Things to learn for C3/C4

Question 1

what does sec x equal?

Answer 1

1/cos x

Question 2

what does cot x equal?

Answer 2

1/tan x

or cos/sin

Question 3

what does cosec x equal?

Answer 3

1/sin x

Question 4

How do you draw sec/cot/cosec graphs?

Answer 4

inverse graphs of cos/tan/sin

Question 5

how do you integrate by parts?

Answer 5

uv- sum of u’v

Question 6

how do you work out the area of a parametric function?

Answer 6

sum of y dx/dt dt

Question 7

how do you work out the volume of a parametric function and normal graph?

Answer 7

sum of piy^2 dx/dt dt

sum of piy^2 dx

Question 8

what does sec^2 equal?

Answer 8

tan^2x + 1

Question 9

what does cosec^2 equal?

Answer 9

1 + cot^2x

Question 10

If siny = x
y = arcsinx
what is arcsinx?

Answer 10

sin^-1x not 1/sinx

Question 11

what does 1 equal in terms of sin and cos?

Answer 11

sin^2 + cos^2

Question 12

what does R equal?

what does alpha equal?

Answer 12

root A^2 + B^2
tan^-1 B/A
B must be the cosx

Question 13

What is the minimum value of a double angle?

Answer 13

-R

Question 14

what does tan2x equal?

Answer 14

sin2x/cos2x

Question 15

what does tanx equal in terms of cot?

Answer 15

cot(90-x)

Question 16

How do you draw f= |f(x)|

Answer 16

reflect in the x axis

Question 17

How do you draw y=f^-1(x)

Answer 17

swap x and y co ordinates of each point

Question 18

What does Sin2A equal?

Answer 18

2SinACosA

Question 19

What does Cos2A equal?

Answer 19

Cos^2A - Sin^2A
2Cos^2A - 1
1 - 2Sin^2A

Question 20

What does Tan2A equal?

Answer 20

2TanA/1 - Tan^2A

Question 21

2Sin^3A

SinA = 5 what is the answer?

Answer 21

2(5)^3

Do not cube 2

Question 22

How do you find an inverse function of x?

Answer 22

swap x for y

rearrange to make y the subject

Question 23

What is the differential of sinkx?

Answer 23

k cos kx

Question 24

What is the differential of coskx?

Answer 24

-k sin kx

Question 25

What is the differential of e^kx

Answer 25

ke^kx

Question 26

What is the integral of Sin kx?

Answer 26

-1/k Cos kx

Question 27

What is the integral of Cos kx?

Answer 27

1/k Sin kx

Question 28

Why does more trapezium give a more accurate value?

Answer 28

With increasing ordinates the line segments at the top of the trapezia are closer to the curve.

Question 29

What is the differential of tanx?

Answer 29

Sec^2 x

Question 30

Hat is the integral of tanx?

Answer 30

ln(Secx) + c

Question 31

What is the integral of cot x?

Answer 31

ln(Sinx) + c

Question 32

What is the differential of Sec x?

Answer 32

Secx tanx

Question 33

What is the domain of an inverse function?

Answer 33

The range of the original function