Core Formula

Question 1

What is the formula to work out the area of a sector?

Answer 1

(1/2)(r^2)(θ)

Question 2

What is the formula to work out the area of a segment?

Answer 2

(1/2)(r^2)(θ - sinθ)

Question 3

What is the sine rule?

Answer 3

a/sinA = b/sinB = c/sinC

Question 4

What is the formula for the area of a triangle?

Answer 4

(1/2)absinC

Question 5

What is the two expressions for logarithms?

Answer 5

a^x = n

Loga(n) = x

Question 6

What is the multiplication law for logarithms?

Answer 6

log(xy) = log(x) + log(y)

Question 7

What is the division law for logarithms?

Answer 7

log(x/y) = log(x) - log(y)

Question 8

What is the power law for logarithms?

Answer 8

log(x)^k = klog(x)

Question 9

What is the formula to work out the midpoint of a line?

Answer 9

((x1 + x2)/2 , (y1 + y2)/2)

Question 10

What is the formula to work out the distance of a line?

Answer 10

d = √((x2 - x1)^2) + (y2 - y1)^2))

Question 11

What is the equation of a circle?

Answer 11

(x ± a)^2 + (y ± b)^2 = r^2

Question 12

What is the formula to work out arc length?

Answer 12

rθ

Question 13

What is tanθ in terms of sin and cos?

Answer 13

sinθ/cosθ

Question 14

What is the basic trig function?

Answer 14

sin^2(θ) + cos^2(θ) = 1

Question 15

What is the manipulations of the basic trig function?

In terms of sec, cosec, cot and tan

Answer 15

1 + cot^2(θ) = cosec^2(θ)

tan^2(θ) + 1 = sec^2(θ)

Question 16

What is the differential of sinx?

Answer 16

cosx

Question 17

What is the differential of cosx?

Answer 17

-sinx

Question 18

What is the sin(2x) in terms of sin and cos?

Answer 18

2sin(x)cos(x)

Question 19

What is the cos(2x) in terms of sin and cos?

Answer 19

cos^2(x) - sin^2(x)

Question 20

What is the cos(2x) in terms of sin?

Answer 20

1 - 2sin^2(x)

Question 21

What is the cos(2x) in terms of cos?

Answer 21

2cos^2(x) - 1

Question 22

What is the differential of ln(x)?

Answer 22

1/x

Question 23

In vectors what is a.b equal to?

Answer 23

a.b = IaI IbI cosx