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Mathematics :fire:, The prelim topics SPA1, copy [π] from here for…
Mathematics :fire:
Algebra
Algebraic Fractions
Algebraic Brackets
Trigonometry & Pythagoras
Trigonometry
In Trigonometry we use Sine and Cosine to find out the Angle or side of any triangle by matching pairs and trios to find Angles, Sides and Areas
Sin(A) / a = Sin(B) / b = Sin(C) / c to find an Angles
If Angle A = 46 degrees, Side a = 34cm and side b = 23cm we use Sin(A) / a = Sin(B) / b to get Sin(46) / 34 = Sin(B) / 23 therefore Sin(B) = (Sin(46) / 34) x 23 so Sin(B) = 0.486612 then Sin^-1(0.486612) and B = 29 Degrees
a / Sin(A) = b / Sin(B) = c / Sin(C) to find our Sides
If Side a is 15cm, Angle A is 35 degrees and Angle B is 42 degrees we use a / Sin(A) = b / Sin(B) we get (15 / SIn(35)) x Sin(42) we get b = 17.5cm
1/2 ab Sin(C) to work out the Area
If we have side a = 10m, side b = 7m and angle C is = 25 Degrees then 1/2 x 10 x 7 x Sin(25) = 1/2 x 70 x Sin(25) we get 35 x Sin(25) therefore Area = 14.8m^2
c^2 = a^2 + b^2 - 2abCos(C) to find the third Angle
A^2 + B^2 - C^2 / AB to find an Angle with three Sides
Pythagoras
C^2 = A^2 + B^2 Is our Formula for The Hypotenuse of A right angled Triangle
If A = 7m, B = 9m and C^2 = A^2 + B^2 then C^2 = 49 + 81 so C^2 = 130m but We need C so we square root 130 To Get C = 11.4m which is the largest side
X^2 = C^2 - A^2 Is our Formula for finding The Adjacent or Opposite sides Of A right Angled triangle
If X^2 = C^2 - A^2 and C = 13, A = 6 Then X^2 =169 - 36 so X^2 = 133 and X is 11.5m Which is Shorter than The Hypotenuse
Pythagorean Theorem Is our Understanding That The Hypotenuse (The Side Opposite The right Angle) Is always The Largest. This Can Be Used To Find All Three Sides As well as Figuring Out if A Triangle is right angled
Reverse Pythagoras Is When We are given two sides and are asked to find out if the triangle is right angled in which the hypotenuse is the largest
Graphs & Equations
Graphs
Equations
Surds & Indices
Surds
Indices
Percentages & Statistics
Percentages
Statistics
Arcs & Sectors
Arc Length
Area Of Sectors
Brackets & Factorising
Brackets
()
Factorising
Volume/Area & Scientific Notation
Volume/Area
Volume
Formulae
Prism V = B × h B = Area of base, (B = side2 or length.breadth) h = Height
Sphere V = (4⁄3)πr^3
Cylinder V = πr2h r = Radius of the circular base h = Height
Area
Formulae
Area of a Triangle: A = 1/2abSinc
Area of a Circle: A = πr^2
Area of a Square/Rectangle : A = LxB
Cuboid: V = l × b × h
Prism: V = A × h
Cylinder: V = π × r
Scientific Notation
Known as Scientific Notation or Standard Form
The prelim topics SPA1
Surds
Indices
Scientific Notation
Brackets and Factorising
Completing the square
Algebraic Fractions
Arcs and Sectors of Circles
Volume
Straight line
Equations and Inequalities
Changing the subject
Percentages
Fractions
Statistics
Functions
Triangle trig
copy [π] from here for formulas :D
salut