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Maths Core > Graphs, (Sketching, Circles, Straight Lines, Stationary Points) > Flashcards

Graphs, (Sketching, Circles, Straight Lines, Stationary Points) Flashcards

1
Q

What does a (y = x) graph look like?

A

/

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2
Q

What does a (y = -x) graph look like?

A

\

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3
Q

What does a (y = x^2) graph look like?

A

\/

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4
Q

What does a (y = -x^2) graph look like?

A

/\

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5
Q

What does a (y = x^3) graph look like?

A

/\/

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6
Q

What does a (y = -x^3) graph look like?

A

\/\

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7
Q

What is the equation for a straight line graph, and what do the symbols stand for?

A 
y = mx + c
y = y co-ordinate
x = x co-ordinate
m = gradient
c = y-intercept
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8
Q

What is the Equation for the mid-point?

A

mp = (x1+x2/2) , (y1+y2/2)

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9
Q

What is the equation for the gradient of a line on a graph?

A

m = (y2-y1) / (x2-x1)

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10
Q

What is the gradient of parallel and perpendicular lines?

A 
Parallel = same gradient
Perpendicular = -1/m
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11
Q

How do you find the distance between two points on a graph?

A

d = /(x2 – x1)^2 + (y2 – y1)^2

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12
Q

What are the equations for direct and inverse proportion?

A

Direct Proportion: y = kx

Inverse Proportion: y = k/x

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13
Q

What is a circle?

A

A 2D line where all the points are equidistant from the centre

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14
Q

How do you find the equation of a tangent of a circle?

A
  1. Find the gradient of AB
  2. Work out the perpendicular gradient
  3. Find the co-ordinate of the centre
  4. Find the equation
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15
Q

What is the equation for a circle?

A

(x – a)^2 + (y – b)^2 = r^2
(a, b) = centre of the circle
r = radius

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16
Q

How do you check if a circle passes through a certain point?

A

Substitute the equations for (x,y)

17
Q

How do you find where the circle meets the x axis?

A

Sub y for 0

18
Q

How do you find where the circle meets the y axis?

A

Sub x for 0

19
Q

How do you find where the circle meets the line?

A

Sub the line equation in the circle equation

20
Q

What does it mean if there are no (x,y) when you sub in the line equation?

A

Line doesn’t intercept circle

21
Q

What does it mean if there is 1 (x,y) when you sub in the line equation?

A

Line intercepts circle once

22
Q

What does it mean if there is 2 (x,y) when you sub in the line equation?

A

Line intercepts circle twice

23
Q

What is the gradient at stationary points?

A

m = 0

24
Q

How do you find the stationary point(s)?

A
  1. Differentiate
  2. Solve to = 0
  3. Substitute
25
Q

How do you find out if the stationary point is a maximum or a minimum?

A

d^(2)y / dx^2
Substitute in co-ordinates
Positive = minimum
Negative = maximum

26
Q

What does a (y = x^4) graph look like?

A

\/\/

27
Q

What does a (y = -x^4) graph look like?

A

/\/\

28
Q

What does a (y = 1/x) graph look like?

A

_\

\

29
Q

What does a (y = -1/x) graph look like?

A

/

_/

30
Q

What does a (y = 3/x) graph look like?

A

_\

\

Maths Core (27 decks)

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