angles you found in question c) to find the measure of one of the angles in PQRS. In each case, give reasons for your answer. P M22 i) R PQR = Q S Reasons: P ii) R = Q S Reasons: P iii) Q R S = Reasons: P iv) = Q R S Reasons: P 16 Grade 9 ssessment of Mathematics

17 e) Look at your results from question d). i) o your results support your hypothesis from question a)? Give reasons for your answer. PS M25 ii) classmate says that your hypothesis works only for parallelograms in which one of the angles is 60. escribe the additional work you would need to do in order to check whether your hypothesis is true for any parallelogram. PS M25 Grade 9 ssessment of Mathematics 17

Activity P07: Acceleration of a Cart (Acceleration Sensor, Motion Sensor)

Activity P07: Acceleration of a Cart (Acceleration Sensor, Motion Sensor) Equipment Needed Qty Equipment Needed Qty Acceleration Sensor (CI-6558) 1 Dynamics Cart (inc. w/ Track) 1 Motion Sensor (CI-6742)