C3

Question 1

When is a function even?

Also give the algebraic form.

Answer 1

If its graph has the y axis as a line of symmetry.

f(x) = f(-x)

Question 2

When is a function odd?

Also give the algebraic form/

Answer 2

If its graph has a rotational symmetry of order 2 about the origin.
f(-x) = -f(x)

Question 3

When is a function periodic?

Answer 3

If it has a repeating pattern.

Question 4

How do you differentiate e^x

How do you integrate e^x

Answer 4

dy/dx = e^x

e^x dx = e^x +c

Question 5

How do you differentiate sinx?

Answer 5

d/dx sinx = cos x

Question 6

How do you differentiate cosx?

Answer 6

d/dx cosx = -sin x

Question 7

How do you differentiate tanx?

Answer 7

d/dx tanx = sec^2 x

In the formula book

Question 8

What is the reciprocal trig function of: 1/cosx

Answer 8

1/cosx = secx

Question 9

What is the reciprocal trig function of: 1/sinx

Answer 9

1/sinx = cosecx

Question 10

What is the reciprocal trig function of: 1/tanx

Answer 10

1/tanx = cotx

Question 11

How do you integrate ln(f(x))

Answer 11

dy/dx = f’(x) / f(x)

Question 12

What is implicit differentiation?

Answer 12

Function containing x and y where y is not the subject.

Question 13

What are the 2 types of integrating and when do you use them?

Answer 13

Integration by substitution; Use when integrating a composite function
Integration by parts; Use for products made up of 2 different types of functions e.g (x^3 + 1) sinx

Question 14

How do you integrate cosx?

Answer 14

cosx dx = sinx + c

Question 15

How don you integrate sinx?

Answer 15

sinx dx = cosx + c