How to do everything in Higher maths Flashcards
be able to do maths haha
Distance Formula
The Square root of
x2-x1) + (y2-y1
m=tana
positive of x axis use angle given
negative of x axis take away from 180
Equation of a straight line
y-b=m(x-a)
Parallel lines
have equal gradients
Perpendicular
flip and change sign
m1 x m2 = -1
Collinearity
Mab = Mbc = Mac
share a common point and have the same gradient
Point of intersection
Simultaneous equations
Medians
Find Midpoint
Find the gradient M
Find equation of line using M and either point
Altitudes
Find M then Mperp
Use third point and Mperp
Perpendicular Bisector
Find Midpoint
Find Gradient M
Find Mperp
use Mperp and Midpoint
Recurrence Relations
Un+1 = aun + b
or
Un-1 = aun + b
Limits
a limit can only occur if - 1< a < 1
Sketching Functions
inside the bracket change the x coordinate
outside the bracket change the y coordinate
Composite Functions
substitute and solve
Differentiation
bring power down
take away one from power
Equations of tangents
need one point and M
one point is ALWAYS given
M is the rate of change f’(x)
x coordinate is the equation of the gradient
Increasing and Decreasing Functions
f’(x) > 0 - increasing
f’(x) < 0 - decreasing
Stationary Points
when f’(x) = 0
use nature table to find nature of curve
Curve Sketching
Work out x-axis intercepts / roots solve y = 0
work out y axis intercepts for x = 0
determine stationary points and their nature
sketch on a graph
Closed Intervals
Max/Min values can occur at stationary points or end points of the closed interval
a range is given -a < x < b
find stationary points - use if in range
sub the interval values and stationary points into f’(x) ti find max / min
Graphs of Derived Functions
All stationary points become roots
when graph is increasing - above x axis
when graph is decreasing - below x axis
plot on graph new curve
Polynomials - factors
is a factor if R=0
Equations for Polynomials
use y=k(x-a)(x-b)
use point on graph to determine y and x and given point for a and b
Completing the square
take the coefficent out of the x^2
then half everything
complete the sqaure as normal
put the coefficent back in
Quadratic Inequations
less than zero = below x axis
greater than zero = above x axis
draw a sketch and solve
The discriminant
< 0 = No real roots
= 0 , = Equal roots (one root)
> 0 = 2 Real roots
Conditions for Tangency
make line and curve equal to each other
make = 0
solve
if one value it is a tangent
Point of Contact
sub point (x) into the line to find y
Integration
Add 1 to power and divide by new power
Indefenite Integrals
must have + c !!
Definite Integrals
have limits
Finding a Limit - Integration
integrate, then upper take away lower limit
Area Under Graph
use graph to find limits if not given
integrate