Higher Course Flashcards by Lauren Thomson

Collinearity

Find gradient of 2 points
Use one of those points and the other one not used
If same then collinear

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Parallel Gradients

Find gradient of given equation

Sub into straight line using given points

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Perpendicular Gradient

Find gradient
Find perpendicular gradient
Sub into straight line equation

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Median

Find midpoint
Find gradient through midpoint and other point
Sub into straight line

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Perpendicular Bisector

Find midpoint
Find gradient with points used to find midpoint
Find perpendicular gradient
Sub straight line equation with gradient and midpoint

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Altitude

Find gradient
Find perpendicular gradient
Sub into straight line equation

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Polynomials

Use synthetic division to find if a factor

Then factorise if asked

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Polynomials with unknown coefficients

Use synthetic division and simplfy to find the coefficients

if 2 unknown coefficients then use simultaneous equations

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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

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Differentiation

Multiply by power

minus 1 off the power

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Rate of Change

Differentiate

Sub in the number asked

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Equation of a tangent

Find y to get coordinates
Find gradients by differentiation
Sub in for straight line equation

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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

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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

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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

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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