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YEAR 11 Mathematics Standard

Assessment Task 2 2020: Sighted Test

Due Date: Thursday 2nd July 2020 (Week 10) Assessment Name: Sighted Test Mark: /45 Weighting: 30 % SYLLABUS OUTCOMES TO BE ASSESSED: MS11-2 represents information in symbolic, graphical and tabular form MS11-3 solves problems involving quantity measurement, including accuracy and the choice of relevant units MS11-4 performs calculations in relation to two-dimensional and three-dimensional figures MS11-7 develops and carries out simple statistical processes to answer questions posed MS11-8 solves probability problems involving multistage events MS11-10 justifies a response to a given problem using appropriate mathematical terminology and/or calculations DIRECTIVES TO BE ASSESSED: Develop: Create in a systematic way Justify: Show or prove to be right or reasonable Perform: Carry out or complete Represent: display or communicate Solve: find an answer to, explanation for, or means of effectively dealing with

TASK DESCRIPTION: You will complete a one period test based on the attached preparation questions. The paper will be a combination of multiple-choice and short-answer questions. You will be given the 2020 Mathematics Standard HSC Reference Sheet (also attached). The topics assessed are:

● S2: Relative Frequency and Probability – Chapter 4 ● M1.2: Perimeter, Area and Volume – Chapter 5 (5.05-5.12), Chapter 6 (6.02) ● S1.1: Classifying and Representing Data – Chapter 1

Recommended Equipment: ❖ NESA approved scientific calculator ❖ Pens, ruler, pencils

ASSESSMENT CRITERIA – STUDENT CHECKLIST: Have you:

o Referred to the above chapters o Checked Google Classroom and the Y11 Standard Maths Google Site for lesson content o Referred to the Marking Criteria below o Completed ALL relevant chapters in the textbook o Completed the attached questions o Asked your teacher for clarification/help with any work o Attended the Maths / STEM Staffroom for help if needed

Preparation Questions – see following pages

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S2: Relative Frequency and Probability – Chapter 4

1 The probability of rain on a given day is 0.75. What word would you use to describe this probability?

2 Which of the following events have outcomes that are equally likely?

3 How many elements are there in the sample space when two cards are selected without replacement from cards labelled 1 to 8?

4 Celeste, Monique, Petra, Mia, Lily and Amira must line up in front of their classroom when the school bell rings each morning. In how many possible ways can they stand in a queue in front of their classroom?

5 A die is biased so that the probability of throwing a 1 is twice that of any other single number. Calculate the probability of throwing a 2 on a single roll of the die.

6 James buys five tickets in a raffle in which 230 tickets were sold. He wins first prize. What is the probability that he also wins second prize?

7 A key ring holds three identical keys. Two keys open the front door of a house and one opens the back door. What is the probability that a key selected at random opens the front door?

8 If a coin is tossed three times, how many different outcomes are possible?

9 An envelope requires 45 cents worth of postage. If I have two 20c stamps, three 10c stamps and four 5c stamps, how many different combinations of stamps can I use to make up the 45c postage?

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10 Which of the following is the number of outcomes possible when two coins and one die are tossed together?

11 If a coin is tossed 300 times, how many tails would you expect?

12 A special pack of cards consists of four aces, four kings, four queens and four jacks. One card is chosen at random. The probability that the card is not a king or a queen is:

13 Janie has three skirts (red, pink, yellow) and two blouses (white and grey). List all the combinations of skirt and blouse Janie can wear. 2

14 Henry, James and Andrew are running in a race. Find the number of possible orders in which they can finish the race. 2

15 A class tallied the different coloured cars in the school car park and tabulated their results.

White 18

Black 21

Silver 14

Red 4

Blue 3

A black. 1 B red or blue. 1 C not silver. 1

16 The probability of hitting a target is 0.7. In 80 attempts, how many hits would you expect? 1

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17 Kate has forgotten her locker combination. The lock has three dials, each numbered 0–9. A How many different combinations are possible on Kate’s lock? 2 B Freddy thinks that the first number is either 0 or 1. Assuming he is correct, how many

combinations are possible on Kate’s lock? 1

18 Two-digit numbers are formed using the numbers 1, 2, 3 and 4, with no number repeated. A How many numbers are possible? 2 B What is the probability of getting a number greater than 23? 1 C What is the probability that the number is a multiple of 3? 1

19 A coin is tossed and a die is rolled. Complete a tree diagram to list the sample space. 2

20 Two dice are rolled. A Draw a table to show the possible totals. 1

B What is the probability of getting a total of 6? 1 C What is the probability that the number is a multiple of 3? 1

21 Mr Martin has 2 pairs of trousers, 3 shirts and 4 ties. By drawing a tree diagram or otherwise, calculate the total number of work outfits he has. 1

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22 In a bag are 10 red marbles (R) and 5 blue marbles (B). Two marbles are selected at random. A partially completed tree diagram in shown. Complete the probability tree and calculate the probability of selecting 2 marbles of the same colour. 3

23 A group of 485 people were surveyed. What is the probability that a person selected randomly is either female or a non-smoker? 1

24 A deck of 52 playing cards contains 12 picture cards. Two cards are drawn at random and placed

on a table. What is the probability, correct to four decimal places, that two picture cards are on the table? 2

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M1.2: Perimeter, Area and Volume – Chapter 5 (5.05-5.12), Chapter 6 (6.02)

1 What is the area of a triangle with a base of 5 m and a perpendicular height of 8 m?

2 A cubic water tank has a side length of 6 m. What is the capacity of the tank?

3 The volume of a sphere with radius of 45 cm is closest to:

4 A sphere fits exactly inside a cylindrical container as shown. The diameter of the sphere is 20 cm. Calculate the volume of the cylindrical container to the nearest cubic centimetre.

5 Use four applications of the Trapezoidal rule to find the approximate area of the shape below, to the nearest square metre.

6 5.23 litres = _________ cm3

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7 Find, in terms of π, the exact circumference of a circle with area 64π m2.

10 If the volume of a cube is 17 576 cm3, what is its surface area?

9 Calculate the shaded area.

11 Find the volume of the rectangular pyramid below, correct to the nearest cm2.

8 The area of the shaded region is closest to: . 9 cm

15 cm

8m 5m

4m

6m

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12 Given the volume of a sphere is 100 cm3, find its radius, correct to two decimal places.

13 A 20 cm label fits exactly around a cylindrical tin of spaghetti with no overlap. What is the radius of the cylinder?

14 Find the area and of the figure ABCD. All measurements are in metres.

16 The surface area of a closed cylinder is 7820 cm2 and the radius is 15 cm. Calculate the height of the cylinder, correct to one decimal place. 2

17 A spherical fishbowl has a radius measuring 12 cm. If the fishbowl is filled to 60 per cent capacity, how many litres of water are required? Give your answer correct to the nearest litre. 2

15 Find the perimeter of the figure in Question 14.

20 cm

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18 A rubbish bin in the shape of a cylinder with only one end open has a radius of 13 cm, shown below. Jack throws his ball towards the bin and it lands on top of the bin as shown. The radius of Jack’s ball is also 13 cm. A Calculate the external surface area of the rubbish bin. Express your answer to the nearest square

centimetre. 2

B Calculate the volume of the solid formed when Jack lands his ball on top of the bin. Express your

answer to the nearest cubic centimetre. 2

19 A pool is in the shape of a rectangle and two semicircles as shown in the diagram.

A How wide is the pool across the centre? 2

B If the pool has a uniform depth of 1.2 m, calculate the capacity of the pool, correct to the nearest

whole kilolitre. 3

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S1.1: Classifying and Representing Data – Chapter 1

1 What is the class centre for the 90–94 class?

Class Class Centre Frequency Cumulative

Frequency 80–84 2 85–89 4 90–94 3 95–99 6

2 An online shop wants to sell T-shirts. It first does a survey of people to determine the demand for each of the following sizes: XS S M L XL What type of data is the survey collecting?

3 Amy wishes to conduct a survey using the school population. She decides to survey every 30th student on the roll. What is this method of sampling?

4 A company employs 400 men and 160 women. If, out of 49 people, 35 men were selected for a survey, this would be an example of:

5 What percentage of scores are above 80 in the following data set?

4 2 7

5 3 5 9 9

6 1 3 7 9

7 0 2 5 7 7

8 3 4 8

9 3 9

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8 The dot plot below indicates how many hours students use their electronic devices for per week.

What percentage of students use their devices for at least 3 hours per week?

The graph below shows the cumulative frequency histogram and polygon (ogive) for a distribution of student marks on a spelling test. Use the graph to answer questions 9-11.

7 A school’s anti-bullying program is run by 20 students, seven teachers and eight parents. A stratified sample of ten people is selected to attend a conference. How many teachers should be in the sample?

l

l l

l l l l

l l l l l l l

l l l l l l l

0 1 2 3 4 5 6

9 How many students scored 40 on the test?

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10 What percentage of students scored 50 on the test?

11 How many students scored less than 20?

12 The table shows the number of students in each year level at Picktown High School.

If 100 students from the school are to be surveyed, how many Year 8 students should be surveyed? 2

13 Alexander decides to survey the school on changing the menu in the canteen. He asks the students at the canteen during lunchtime. Comment on the fairness of this situation and suggest a more appropriate way of collecting a sample of students. 2

14 Give the correct name for: A data that is a number. 1 B data measured on a continuous scale. 1 C non-numerical data. 1 D data that can be described in words and ordered. 1

Year Number of students

7 102

8 120

9 105

10 116

11 87

12 70

Total 600

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15 A school surveyed the students arriving late. The reasons are summarised in a Pareto chart below. What percentage was due to “traffic problems” or “car breakdown”?

16 The graph below shows a frequency distribution polygon from a sample of patrons viewing a movie. A Use the information in the graph to complete the following table. 1 C Construct a cumulative frequency histogram and polygon for the data set. 3 D What percentage of patrons were over 18? 1

E How many patrons were aged between 14 and 18 inclusive? 1

Age Cumulative frequency

12

13

14

15

16

17

18

19

20

0

5

10

15

20

25

30

35

40

12 13 14 15 16 17 18 19 20

Frequency

Age

Agesofpatronsinamoviecinema

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END OF PREPARATION QUESTIONS

17 A restaurant owner wants to find out what the customers like best about the restaurant. Each customer is asked to complete this questionnaire at the end of their meal.

a) Outline TWO reasons showing why this questionnaire can be considered to be

poorly designed for its purpose. 2

b) Create two categorical questions that could be added to improve the survey. 2

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NSW Education Standards Authority

2020 HIGHER SCHOOL CERTIFICATE EXAMINATION

Mathematics Standard 1Mathematics Standard 2