Formulas

Formulas

Further Trigonometry
1. Right-Angled Trig
  1. Sin θ = O/H θ =sin-1(O/H)
  2. Cosθ = A/H θ=Cos-1 (A/H)
2. Further Trig
  1. Cos Rule
    1. Side: a² = b² + c² - 2bc cosA
    2. Angle: cosA = (b² + c² - a²)/2bc
    3. USE WHEN: 3 sides + 1 angle
  2. Sin Rule:
    1. Sin rule: a/SinA = b/SinB = c/SinC
3. Complimentary Ratios:
  1. Sin alpha = cos(90-alpha)
  2. Cos alpha = sin(90-alpha)
  3. Tan alpha = (sin alpha/cos alpha)
4. Supplementary Ratios
  1. Sin(180-θ) = Sinθ
  2. Cos(180-θ)= - cosθ
  3. Tan(180-θ)= - tanθ
5. Area of a Triangle
  1. A = 1/2*a*b*sinC (2 sides + included angle)
Quadratic Equations
1. Quadratic Formula
  1. x = (-b +/- √b² - 4ac)/2a
2. Discrminant (Δ)
  1. For finding amount of possible solutions.
    1. Δ > 0 = 2
    2. Δ = 0 = 1
    3. Δ < 0 = none
  2. b² - 4ac
Coordinate Geometry
1. Distance
  1. d = √(x₂- x₁)² + (y₂- y₁)²
2. Midpoint
  1. MP = (x₁+ x₂/ 2 , y₁+ y₂/2 )
3. Gradient
  1. m = (y₂- y₁) / (x₂- x₁)
4. Parallel: Same gradient
5. Perpendicular: negative reciprocal
6. y-int: Let x = 0
7. x-int = Let y = 0
8. General form of a linear equation: ax + by + c = 0
9. Point Gradient
  1. WIth the gradient of the line and points it passes
  2. y - y₁= m ( x - x₁)
10. Two point
  1. 2 points are given
  2. (y - y₁) / (x - x₁) = (y₂- y₁) / (x₂- x₁)
Parabolas
1. Axis of Symmetry
  1. x = h (x coordinate of the vertex)
  2. x = -b / 2a
  3. x = x-int + x-int / 2
2. x-ints: factorise
Consumer Arithmetic
1. Simple Interest
  1. I = PRT
    Nota:
    - I = Interest P = Principa lR = rate of interest as a decimal T = time periods
2. Compound Interest
  1. A = P(1 + r)^n
3. Depreciation
  1. A = P(1 - r)^n
4. Balance owing = cost - deposit
5. Total repaid = Balance + interest
6. Total price = Total repayments + deposit
7. Credit Cards
  1. Closing Balance = Opening + purchases - payments
Surface Area and Volume
1. Surface Area
  1. Prism
    1. Sum of the area of the faces. Draw a net.
  2. Cylinder
    1. SA = 2 π r² + 2π r h
  3. Composite Shapes
    1. Write in words what needs to be found
  4. Rhombus/Kite
    1. A = xy/2
  5. Trapezium
    1. A = 1/2*h*(a+b)
  6. Parallelogram
    1. A = bh (h = perpen.)
  7. Spheres
    1. SA = 4π r²
  8. Hemispheres
    1. SA = 2π r²
  9. units²
  10. Cones
    1. SA = π r² + π r l (l = slant height)
2. Volume
  1. units³
    1. Prism
      1. V = Ah
  2. Cones
    1. V = 1/3 Ah
  3. Cylinders
    1. V = π r² h
  4. Spheres
    1. 4/3 π r³
3. For weird cut circles: n/360 x π r²
Functions
1. Inverse Functions
  1. 1. Swap x and y 2. Make y the subject
  2. Reflect along y=x Swap x & y pts
2. Line Tests
  1. Vertical line test
  2. Horizontal line test
    1. To check whether the inverse of a graph is a function
3. Function: Each x value only has 1 y value
Further Graphs
1. Effects to graphs
  1. h(2x)
    1. horizontal -><-
  2. h(0.5x)
    1. horizontal <-->
  3. 2h(x)
    1. vertical stretch
  4. -h(x)
    1. vertical flip
  5. h(-x)
    1. horizontal flip
2. Effects to asymptotes
  1. -f(x)
    1. y= 2-->y= -2
  2. f(-x)
    1. x= 3-->x= -3
  3. f(x-2)
    1. x= 3--> x=5 (opp.)
  4. f(x)-2
    1. y=2 --> y=0
  5. f(2x)
    1. x=100 --> x=50
  6. 2f(x)
    1. y=50 --> y=100
3. in bracket: x (horizontal)
4. Out of bracket: y (vertical)
Deductive Geometry
1. Congruence
  1. SSS
  2. SAS
  3. AAS
  4. RHS
2. Similarity
  1. Scale Factor
    1. sf = image length/original length
  2. SSS
  3. AA
  4. RHS
  5. SAS
Surds
1. √ab = √ a*√ b
2. (√5)² = √5*√5
Logarithms:
1. Log Laws
  1. 1) Multiplication inside the log can be turned into addition outside the log, and vice versa.
  2. 2) Division inside the log can be turned into subtraction outside the log, and vice versa.
  3. 3) An exponent on everything inside a log can be moved out front as a multiplier, and vice versa.
  4. Log a a = 1
  5. Log a 1 = 0
Index Laws
1. a^m x a^n = a^m+n
2. a^m / a^n = a^m-n
3. (a^m)^n = a^m*n
4. a^1/m = m√a
5. a^0 = 1

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