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1 Brisbane School of Distance Education Task Sheet - Exam Student name Class Name Year level/ Subject 9 Maths Teacher name Task title SA6 - Exam Due Date To be received by 5pm Friday 18th November Technique Supervised exam Mode Written Text type Short answer response Duration Up to 60 minutes Task Purpose Students will apply the proficiencies of understanding and fluency and reasoning and problem solving across the topics of Statistics and Probability. Students will apply mathematical processes, solve problems and communicate their understanding of Statistics and Probability. Task details/ Instructions • Write your name on this cover page and circle your teacher’s name. • Complete all questions with full working and answers, in the spaces provided. • Use a black or blue pen, or a dark pencil. Be sure that your handwriting is legible for scanning. • Read all questions carefully. • If extra paper is needed, write your name on the top of each page and label questions clearly. • On completion of the exam, sign the student declaration and date it. • The supervisor is also required to sign the declaration and date it. • The supervisor is required to scan the completed task sheets and any extra pages into a single multi- page pdf document and save as “MAT_09_SA6_Lastname_Firstname”. This file should then be uploaded to Blackboard. The original documents should be kept safe until results have been returned. Conditions Perusal is for reading the paper only. No notes can be made or writing on any paper. No exam supervisor input is permitted. No access to computers, textbooks or student notes are permitted. Scientific calculators are permitted. Blank lined paper may be supplied by the student. The supervisor should be present for the duration of the exam. Supervisor/Parent declaration Student declaration of Academic Integrity I declare that this assessment has been completed in accordance with the conditions and instructions above and the work submitted is the student’s own work, and has not been written by any other person. Supervisor name: __________________________ Signature:__________________ Date:__________ I declare that this exam has been completed in accordance with the instructions and the work submitted is my own work and has not been written nor assistance given by any other person. NB: Your work will not be marked if the student declaration is not signed and dated. Student name: ________________________________ Signature:___________________ Date:____________ 2 Topic: Statistics and Probability Purpose: Students will demonstrate the application of the proficiencies of understanding and fluency and reasoning and problem solving across the topics of Statistics and Probability. Students will apply mathematical processes, solve problems and communicate their understanding. A B C D E U n d er st an d in g an d F lu en cy C o n ce p tu al u n d er st an d in g connection and description of mathematical concepts and relationships in unfamiliar situations connection and description of mathematical concepts and relationships in complex familiar situations recognition and identification of mathematical concepts and relationships in simple familiar situations some identification of simple mathematical concepts statements about obvious mathematical concepts P ro ce d u ra l fl u en cy recall and use of facts, definitions, technologies and procedures to find solutions in unfamiliar situations recall and use of facts, definitions, technologies and procedures to find solutions in complex familiar situations recall and use of facts, definitions, technologies and procedures to find solutions in simple familiar situations some recall and use of facts, definitions, technologies and simple procedures partial recall of facts, definitions or simple procedures M at h em at ic al la n g u ag e an d sy m b o ls effective and clear use of appropriate mathematical terminology, diagrams, conventions and symbols consistent use of appropriate mathematical terminology, diagrams, conventions and symbols use of appropriate mathematical terminology, diagrams, conventions and symbols use of aspects of mathematical terminology, diagrams and symbols use of everyday language Questions 11 13 7b 10a 1 2a 2b 3 4a 4b 7a 8a 9a 9b P ro b le m S o lv in g & R ea so n in g P ro b le m - so lv in g ap p ro ac h es systematic application of relevant problem-solving approaches to investigate unfamiliar situations application of relevant problem- solving approaches to investigate complex familiar situations application of problem-solving approaches to investigate simple familiar situations some selection and application of problem- solving approaches in simple familiar situations. partial selection of problem-solving approaches M at h em at ic al m o d el lin g development of mathematical models and representations in unfamiliar situations development of mathematical models and representations in complex familiar situations development of mathematical models and representations in simple familiar situations statements about simple mathematical models and representations isolated statements about given mathematical models and representations R ea so n in g a n d ju st if ic at io n clear explanation of mathematical thinking and reasoning, including justification of choices made, evaluation of strategies used and conclusions reached explanation of mathematical thinking and reasoning, including reasons for choices made, strategies used and conclusions reached description of mathematical thinking and reasoning, including discussion of choices made, strategies used and conclusions reached statements about choices made, strategies used and conclusions reached isolated statements about given strategies or conclusions Questions 12 8b 5 6 10b Comment Understanding & Fluency Problem Solving & Reasoning Overall Results 3 Fluency and Understanding Simple Familiar Question 1 The following table shows the total number of State of Origin games won by each team in the last 20 years. Queensland New South Wales 27 15 Circle the correct probability of Queensland winning a game at the State of Origin. A. 9 5 B. 5 14 C. 9 14 D. 15 17 Question 2 In a survey of 50 coffee drinkers, 33 have milk and 11 have sugar with their coffee. The information is summarised in a Venn Diagram below. a. What is the probability that a coffee drinker has sugar only? A. 3 14 B. 36 50 C. 11 50 D. 3 50 b. What is the probability that a coffee drinker has milk or sugar? A. 11 14 B. 36 50 C. 28 50 D. 28 14 Question 3 Students at BrisbaneSDE conducted a survey on Australia’s most popular TV shows by surveying Year 9 students. Circle the classification(s) that best describe this type of data. A. Population B. Categorical C. Sample D. Numerical 4 Question 4 A bag of balls contains 5 black balls and 5 red balls. Two balls are selected (without replacement). a) Complete the tree diagram below to list all possible outcomes. b) Calculate the probability of selecting two red balls. Problem Solving and Reasoning Simple Familiar Question 5 You roll two dice. The first die lands on the table and the other die rolls under a chair and you cannot see it. What is the probability that both dice show a three? 5 Question 6 The following are daily wages in dollars for 11 workers. $195, $280, $275, $315, $420, $275, $160, $842, $359, $275, $740 Ann says that the average wage is $280. Harry says the average wage is $376. Show how they can both be correct. Fluency and Understanding Simple Familiar / Complex Familiar Question 7 A box claims to contain 100 matches. A survey of 200 boxes had the following results. If you were to purchase a box of matches, what is the probability that: a. The box would contain exactly 100 matches b. The box would contain at least 100 matches Number of matches 95 96 97 98 99 100 101 102 103 104 Frequency 1 8 14 7 27 75 25 16 13 14 6 Question 8 Arathi purchases 7 computer games at a sale. Three games cost $20 each, two games cost $30, one game costs $50, and the last game cost $200. a. Calculate the mean, median, and the mode, and range. Mean = Median = Mode = Range = b. Which of the mean, median or mode gives the best ‘average’ for the cost of Arathi’s games? Justify your response using statistical reasoning. 7 Question 9 A shop owner has two jeans shops. The daily sales in each shop over a 7-day period are recorded in the table below. a. Construct a stem-and-leaf plot for the Daily Jean Sale. b. The mean for Shop A is 18.7 and the mean for Shop B is 10.3. Compare and comment on the differences between the sales made by the two shops. Refer to the mean, mode, median, and range. Shop A 32 24 15 12 3 24 21 Shop B 23 7 10 7 14 4 7 8 Question 10 The table below represents the data collected over a month of 30 consecutive days displaying the delay time (in minutes) of an Airline’s flight departures. Airline A Frequency Number of minutes delayed 0-10 11-20 21-30 31-40 41-50 51-60 Number flights 13 14 2 0 0 1 a. Construct a histogram using the data provided in the frequency table. b. Circle the term that best describes the histogram. A. Skewed B. Symmetric C. Mode D. Bimodal 9 Question 11 There are two classes at a High School. Both classes completed the same exam. The sum of the scores of Class A was identical to the sum of the scores of Class B. Given that; • Class A has 20 students and a mean score of 60. • Class B has 24 students Find the mean score of class B. Problem Solving and Reasoning Complex Unfamiliar 10 Question 12 Each standard box contains 12 chocolates. One chocolate is selected at random from 60 different boxes and the results are shown in the table. Using these results, predict how many chocolates of each type of filling are likely to be in a standard box placing your answers in the table below. (Show working below) Strawberry Caramel Coconut Nut Crunch Mint Filling Total Strawberry 11 Caramel 14 Coconut 9 Nut Crunch 19 Mint 7 11 Question 13 Stacey and Christine compete against each other in a duathlon. A duathlon consists of a run and then a bike ride. • Stacey and Christine each have an equal chance of winning the run. • If Stacey wins the run, the probability that she wins the bike ride rises to 0.7 • If Stacey loses the run, the probability that she wins the bike ride is 0.4. Construct a tree diagram to determine the probability that Stacey wins both the run and the bike ride. Understanding and Fluency Complex Unfamiliar