3.1

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

• Prove that vector AB is a multiple of vector BC

AB = k BC• And state that B is common to both vectors

3.1

Unit 3 Question 2

•How do you add or subtract vectors ?

Answer to Unit 3 Question 2

• add or subtract matching components

• add or subtract matching components

3.3

Unit 3 Question 3

•State the three rules of logs ?

Answer to Unit 3 Question 3

• (i) logaxy = logax + logay

• (ii) loga = logax – logay

• (iii) logaxn = nlogax

• (i) logaxy = logax + logay

• (ii) loga = logax – logay

• (iii) logaxn = nlogax

xy

3.4

Unit 3 Question 4

•What does ksin(x-a) expand out to?

Answer to Unit 3 Question 4

• ksinxcosa-kcosxsina

3.1

Unit 3 Question 5

•If u =

then what is u ?

abc

Answer to Unit 3 Question 5

• work out length

√(a2+b2+c2)

• work out length

√(a2+b2+c2)

3.1

Unit 3 Question 6

•What does•a.a equal ?

Answer to Unit 3 Question 6

• a ²

3.3

Unit 3 Question 7

•Express the equation y=kxn in the form of the equation of a straight line, Y=nX+c.

Answer to Unit 3 Question 7

• logy = nlogx + logk• logy = nlogx + logk

3.1

Unit 3 Question 8

•How do you show that two vectors are perpendicular ?

Answer to Unit 3 Question 8

•Show that a.b=0

a

b

3.2

Unit 3 Question 9

•What do you get when you differentiate cosx ?

Answer to Unit 3 Question 9

• -sinx

3.3

Unit 3 Question 10

•What is

•logax – logay

equal to ?

Answer to Unit 3 Question 10

• x

loglogaa yy

3.1

Unit 3 Question 11

•How do you name the angle between a line and a plane ?

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

3.1

Unit 3 Question 12

•What is a position vector ?

Answer to Unit 3 Question 12

•A vector which starts at the origin

3.2

Unit 3 Question 13

•What do you get when you differentiate sin x ?

Answer to Unit 3 Question 13

•cos x•cos x

3.2

Unit 3 Question 14

•How do you integrate cos ax ?

Answer to Unit 3 Question 14

• 1/a sin ax + C

3.2

Unit 3 Question 15

•What do you get when you differentiate

•cosax ?

Answer to Unit 3 Question 15

•-asinax

3.2

Unit 3 Question 16

•How would you differentiate a function like

y = sin ax ?

Answer to Unit 3 Question 16

• dy/dx = acos ax• dy/dx = acos ax

3.3 and 1.2

Unit 3 Question 17

•What is logaa

equal to ?

Answer to Unit 3 Question 17

•1

3.3 and 1.2

Unit 3 Question 18

•What is loga1

equal to ?

Answer to Unit 3 Question 18

•0

3.4

Unit 3 Question 19

•How do you express acosx+bsinx+cin the formkcos(x- α)?

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

ATS

C

3.4

Unit 3 Question 20

•How do you solve an equation of the form acosx + bsinx + c=0 ?

Answer to Unit 3 Question 20

•Change acosx+bsinx into Rcos(x- )

•rearrange and solve

•Change acosx+bsinx into Rcos(x- )

•rearrange and solve