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    18 Logs and Exponentials Integration

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    18 Logs and Exponentials Integration

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    24 views6 pages

    18 Logs and Exponentials Integration

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    of 6

    Questions

    ADV: Calculus (Adv), C4 Integration (Adv), Integration (Y12)


    L&E Integration 1. Calculus, 2ADV C4 2014 HSC 4 MC

    Teacher: Robert Trenwith Which expression is equal to ?


    Exam Equivalent Time: 72 minutes (based on HSC allocation of 1.5 minutes approx. per
    mark)
    (A)

    (B)

    (C)

    (D)

    2. Calculus, 2ADV C4 2020 HSC 4 MC

    What is ?

    A.
    HISTORICAL CONTRIBUTION
    B.
    C4 Integration has contributed a substantial 13.2% to past Mathematics exams, on
    average over the past decade. C.

    This topic has been split into four sub-topics for analysis purposes: 1-Integrals (5.3%),
    D.
    2-Areas Under Curves (4.1%), 3-Trapezoidal Rule (2.3%) and 4-Other Integration
    Examples (1.5%).
    This analysis looks at Integrals. 3. Calculus, 2ADV C4 2012 HSC 9 MC

    HSC ANALYSIS - What to expect and common pitfalls What is the value of ?

    Integrals (5.3%) is made up of standard integration (1.5%), log and exponential


    integration (2.6%) and trig integration (1.2%). (A)

    Dedicated questions testing log and exponential integration have consistently


    appeared in past HSC exams - absent in just 1 exam of the past decade and (B)
    including a record 3 separate questions in the 2020 exam. (C)
    Questions requiring students to differentiate then integrate have easily been the worst (D)
    answered question type in this area, causing surprising problems in 2020 and 2019 -
    an important revision area.
    Integration of a fraction that results in a logarithm is a 2-3 mark question type that
    4. Calculus, 2ADV C4 2013 HSC 11e
    has appeared 5 times in the last decade, but just once in the last 5 years (2020 Adv
    17).
    Find (2 marks)
    We note 2019 HSC 13c(ii) surprisingly produced a sub-50% mean mark and deserves
    attention.
    5. Calculus, 2ADV C4 2004 HSC 3bi 13. Calculus, 2ADV C4 2020 HSC 17

    Evaluate . (2 marks) Find . (2 marks)

    6. Calculus, 2ADV C4 2006 HSC 2bi 14. Calculus, 2ADV C4 SM-Bank 1

    Find . (2 marks) If , express in its simplest form. (2 marks)

    7. Calculus, 2ADV C4 2015 HSC 11h 15. Calculus, 2ADV C4 SM-Bank 3

    Find . (2 marks) If and find . (3 marks)

    8. Calculus, 2ADV C4 2018 HSC 11e 16. Calculus, 2ADV C4 2005 HSC 2ci

    Evaluate . (2 marks) Find . (2 marks)

    9. Calculus, 2ADV C4 2016 HSC 12d 17. Calculus, 2ADV C4 2008 HSC 2ci

    i. Differentiate . (1 mark)
    Find . (1 mark)

    ii. Hence find the exact value of . (2 marks)

    18. Calculus, 2ADV C4 2010 HSC 2dii

    10. Calculus, 2ADV C4 2004 HSC 3bii Find . (2 marks)

    Find . (2 marks)

    19. Calculus, 2ADV C4 2011 HSC 4b

    11. Calculus, 2ADV C4 2006 HSC 2bii


    Evaluate (2 marks)

    Evaluate . (3 marks)

    20. Calculus, 2ADV C4 2012 HSC 12b


    12. Calculus, 2ADV C4 2019 MET1-N 3
    Find . (2 marks)

    Evaluate . (2 marks)
    21. Calculus, 2ADV C4 2013 HSC 11f Worked Solutions

    Evaluate (3 marks)
    1. Calculus, 2ADV C4 2014 HSC 4 MC

    22. Calculus, 2ADV C4 2019 HSC 13c

    i. Differentiate . (2 marks)

    ii. Hence, or otherwise, find . (1 mark)


    2. Calculus, 2ADV C4 2020 HSC 4 MC

    23. Calculus, 2ADV C4 2020 HSC 18

    a. Differentiate . (2 marks)

    b. Hence, find . (1 marks)

    3. Calculus, 2ADV C4 2012 HSC 9 MC


    Copyright © 2004-20 The State of New South Wales (Board of Studies, Teaching and Educational Standards NSW)

    TIP: Note that , as

    4. Calculus, 2ADV C4 2013 HSC 11e

    5. Calculus, 2ADV C4 2004 HSC 3bi


    6. Calculus, 2ADV C4 2006 HSC 2bi 10. Calculus, 2ADV C4 2004 HSC 3bii

    7. Calculus, 2ADV C4 2015 HSC 11h

    11. Calculus, 2ADV C4 2006 HSC 2bii

    8. Calculus, 2ADV C4 2018 HSC 11e

    12. Calculus, 2ADV C4 2019 MET1-N 3

    9. Calculus, 2ADV C4 2016 HSC 12d

    i.

    13. Calculus, 2ADV C4 2020 HSC 17

    ii.
    14. Calculus, 2ADV C4 SM-Bank 1 17. Calculus, 2ADV C4 2008 HSC 2ci

    18. Calculus, 2ADV C4 2010 HSC 2dii

    IMPORTANT: Minimise errors by


    adjusting the integral to fit the

    15. Calculus, 2ADV C4 SM-Bank 3 form before integrating.

    19. Calculus, 2ADV C4 2011 HSC 4b

    MARKER'S COMMENT: Most


    common error was .
    Minimize errors by getting the

    integral in the form of

    before integrating.

    20. Calculus, 2ADV C4 2012 HSC 12b

    16. Calculus, 2ADV C4 2005 HSC 2ci


    21. Calculus, 2ADV C4 2013 HSC 11f 23. Calculus, 2ADV C4 2020 HSC 18

    a.

    TIP: Note that , ♦ Mean mark part (b) 40%.


    because
    b.

    22. Calculus, 2ADV C4 2019 HSC 13c


    Copyright © 2016-2021 M2 Mathematics Pty Ltd (SmarterMaths.com.au)

    i.

    ♦ Mean mark part (ii) 49%.


    ii.

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