WORKSHEET - Mathematics (Advanced) 8. Differentiation Logs and Exponentials - Differentiation Standard / 1st Principles Trig Differentiation Teacher: James Butterworth Exam Equivalent Time: 103.5 minutes (based on HSC allocation of 1.5 minutes approx. per mark) Questions 3. Trig Calculus, 2UA 2013 HSC 4 MC What is the derivative of ? (A) (B) (C) (D) 1. L&E, 2UA 2016 HSC 5 MC 4. Differentiation, 2UA 2016 HSC 11b What is the derivative of (A) Differentiate (B) (C) (2 marks) 5. L&E, 2UA 2008 HSC 2aii (D) Differentiate with respect to 2. L&E, 2UA 2017 HSC 3 MC What is the derivative of (A) (B) (C) (D) : (2 marks) ? 6. Trig Calculus, 2UA 2012 HSC 12aii Differentiate with respect to . . (2 marks) 7. Differentiation, 2UA 2004 HSC 1b Differentiate with respect to . 8. Differentiation, 2UA 2005 HSC 2bii Differentiate with respect to : (2 marks) (2 marks) 18. L&E, 2UA 2017 HSC 11d 9. Differentiation, 2UA 2014 HSC 11c Differentiate . Differentiate (2 marks) , where Differentiate with respect to . (2 marks) . (2 marks) 13. L&E, 2UA 2012 HSC 11d Differentiate . (2 marks) 14. L&E, 2UA 2012 HSC 12ai Differentiate with respect to (2 marks) 21. Trig Calculus, 2UA 2009 HSC 2ai 12. L&E, 2UA 2011 HSC 1d with respect to . (2 marks) Differentiate with respect to : Differentiate with respect to . Differentiate : 20. Trig Calculus, 2UA 2007 HSC 2a(ii) 11. L&E, 2UA 2009 HSC 2aii . (2 marks) 19. Trig Calculus, 2UA 2004 HSC 3aii 10. Differentiation, 2UA 2015 HSC 12c Find . (2 marks) Differentiate with respect to : (2 marks) 22. Trig Calculus, 2UA 2010 HSC 1e Differentiate with respect to . (2 marks) 23. Trig Calculus, 2UA 2010 HSC 2a Differentiate with respect to . (2 marks) (2 marks) 15. L&E, 2UA 2013 HSC 11d Differentiate (2 marks) 16. L&E, 2UA 2007 HSC 2ai Differentiate with respect to : 24. Trig Calculus, 2UA 2011 HSC 4a Differentiate with respect to . (2 marks) 25. Trig Calculus, 2UA 2013 HSC 11c Differentiate . (2 marks) (2 marks) 26. Trig Calculus, 2UA 2017 HSC 11c 17. L&E, 2UA 2015 HSC 11e Differentiate . (2 marks) Differentiate . (2 marks) 33. Differentiation, 2UA 2013 HSC 11b 27. Trig Calculus, 2UA 2008 HSC 2aiii Differentiate with respect to . : Evaluate . (2 marks) (2 marks) Copyright © 2004-16 The State of New South Wales (Board of Studies, Teaching and Educational Standards NSW) 28. L&E, 2UA 2016 HSC 12d i. Differentiate (1 mark) ii. Hence find the exact value of (2 marks) 29. Trig Calculus, 2UA 2006 HSC 2a Differentiate with respect to : (i) (ii) (2 marks) (2 marks) 30. L&E, 2UA 2015 HSC 11f Differentiate . (2 marks) 31. Trig Calculus, 2UA 2014 HSC 13a (i) Differentiate . (1 mark) (ii) Hence, or otherwise, find . (2 marks) 32. Integration, 2UA 2011 HSC 4d (i) Differentiate with respect to (ii) Hence, or otherwise, find . (2 marks) . (2 marks) Worked Solutions 4. Differentiation, 2UA 2016 HSC 11b 1. L&E, 2UA 2016 HSC 5 MC 2. L&E, 2UA 2017 HSC 3 MC 5. L&E, 2UA 2008 HSC 2aii 3. Trig Calculus, 2UA 2013 HSC 4 MC 6. Trig Calculus, 2UA 2012 HSC 12aii 7. Differentiation, 2UA 2004 HSC 1b 8. Differentiation, 2UA 2005 HSC 2bii 9. Differentiation, 2UA 2014 HSC 11c 10. Differentiation, 2UA 2015 HSC 12c 13. L&E, 2UA 2012 HSC 11d 14. L&E, 2UA 2012 HSC 12ai 11. L&E, 2UA 2009 HSC 2aii 12. L&E, 2UA 2011 HSC 1d 15. L&E, 2UA 2013 HSC 11d 16. L&E, 2UA 2007 HSC 2ai 19. Trig Calculus, 2UA 2004 HSC 3aii 20. Trig Calculus, 2UA 2007 HSC 2a(ii) 21. Trig Calculus, 2UA 2009 HSC 2ai 17. L&E, 2UA 2015 HSC 11e 22. Trig Calculus, 2UA 2010 HSC 1e 18. L&E, 2UA 2017 HSC 11d COMMENT: There is no necessity to take out the common factor in this case. 25. Trig Calculus, 2UA 2013 HSC 11c 23. Trig Calculus, 2UA 2010 HSC 2a MARKER'S COMMENT: A significant number of students did not know the quotient rule and many found assistance by writing out before going into calculations. 26. Trig Calculus, 2UA 2017 HSC 11c 24. Trig Calculus, 2UA 2011 HSC 4a 27. Trig Calculus, 2UA 2008 HSC 2aiii 28. L&E, 2UA 2016 HSC 12d 30. L&E, 2UA 2015 HSC 11f i. ii. 31. Trig Calculus, 2UA 2014 HSC 13a (i) 29. Trig Calculus, 2UA 2006 HSC 2a (i) (ii) (ii) 32. Integration, 2UA 2011 HSC 4d (i) IMPORTANT: Some students might find calculations easier by rewriting the equation as . (ii) 33. Differentiation, 2UA 2013 HSC 11b ♦ Mean mark 47% MARKER'S COMMENT: A poorly answered question that showed up a weakness in cubic factorisation. Copyright © 2014-2017 M2 Mathematics Pty Ltd (SmarterMaths.com.au)