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Maths formulas Flash Cards
Fichas del conjunto (23)
- 1Basic trigonometry
- 2SOHCAHTOA
- 3Trigonometry Finding anglesEquation: tan{x} = o/a
tan{x} = 5/7
tan{x} = 0.714285... Do not round this answer yet.
To calculate the angle use the inverse tan button on the calculator (Equation: tan^{-1})
x = 35.5 degrees - 4Trigonometry Finding LengthsEquation: sin{x} = o/h
sin{32} =o/8
Make AB (Equation: o) the subject by multiplying both sides by 8.
AB = 8 x sin{32}
AB = 4.2 cm - 5Pythagoras Formula
- 6Pythagoras TripletA "Pythagorean Triple" is a set of positive integers, a, b and c that fits the rule:
a^2 + b^2 = c^2
a Pythagorean Triple always consists of:
all even numbers, or
two odd numbers and an even number
A Pythagorean Triple can never be made up of all odd numbers or two even numbers and one odd number. This is true because:
The square of an odd number is an odd number and the square of an even number is an even number.
The sum of two even numbers is an even number and the sum of an odd number and an even number is in odd number
- 7Circle TheoremsInscribed Angle: an angle made from points sitting on the circle's circumference.
A and C are "end points"
B is the "apex point"
- 8Circle TheoremsAn inscribed angle a° is half of the central angle 2a°
Angle at the Center Theorem
- 9Circle TheoremsThe angle a° is always the same, no matter where it is on the circumference.
Angles Subtended by Same Arc Theorem
- 10Circle TheoremsAn angle inscribed in a semicircle is always a right angle
The inscribed angle 90° is half of the central angle 180°
- 11Circle TheoremsA "Cyclic" Quadrilateral has every vertex on a circle's circumference
A Cyclic Quadrilateral's opposite angles add to 180°
a + c = 180°
b + d = 180°
- 12Circle TheoremsA tangent is a line that just touches a circle at one point.
It always forms a right angle with the circle's radius
- 13Circles Sectors & SegmentThere are two main "slices" of a circle
The "pizza" slice is called a Sector.
And the Segment, which is cut from the circle by a "chord" (a line between two points on the circle).
- 14Area of SectorArea of Sector = θ/2 × r^2
when θ is in radians
Area of Sector = θ × π/360 × r^2
when θ is in degrees - 15Area of SegmentArea of Segment = θ − sin(θ)/2 × r^2
when θ is in radians
( θ /360 × π − sin(θ)/2 ) × r^2
when θ is in degrees - 16Circles ArcThe arc length (of a Sector or Segment) is
L = θ × r
when θ is in radians
L = (θ × π/180) × r
when θ is in degrees
- 17Circles AnnulusAn annulus is a flat shape like a ring
Its edges are two circles that have the same center.
Because it is a circle with a circular hole, you can calculate the area by subtracting the area of the "hole" from the big circle's area
Area = πR^2 − πr^2 or π( R^2 − r^2 )
- 18Circles BasicsA line that goes from one point to another on the circle's circumference is called a Chord.
If that line passes through the center it is called a Diameter.
A line that "just touches" the circle as it passes by is called a Tangent.
And a part of the circumference is called an Arc
- 19Sine RuleTo be able to the find the length of any triangle
- 20Sine RuleTo be able to find the angle of the triangles
- 21Quadratic Formula
- 22Functions of Graphsy=f(x + or - a)
translation in the x direction
y=f(x) + or - a
translation in the y direction
y=f(xa)
enlargement in the x direction
y=af(x)
enlargement in the y direction
y=f(-x)
reflection in the y axis
y=f(x)
reflection in the x axis
y=af(x)
stretch in y direction sf=a
y=f(ax)
squash in the x direction sf=a
- 23Stratified Sampling The number in the sample are in proportion for each categorySample size/population size x Stratum size