1.1

Question 1

How do you find the equation of a perpendicular bisector of a straight line ?

Answer to Question 1

(i) find the midpoint of the line(ii) find the gradient of the line(iii) find the gradient

perpendicular to the given line

(iv) Use midpoint and gradient in y-b = m(x-a)

M(a,b)

1.1

Question 2

How do you find the midpoint of a line joining two points ?

Answer to Question 2

Add the coordinates and divide by two

x1+ x

2 , y1+ y

2

2 2( )x

y(x2,y2)

(x1,y1)

1.1

Question 3

How do you find the altitude AN of ΔABC ?

Answer to Question 3

(i) find the gradient of BC(ii) find the gradient of AN, perpendicular to BC

(iii) use y-b=m(x-a), using A as (a,b)

A

NB

C

2.1

Question 4

How do you show that x-1 is a factor of the function f(x)=x3-3x+2 ?

Answer to Question 4

(i) rewrite the function asf(x)=x3+0x2-3x+2

(ii) use synthetic division with 1 on the outside

(iii) show thatremainder = 0

1.2

Question 5

For what values is this function undefined ?f(x) = x

(x+2)(x-3)

Answer to Question 5

-2 and 3

1.2

Question 6

How do you draw the graph of 2f(x) given the graph of f(x) ?

Answer to Question 6

Double the y-coordinates

2.3

Question 7

How do you find theexact value ofsin (α-β),given that sinα =4/5

and cosβ = 12/13 ?

Answer to Question 7

(i) draw triangles for α and β

(ii) work out cosα and sinβ

(iii) expand formula for sin(α-β)

(iv) insert exact values

αα

4

5

12

13

ββ

2.1

Question 8

What is the turning point ofy=2(x-a)2+b ?Max or min ?

Answer to Question 8

(i) (a,b)minimum

(a,b)

1.2

Question 9

How do you draw the graph of f(-x) given the graph of f(x) ?

Answer to Question 9

Reflect the graph in the y-axis

1.2

Question 10

How do you draw a graph of the form y = cos(x+a) or y = sin(x+a) ?

Answer to Question 10

Move the graph of y=cosx or y=sinx

a units to the LEFT

Move the graph of y=cosx or y=sinx

a units to the LEFT

1.3

Question 11

Name the steps you take in order to differentiate functions likef(x) = x2+ 3x + 1

√x

Answer to Question 11

(i) Change roots to powers

(ii) split up into 3 fractions

(iii) simplify each term(iv) differentiate

1.3

Question 12

If f(t) is the distance travelled in a certain time t seconds, then what does f’(t) represent ?

Answer to Question 12

Speed (velocity)

2.2

Question 13

Given f’(x) and a point on the curve, how do you findf(x) ?

Answer to Question 13

(i) integrate(ii) substitute in a

given point to work out value

of C

1.1

Question 14

What do you know about the gradients of two parallel lines?

Answer to Question 14

They are the same

1.1

Question 15

How do you find the equation of a tangent to a curve at the point when x = a ?

Answer to Question 15

(i) Differentiate(ii) fit a into f’(x) to get

the gradient (m) (iii) fit a into f(x) to get

the tangent point (a,b)

(iv) use y-b=m(x-a)

1.3

Question 16

How do you find the rate of change of a function at a particular point ?

Answer to Question 16

(i) differentiate (ii) fit in given x

value

1.3

Question 17

If y is the equation of a curve, what is represented by dy/dx ?

Answer to Question 17

The gradient

1.3

Question 18

How do you find where a curve is increasing ?

Answer to Question 18

(i) differentiate(ii) let f’(x) = 0(iii)solve to find stationary

points(iv) draw nature table(v) read values for which

graph is increasing

1.3

Question 19

How would you find the maximum or minimum value of a function given its equation?

Answer to Question 19

(i) differentiate(ii) let f’(x) = 0(iii) solve to find the

stationary points(iv) draw the nature table(v) read off max or min

1.4

Question 20

Given a rec. relation in the form un+1 = aun + b and 3 consecutive terms, how do you find the values of a and b?

Answer to Question 20

(i) fit 1st term into un and 2nd term into un+1

(ii) fit 2nd term into un and the 3rd term into un+1

(iii) solve simultaneous equations

2.1

Question 21

How do you find the value of a in the polynomial x3+ax2+4x+3 given either a factor of the polynomial, or the remainder when the polynomial is divided by a number ?

Answer to Question 21

(i) do synthetic division(ii)let the expression

= 0 or the remainder(iii) solve the equation

3.2

Question 22

How do you find

∫ (ax + b)n dx ?

Answer to Question 22

(i) increase power by 1(ii) divide by new power(iii) divide by the

derivative ofthe bracket

i.e. (ax+b)n+1

a(n+1)+ C+ C

2.3

Question 23

How do you solve equations of the form

sin2xo = 0.5 ?(0≤x≤360)

Answer to Question 23

(i) decide on the 2 quadrants (sin is +ve)(ii) press INV sin to get

angle(iii) work out your 2 angles

(iv) divide each by 2

2.3

Question 24

How do you solve equations like

cos2xo-5sinxo = 0 ?(0≤x≤360)

Answer to Question 24

(i) fit in 1-2sin2xo for cos2xo

(ii) factorise(iii) solve equation

3.1

Question 25

How do you find a unit vector parallel to a given vector ?

Answer to Question 25

(i) find the length of the given vector

(ii) divide all the components by

this length

2.4

Question 26

How do you prove that a line is a tangent to a circle ?

Answer to Question 26

Rearrange line to makey = or x =

Substitute line into circleProve it has equal roots using b2-4ac = 0 or repeated roots

3.1

Question 27

How do you find the angle between two vectors ?

Answer to Question 27

a.b

a b

a.b

a bcos=

a

b

3.1

Question 28

What is a unit vector ?

Answer to Question 28

A vector of length 1 unitA vector of length 1 unit

3.1

Question 29

What vector is equal to

AB + CD + BC ?

Answer to Question 29

AD

3.1

Question 30

If u = ai+bj+ckthen what is u in component form ?

Answer to Question 30

U =abc

3.2

Question 31

How do you integrate sin ax ?

Answer to Question 31

-1/a cos ax + C

3.2

Question 32

How would you differentiate a function likey = sin3 x ?

Answer to Question 32

(i) write as (sin x)3

(ii) multiply by the power(iii) decrease power by one(iv) multiply by the derivative of

the bracketi.e. 3 sin2x cosx

(i) write as (sin x)3

(ii) multiply by the power(iii) decrease power by one(iv) multiply by the derivative of

the bracketi.e. 3 sin2x cosx

3.3

Question 33

Given experimental data, how do you find an equation in the form y=abx or y=axb ?

Answer to Question 33

(i) take logs of both sides

(ii) rearrange to get a straight line equation

(iii) determine type(iv) Equate and solve for a

and b

(i) take logs of both sides

(ii) rearrange to get a straight line equation

(iii) determine type(iv) Equate and solve for a

and b

3.2

Question 34

How do you differentiate an expression like

without multiplying it out ?

432 x

Answer to Question 34

(i) multiply by the power

(ii) decrease power by 1

(iii) multiply by derivative of bracket

3.3

Question 35

Given an equation like m = moe-3k and an amount by which it has been decayed, how do you find k ?

Answer to Question 35

(i) fit in m and mo

(ii) rearrange to get e-3k =

(iii) take logs to get -3k =

(iv) solve for k

(i) fit in m and mo

(ii) rearrange to get e-3k =

(iii) take logs to get -3k =

(iv) solve for k

3.3

Question 36

What isloga x + loga y equal to ?

Answer to Question 36

Loga xyLoga xy

3.3

Question 37

How do you solve equations of the form

3x = 0.155 ?

Answer to Question 37

(i) take logs of both sides

(ii) bring x down to front

(iii) solve the equation

(i) take logs of both sides

(ii) bring x down to front

(iii) solve the equation

3.3

Question 38

What is loga xn equal to ?

Answer to Question 38

nloga xnloga x

1.3

Question 39

If y =

How should you rewrite y so it is ready to differentiate?

x2

1

Answer to Question 39

1

2

1 x

3.4

Question 40

How do you find the maximum or minimum values ofacosx + bsinx + c ?

Answer to Question 40

(i) change acosx+bsinx into Rcos(x-a)

(ii) max is R+c