Higher Course Flashcards
Collinearity
Find gradient of 2 points
Use one of those points and the other one not used
If same then collinear
Parallel Gradients
Find gradient of given equation
Sub into straight line using given points
Perpendicular Gradient
Find gradient
Find perpendicular gradient
Sub into straight line equation
Median
Find midpoint
Find gradient through midpoint and other point
Sub into straight line
Perpendicular Bisector
Find midpoint
Find gradient with points used to find midpoint
Find perpendicular gradient
Sub straight line equation with gradient and midpoint
Altitude
Find gradient
Find perpendicular gradient
Sub into straight line equation
Polynomials
Use synthetic division to find if a factor
Then factorise if asked
Polynomials with unknown coefficients
Use synthetic division and simplfy to find the coefficients
if 2 unknown coefficients then use simultaneous equations
Determining the equation from a graph
Find roots (3) Sub roots into K(x-a)(x-b)(x-c) to find k (x=0) Use K in f(x)=K(x-a)(x-b)(x-c) and multiply out
Differentiation
Multiply by power
minus 1 off the power
Rate of Change
Differentiate
Sub in the number asked
Equation of a tangent
Find y to get coordinates
Find gradients by differentiation
Sub in for straight line equation
Stationary Points
Find f’(x)
Find f’(x) =0 to get x
Sub x into original equation
Use nature table to determine the nature of roots
Curve Sketching
Find y intercept when x=0
Find x intercept when y=0
Find stationary points
Sketch a graph using x and y intercept and results of nature table
Optimisation
Find area using A=LxB
Find S.P’s of original equation
Find x
Use nature table to get value asked
Sub back into length or breadth of the room
Trig Exact Values
SIN
0° = 0 30° = 1/2 45° = 1/√2 60° = √3/2
Trig Exact Values
COS
0° = 1 30° = √3/2 45°= 1\√2 60° = 1/2
Trig Exact Values
TAN
0° = 0 30° = 1/√3 45°= 1 60° = √3
Radians Values
360° = 2π 180° = π 90° = π/2 60° = π/3 45° = π/4 30° = π/6
Inverse Functions
Replace f(x) with y
Change the subject to x
Replace y with x
Replace x with f’(x)
Quadratic Inequations
Factorise to find roots
Draw a sketch
If bounded is between the 2 roots
If unbounded 2 separate values
The discriminat
b²-4ac
If below 0 - no real roots
If equal to 0 - 2 real and distinct roots
If over 0 - roots are real and distinct
Find intersection of a line and curve
Simply equation Use discriminate If 0 - then a tangent If less than 0 - no intersection If over 0 - 2 points of intersection
Find intersection of a line and curve with 2 points
Simply equation
Factorise to find 2 x points
Sub into original equation
Find coordinates of 2 points of intersection
Distance Formula
√(x2-x1)²+(y2-y1)²
Circle Equation
(x-a)²+(x-b)²=r²
(a,b) is the centre
r is the radius
General Formula of a Cricle
x²+y²+2gx+2fy+c=0
centre = (-g,-f)
Radius -√g²+f²-c
Coordinates and the Circle
Sub coordinates into equation
Determine LHS and compare to RHS
Nature of intersection of line and curve
Sub equation of line into circle equation
Simplify and rearrange to 0
Use discriminate to determine nature
Find the points of intersection of line and circle
Sub equation of line into circle equation
Simplify and rearrange to 0
Factorise for 2 x points
Sub into line equation to get coordinates
Equation of a tangent to a curve
Find the centre to get the points
Use points to find the gradient
Sub into line equation
The intersection of 2 circles
Find the radius and circle of both equations
Find the distance between the centres
Add the radius
compare centre distances and add the radius to determine the intersection
The intersection of 2 points - Intersections
r1+r2 less than AB - 2 points of intersection
r2-r1=AB - one circle is inside the other
r1+r2 more than AB 2 points of intersection
Integration
Add one to the power
Divide by new power
Definite Integration
f(b) - F(a)
Integrate by subbing in (b) then sub in (a) into x
Area under a curve
Integrate
If negative the under x-axis
Use units²
