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Unit 3 Question 1

Unit 3 Question 1. How do you prove that three 3-D points, A, B and C, are collinear ?. Answer to Unit 3 Question 1. Prove that vector AB is a multiple of vector BC AB = k BC And state that B is common to both vectors. Unit 3 Question 2. How do you add or subtract vectors ?.

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Unit 3 Question 1

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  1. Unit 3 Question 1 • How do you prove that three 3-D points, A, B and C, are collinear ? 3.1

  2. Answer to Unit 3 Question 1 • Prove that vector AB is a multiple of vector BC AB = k BC • And state that B is common to both vectors

  3. Unit 3 Question 2 • How do you add or subtract vectors ? 3.1

  4. Answer to Unit 3 Question 2 • add or subtract matching components

  5. Unit 3 Question 3 • State the three rules of logs? 3.3

  6. Answer to Unit 3 Question 3 • (i) logaxy = logax + logay • (ii) loga = logax – logay • (iii) logaxn = nlogax x y

  7. Unit 3 Question 4 • What does ksin(x-a) expand out to? 3.4

  8. Answer to Unit 3 Question 4 • ksinxcosa-kcosxsina

  9. Unit 3 Question 5 a b c • If u = then what is u? 3.1

  10. Answer to Unit 3 Question 5 • work out length √(a2+b2+c2)

  11. Unit 3 Question 6 • What does • a.aequal ? 3.1

  12. Answer to Unit 3 Question 6 • a ²

  13. Unit 3 Question 7 • Express the equation y=kxn in the form of the equation of a straight line, Y=nX+c. 3.3

  14. Answer to Unit 3 Question 7 • logy = nlogx + logk

  15. Unit 3 Question 8 • How do you show that two vectors are perpendicular ? 3.1

  16. a b Answer to Unit 3 Question 8 • Show that a.b=0

  17. Unit 3 Question 9 • What do you get when you differentiate cosx ? 3.2

  18. Answer to Unit 3 Question 9 • -sinx

  19. Unit 3 Question 10 • What is • logax – logay equal to ? 3.3

  20. Answer to Unit 3 Question 10 • x loga y

  21. Unit 3 Question 11 • How do you name the angle between a line and a plane ? 3.1

  22. A C B Answer to Unit 3 Question 11 • (i) start at end of line (A) • (ii) go to where line meets the plane (B) • (iii) go to the point on the plane directly under the start of the line (C) • (iv) Answer is ABC

  23. Unit 3 Question 12 • What is a position vector ? 3.1

  24. Answer to Unit 3 Question 12 • A vector which startsat the origin

  25. Unit 3 Question 13 • What do you get when you differentiatesin x? 3.2

  26. Answer to Unit 3 Question 13 • cos x

  27. Unit 3 Question 14 • How do you integrate cos ax ? 3.2

  28. Answer to Unit 3 Question 14 • 1/a sin ax + C

  29. Unit 3 Question 15 • What do you get when you differentiate • cosax ? 3.2

  30. Answer to Unit 3 Question 15 • -asinax

  31. Unit 3 Question 16 • How would you differentiate a function like y = sin ax? 3.2

  32. Answer to Unit 3 Question 16 • dy/dx = acos ax

  33. Unit 3 Question 17 • What is logaa equal to ? 3.3 and 1.2

  34. Answer to Unit 3 Question 17 • 1

  35. Unit 3 Question 18 • What is loga1 equal to ? 3.3 and 1.2

  36. Answer to Unit 3 Question 18 • 0

  37. Unit 3 Question 19 • How do you express acosx+bsinx+c in the form kcos(x- α)? 3.4

  38. Answer to Unit 3 Question 19 • (i) expand brackets and equate like terms • (ii) find k =√(a2+b2) • (iii) identify quadrant α is in • (iv) find α using tanα = sinα cosα S A T C

  39. Unit 3 Question 20 • How do you solve an equation of the form acosx + bsinx + c=0? 3.4

  40. Answer to Unit 3 Question 20 • Change acosx+bsinx into Rcos(x- a) • rearrange and solve

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