C3

Question 1

What is the exponential relationship function?

Answer 1

y = a^x

Question 2

What is the inverse of the exponential function?

Answer 2

y = ln(x)

Question 3

What is the transformation f(x)+a?

Answer 3

VERTICAL shift of a units

Question 4

What is the transformation f(x+a)?

Answer 4

Horizontal shift of -a units

Question 5

What is the transformation af(x)?

Answer 5

VERTICAL stretch of scale factor a

Question 6

What is the transformation f(ax)?

Answer 6

HORIZONTAL stretch of scale factor 1/a

Question 7

What is the transformation -f(x)?

Answer 7

REFLECTION in the X axis

Question 8

What is the transformation f(-x)?

Answer 8

REFLECTION in the y axis

Question 9

When you have a complex transformation what should you do?

Answer 9

Take it one step at a time

Question 10

How do you use numerical methods to find the intercept between f(x) and g(x)?

Answer 10

1) Note the number of solutions (intersects)
2) Let f(x) = g(x)
3) Rearrange f(x) = g(x) into f(x) - g(x) = h(x)
4) Sub in x for two values on the graph, a and b. If there is a sign change between these two values then there is a solution between them.
5) Rearrange the f(x) = 0 formula into x= something, allowing the iterative form to be used to narrow down what x is.

Question 11

What is the Modulus function?

Answer 11

It ensures a value is always positive

Question 12

What does |f(x)| mean?

Answer 12

No value of f(x) will drop below the x axis, the negative y value will become a positive y value.

Question 13

What does f(|x|) mean?

Answer 13

When the graph touches the y axis, the positive x data points are reflected in y axis again.

Question 14

How do we solve a modulus equation?

Answer 14

1) Draw both graphs.
2) Complete the square of whats in the modulus sign.
3) Split the graph into what the modulus has effected and what it hasnt.
4) Solve the regular bit like normal. Solve the moduled bit accounting for any reflection which has occurred.

Question 15

What does sin^2 + cos^2 equal?

Answer 15

1

Question 16

What is cosec?

Answer 16

1/sin

Question 17

what is sec?

Answer 17

1/cos

Question 18

what is cot?

Answer 18

1/tan

Question 19

what is sin/cos?

Answer 19

tan

Question 20

What does the cosec graph look like?

Answer 20

U’s between -2pi and pi, 0 and pi. n’s between -pi and 0, pi and 2pi.

Question 21

What does the sec graph look like?

Answer 21

the cosec graph with horizontal shift of 1/2pi. A U centered on 0, two n’s centered on -pi and pi, and two half U’s on 2pi and -2pi.

Question 22

What does the Cot Graph look like?

Answer 22

When tan would tend to infinity, it is 0. When tan would be 0, it is infinity. There are assentotes at-2pi, -pi, 0, pi and 2pi. With the tan like curves going from top left to bottom right.

Question 23

What does 1 + tan^2 equal?

Answer 23

sec^2

Question 24

what does 1 + cot^2 equal?

Answer 24

cosec^2

Question 25

what is sin^-1?

Answer 25

arcsin

Question 26

what is cos^1?

Answer 26

arccos

Question 27

what is tan^-1?

Answer 27

arctan

Question 28

Are the "arc" graphs infinite, like the normal sin cos tan graphs?

Answer 28

NOOOOO

Question 29

What does arcsin look like?

Answer 29

A reflected sinx in the line y = x, where the domain is now -1 =< x =< 1 and the range is -1/2pi and 1/2pi

Question 30

What does arccos look like?

Answer 30

A reflection of y = cosx in the line y=x, where the domain is -1 tp 1 and the range is 0 to pi

Question 31

What does arctan look like?

Answer 31

A reflection of y = tanx in the line y = x, where the domain is any real value, and the range is between -1/2pi to 1/2pi

Question 32

What is the double angle formula for sin?

Answer 32

Sin(2A) = 2sinACosA

Question 33

What is the double angle formula for cos?

Answer 33

Cos(2A) = cos^2(A) - sin^2(A)

Question 34

What is the double angle formula for tan?

Answer 34

tan(2A) = (2tanA)/(1-tan^2(A))

Question 35

What is the Harmonic form?

Answer 35

The idea that anything in the form acos(x) + bsin(x) can be expressed in the form Rsin(X+R) or Rcos(X-R).

Question 36

What do you need to be careful of in the Harmonic form?`

Answer 36

If you are expressing it in the form Cos, then it is X-R if it is acos + bsin, and it is X+R if it is acos - bsin.

Question 37

How do we apply harmonic form?

Answer 37

1) Make left equal right 2) Equate coefficients 3) Divide coefficient equations to make tan 4) Use a^2 + b^2 = c^2 formula on coefficient formulas to find what R is. 5) Write out answers.

Question 38

What is the chain rule?

Answer 38

For y = f(g(x)), dy/dx = f'(g(x)) multiplied by g'(x).

Question 39

What is the product rule?

Answer 39

for y= f(x) g(x), dy/dx = f'(x) g(x) multiplied by f(x) g'(x)

Question 40

What is the quotient rule?

Answer 40

For y = f(x)/g(x), dy/dx = [ f'(x) g(x) - f(x) g'(x) ]/ g(x)^2

Question 41

What is the derivative of y = e^x?

Answer 41

dy/dx = e^x

Question 42

What is the derivative of y = ln(x)?

Answer 42

dy/dx = 1/x

Question 43

What is the derivative of y = sinx?

Answer 43

dy/dx = cosx

Question 44

What is the derivative of y = cosx?

Answer 44

dy/dx = -sinx

Question 45

What is the derivative of y = tanx?

Answer 45

dy/dx = sec^2 x