C1 Flashcards
When an equation has 2 real, distinct roots..
b^2-4ac > 0
When an equation has 1 root
b^2-4ac = 0
When an equation has no real roots…
b^2-4ac
How do you find the points of intersection on the axis
For x axis - set y = 0
For y axis - set x = 0
How to find the maximum of minimum of a curve?
Complete the square
Solve f’(x) = 0
Gradient of a line
(Y2 - Y1) / (x2 - x1)
Distance from 2 points
Square root of
(x2-x1)^2 + (y2-y1)^2
Nth term of an arithmetic series
a + (n-1)d
Sn of arithmetic sequence
n/2 [2a+(n-1)d]
Or
n/2(a+l)
Gradient of a tangent to a curve =
dy / dx
The normal to a curve at a point is …… To the tangent at that point
Perpendicular
The discriminant
b^2-4ac
What not to forget in integration
The c value at the end
How to find the area under a curve
Integrate between the x values wanted
eg
[3/2 + 3 x 4] - [1/2 + 1 x4]
Area between 2 lines
Rearrange/combine the 2 integrated equations before subbing in the values
2nd differential - the maximum point
d2y / dx2
2nd differential - minimum point
d2y / dx2 > 0
Define arithmetic series
A series where each term is obtained by adding on a constant to the previous term
Transforming graphs
f(x) + a
Moves the graph up and down by a units
Transforming graphs
f(x+a)
Moves the graph left by a units
Transforming graphs
af(x)
Stretches the graph in the y axis by a scale factor a
Transforming graphs
f(ax)
Stretches the graph in the x axis by a scale factor 1/a
