Maths/science equations

• Pythagorean Identity


  sin^2(A) + cos^2(A) = 1, balance of squares of sine and cosine
• Tangent Formula


  tan(A) = sin(A) / cos(A), ratio of sine to cosine
• Pythagorean Theorem


  a squared + b squared = c squared, find hypotenuse when given adjacent and opposite sides
• Area of a Square


  find area by squaring the side length
• Area of a Triangle


  A = (base × height) / 2, find area by multiplying base and height, then dividing by 2
• Area of a Circle


  A = π × radius squared, find area by multiplying pi by the square of the radius
• Circumference of a Circle


  C = 2 × π × r, find circumference by multiplying 2 times pi times the radius
• How do probabilities in each branch of a probability tree relate to each other?


  They add up to 1.
• What are the key principles to remember when working with probabilities in branches?


  • At each branch, probabilities add up to 1.
  • Multiply along the branches.
• If the probability of being late if they cycle is $0.25 \times 0.2$, what is the result?


  $0.05$
• If the probability of being late if they do not cycle is $0.75 \times 0.25$, what is the result?


  $0.1875$
• How do you calculate the overall probability of being late from the probabilities of cycling and not cycling?


  By adding the separate probabilities.
• surface area of a cone

  surface area of a cone= area of base + lateral(side) surface area

  Area = πr x side length + πr²

  Area = πrl + πr²
• The surface area of a sphere is equal to=4πr² If you are looking for the surface area of a semicircle that is equal to 2πr²
• • volume of cone



  volume of cone=1/3πr²h
• volume of a sphere


  volume of a sphere=4/3πr³
• area of trapezium


  area of trapezium = 1/2(a+b) x height

  height is the distance between the parallel lines
• circumference of a circle


  C = π d

  or

  C = 2 π r
• volume of a cuboid

  volume of a cuboid = L x W x H

  
• volume of a cylinder

  volume of a cylinder = πr²h

  
• volume of a pyramid


  volume of a pyramid = 1/3 x area of base x height

  
• speed (velocity)


  speed = distance/time

  metres per second

  km per hour

  miles per hour

  
• density


  density = mass/volume

  the greek symbol "rho" is sometimes used instead of the letter "d"

  grams per cubic centimetre

  gold is very dense at 19.32 g/cm3

  paper is much less dense at 1.20 g/cm3

  
• pressure


  pressure = force/area

  Newtons per cm²

  Newtons per m²

  1 Pascal = 1 Newton per square metre

  
• Pythagoras' Theorem


  hypotenuse is longest side and always

  opposite the right angle

  
• Quadratic Formula


  when ax² + bx + c = 0

  negative of b plus/minus square root of b-squared minus 4ac all divided by 2a

  doesn't work if a negative under the square root as the curve doesn't cross the x-axis
• Sine rule (for non-right angle triangles)


  use top version for finding a side

  use bottom version for finding an angle

  
• Cosine rule (for non-right angle triangles)


  Like Super-Pythagoras for non-right angle triangles!

  a² = b² + c² - 2bcCosA

  Angle A must always be opposite side a

  
• Area of a triangle given Side-Angle-Side


  (trig version when height is unknown)

  A = 1/2 x a x b x sinC

  
• area of a sector

  angle/360 x area of full circle

  
• segment area


  segment are = sector area - area of triangle

  
• vertically opposite angles


  Angles A and B are equal because

  vertically opposite angles are equal

  
• corresponding angles


  corresponding angles are equal

  
• Interior alternate angles


  angles 5 and 6 are equal

  angles 7 and 8 are equal

  Because Interior alternate angles are equal

  Interior means inside the parallel lines.

  
• Exterior alternate Angles

  Angles 1 and 2 are equal to each other.

  Angles 3 and 4 are equal to each other.

  Because Exterior alternate angles are equal

  Exterior means outside the parallel lines.

  
• co-interior angles


  co-interior angles add to 180

  co-interior angles are inside the parallel lines on the same side as the traversal

  
• Sum of exterior angles of a regular polygon


  Exterior angles sum to 360 degrees

  
• Size of one exterior angle of a regular polygon

  360/number of sides

  
• Sum of interior angles of a polygon


  (number of sides - 2) x 180

  
• Exact value triangle for sin/cos/tan 45, lengths=