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Pure Mathematics Term 1 topics - Coggle Diagram
Pure Mathematics Term 1 topics
Coordinate Geometry
Equation of a straight line
y = mx + c
m = gradient
x = x-coordinate
y = y- coordinate
c = y-intercept
y - y1 = m(x-x1)
Intersections of two lines
equate both equations
Coordinates: Plot, Sketch, Draw
Gradient = m (y2 - y1)/(x2-x1)
Distance between two poitns = sqrt(a^2 + b^2)
Midpoint Formula = ( (x1+x2)/2 , (y1 + y2)/2)
Perp m = -1/m
Parallel -> m = m
Drawing Curves
Type 1: y = x^n for n = 1,2,3,4
Type 2: y = 1/x^n ( for x ≠0)
Type 3: y = kx^0.5 and kx^-0.5
Circle
Equation of a circle: r^2 = (x-h)^2 + (y-k)^2
Algebra and Quadratics
Quadratic equation
-b +_ /b^2 - 4ac / 2a
Factorisation
Example : 21x + 7y = 7(3x + y)
Completing the square
(x+a)^2 + b
(x+b/2)^2 - ( b/2)^2 + c
Simultaneous equations
Inequalities
F(x) > 0 Two equations
F(x) = 0 One equation
F(x) < 0 Zero equations
Functions
b^2 - 4ac
Functions and Transformations
Functions
Output (range) Input (domain)
One input can only have one output, but two inputs can have the same output.
If it is possible for a vertical line to intersect a graph at more than one point, then the graph is NOT the graph of a function.
Example of a funciton
NOT an Example of a function
Transformations
y=f(x)+a
0/a
moves the graph (a) units up
y=f(x)-a
0/-a
moves graph (a) units down
y=f(x+a)
-a/0
moves graph a units left
y=f(x-a)
a/0
moves graph a units right
y=-f(x)
reflection in x axis
y= af(x)
switch parallel to the y axis with a scale factor of a
y=f(-x)
reflection in y axis
y=f(ax)
stretch parallel to x axis with scale factor 1/a
Trigonometry
identities
sin θ+ cos θ= 1
tanθ=sinθ/cosθ
degree to radian
cosine tangent graph
