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Higher Mathematics > Higher Course > Flashcards

Higher Course Flashcards

1
Q

Collinearity

A

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

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2
Q

Parallel Gradients

A

Find gradient of given equation

Sub into straight line using given points

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3
Q

Perpendicular Gradient

A

Find gradient
Find perpendicular gradient
Sub into straight line equation

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4
Q

Median

A

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

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5
Q

Perpendicular Bisector

A

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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6
Q

Altitude

A

Find gradient
Find perpendicular gradient
Sub into straight line equation

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7
Q

Polynomials

A

Use synthetic division to find if a factor

Then factorise if asked

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8
Q

Polynomials with unknown coefficients

A

Use synthetic division and simplfy to find the coefficients

if 2 unknown coefficients then use simultaneous equations

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9
Q

Determining the equation from a graph

A 
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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10
Q

Differentiation

A

Multiply by power

minus 1 off the power

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11
Q

Rate of Change

A

Differentiate

Sub in the number asked

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12
Q

Equation of a tangent

A

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

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13
Q

Stationary Points

A

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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14
Q

Curve Sketching

A

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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15
Q

Optimisation

A

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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16
Q

Trig Exact Values

SIN

A 
0° = 0 
30° = 1/2
45° = 1/√2
60° = √3/2
17
Q

Trig Exact Values

COS

A 
0° = 1 
30° = √3/2 
45°= 1\√2
60° = 1/2
18
Q

Trig Exact Values

TAN

A 
0° = 0 
30° = 1/√3
45°= 1 
60° = √3
19
Q

Radians Values

A 
360° = 2π
180° = π
90° = π/2 
60° = π/3 
45° = π/4 
30° = π/6
20
Q

Inverse Functions

A

Replace f(x) with y
Change the subject to x
Replace y with x
Replace x with f’(x)

21
Q

Quadratic Inequations

A

Factorise to find roots
Draw a sketch
If bounded is between the 2 roots
If unbounded 2 separate values

22
Q

The discriminat

A

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

23
Q

Find intersection of a line and curve

A 
Simply equation 
Use discriminate 
If 0 - then a tangent 
If less than 0 - no intersection 
If over 0 - 2 points of intersection
24
Q

Find intersection of a line and curve with 2 points

A

Simply equation
Factorise to find 2 x points
Sub into original equation
Find coordinates of 2 points of intersection

25
Q

Distance Formula

A

√(x2-x1)²+(y2-y1)²

26
Q

Circle Equation

A

(x-a)²+(x-b)²=r²
(a,b) is the centre
r is the radius

27
Q

General Formula of a Cricle

A

x²+y²+2gx+2fy+c=0
centre = (-g,-f)
Radius -√g²+f²-c

28
Q

Coordinates and the Circle

A

Sub coordinates into equation

Determine LHS and compare to RHS

29
Q

Nature of intersection of line and curve

A

Sub equation of line into circle equation
Simplify and rearrange to 0
Use discriminate to determine nature

30
Q

Find the points of intersection of line and circle

A

Sub equation of line into circle equation
Simplify and rearrange to 0
Factorise for 2 x points
Sub into line equation to get coordinates

31
Q

Equation of a tangent to a curve

A

Find the centre to get the points
Use points to find the gradient
Sub into line equation

32
Q

The intersection of 2 circles

A

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

33
Q

The intersection of 2 points - Intersections

A

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

34
Q

Integration

A

Add one to the power

Divide by new power

35
Q

Definite Integration

A

f(b) - F(a)

Integrate by subbing in (b) then sub in (a) into x

36
Q

Area under a curve

A

Integrate
If negative the under x-axis
Use units²

Higher Mathematics (1 decks)

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