Random A level maths stuff

Question 1

Area of a sector in radians formula?

Answer 1

1/2 * r^2 * θ

Question 2

Area of a segment in radians formula?

Answer 2

1/2 * r^2 * (θ - sinθ)

Question 3

Cosine rule for a side?

Answer 3

a^2 = b^2 + c^2 - 2bc * cos(A)

Question 4

Cosine rule for an angle?

Answer 4

cos(A) = (b^2 + c^2 - a^2) / (2 * b * c)

Question 5

Discriminant formula?

Answer 5

B^2 - 4 * a * c

Question 6

Quadratic formula?

Answer 6

(-b +- sqrt(b^2 - 4 * a * c )) / 2a

Question 7

Double angle formula for sin(2x)?

Answer 7

Sin(2x) = 2sinxcosx

Question 8

Double angle formulae for cos(2x)?

Answer 8

Cos(2x) = cos^2x - sin^2x
1 - 2sin^2x
2cos^2x - 1

Question 9

Double angle formula for tan2x?

Answer 9

(2tanx) / (1 - tan^2x)

Question 10

What is the pythagorean identity for 1?

Answer 10

Sin^2x + Cos^2x = 1

Question 11

What is the pythagorean identity for sec^2x

Answer 11

1 + tan^2x = sec^2x

Question 12

What is the pythagorean identity for cosec^2x

Answer 12

1 + cot^2x = cosec^2x

Question 13

What is the formula for finding the angle a vector makes with an axis?

Answer 13

Theta(x) = arccos(x component of vector/|vector|)
Where x can be x, y or z depending on the axis

Question 14

When does the newton-raphson method not work?

Answer 14

When choosing a starting value near to a point of inflection or a root

Question 15

What is the formula for the unit vector of vector a, and its symbol?

Answer 15

= a/|a|, a with Chinese hat, < rotated 90° clockwise