Memorise for IGCSE Maths Flashcards
HCF
Multiply all numbers in the middle of venn diagram
LCF
Multiply all the numbers in th whole venn diagram
Adding + Subtracting Fractions
Find a common denominator
Multiplication of Fractions
Top x Top and Bottom x Bottom
Division of Fractions
KFC - Keep, flip, change
Sum of all outcomes - Probability
Equals to 1
Nth Term - Sequences
difference x n + 0th term
Translation - Transformations
By vector (a/b) a = right, -a = left, b = up, -b = down
Reflection - Transformations
In line x = a (horizontal) y = b (vertical)
Rotation - Transformations
centre, angle, driection (CW or ACW)
Enlargement - Transformations
Centre, scale factor
Multiplier - Percentages
Increase = 100+x/100, Decrease = 100-x/100
% Change - Percentages
Change/Original x 100
Reverse % - Percentages
Original = New/Multiplier
Inequalities
y<mx+c = shade below the line, y>mx+x = shade above the line
Indicies
(a^m)^n = a^mxn
a^-m = 1/a^m
a^1/n = ^n\sqrt{a}
a^m/n = ^n\sqrt{a^m}
Measuring Speed, Density + Pressure
Speed = Distance/Time
Density = Mass/Volume
Pressure = Force/Area
Angles
Straight line - Adds to 180
Around a point - Adds to 360
Corresponding - Equal
Alternate - Equal
Vertically opposite - Equal
CO-interior - Adds to 180
Angles in Polygons
Interior angles = (n-2) x 180
Exterior angles = 360
Interior + Exterior = 180
Bearings
Meaured - From North and clockwise
Back bearings - Differ by 180
Area
Parallelograms = bxh
Triangle = bxh/2
Trapezium = 1/2(a+b)xh
Circle = Pi x r^2
Circumference = 2 x Pi x r
Volume
Prism = Cross-Sectional Area x Height
Surface Area = Sum the areas of all the faces
Cylinder = Pi x r^2 x h
Curved Surface Area = 2 x Pi x r x h
Total Surface Area = 2 x Pi x r x h + 2 x Pi x r^2
Straight Lines
y=mx+c where m = gradient and c = y-intercept
Gradient = y2-y1/x2-x1
Length of line = Square root of (x2-1)^2+(y2+y1)^2
Midpoint = (x1+x2/2, y1+y2/2)
Parallel = Same Gradient
Probability
And = Multiply
Or = Add
At least 1 = 1-none
Circle Theorms
- Angles from same segment are equal
- Angle at centre twice circumference angle
- Opposites in cyclic quadrilateral add to 180
- Tangent and radius 90
- Tangents that meet are equal
- Alternate segment Theorem
- 2 radii make isoscleles triangle
Set Theory
AnB - Intersection - Both
AuB - Union - Either
A’ - Not A
Q - Empty
E - Univeral Set
n(A) - Number of elements in A
AcB - A is subset of B
Proportion
Directly Proportional - y=kx
Inversely Proportional - y=k/x
Histograms
Frequenncy Density = Frequency/Class Width
Similar Shapes
Linear Scale factor - k
Area Scale Factor - k^2
Volume Scale Factor - k^3
Surds
root a x root b = root axb
root a/b = root a/root b
x/root a = multiply top and bottom by root a
x/root a + b = Multiply top and bottom by root a - b
Cones and Spheres
Volume of Cone = 1/3 x Pi x r^2 x h
Curved Surface Area = Pi x r x L
Total Surface Area = Pi x r^2 + Pi x r x L
Volume of Sphere = 4/3 x Pi x r^3
Surface Area = 4x Pir x r^2
Sectors
Arc length = O/360 x 2 x Pi x r
Area = O/360 x Pi x r^2
3D Pythagoras
Long diagonal of a Cubiod - d = root a^2+b^2+c^2
Completing the Square
Minimum point (x+p)^2+q = (-p,q)
Symmetry line - x=-p
Perpendicular lines
Perpendicular Gradients - Negative reciprocal, m2 = -1/m1
Alternate Equation of line - y-y1 = m(x-x1)
Funcntions
Composite Functions - fg(x) Means do g then f
Inverse Functions - y=f(x) — x=f^-1(y)
Differentiation
Differentiating y = ax^n - dy/dx = nax^n-1
Stationary Points - dy/dx = 0
Kinematics
Differentiate = Displacement - Velocity - Acceleration
Sequences
Notation - a = first term, d = difference, n = position
Summation - Sn = n/2(2a+(n-1)d)
Nth Term - an = a +(n-1)d
