# Formulas

Mind Map by , created almost 6 years ago

## Year 10 Mathematics Mind Map on Formulas, created by joyceex on 10/26/2013.

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 Created by joyceex almost 6 years ago
C2 - Formulae to learn
Maths C4 Trig formulae (OCR MEI)
TYPES OF DATA
Cognitive Psychology - Loftus and Palmer (1974)
GCSE AQA Chemistry Atomic Structure and Bonding
Geometry Formulas (Perimeters)
Discriminant
FREQUENCY TABLES: MODE, MEDIAN AND MEAN
HISTOGRAMS
MODE, MEDIAN, MEAN, AND RANGE
Formulas
1 Further Trigonometry
1.1 Right-Angled Trig
1.1.1 Sin θ = O/H θ =sin-1(O/H)
1.1.2 Cosθ = A/H θ=Cos-1 (A/H)
1.2 Further Trig
1.2.1 Cos Rule
1.2.1.1 Side: a² = b² + c² - 2bc cosA
1.2.1.2 Angle: cosA = (b² + c² - a²)/2bc
1.2.1.3 USE WHEN: 3 sides + 1 angle
1.2.2 Sin Rule:
1.2.2.1 Sin rule: a/SinA = b/SinB = c/SinC
1.3 Complimentary Ratios:
1.3.1 Sin alpha = cos(90-alpha)
1.3.2 Cos alpha = sin(90-alpha)
1.3.3 Tan alpha = (sin alpha/cos alpha)
1.4 Supplementary Ratios
1.4.1 Sin(180-θ) = Sinθ
1.4.2 Cos(180-θ)= - cosθ
1.4.3 Tan(180-θ)= - tanθ
1.5 Area of a Triangle
1.5.1 A = 1/2*a*b*sinC (2 sides + included angle)
2.1.1 x = (-b +/- √b² - 4ac)/2a
2.2 Discrminant (Δ)
2.2.1 For finding amount of possible solutions.
2.2.1.1 Δ > 0 = 2
2.2.1.2 Δ = 0 = 1
2.2.1.3 Δ < 0 = none
2.2.2 b² - 4ac
3 Coordinate Geometry
3.1 Distance
3.1.1 d = √(x₂- x₁)² + (y₂- y₁)²
3.2 Midpoint
3.2.1 MP = (x₁+ x₂/ 2 , y₁+ y₂/2 )
3.3.1 m = (y₂- y₁) / (x₂- x₁)
3.5 Perpendicular: negative reciprocal
3.6 y-int: Let x = 0
3.7 x-int = Let y = 0
3.8 General form of a linear equation: ax + by + c = 0
3.9.1 WIth the gradient of the line and points it passes
3.9.2 y - y₁= m ( x - x₁)
3.10 Two point
3.10.1 2 points are given
3.10.2 (y - y₁) / (x - x₁) = (y₂- y₁) / (x₂- x₁)
4 Parabolas
4.1 Axis of Symmetry
4.1.1 x = h (x coordinate of the vertex)
4.1.2 x = -b / 2a
4.1.3 x = x-int + x-int / 2
4.2 x-ints: factorise
5 Consumer Arithmetic
5.1 Simple Interest
5.1.1 I = PRT

Annotations:

• I = Interest P = Principa lR = rate of interest as a decimal                                         T = time periods
5.2 Compound Interest
5.2.1 A = P(1 + r)^n
5.3 Depreciation
5.3.1 A = P(1 - r)^n
5.4 Balance owing = cost - deposit
5.5 Total repaid = Balance + interest
5.6 Total price = Total repayments + deposit
5.7 Credit Cards
5.7.1 Closing Balance = Opening + purchases - payments
6 Surface Area and Volume
6.1 Surface Area
6.1.1 Prism
6.1.1.1 Sum of the area of the faces. Draw a net.
6.1.2 Cylinder
6.1.2.1 SA = 2 π r² + 2π r h
6.1.3 Composite Shapes
6.1.3.1 Write in words what needs to be found
6.1.4 Rhombus/Kite
6.1.4.1 A = xy/2
6.1.5 Trapezium
6.1.5.1 A = 1/2*h*(a+b)
6.1.6 Parallelogram
6.1.6.1 A = bh (h = perpen.)
6.1.7 Spheres
6.1.7.1 SA = 4π r²
6.1.8 Hemispheres
6.1.8.1 SA = 2π r²
6.1.9 units²
6.1.10 Cones
6.1.10.1 SA = π r² + π r l (l = slant height)
6.2 Volume
6.2.1 units³
6.2.1.1 Prism
6.2.1.1.1 V = Ah
6.2.2 Cones
6.2.2.1 V = 1/3 Ah
6.2.3 Cylinders
6.2.3.1 V = π r² h
6.2.4 Spheres
6.2.4.1 4/3 π r³
6.3 For weird cut circles: n/360 x π r²
7 Functions
7.1 Inverse Functions
7.1.1 1. Swap x and y 2. Make y the subject
7.1.2 Reflect along y=x Swap x & y pts
7.2 Line Tests
7.2.1 Vertical line test
7.2.2 Horizontal line test
7.2.2.1 To check whether the inverse of a graph is a function
7.3 Function: Each x value only has 1 y value
8 Further Graphs
8.1 Effects to graphs
8.1.1 h(2x)
8.1.1.1 horizontal -><-
8.1.2 h(0.5x)
8.1.2.1 horizontal <-->
8.1.3 2h(x)
8.1.3.1 vertical stretch
8.1.4 -h(x)
8.1.4.1 vertical flip
8.1.5 h(-x)
8.1.5.1 horizontal flip
8.2 Effects to asymptotes
8.2.1 -f(x)
8.2.1.1 y= 2-->y= -2
8.2.2 f(-x)
8.2.2.1 x= 3-->x= -3
8.2.3 f(x-2)
8.2.3.1 x= 3--> x=5 (opp.)
8.2.4 f(x)-2
8.2.4.1 y=2 --> y=0
8.2.5 f(2x)
8.2.5.1 x=100 --> x=50
8.2.6 2f(x)
8.2.6.1 y=50 --> y=100
8.3 in bracket: x (horizontal)
8.4 Out of bracket: y (vertical)
9 Deductive Geometry
9.1 Congruence
9.1.1 SSS
9.1.2 SAS
9.1.3 AAS
9.1.4 RHS
9.2 Similarity
9.2.1 Scale Factor
9.2.1.1 sf = image length/original length
9.2.2 SSS
9.2.3 AA
9.2.4 RHS
9.2.5 SAS
10 Surds
10.1 √ab = √ a*√ b
10.2 (√5)² = √5*√5
11 Logarithms:
11.1 Log Laws
11.1.1 1) Multiplication inside the log can be turned into addition outside the log, and vice versa.
11.1.2 2) Division inside the log can be turned into subtraction outside the log, and vice versa.
11.1.3 3) An exponent on everything inside a log can be moved out front as a multiplier, and vice versa.
11.1.4 Log a a = 1
11.1.5 Log a 1 = 0
12 Index Laws
12.1 a^m x a^n = a^m+n
12.2 a^m / a^n = a^m-n
12.3 (a^m)^n = a^m*n
12.4 a^1/m = m√a
12.5 a^0 = 1