SAMPLE ASSESSMENT TASKS MATHEMATICS METHODS ATAR YEAR 11

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1 AMPLE AEMENT TAK MATHEMATI METHOD ATAR YEAR

2 opyright chool urriculum and tandards Authority, 208 This document apart from any third party copyright material contained in it may be freely copied, or communicated on an intranet, for non-commercial purposes in educational institutions, provided that the chool urriculum and tandards Authority is acknowledged as the copyright owner, and that the Authority s moral rights are not infringed. opying or communication for any other purpose can be done only within the terms of the opyright Act 968 or with prior written permission of the chool urriculum and tandards Authority. opying or communication of any third party copyright material can be done only within the terms of the opyright Act 968 or with permission of the copyright owners. Any content in this document that has been derived from the Australian urriculum may be used under the terms of the reative ommons Attribution 4.0 International ( BY) licence. Disclaimer Any resources such as texts, websites and so on that may be referred to in this document are provided as examples of resources that teachers can use to support their learning programs. Their inclusion does not imply that they are mandatory or that they are the only resources relevant to the course. 204/4296v7

3 ample assessment task Mathematics Methods ATAR Year 7 (Test 3) Unit Assessment type: Response onditions: Time for the task: Up to 50 minutes, in-class, under test conditions Materials required: ection One: alculator-free tandard writing equipment ection Two: alculator-assumed alculator (to be provided by the student) Other materials allowed: Marks available: Drawing templates, page of notes in ection Two 52 marks ection One: alculator-free ection Two: alculator-assumed (27 marks) (25 marks) weighting: 5.5% ample assessment tasks Mathematics Methods ATAR Year

4 2 ection One: alculator-free (27 marks) uggested time: 25 minutes Question (7 marks) The spinners A and B are divided into 4 and 5 equal sectors respectively. They are spun at the same time and the numbers to which the arrows point are added. Use a suitable sample space to show all possible outcomes. (2 marks) What is the probability that the total is even? ( mark) (c) What is the probability that the total is 2? ( mark) (d) Which total(s) has(have) a 0.5 probability of occurring? ( mark) (e) What is the probability that the total is even when the result on spinner A is an even number? ( mark) (f) What is the probability that the total is at least 0 when it is known that the total is greater than or equal to 7? ( mark) ample assessment tasks Mathematics Methods ATAR Year

5 3 Question 2 (3 marks) tudents in Year were surveyed to determine the number who had played competition sport and undertaken paid work the previous weekend. The results are provided in the table. Played competition sport Yes No Total Undertaken paid work Yes No Total If a student is selected at random from this Year group, what is the probability that: they played competition sport and undertook paid work? ( mark) they either played competition sport or undertook paid work? ( mark) (c) they did not play competitive sport, given that they had undertaken paid work? ( mark) Question 3 (5 marks) The universal set is the set of integers from to 20, A is the set of numbers divisible by 3, B is the set of square numbers and is the set of prime numbers. Describe the set A B ( mark) Determine A B (2 marks) ample assessment tasks Mathematics Methods ATAR Year

6 4 (c) Determine na ( B ) ( mark) (d) A number is selected at random from the universal set, determine PAB ( ) ( mark) Question 4 Expand and simplify (5 marks) 3 (2x + 5) (3 marks) Part of Pascal s triangle is printed below. Row Use the triangle to write out the expansion of ( m ) 7 + k (2 marks) ample assessment tasks Mathematics Methods ATAR Year

7 5 Question 5 A function is defined as f( x) = x + 2x 8. 2 (3 marks) Write an expanded expression for f(2 x ) ( mark) f(2 x) represents a transformation of f( x ). Describe this transformation. (2 marks) Question 6 (4 marks) For the line 3x+ 3y= 2 ketch the line (2 marks) Mark the angle of inclination the line makes with the xx-axis. Determine this angle. Justify your answer. (2 marks) ample assessment tasks Mathematics Methods ATAR Year

8 6 ection Two: alculator-assumed (25 marks) uggested time: 25 minutes Question 7 (4 marks) tate the coefficient of 4 2 x y in the expansion of (3x 2 ) 6 y ( mark) Express the coefficient of n r 4 2 m xy in Part in terms of a b n (3 marks) Question 8 (5 marks) Ten Year students are to be given an opportunity to go overseas to help paint a village school. There were 20 applicants for the trip, 2 girls and eight boys. How many different combinations of students are possible? ( mark) If there have to be five girls and five boys, how many different combinations are possible? (2 marks) (c) Tess and Lisa were two of the applicants and they heard that eight girls and two boys had been chosen. What was the probability that both girls, Tess and Lisa, were chosen? (2 marks) ample assessment tasks Mathematics Methods ATAR Year

9 7 Question 9 (7 marks) To qualify as an umpire, candidates had to pass both a written test and a practical test. Data from previous tests indicated that 90% of candidates passed the written test and of these 70% passed the practical test. Of those who failed the written test, 40% also failed the practical test. What percentage of candidates passed both tests? ( mark) What percentage of candidates passed at least one test? (2 marks) (c) Of those who did not qualify as an umpire what fraction of the candidates failed the written test? (2 marks) (d) Are the events Pass the written test and Pass the practical test independent? Justify your answer. (2 marks) ample assessment tasks Mathematics Methods ATAR Year

10 8 Question 0 (3 marks) A test containing five questions was given to a group of students. The table below shows the probability of the number of questions (out of 5) being answered correctly. Number of questions answered correctly ( n ) Probability that this number of questions were answered correctly x Determine x ( mark) Evaluate P(3 n 4 n> 2) (2 marks) Question (6 marks) For two events M and K, PM ( ) = 0.4 and PM ( M K) = 0.8. Determine PK ( ) if events M and K are mutually exclusive. (3 marks) events M and K are independent. (3 marks) END OF TET QUETION ample assessment tasks Mathematics Methods ATAR Year

11 9 ummary table of syllabus content assessed by 7 (Test 3) Question yllabus reference use everyday occurrences to illustrate set descriptions and representations of events and set operations review probability as a measure of the likelihood of occurrence of an event understand the notion of a conditional probability and recognise and use language that indicates conditionality review probability as a measure of the likelihood of occurrence of an event understand the notion of a conditional probability and recognise and use language that indicates conditionality use set language and notation for events use the notation PP(AA BB)... expand (xx + yy) nn for small positive integers nn use Pascal s triangle and its properties use function notation... examine dilations and the graphs of yy = cccc(xx) and yy = ff(dddd) recognise features of the graph of yy = mmmm + cc, including its linear nature, its intercepts and its slope or gradient examine the relationship between the angle of inclination of a line and the gradient of that line recognise the exact values of sin θθ, cos θθ... recognise the numbers nn as binomial coefficients (as coefficients in the rr expansion of (xx + yy) nn ) understand the notion of a combination as a set of rr objects taken from a set 8.3. of n distinct objects use the notation nn.3.2 rr and the formula nn rr = nn! for the number of rr!(nn rr)! combinations of rr objects taken from a set of nn distinct object establish and use the formula PA ( B) = PAPB ( ) ( ) for independence of events A and B, and recognise the symmetry of independence use relative frequencies obtained from data as estimates of probabilities.3.4 use the notation PP(AA BB) and the formula PP(AA BB) = PP(AA BB)PP(BB).3.4 use the notation PP(AA BB) and the formula PP(AA BB) = PP(AA BB)PP(BB) ample assessment tasks Mathematics Methods ATAR Year

12 0 Marking key for sample assessment task 7 (Test 3) Unit *Note: Each item has been classified as imple() or omplex() to provide teachers with some indication of the anticipated difficulty, which may be helpful with grading. However, it must be recognised that the classifications have been provided a-priori and will need refining once the tasks have been administered (that is, after evidence as to the effect has been gathered). ection One: alculator-free (27 marks) Question (7 marks) olution Behaviours Marks Item* (/) pinner B elects correctly labelled rows and columns A Accurately adds numbers on each spinner Determines probability (c) 20 Determines probability (d) 5, 6, 7, 8 Works backwards when given probability (e) 00% or Recognises the event is certain (f) 4 2 elects correct number of outcomes and elements in the sample space Question 2 (c) = (3 marks) olution Behaviours Marks (/) Reads the table to locate correct number of outcomes in the event and in the sample space Applies the complementary principle (or addition principle) Determines conditional probability ample assessment tasks Mathematics Methods ATAR Year

13 Question 3 olution Behaviours Marks Uses correct terminology for sets with no Empty set elements {,3, 4,6,9,2,5,6,8 } Includes all numbers divisible by three Includes all square numbers [no repeats] (c) 4 (d) 4 ounts the number of elements outside the three sets described Identifies there is one element in the intersection and four elements in set B (5 marks) (/) Question 4 (5 marks) olution Behaviours Marks (/) 3 2 (2x+ 5) = (2x+ 5)(2x+ 5) quares one pair of bracket 2 accurately = (2x+ 5)(4x + 20x+ 25) Expands second pair of brackets = 8x + 20x + 40x + 00x+ 50x+ 25 implifies expression = x + x + x m + 7mk+ 2mk + 35mk + 35mk + 2mk + 7mk + k Identifies correct terms and powers elects correct row and coefficients Question 5 (3 marks) olution Behaviours Marks (/) 2 4x + 4x 8 ubstitutes 2x into expression and simplifies Dilation parallel to the xx-axis by a scale factor of ½ Describes dilation fully Nominates correct scale factor ample assessment tasks Mathematics Methods ATAR Year

14 2 Question 6 (4 marks) olution Behaviours Marks (/) (0,4) 0 (4,0) Draws a line with a negative gradient Labels the x and yy-intercept with the correct coordinates Gradient = 4 = 4 Determines gradient of the line Evaluates the angle with a tangent of - Ɵ Tan θ = - θ = 35 o ample assessment tasks Mathematics Methods ATAR Year

15 3 ection Two: alculator-assumed Question ( 2) olution Marks (25 marks) (4 marks) (/) Behaviours: elects the correct coefficient from the expanded expression on a calculator Recognises combinations as coefficients of expansion Allows for power of the coefficients in original expression Question 8 (5 marks) olution Behaviours Marks (/) 20 Uses combination notation and calculates = number of combinations 2 8 Identifies number of ways for girls = Multiplies this by number of ways for boys (c) elects number of ways these two girls can be chosen = 2 8 Divides by the number of ways that eight girls 33 can be chosen 8 2 Question 9 (7 marks) olution Behaviours Marks (/) 0.9 x 0.7 = 0.63 so 63% Uses the multiplication principle (c) (d) (0. x 0.4) = 0.96 so 96% Identifies those failing both tests Uses the fact that probability sums to 0. = P(Pass written) = 0.9 P(Pass practical) = 0.69 P(Passing both) = o events not independent Identifies proportion of the intersection of the two sets Identifies proportion of students not passing both tests. Uses correct rule to test for independence elects correct probabilities to substitute into the rule ample assessment tasks Mathematics Methods ATAR Year

16 4 Question 0 olution Behaviours Marks x = ( ) = = (3 marks) (/) Identifies probability sums to Applies the conditional probability formula Evaluates correctly Question olution PM ( ( M K)) PM ( M K) = 0.8 = 0.8 PM ( K) PM ( ) 0.4 = = 0.8 PM ( K) PM ( K) o PM ( K) = 0.5 If M and K are mutually exclusive then PM ( K) = 0 PK ( ) = 0. Behaviours Applies the formula for conditional probability alculates PM ( K) Uses the fact that the intersection is empty if sets are mutually exclusive If sets are independent, then PM ( ) PK ( ) = PM ( K) o 0.4 PK ( ) = PM ( ) + PK ( ) PM ( K) 0.4 PK ( ) = PK ( ) 0.5 o PK ( ) = 6 Behaviours Applies rule for independence Expands PM ( K) and substitutes the value for PM ( ) olves the equation for PK ( ) (6 marks) Marks (/) ample assessment tasks Mathematics Methods ATAR Year

SAMPLE COURSE OUTLINE MATHEMATICS METHODS ATAR YEAR 11

SAMPLE COURSE OUTLINE MATHEMATICS METHODS ATAR YEAR 11 Copyright School Curriculum and Standards Authority, 2017 This document apart from any third party copyright material contained in it may be freely