Maths Formulas

Question 1

What is the formula for the area of a sector?

Answer 1

Area = 0.5 * r^2 * θ, where r is the radius and θ is in radians.

Question 2

What is The derivative of sin(x)

Answer 2

cos(x)

Question 3

Integrate e^x

Answer 3

e^x + C

Question 4

What is the formula for the area of a triangle using two sides and the included angle?

Answer 4

Area = 0.5 * a * b * sin(C), where a and b are sides and C is the included angle.

Question 5

Fill in the blank: The formula for the distance between two points (x1, y1) and (x2, y2) is _____.

Answer 5

d = √((x2 - x1)² + (y2 - y1)²).

Question 6

What is the formula for the derivative of a product of two functions?

Answer 6

f’(x) = u’v + uv’, where u and v are functions of x.

Question 7

Fill in the blank: The formula for the circumference of a circle is _____.

Answer 7

C = 2 * π * r.

Question 8

What is the formula for the arithmetic mean of a set of numbers?

Answer 8

Mean = (sum of all values) / (number of values).

Question 9

What is the formula for the area of a trapezium?

Answer 9

Area = 0.5 * (a + b) * h, where a and b are the lengths of the parallel sides and h is the height.

Question 10

Fill in the blank: The formula for the midpoint of a line segment between points (x1, y1) and (x2, y2) is _____.

Answer 10

Midpoint = ((x1 + x2)/2, (y1 + y2)/2).

Question 11

What is the formula for the law of cosines?

Answer 11

c² = a² + b² - 2ab * cos(C), where a, b, and c are the sides of a triangle and C is the included angle.

Question 12

What is the formula for arc length when θ is in radians

Answer 12

r θ

Question 13

sin^2x + cos^2x =?

Answer 13

1

Question 14

1 + tan^2x = ?

Answer 14

sec^2x
(tan = sexy)

Question 15

1 + cot^2x = ?

Answer 15

cosec^2x
(cot = cozy)

Question 16

tanx =?

Answer 16

sinx/cosx

Question 17

sin(2x) = ?

Answer 17

2sinxcosx

Question 18

cos(2x) = ?

Answer 18

cos^2x - sin^2x
2cos^2x -1
1-2sin^x

Question 19

tan(2x) = ?

Answer 19

2tanx / 1 - tan^2x

Question 20

sin(A±B) = ?

Answer 20

sinAcosB ± cosAsinB

Question 21

cos(A±B) = ?

Answer 21

cosAcosB ∓ sinAsinB

Question 22

What does lnx differentiate to?

Answer 22

1/x

Question 23

What does 1/x integrate to?

Answer 23

ln(x) + c

Question 24

When would you use integration by parts?

Answer 24

When integrating a product of two functions e.g. (xsinx)

Question 25

What does LATE stand for

Answer 25

Logs, Algebra, Trig, Exponentials

Question 26

When do you integrate with substitution

Answer 26

When there is a function inside another one, or see a function and its derivative

Question 27

When do you integrate with partial fractions?

Answer 27

when there are functions on the top and bottom of the fraction and the denominator can be factorized

Question 28

How do you integrate kf'(x) / f(x)

Answer 28

kln|f(x)| + c

Question 29

How do you find the area of a triangle with height and base

Answer 29

A = 1/2 * b * h