C3

Question 1

Differentiating Trig Functions

Answer 1

y = sinx ^dy/_dx = cosx

y = cosx ^dy/_dx = -sinx

y = tanx ^dy/_dx = sec²x

Question 2

Graph Transformations

Answer 2

Reflection in x axis = -f(x)

Reflection in y axis = f(-x)

Stretch with scale factor a, parallel to x axis = f (¹/_ax)

Stretch with scale factor a, parallel to y axis = af(x)

Translation (^a₀) = f(x-a)

Translation (⁰_a) = f(x)+a

Question 3

Definitions of Even and Odd Functions

Answer 3

Even: There is a line of symmetry on the y axis.

Odd: The graph has a rotational symmetry of order 2.

Question 4

Differentiating Natural Logs

Answer 4

y = aln(x) ^dy/_dx = ^a/_x

y = ln(ax) ^dy/_dx = ¹/_x

y = ln(f(x)) ^dy/_dx = ^f’(x)/_f(x)

Question 5

Differentiating Exponentials

Answer 5

y = ae^xdy/_dx = ae^x

y = e^axdy/_dx = ae^ax

y = e^f(x)dy/_dx = f’(x)e^f(x)

Question 6

Exponential relationship

Answer 6

e^x+y = e^x e^y

Question 7

Natural logarithm relationship

Answer 7

ln(a) + ln(b) = ln(ab)

ln(a) - ln(b) = ln(^a/_b)