Unit 1 Flashcards
Distance formula
d= √(x2-x1)²+(y2-y1)²
Midpoint formula
(x1+x2/2),(y1+y2/2)
Gradient formulas
m=y2-y1/x2-x1
m=tanø
When are points collinear
When they lie on the same straight line
Gradients of perpendicular lines
m x m_ = -1
How to find a median
Midpoint
Gradient
Equation
How to find an Altitude
Gradient
Perpendicular gradient
Equation
How to find a perpendicular bisector
Midpoint
Gradient
Perpendicular gradient
Equation
When are lines concurrent
If there is a point through which they all pass
What is this
f^-1(x)
Inverse
How to find the inverse of a function
Change notation from f(x) to y
Change subject to x
Change notation back to f^-1(x)
Change y in equation to x
How to draw the graph of an inverse
Reflect it over the line y=x
What is this
f(x)=a^x
Exponential function
What points do the graphs of an exponential function always pass through
(0,1) (1,a)
How to sketch the graph of an exponential function
Sub in x=0
Sub in x=1
What is this
f(x)=log a x
Logarithm
What points to the graph of a logarithmic function always pass through
(1,0) (a,1)
How to change degrees to radians and radians to degrees
x 3.14 x 180
180 3.14
Exact values table
30 45 60
sinx 1/2 1/√2 √3/√2
cosx √3/2 1/√2 1/2
tanx 1/√3 1 √3/1
f(x)+a
Shifts graph up y axis
f(x+a)
Shifts graph -a along x axis
-f(x)
Reflects graph in x axis
f(-x)
Reflects graph in y axis
kf(x)
Scales graph vertically
Stretches if k>1
Compresses if k<1
f(kx)
Scales graph horizontally
compresses if k>1
stretches if k<1
How to differentiate
Multiply first term by power
Minus 1 from power
3 types of notation when differentiating
f’(x)
dy/dx
d/dx (term)
How to find the rate of change/velocity of a function
Differentiate
Sub in x coordinate
What is a tangent
A straight line that touches a curve
How to find the equation of a tangent
Find coordinates of point
Differentiate curve equation
Sub in x coordinate to get gradient
Write out equation
When is a curve strictly increasing
derivative > 0
When is a curve strictly decreasing
Derivative < 0
How to find if a curve is strictly increasing/decreasing
Differentiate equation of curve
Sub in x coordinate
Look if dy/dx is < or >0
How to find stationary points and determine their nature
Differentiate equation of curve
Make derivative equal to zero
Factories for x coordinates
Sub each x coordinate into original equation of curve for y coordinates
Draw nature table using x coordinates and derivative to determine nature
How to sketch a curve
Find where cuts y axis when x=0 Find where cuts x axis when y=0 Find stationary points Do nature table Draw graph
How to find the closed interval of a graph
Find stationary points
Do nature table
State interval ends by subbing values into original equation
Find where cuts the x and y axis by subbing in zero
Draw graph
How to draw the graph of a derivative
Switch line directions when drawing
What do A and B represent?
Un+1 = AUn + B
A is percent increase/decrease added/subtracted from 100, divided by 100
B is variable being introduced
Limit of a sequence formula
l = b/1-a
