Adv - Week 01 PDF

Questions ADV: Functions (Adv), F1 Working with Functions (Adv) Algebraic Techniques (Y11) 1. Functions, 2...

Questions ADV: Functions (Adv), F1 Working with Functions (Adv) Algebraic Techniques (Y11) 1. Functions, 2ADV F1 2018 HSC 1 MC Teacher: Morgen Sugiharto What is the value of correct to two decimal places? Exam Equivalent Time: 76.5 minutes (based on HSC allocation of 1.5 minutes approx. (A) 0.07 per mark) (B) 0.08 (C) -12.54 F1 Working With Functions (D) -12.55 2. Functions, 2ADV F1 2012 HSC 1 MC What is correct to three significant figures? 1% 2% 3% 4% 5% 6% 7% 8% (A) Algebraic Techniques *Analytics based on the average (B) contribution to Advanced HSC Linear Functions exams over the last decade. (C) Quadratics and Cubic Functions Further Functions and Relations (D) 3. Functions, 2ADV F1 2014 HSC 1 MC HISTORICAL CONTRIBUTION F1 Working with Functions is a Year 11 topic whose content represents the lowest of low hanging What is the value of , correct to 3 significant figures? fruit in the new Advanced course. F1 Working with Functions has seen significant re-categorisation of content in the new syllabus. Our (A) analysis has it accounting for approximately 7.1% per exam over the last decade. (B) We have split the topic into 5 categories for analysis purposes: 1-Algebraic Techniques, 2-Linear (C) Functions, 3-Quadratics and Cubic Functions, 4-Composite Functions and 5-Further Functions and Relations. (D) This analysis looks at Algebraic Techniques (1.7%). 4. Functions, 2ADV F1 2015 HSC 1 MC HSC ANALYSIS - What to expect and common pitfalls What is written in scientific notation, correct to 4 significant figures? Algebraic Techniques were regularly tested in the old Mathematics course, with surd calculations representing the dominant question type. (A) Surds have historically been examined in 2 out of every 3 years (not examined in 2021 or 2020). Note (B) that virtually all past questions have involved compound surds in the denominator which are no longer examinable. This fact is reflected in the database along with supplementary questions that (C) look at examinable surd denominators (i.e. non-compound surds). (D) Algebraic Fractions were examined in the 2021 Advanced paper and deserve attention, particularly as they represent an overlap between the new Advanced and Standard 2 content. Rounding questions can require students to know standard decimal place rounding, significant figures (2019) and scientific notation (2015). 5. Functions, 2ADV F1 2019 HSC 1 MC 12. Functions, 2ADV F1 2011 HSC 1a What is the value of to two significant figures? Evaluate correct to four significant figures. (2 marks) (A) (B) 13. Functions, 2ADV F1 2013 HSC 11a (C) Evaluate correct to three significant figures. (1 mark) (D) 14. Functions, 2ADV F1 2008 HSC 1a 6. Functions, 2ADV F1 2005 HSC 1a Evaluate correct to three significant figures. (2 marks) Evaluate correct to two significant figures. (2 marks) 15. Functions, 2ADV F1 2008 HSC 1e 7. Functions, 2ADV F1 2007 HSC 1a Expand and simplify. (2 marks) Evaluate correct to two decimal places. (2 marks) 16. Functions, 2ADV F1 2021 HSC 11 8. Functions, 2ADV F1 SM-Bank 50 Solve (2 marks) Rationalise the denominator of. (2 marks) 17. Functions, 2ADV F1 SM-Bank 46 9. Functions, 2ADV F1 SM-Bank 53 Find and such that are real numbers and i. If , find. (1 mark). (2 marks) ii. Calculate the value of to 3 significant figures. (1 mark) 18. Functions, 2ADV F1 SM-Bank 47 10. Functions, 2ADV F1 2004 HSC 1c Find and such that are real numbers and Solve. (2 marks) (2 marks) 11. Functions, 2ADV F1 2005 HSC 1d 19. Functions, 2ADV F1 SM-Bank 51 Express as a single fraction in its simplest form. (2 marks) Find and such that are real numbers and. (2 marks) 20. Functions, 2ADV F1 SM-Bank 52 28. Functions, 2ADV F1 EQ-Bank 21 Find and such that are real numbers and Simplify. (2 marks). (2 marks) Copyright © 2004-21 The State of New South Wales (Board of Studies, Teaching and Educational Standards NSW) 21. Functions, 2ADV F1 SM-Bank 54 Find the reciprocal of. (2 marks) 22. Functions, 2ADV F1 SM-Bank 56 Simplify. (2 marks) 23. Functions, 2ADV F1 SM-Bank 55 Simplify. (2 marks) 24. Functions, 2ADV F1 EQ-Bank 22 Worker A picks a bucket of blueberries in hours. Worker B picks a bucket of blueberries in hours. i. Write an algebraic expression for the fraction of a bucket of blueberries that could be picked in one hour if A and B worked together. (2 marks) ii. What does the reciprocal of this fraction represent? (1 mark) 25. Functions, 2ADV F1 2004 HSC 1a The radius of Mars is approximately. Write this number in scientific notation, correct to two significant figures. (2 marks) 26. Functions, 2ADV F1 2004 HSC 1d Find integers and such that. (2 marks) 27. Functions, 2ADV F1 2008 HSC 1c Simplify. (2 marks) Worked Solutions 7. Functions, 2ADV F1 2007 HSC 1a 1. Functions, 2ADV F1 2018 HSC 1 MC 8. Functions, 2ADV F1 SM-Bank 50 2. Functions, 2ADV F1 2012 HSC 1 MC 9. Functions, 2ADV F1 SM-Bank 53 3. Functions, 2ADV F1 2014 HSC 1 MC i. ii. 4. Functions, 2ADV F1 2015 HSC 1 MC 10. Functions, 2ADV F1 2004 HSC 1c 5. Functions, 2ADV F1 2019 HSC 1 MC 6. Functions, 2ADV F1 2005 HSC 1a 11. Functions, 2ADV F1 2005 HSC 1d 16. Functions, 2ADV F1 2021 HSC 11 17. Functions, 2ADV F1 SM-Bank 46 12. Functions, 2ADV F1 2011 HSC 1a MARKER'S COMMENT: Show answer to 5 or 6 decimals before rounding. Correct rounding of a wrong answer still receives half marks. 13. Functions, 2ADV F1 2013 HSC 11a 18. Functions, 2ADV F1 SM-Bank 47 14. Functions, 2ADV F1 2008 HSC 1a 15. Functions, 2ADV F1 2008 HSC 1e 19. Functions, 2ADV F1 SM-Bank 51 22. Functions, 2ADV F1 SM-Bank 56 23. Functions, 2ADV F1 SM-Bank 55 20. Functions, 2ADV F1 SM-Bank 52 24. Functions, 2ADV F1 EQ-Bank 22 i. COMMENT: Note that the question asks for "a fraction". 21. Functions, 2ADV F1 SM-Bank 54 ii. 25. Functions, 2ADV F1 2004 HSC 1a 26. Functions, 2ADV F1 2004 HSC 1d 27. Functions, 2ADV F1 2008 HSC 1c 28. Functions, 2ADV F1 EQ-Bank 21 Copyright © 2016-2022 M2 Mathematics Pty Ltd (SmarterMaths.com.au)  Composite functions been examined in both new syllabus Advanced exams within a ADV: Functions (Adv), F1 Working with Functions (Adv) calculus context which proved very challenging to most students. These are covered Composite Functions (Y11) in later topics. Teacher: Morgen Sugiharto Exam Equivalent Time: 54 minutes (based on HSC allocation of 1.5 minutes approx. per mark) F1 Working With Functions 1% 2% 3% 4% 5% 6% 7% 8% Algebraic Techniques *Analytics based on the average contribution to Advanced HSC Linear Functions exams over the last decade. Quadratics and Cubic Functions Further Functions and Relations HISTORICAL CONTRIBUTION F1 Working with Functions is a Year 11 topic whose content represents the lowest of low hanging fruit in the new Advanced course. F1 Working with Functions includes new and a significant re-categorisation of old syllabus content. We have split the topic into 5 categories for analysis purposes: 1-Algebraic Techniques, 2-Linear Functions, 3-Quadratics and Cubic Functions, 4-Composite Functions and 5-Further Functions and Relations. This analysis looks at Composite Functions. HSC ANALYSIS - What to expect and common pitfalls Composite Functions is brand new content that is therefore absent from the "past contributions" bar chart above. Our analysis has found composite functions to be a highly examinable topic area. By this we mean it lends itself to a broad spectrum of questions at varying degrees of difficulty - which has been the experience of other States with an exam history in this topic. We recommend a close revision of examples where students need to state the domain and range of composite functions. Numerous examples in the database look at this. Questions 4. Functions, 2ADV F1 SM-Bank 16 MC 1. Functions, 2ADV F1 SM-Bank 2 MC Let and be functions such that and. Let and be functions such that , , , and The value of is. A. 2 The value of is B. 4 A. C. 5 B. D. 6 C. D. 5. Functions, 2ADV F1 SM-Bank 13 MC 2. Functions, 2ADV F1 SM-Bank 5 MC Which one of the following functions satisfies the functional equation ? A. Let and B. Then is given by C. A. D. B. 6. Functions, 2ADV F1 SM-Bank 8 MC C. Let D. Which one of the following is not true? 3. Functions, 2ADV F1 SM-Bank 9 MC A. B. If then is equal to C. D. A. B. 7. Functions, 2ADV F1 SM-Bank 12 MC C. If , then is equal to D. A. B. C. D. 8. Functions, 2ADV F1 SM-Bank 15 MC 11. Functions, 2ADV F1 SM-Bank 6 MC If the equation is true for all real values of , then could equal Let is equal to A. B. A. C. B. D. C. D. 9. Functions, 2ADV F1 SM-Bank 1 MC 12. Functions, 2ADV F1 SM-Bank 14 MC Let for. Let Which one of the following statements about is not true? Which one of the following equations is true for all positive real values of A. A. B. B. C. C. D. D. 10. Functions, 2ADV F1 SM-Bank 4 MC 13. Functions, 2ADV F1 SM-Bank 10 The function satisfies the functional equation for. Let Write down the rule of (1 mark) The rule for the function is A. 14. Functions, 2ADV F1 2019 MET1-N 2 B. Let and. C. a. Find. (2 marks) b. Express in the form , where , and are non-zero integers. (2 marks) D. 15. Functions, 2ADV F1 SM-Bank 30 Given and i. Find. (1 mark) ii. Find the domain and range of. (2 marks) 16. Functions, 2ADV F1 EQ-Bank 11 Worked Solutions Given the function and , sketch over its natural domain. (2 marks) 1. Functions, 2ADV F1 SM-Bank 2 MC 17. Functions, 2ADV F1 SM-Bank 31 Find the domain and range of given and. (2 marks) 2. Functions, 2ADV F1 SM-Bank 5 MC 18. Functions, 2ADV F1 SM-Bank 3 Let for i. State the range of. (1 mark) ii. Let , where and. Find the largest possible value of such that the range of g(x) is a subset of the domain of. (2 marks) 19. Functions, 2ADV F1 SM-Bank 7 3. Functions, 2ADV F1 SM-Bank 9 MC Let for and for all. i. Find , where. (1 mark) ii. State the domain and range of. (2 marks) iii. Show that. (2 marks) 20. Functions, 2ADV F1 SM-Bank 11 Given and 4. Functions, 2ADV F1 SM-Bank 16 MC a. Find integers and such that (2 marks) b. State the domain for which is defined. (2 marks) Copyright © 2004-21 The State of New South Wales (Board of Studies, Teaching and Educational Standards NSW) 5. Functions, 2ADV F1 SM-Bank 13 MC 8. Functions, 2ADV F1 SM-Bank 15 MC 6. Functions, 2ADV F1 SM-Bank 8 MC 9. Functions, 2ADV F1 SM-Bank 1 MC ♦ Mean mark 46%. 7. Functions, 2ADV F1 SM-Bank 12 MC 10. Functions, 2ADV F1 SM-Bank 4 MC ♦ Mean mark 47%. 11. Functions, 2ADV F1 SM-Bank 6 MC 14. Functions, 2ADV F1 2019 MET1-N 2 a. ♦ Mean mark 44%. b. 12. Functions, 2ADV F1 SM-Bank 14 MC ♦♦ Mean mark 35%. 15. Functions, 2ADV F1 SM-Bank 30 i. ii. 13. Functions, 2ADV F1 SM-Bank 10 16. Functions, 2ADV F1 EQ-Bank 11 18. Functions, 2ADV F1 SM-Bank 3 i. f (x) (0, 1) x ii. g (x) x _ _ 3 1 17. Functions, 2ADV F1 SM-Bank 31 19. Functions, 2ADV F1 SM-Bank 7 20. Functions, 2ADV F1 SM-Bank 11 i. a. ii. ♦♦ Mean mark part (a)(ii) 30%. b. ♦♦♦ Mean mark 13%. MARKER'S COMMENT: "Very poorly answered" with a common iii. MARKER'S COMMENT: Many response of that students were unsure of how to ignored the information from part present their working in this (a). question. Note the layout in the solution. Copyright © 2016-2022 M2 Mathematics Pty Ltd (SmarterMaths.com.au)  Questions ADV: Functions (Adv), F1 Working with Functions (Adv) Further Functions and Relations (Y11) 1. Functions, 2ADV F1 2019 HSC 2 MC Teacher: Morgen Sugiharto What values of satisfy ? Exam Equivalent Time: 93 minutes (based on HSC allocation of 1.5 minutes approx. per mark) (A) (B) F1 Working With Functions (C) (D) 1% 2% 3% 4% 5% 6% 7% 8% Algebraic Techniques *Analytics based on the average 2. Functions, 2ADV F1 2013 HSC 3 MC contribution to Advanced HSC Linear Functions exams over the last decade. Quadratics and Cubic Functions Which inequality defines the domain of the function ? Further Functions and Relations (A) (B) HISTORICAL CONTRIBUTION (C) F1 Working with Functions is a Year 11 topic that includes some new content and a significant re- categorisation of old syllabus content. (D) We have split the topic into 5 categories for analysis purposes: 1-Algebraic Techniques, 2-Linear Functions, 3-Quadratics and Cubic Functions, 4-Composite Functions and 5-Further Functions and 3. Functions, 2ADV F1 2020 HSC 1 MC Relations. This analysis looks at Further Functions and Relations (1.9%). Which inequality gives the domain of ? A. HSC ANALYSIS - What to expect and common pitfalls Absolute value equations can be examined in the new course, although it must be emphasised that absolute value inequality equations, which were the more common question type in the old syllabus, B. have moved to the Ext1 course. Graphing absolute value equations should be a revision focus in our view, as we expect this skill to be C. examined more frequently going forward. Inequalities involving linear (and square root) equations have been examined in 3 of the past 4 D. Advanced papers, notably absent in 2021. A great opportunity for scoring highly. Reflections require students to graph and of certain equations. Examined in the first new syllabus paper (2020 Adv 24), this question type warrants attention as we expect it to be regularly examined going forward. Circle functions were examined within the same question (2020 Adv 24) and surprisingly caused problems - we recommend a careful review of this area. Proportional (non-linear) relationships appear in the topic guidance exemplar questions and deserve attention. 4. Functions, 2ADV F1 SM-Bank 21 MC 13. Functions, 2ADV F1 SM-Bank 33 A circle with centre and radius 5 units has equation i. State the domain and range of. (2 marks) where and are real constants. ii. Sketch the graph. (1 mark) The values of and are respectively A. −3 and 38 14. Functions, 2ADV F1 SM-Bank 41 B. 3 and 12 Find the values of for which. (2 marks) C. −3 and −8 D. 3 and 18 15. Functions, 2ADV F1 SM-Bank 42 Find the values of for which. (2 marks) 5. Functions, 2ADV F1 2007 HSC 1b Solve and graph the solution on a number line. (2 marks) 16. Functions, 2ADV F1 SM-Bank 44 Solve (2 marks) 6. Functions, 2ADV F1 2009 HSC 1c Solve. (2 marks) 17. Functions, 2ADV F1 SM-Bank 37 7. Functions, 2ADV F1 2010 HSC 1d Find all values of for which. (3 marks) Solve. (2 marks) 18. Functions, 2ADV F1 2016 HSC 11a 8. Functions, 2ADV F1 2006 HSC 1e Sketch the graph of (2 marks) Solve. (2 marks) 9. Functions, 2ADV F1 2011 HSC 1e Solve. (2 marks) 10. Functions, 2ADV F1 2017 HSC 11g Solve. (2 marks) 11. Functions, 2ADV F1 2018 HSC 11b Solve. (2 marks) 12. Functions, 2ADV F1 2008 HSC 1d Solve. (2 marks) 19. Functions, 2ADV F1 SM-Bank 36 21. Functions, 2ADV F1 EQ-Bank 6 The graph of is shown below. It has asymptotes at and. Consider the function. Using interval notation, state the domain and range of. (2 marks) i. Sketch the graph. (2 marks) 22. Functions, 2ADV F1 EQ-Bank 7 ii. On the same graph, sketch. (2 marks) The current of an electrical circuit, measured in amps (A), varies inversely with its resistance, measured in ohms (R). When the resistance of a circuit is 28 ohms, the current is 3 amps. 20. Functions, 2ADV F1 2019 HSC 13e What is the current when the resistance is 8 ohms? (2 marks) i. Sketch the graph of for. (1 mark) ii. Using the sketch from part i, or otherwise, solve. (2 marks) 23. Functions, 2ADV F1 EQ-Bank 8 Jacques is a marine biologist and finds that the mass of a crab is directly proportional to the cube of the diameter of its shell. If a crab with a shell diameter of 15 cm weighs 680 grams, what will be the diameter of a crab that weighs 1.1 kilograms? Give your answer to 1 decimal place. (2 marks) 24. Functions, 2ADV F1 EQ-Bank 26 Fuifui finds that for Giant moray eels, the mass of an eel is directly proportional to the cube of its length. An eel of this species has a length of 25 cm and a mass of 4350 grams. What is the expected length of a Giant moray eel with a mass of 6.2 kg? Give your answer to one decimal place. (3 marks) 25. Functions, 2ADV F1 EQ-Bank 27 Worked Solutions The stopping distance of a car on a certain road, once the brakes are applied, is directly proportional to the square of the speed of the car when the brakes are first applied. 1. Functions, 2ADV F1 2019 HSC 2 MC A car travelling at 70 km/h takes 58.8 metres to stop. How far does it take to stop if it is travelling at 105 km/h? (3 marks) 26. Functions, 2ADV F1 SM-Bank 32 Find the centre and radius of the circle with the equation (2 marks) 2. Functions, 2ADV F1 2013 HSC 3 MC 27. Functions, 2ADV F1 2010 HSC 1c Write down the equation of the circle with centre (–1, 2) and radius 5. (1 mark) 28. Functions, 2ADV F1 2010 HSC 1g Let. What is the domain of ? (1 mark) 29. Functions, 2ADV F1 2017 HSC 11h Find the domain of the function. (2 marks) 3. Functions, 2ADV F1 2020 HSC 1 MC 30. Functions, 2ADV F1 2020 HSC 24 The circle of is reflected in the -axis. Sketch the reflected circle, showing the coordinates of the centre and the radius. (3 marks) Copyright © 2004-21 The State of New South Wales (Board of Studies, Teaching and Educational Standards NSW) 4. Functions, 2ADV F1 SM-Bank 21 MC 8. Functions, 2ADV F1 2006 HSC 1e 9. Functions, 2ADV F1 2011 HSC 1e 5. Functions, 2ADV F1 2007 HSC 1b 10. Functions, 2ADV F1 2017 HSC 11g MARKER'S COMMENT: Note that both conditions must be satisfied! Dealing with negative signs and division for inequalities produced many errors. 6. Functions, 2ADV F1 2009 HSC 1c 11. Functions, 2ADV F1 2018 HSC 11b 7. Functions, 2ADV F1 2010 HSC 1d 12. Functions, 2ADV F1 2008 HSC 1d 15. Functions, 2ADV F1 SM-Bank 42 13. Functions, 2ADV F1 SM-Bank 33 i. 16. Functions, 2ADV F1 SM-Bank 44 ii. 17. Functions, 2ADV F1 SM-Bank 37 14. Functions, 2ADV F1 SM-Bank 41 18. Functions, 2ADV F1 2016 HSC 11a 19. Functions, 2ADV F1 SM-Bank 36 i. ii. 20. Functions, 2ADV F1 2019 HSC 13e 23. Functions, 2ADV F1 EQ-Bank 8 (i) ii. 24. Functions, 2ADV F1 EQ-Bank 26 21. Functions, 2ADV F1 EQ-Bank 6 22. Functions, 2ADV F1 EQ-Bank 7 25. Functions, 2ADV F1 EQ-Bank 27 29. Functions, 2ADV F1 2017 HSC 11h 30. Functions, 2ADV F1 2020 HSC 24 26. Functions, 2ADV F1 SM-Bank 32 ♦ Mean mark 48%. 27. Functions, 2ADV F1 2010 HSC 1c MARKER'S COMMENT: Expanding this equation is not necessary! 28. Functions, 2ADV F1 2010 HSC 1g Copyright © 2016-2022 M2 Mathematics Pty Ltd (SmarterMaths.com.au) ♦ Mean mark 49%. MARKER'S COMMENT: was a common incorrect answer.  Questions ADV: Functions (Adv), F1 Working with Functions (Adv) Linear Functions (Y11) 1. Algebra, STD2 A4 SM-Bank 6 MC Teacher: Morgen Sugiharto A computer application was used to draw the graphs of the equations Exam Equivalent Time: 90 minutes (based on HSC allocation of 1.5 minutes approx. per and mark) Part of the screen is shown. F1 Working With Functions 1% 2% 3% 4% 5% 6% 7% 8% Algebraic Techniques *Analytics based on the average contribution to Advanced HSC Linear Functions exams over the last decade. Quadratics and Cubic Functions Further Functions and Relations HISTORICAL CONTRIBUTION F1 Working with Functions is a Year 11 topic whose content represents the lowest of low hanging fruit in the new Advanced course. F1 Working with Functions includes new and a significant re-categorisation of old syllabus content. Any insights from past contributions in this topic area are unavoidably limited. However, with the What is the solution when the equations are solved simultaneously? information available, our analysis has it accounting for ~7.1%. A. We have split the topic into 5 categories for analysis purposes: 1-Algebraic Techniques, 2-Linear B. Functions, 3-Quadratics and Cubic Functions, 4-Composite Functions and 5-Further Functions and Relations. C. This analysis looks at Linear Functions (2.1%). D. HSC ANALYSIS - What to expect and common pitfalls 2. Functions, 2ADV F1 2015 HSC 2 MC Linear Functions will primarily look at analysing and modelling linear relationships, with a significant What is the slope of the line with equation ? shift away from the old course Plane Geometry content. (A) This area represents common Adv/Std2 content and the 2020 HSC exams included a 4-mark common question (2020 Adv 11). (B) Modelling and analysis of linear equations looks at numerous Std2 past HSC questions which proved challenging, including breakeven analysis. (C) Although co-ordinate geometry content is diminished, some important areas remain examinable in this area and should be reviewed. (D) NESA's HSC sample exam included a challenging simultaneous equation question. Review F1 EQ- Bank 12 to cover this area. 3. Functions, 2ADV F1 2017 HSC 1 MC 6. Functions, 2ADV F1 2014 HSC 5 MC What is the gradient of the line ? Which equation represents the line perpendicular to , passing through the point ? (A) (A) (B) (B) (C) (C) (D) (D) 7. Algebra, STD2 A4 2011 HSC 20 MC A function centre hosts events for up to 500 people. The cost , in dollars, for the centre to host an event, where people attend, is given by: 4. Functions, 2ADV F1 2018 HSC 3 MC What is the -intercept of the line ? The centre charges $100 per person. Its income , in dollars, is given by: (A) (B) (C) (D) 5. Algebra, STD2 A2 2019 HSC 14 MC Last Saturday, Luke had 165 followers on social media. Rhys had 537 followers. On average, Luke gains another 3 followers per day and Rhys loses 2 followers per day. If represents the number of days since last Saturday and represents the number of followers, which pair of equations model this situation? A. B. C. How much greater is the income of the function centre when 500 people attend an event, than its income at the breakeven point? D. (A) (B) (C) (D) 8. Functions, 2ADV F1 2016 HSC 12a 13. Functions, 2ADV F1 2020 HSC 11 The diagram shows points and The point lies on such that There are two tanks on a property, Tank and Tank. Initially, Tank holds 1000 litres of water and Tank B is empty. a. Tank begins to lose water at a constant rate of 20 litres per minute. The volume of water in Tank is modelled by where is the volume in litres and is the time in minutes from when the tank begins to lose water. (1 mark) On the grid below, draw the graph of this model and label it as Tank. i. Show that the equation of is. (2 marks) NB. Parts ii-iii are not in the new syllabus. 9. Functions, 2ADV F1 2015 HSC 11a Simplify. (1 mark) 10. Functions, 2ADV F1 SM-Bank 24 Ita publishes and sells calendars for $25 each. The cost of producing the calendars is $8 each plus a set up cost of $5950. How many calendars does Ita need to sell to breakeven? (2 marks) 11. Functions, 2ADV F1 2007 HSC 1f Find the equation of the line that passes through the point and is perpendicular to. (2 marks) 12. Functions, 2ADV F1 2009 HSC 1a Sketch the graph of , showing the intercepts on both axes. (2 marks) b. Tank remains empty until when water is added to it at a constant rate of 30 litres per minute. By drawing a line on the grid (above), or otherwise, find the value of when the two tanks contain the same volume of water. (2 marks) c. Using the graphs drawn, or otherwise, find the value of (where ) when the total volume of water in the two tanks is 1000 litres. (1 mark) 14. Functions, 2ADV F1 SM-Bank 25 16. Functions, 2ADV F1 EQ-Bank 12 Damon owns a swim school and purchased a new pool pump for $3250. Two archers play a game where each can aim for a large target or a small target. He writes down the value of the pool pump by 8% of the original price each year. If an arrow hits the large target it scores points, and if it hits the small target, it scores points. i. Construct a function to represent the value of the pool pump after years. (1 mark) The results of a game are shown in the table below. ii. Draw the graph of the function and state its domain and range. (2 marks) 15. Functions, STD2 A4 SM-Bank 27 Fiona and John are planning to hold a fund-raising event for cancer research. They can hire a function room for $650 and a band for $850. Drinks will cost them $25 per person. i. Write a formula for the cost ($C) of holding the charity event for people. (1 mark) By forming a pair of simultaneous equations, or otherwise, find the value of and. (3 marks) ii. The graph below shows the planned income and costs if they charge $50 per ticket. Estimate the number of guests they need to break even. (1 mark) 17. Functions, 2ADV F1 2009 HSC 5a In the diagram, the points and lie on the -axis and the point lies on the -axis. The line has equation. The line is perpendicular to. iii. How much profit will Fiona and John make if 80 people attend their event? (1 mark) i. Find the equation of the line. (2 marks) ii. Find the area of the triangle. (2 marks) 18. Algebra, STD2 A2 2007 HSC 27b 20. Algebra, STD2 A2 2019 HSC 34 A clubhouse uses four long-life light globes for five hours every night of the year. The purchase price The relationship between British pounds and Australian dollars on a particular day is shown of each light globe is $6.00 and they each cost per hour to run. in the graph. i. Write an equation for the total cost ( ) of purchasing and running these four light globes for one year in terms of. (2 marks) ii. Find the value of (correct to three decimal places) if the total cost of running these four light globes for one year is $250. (1 mark) iii. If the use of the light globes increases to ten hours per night every night of the year, does the total cost double? Justify your answer with appropriate calculations. (1 mark) iv. The manufacturer’s specifications state that the expected life of the light globes is normally distributed with a standard deviation of 170 hours. What is the mean life, in hours, of these light globes if 97.5% will last up to 5000 hours? (1 mark) 19. Algebra, STD2 A4 2005 HSC 28b Sue and Mikey are planning a fund-raising dance. They can hire a hall for $400 and a band for $300. Refreshments will cost them $12 per person. i. Write a formula for the cost ($C) of running the dance for people. (1 mark) The graph shows planned income and costs when the ticket price is $20 a. Write the direct variation equation relating British pounds to Australian dollars in the form. Leave as a fraction. (1 mark) b. The relationship between Japanese yen and Australian dollars on the same day is given by the equation. Convert 93 100 Japanese yen to British pounds. (2 marks) ii. Estimate the minimum number of people needed at the dance to cover the costs. (1 mark) iii. How much profit will be made if 150 people attend the dance? (1 mark) Sue and Mikey plan to sell 200 tickets. They want to make a profit of $1500. iv. What should be the price of a ticket, assuming all 200 tickets will be sold? (3 marks) 21. Algebra, STD2 A2 2015 HSC 27c 22. Algebra, STD2 A2 2010 HSC 27c Ariana’s parents have given her an interest‑free loan of $4800 to buy a car. She will pay them back by The graph shows tax payable against taxable income, in thousands of dollars. paying immediately and every month until she has repaid the loan in full. After 18 months Ariana has paid back $1510, and after 36 months she has paid back $2770. This information can be represented by the following equations. i. Graph these equations below and use to solve simultaneously for the values of and. (2 marks) i. Use the graph to find the tax payable on a taxable income of $21 000. (1 mark) ii. How many months will it take Ariana to repay the loan in full? (2 marks) ii. Use suitable points from the graph to show that the gradient of the section of the graph marked is. (1 mark) iii. How much of each dollar earned between $21 000 and $39 000 is payable in tax? (1 mark) iv. Write an equation that could be used to calculate the tax payable, , in terms of the taxable income, , for taxable incomes between $21 000 and $39 000. (2 marks) 23. Algebra, STD2 A2 2009 HSC 24d Worked Solutions A factory makes boots and sandals. In any week the total number of pairs of boots and sandals that are made is 200 1. Algebra, STD2 A4 SM-Bank 6 MC the maximum number of pairs of boots made is 120 the maximum number of pairs of sandals made is 150. The factory manager has drawn a graph to show the numbers of pairs of boots ( ) and sandals ( ) that can be made. 2. Functions, 2ADV F1 2015 HSC 2 MC 3. Functions, 2ADV F1 2017 HSC 1 MC i. Find the equation of the line. (1 mark) ii. Explain why this line is only relevant between and for this factory. (1 mark) iii. The profit per week, , can be found by using the equation. Compare the profits at and. (2 marks) Copyright © 2004-21 The State of New South Wales (Board of Studies, Teaching and Educational Standards NSW) 4. Functions, 2ADV F1 2018 HSC 3 MC 5. Algebra, STD2 A2 2019 HSC 14 MC 7. Algebra, STD2 A4 2011 HSC 20 MC ♦ Mean mark 50% COMMENT: Students can read the income levels directly off the graph to save time and then check with the equations given. 6. Functions, 2ADV F1 2014 HSC 5 MC 8. Functions, 2ADV F1 2016 HSC 12a a.i. 9. Functions, 2ADV F1 2015 HSC 11a 10. Functions, 2ADV F1 SM-Bank 24 12. Functions, 2ADV F1 2009 HSC 1a 11. Functions, 2ADV F1 2007 HSC 1f 13. Functions, 2ADV F1 2020 HSC 11 a. Tank A Tank A Tank B c. b. 14. Functions, 2ADV F1 SM-Bank 25 15. Functions, STD2 A4 SM-Bank 27 i. i. ii. ii. iii. 16. Functions, 2ADV F1 EQ-Bank 12 17. Functions, 2ADV F1 2009 HSC 5a i. ii. ² 18. Algebra, STD2 A2 2007 HSC 27b i. 19. Algebra, STD2 A4 2005 HSC 28b i. ii. ii. iii. iii. iv. iv. 20. Algebra, STD2 A2 2019 HSC 34 21. Algebra, STD2 A2 2015 HSC 27c i. a. ♦ Mean mark 42%. b. ii. ♦ Mean mark 44%. 22. Algebra, STD2 A2 2010 HSC 27c i. ii. ♦♦ Mean mark 25% iii. ♦♦♦ Mean mark 12%! MARKER'S COMMENT: Interpreting gradients  is an examiner favourite, so make Copyright © 2016-2022 M2 Mathematics Pty Ltd (SmarterMaths.com.au) sure you are confident in this area. iv. ♦♦♦ Mean mark 15%. STRATEGY: The earlier parts of this question direct students to the most efficient way to solve this question. Make sure earlier parts of a question are front and centre of your mind when devising strategy. 23. Algebra, STD2 A2 2009 HSC 24d i. ♦♦♦ Mean mark part (i) 14%. Using is a less efficient but equally valid method, using and ( -intercept). ii. ♦ Mean mark 49% iii. ♦ Mean mark 40%.  Questions ADV: Functions (Adv), F1 Working with Functions (Adv) Quadratics and Cubic Functions (Y11) 1. Functions, 2ADV F1 2013 HSC 1 MC Teacher: Morgen Sugiharto What are the solutions of ? Exam Equivalent Time: 34.5 minutes (based on HSC allocation of 1.5 minutes approx. per mark) (A) (B) F1 Working With Functions (C) (D) 1% 2% 3% 4% 5% 6% 7% 8% Algebraic Techniques *Analytics based on the average contribution to Advanced HSC Linear Functions exams over the last decade. 2. Functions, 2ADV F1 2014 HSC 6 MC Quadratics and Cubic Functions Further Functions and Relations Which expression is a factorisation of ? (A) HISTORICAL CONTRIBUTION (B) F1 Working with Functions is a Year 11 topic whose content represents the lowest of low hanging (C) fruit in the new Advanced course. (D) F1 Working with Functions includes new and a significant re-categorisation of old syllabus content. Any insights from past contributions in this topic area are unavoidably limited. However, with the information available, our analysis has it accounting for ~7.1%. 3. Functions, 2ADV F1 2017 HSC 2 MC We have split the topic into 5 categories for analysis purposes: 1-Algebraic Techniques, 2-Linear Functions, 3-Quadratics and Cubic Functions, 4-Composite Functions and 5-Further Functions and Which expression is equal to ? Relations. (A) This analysis looks at Quadratics and Cubic Functions (1.4%). (B) HSC ANALYSIS - What to expect and common pitfalls (C) Quadratic factorisation has easily been the most common question style in this sub-topic, offering up (D) easy marks in 5 exams within the last decade. Students have also been asked to solve quadratics using the general formula and to find the intersection of quadratic and linear equations. Cubic questions that fall within this sub-topic are rare, with the graphing of cubics typically requiring calculus - a question type covered within the Calculus topic. The graphic representation of an odd function was poorly answered in 2016 and should be reviewed. 4. Functions, 2ADV F1 2016 HSC 4 MC 10. Functions, 2ADV F1 2012 HSC 11a Which diagram shows the graph of an odd function? Factorise (2 marks) 11. Functions, 2ADV F1 2014 HSC 11b Factorise. (2 marks) 12. Functions, 2ADV F1 2015 HSC 11b Factorise fully. (2 marks) 13. Functions, 2ADV F1 SM-Bank 23 Find the values of for which the expression is always positive. (3 marks) Copyright © 2004-21 The State of New South Wales (Board of Studies, Teaching and Educational Standards NSW) 5. Functions, 2ADV F1 2006 HSC 1b Factorise. (2 marks) 6. Functions, 2ADV F1 2007 HSC 1e Factorise. (2 marks) 7. Functions, 2ADV F1 2016 HSC 11e Find the points of intersection of and (3 marks) 8. Functions, 2ADV F1 2010 HSC 1a Solve. (2 marks) 9. Functions, 2ADV F1 2011 HSC 1b Simplify. (1 mark) Worked Solutions 5. Functions, 2ADV F1 2006 HSC 1b 1. Functions, 2ADV F1 2013 HSC 1 MC 6. Functions, 2ADV F1 2007 HSC 1e 7. Functions, 2ADV F1 2016 HSC 11e 2. Functions, 2ADV F1 2014 HSC 6 MC COMMENT: Factorising a cubic is only examinable with scaffolding, as provided here by expanding the answer options. 3. Functions, 2ADV F1 2017 HSC 2 MC 8. Functions, 2ADV F1 2010 HSC 1a 4. Functions, 2ADV F1 2016 HSC 4 MC ♦ Mean mark 38%. 9. Functions, 2ADV F1 2011 HSC 1b 10. Functions, 2ADV F1 2012 HSC 11a STRATEGY: Check your answer by expanding factors. 11. Functions, 2ADV F1 2014 HSC 11b 12. Functions, 2ADV F1 2015 HSC 11b 13. Functions, 2ADV F1 SM-Bank 23 Copyright © 2016-2022 M2 Mathematics Pty Ltd (SmarterMaths.com.au)  Questions ADV: Functions (Adv), F2 Graphing (Adv) Non-Calculus Graphing (Y12) 1. Functions, 2ADV F2 SM-Bank 9 MC Teacher: Morgen Sugiharto The graph of the function , has asymptotes at Exam Equivalent Time: 61.5 minutes (based on HSC allocation of 1.5 minutes approx. per mark) A. F2 Graphing B. C. D. 1% 2% 3% 4% 2. Functions, 2ADV’ F2 2019 HSC 4 MC *Analytics based on the average Transformations contribution to Advanced HSC The diagram shows the graph of. Non- Calculus Graphing exams since 2020. HISTORICAL CONTRIBUTION F2 Graphing Techniques is a Year 12 topic whose content includes a mixture of new content and old course Mathematics and Ext1 content. We have split the topic into 2 categories for analysis purposes: 1-Transformations (1.5%) and 2-Non-Calculus Graphing (2.0%). This analysis looks at Non-Calculus Graphing. HSC ANALYSIS - What to expect and common pitfalls Non-Calculus Graphing looks at a variety of functions that can be graphed without using calculus to find turning points and points of inflection etc... The most common question type is easily the graphing of quotient functions that require students to find intercepts and both vertical and horizontal asymptotes. This was last examined in the 2021 exam and relatively well answered. The old Ext1 course provides a number of past HSC examples that have been recategorised into this Advanced topic. These will prove challenging and provide high Which equation best describes the graph? quality revision. They are identified by the inclusion of ADV' in their title. A. The algebraic manipulation of some quotient functions before graphing can save significant time. We recommend reviewing F2 EQ-Bank 11 to illustrate this. B. Students should be looking for the possibility of functions being odd or even. When identified, graphing solutions can be produced much more efficiently (see 2ADV′ F2 C. 2012 HSC 13b). D. 3. Functions, 2ADV F2 2021 HSC 5 MC 6. Functions, 2ADV’ F2 2017 HSC 5 MC Which of the following best represents the graph of ? Which graph best represents the function ? A. y B. y A. y B. y 10 8 x x –1 1 x –1 1 x C. y D. y C. y D. y 2 10 8 x x –1 1 x –1 1 x –2 4. Functions, 2ADV F2 SM-Bank 10 MC The graph of the function has asymptotes A. 7. Functions, 2ADV F1 SM-Bank 35 B. i. Sketch the function where on a number plane, labelling all C. intercepts. (1 mark) D. ii. On the same graph, sketch. Label all intercepts. (2 marks) 5. Functions, 2ADV’ F2 2015 HSC 5 MC 8. Functions, 2ADV F2 EQ-Bank 9 What are the asymptotes of Consider the function. i. Find the domain of. (1 mark) (A) ii. Sketch , showing all asymptotes and intercepts? (2 marks) (B) (C) (D) 9. Functions, 2ADV’ F2 2012 HSC 13b 13. Functions, 2ADV F2 EQ-Bank 11 i. Find the horizontal asymptote of the graph. (1 mark) On the axes below, sketch the graph of. Label all axis intercepts. Label each asymptote with its equation. (4 marks) ii. Without the use of calculus, sketch the graph , showing the asymptote found in part (i). (2 marks) 10. Functions, 2ADV F2 2021 HSC 19 Without using calculus, sketch the graph of , showing the asymptotes and the and intercepts. (3 marks) 11. Functions, 2ADV F2 SM-Bank 13 i. Show that the function is an odd function? (1 mark) ii. Sketch , labelling all intercepts and asymptotes. (2 marks) 12. Functions, 2ADV F2 SM-Bank 10 Consider the function. i. Identify the domain of. (1 mark) ii. Sketch the graph , showing all intercepts and asymptotes. (3 marks) 14. Functions, 2ADV F2 SM-Bank 12 16. Functions, 2ADV F2 SM-Bank 20 Sketch the graph of. Label the axis intercepts with their coordinates and label a. Sketch the graph of on the axes below. Label asymptotes with their equations any asymptotes with the appropriate equation. (4 marks) and axis intercepts with their coordinates. (3 marks) y 6 5 4 3 2 1 x 0 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 –1 –2 –3 –4 –5 –6 b. Find the values of for which. (1 mark) Copyright © 2004-21 The State of New South Wales (Board of Studies, Teaching and Educational Standards NSW) 15. Functions, 2ADV’ F2 2007 HSC 3b i. Find the vertical and horizontal asymptotes of the hyperbola and hence sketch the graph of. (3 marks) ii. Hence, or otherwise, find the values of for which. (2 marks) Worked Solutions 4. Functions, 2ADV F2 SM-Bank 10 MC 1. Functions, 2ADV F2 SM-Bank 9 MC 5. Functions, 2ADV’ F2 2015 HSC 5 MC 2. Functions, 2ADV’ F2 2019 HSC 4 MC 6. Functions, 2ADV’ F2 2017 HSC 5 MC 3. Functions, 2ADV F2 2021 HSC 5 MC 7. Functions, 2ADV F1 SM-Bank 35 8. Functions, 2ADV F2 EQ-Bank 9 i. i. ii. ii. 9. Functions, 2ADV’ F2 2012 HSC 13b 10. Functions, 2ADV F2 2021 HSC 19 i. y ii. 2.25 y=2 x _ 4.5 x =_4 11. Functions, 2ADV F2 SM-Bank 13 12. Functions, 2ADV F2 SM-Bank 10 i. i. ii. COMMENT: Note that is a short way of writing as approaches 2 from the negative (or left-hand) side. This notation can save time when required. ii. 13. Functions, 2ADV F2 EQ-Bank 11 14. Functions, 2ADV F2 SM-Bank 12 15. Functions, 2ADV’ F2 2007 HSC 3b 16. Functions, 2ADV F2 SM-Bank 20 a. i. x=2 (1, 3) (0, 2) y=1 (4, 0) b. ii. Copyright © 2016-2022 M2 Mathematics Pty Ltd (SmarterMaths.com.au)  Questions ADV: Functions (Adv), F2 Graphing (Adv) Transformations (Y12) 1. Functions, 2ADV F2 2016 HSC 3 MC Teacher: Morgen Sugiharto Which diagram best shows the graph of the parabola Exam Equivalent Time: 66 minutes (based on HSC allocation of 1.5 minutes approx. per mark) F2 Graphing 1% 2% 3% 4% *Analytics based on the average Transformations contribution to Advanced HSC Non- Calculus Graphing exams since 2020. HISTORICAL CONTRIBUTION F2 Graphing Techniques is a Year 12 topic whose content includes a mixture of new content and old course Mathematics and Ext1 content. We have split the topic into 2 categories for analysis purposes: 1-Transformations (1.5%) and 2-Non-Calculus Graphing (2.0%). This analysis looks at Transformations. HSC ANALYSIS - What to expect and common pitfalls Transformations represents new syllabus content that explicitly looks at translations and dilations of several function types, including the introduction of the aforementioned terminology. This topic has been examined in both new syllabus exams, with 2021 Q21 causing problems with a 48% state mean mark. The NESA sample HSC exam, released in March 2020, has been instructive in developing this challenging database area. Pay careful attention to F2 EQ-Bank questions. There have been some examples in past HSC exams that looked at similar content. Please review of F2 2013 HSC 15c which proved very challenging for a majority of students. We note that Trig transformations, which we regard as an extremely important transformation sub-topic, are covered separately under T3 Trig Graphs. This topic area provides scope for examiners to ask both low and high difficulty questions, with a variety of underlying functions. 2. Functions, 2ADV F2 EQ-Bank 2 MC 4. Functions, 2ADV F2 SM-Bank 5 MC Which diagram best shows the graph The point lies on the graph of a function. The graph of is translated four units vertically up and then reflected in the -axis. The coordinates of the final image of are A. B. A. B. C. D. 5. Functions, 2ADV F2 2014 HSC 2 MC Which graph best represents ? C. D. 3. Functions, 2ADV F2 2020 HSC 2 MC The function is transformed to by a horizontal translation of 2 units followed by a vertical translation of 5 units. Which row of the table shows the directions of the translations? 6. Functions, 2ADV F2 SM-Bank 6 MC 9. Functions, 2ADV F2 SM-Bank 8 MC The graph of a function is obtained from the graph of the function by a The transformation that maps the graph of onto the graph of is a reflection in the -axis followed by a dilation from the -axis by a factor of. A. dilation by a factor of from the -axis. Which one of the following is the function ? B. dilation by a factor of from the -axis. A. C. dilation by a factor of from the -axis. B. C. D. dilation by a factor of from the -axis. D. 10. Functions, 2ADV F2 2006 HSC 1c 7. Functions, 2ADV F2 SM-Bank 4 MC Sketch the graph of. (2 marks) The graph of the function is reflected in the -axis and then translated 3 units to the right and 4 units down. 11. Functions, 2ADV F2 SM-Bank 1 The equation of the new graph is i. Draw the graph. (1 mark) A. ii. Explain how the above graph can be transformed to produce the graph B. C. and sketch the graph, clearly identifying all intercepts. (3 marks) D. 12. Functions, 2ADV F1 SM-Bank 35 8. Functions, 2ADV F2 SM-Bank 7 MC i. Sketch the function where on a number plane, labelling all The point lies on the graph of the function. A transformation maps the graph of intercepts. (1 mark) to the graph of , ii. On the same graph, sketch. Label all intercepts. (2 marks) where. The same transformation maps the point to the point. 13. Functions, 2ADV F2 EQ-Bank 9 The coordinates of the point are A. has been produced by three successive transformations: a translation, a B. dilation and then a reflection. C. i. Describe each transformation and state the equation of the graph after each transformation. (2 marks) D. ii. Sketch the graph. (1 mark) 14. Functions, 2ADV F2 EQ-Bank 1 18. Functions, 2ADV F2 SM-Bank 3 The function is transformed and the equation of the new function is. The diagram below shows part of the graph of the function with rule The graph of the new function is shown below. , where , and are real constants. The graph has a vertical asymptote with equation. The graph has a y-axis intercept at 1. The point on the graph has coordinates , where is another real constant. What are the values of , and. (2 marks) 15. Functions, 2ADV F2 EQ-Bank 14 List a set of transformations that, when applied in order, would transform to the graph with equation. (3 marks) 16. Functions, 2ADV F2 SM-Bank 16 i. State the value of. (1 mark) Let ii. Find the value of. (1 mark) Let the graph of be a transformation of the graph of where the transformations have been iii. Show that. (2 marks) applied in the following order: dilation by a factor of from the vertical axis (parallel to the horizontal axis) translation by two units to the right (in the direction of the positive horizontal axis 19. Functions, 2ADV F2 EQ-Bank 13 Find and the coordinates of the horizontal axis intercepts of the graph of. (3 marks) The curve is subject to the following transformations Translated 2 units in the positive -direction 17. Functions, 2ADV F2 SM-Bank 2 Dilated in the positive -direction by a factor of 4 Sketch the graph. Reflected in the -axis Show all asymptotes and state its domain and range. (3 marks) The final equation of the curve is. i. Find the equation of the graph after the dilation. (1 mark) ii. Find the values of and. (2 marks) 20. Functions, 2ADV F2 2021 HSC 21 Worked Solutions Consider the graph of as shown. 1. Functions, 2ADV F2 2016 HSC 3 MC y NOT TO SCALE O 6 x 2. Functions, 2ADV F2 EQ-Bank 2 MC (4, −8) Sketch the graph of showing the -intercepts and the coordinates of the turning points. (2 marks) 21. Functions, 2ADV F2 2013 HSC 15c i. Sketch the graph. (1 mark) ii. Using the graph from part (i), or otherwise, find all values of for which the equation has exactly one solution. (2 marks) 3. Functions, 2ADV F2 2020 HSC 2 MC Copyright © 2004-21 The State of New South Wales (Board of Studies, Teaching and Educational Standards NSW) 4. Functions, 2ADV F2 SM-Bank 5 MC 5. Functions, 2ADV F2 2014 HSC 2 MC 8. Functions, 2ADV F2 SM-Bank 7 MC 6. Functions, 2ADV F2 SM-Bank 6 MC COMMENT: Using "swap" terminology for dilations from the y-axis is simpler and more intelligible for students in our view. 9. Functions, 2ADV F2 SM-Bank 8 MC 7. Functions, 2ADV F2 SM-Bank 4 MC 10. Functions, 2ADV F2 2006 HSC 1c 11. Functions, 2ADV F2 SM-Bank 1 12. Functions, 2ADV F1 SM-Bank 35 i. i. ii. ii. 13. Functions, 2ADV F2 EQ-Bank 9 14. Functions, 2ADV F2 EQ-Bank 1 i. 15. Functions, 2ADV F2 EQ-Bank 14 ii. 16. Functions, 2ADV F2 SM-Bank 16 18. Functions, 2ADV F2 SM-Bank 3 i. ii. iii. 17. Functions, 2ADV F2 SM-Bank 2 19. Functions, 2ADV F2 EQ-Bank 13 21. Functions, 2ADV F2 2013 HSC 15c i. i. ♦ Mean mark 49% MARKER'S COMMENT: Many students drew diagrams that were "too small", didn't use rulers or didn't use a consistent scale on the axes! ii. COMMENT: Using "swap" ii. terminology for reflections in the y-axis is simpler and more intelligible for students in our view. ♦♦ Mean mark 25%. COMMENT: Students need a clear 20. Functions, 2ADV F2 2021 HSC 21 graphical understanding of what they are finding to solve this very challenging, Band 6 question. y ♦ Mean mark 48%. − − − − O 1 2 3 x (2, −32) Copyright © 2016-2022 M2 Mathematics Pty Ltd (SmarterMaths.com.au)