1. How do you prove that three 3-D points, A, B and C, are collinear ?
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. How do you add or subtract vectors ?
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. State the three rules of logs ?
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. What does ksin(x-a) expand out to?
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
If u =
then what is u ? a b c
3.1

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

11. Unit 3 Question 6
What does
a.a equal ?
3.1

12. Answer to Unit 3 Question 6

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

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

17. What do you get when you differentiate cosx ?
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 10x
loga y

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

22. 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 A B C

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

24. Answer to Unit 3 Question 12
A vector which starts at the origin

25. What do you get when you differentiate sin x ?
Unit 3 Question 13
What do you get when you differentiate sin x ?
3.2

26. Answer to Unit 3 Question 13
cos x

27. How do you integrate cos ax ?
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. What do you get when you differentiate
Unit 3 Question 15
What do you get when you differentiate
cosax ?
3.2

30. Answer to Unit 3 Question 15
-asinax

31. How would you differentiate a function like
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

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

36. Answer to Unit 3 Question 18

37. How do you express acosx+bsinx+c in the form kcos(x- α)?
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. How do you solve an equation of the form acosx + bsinx + c=0 ?
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