All

Question 1

sin(A ± B) =

Answer 1

sinAcosB ± cosAsinB

Question 2

cos(A ± B) =

Answer 2

cosAcosB ∓ sinAsinB

Question 3

sin2A =

Answer 3

2sinAcosA

Question 4

cos2A =

Answer 4

cos(squared)A - sin(squared)A

or

2cos(squared)A - 1

or

1 - 2sin(squared)A

Question 5

sin(squared)A + cos (squared)A =

Answer 5

1

Question 6

sinA / cosA =

Answer 6

tanA

Question 7

Partial Fractions: distinct linear factors

ax + b / (cx + d)(ex + f) =

Answer 7

A / (cx + d) + B / (ex + f)

Question 8

Partial Fractions: repeated linear factor

ax(squared) + bx + c /(dx + e) (fx +g)(squared)

Answer 8

A / (dx + e) + B / (fx + g) + C / (fx + g)(squared)

Question 9

Partial Fractions: irreducible quadratic

ax(squared) + bx + c / (dx + e)(fx(squared) + gx + h)

Answer 9

A / (dx + e) + Bx + C / (fx(squared) + gx + h)

Question 10

Calculus is always done in degrees or radians?

Answer 10

Radians

Question 11

Product Rule:

k(x) = f(x) . g(x)

k’(x) =

Answer 11

f’(x) . g(x) + f(x) . g’(x)

Question 12

Quotient Rule:

k(x) = f(x) / g(x)

k’(x) =

Answer 12

f’(x) . g(x) - f(x) . g’(x) / (g(x))(squared)

Question 13

1 / cos(x) =

Answer 13

sec(x)

Question 14

1 / sin(x) =

Answer 14

cosec(x)

Question 15

1 / tan(x) = cos(x) / sin(x) =

Answer 15

cot(x)

Question 16

tan(squared)x =

Answer 16

sec(squared)x - 1

Question 17

f’‘(x) > 0, curve lies…

f’‘(x) < 0, curve lies…

Answer 17

…above tangent, gradient increasing.

…below tangent, gradient decreasing.

Question 18

Implicit differentiation:

Answer 18

Same as normal differentiation, where d (y) / dx = dy/dx

Question 19

Second derivative of implicit functions are easier to find if you…

Answer 19

…differentiate dy/dx again before simplifying.

Question 20

Parametric Differentiation:

dy/dx =

d(squared)y/dx(squared) =

Answer 20

dy/dt / dx/dt

d(dy/dx) / dt . 1 / dx/dt - Differentiate first derivative with respect to t then divide by dx/dt.