pure Y1 Flashcards
How to use discriminant to see if equation has one repeated root
b² - 4ac = 0
How to use discriminant to see if equation has no roots
b² - 4ac < 0
How to use discriminant to see if equation has two distinct real roots
b² - 4ac > 0
How to use set notation for inequalities
{x: x>3 }
n is and, u is or
How to draw positive and negative quadratics
Positive is U shaped. Negative is n shaped
How to draw positive and negative cubics
Positive point upwards. Negative point downwards. The graph is a sideways s shape.
How to draw positive and negative quartics
The positive graphs are W shaped. The negative graphs are M shaped.
How does
y = f(x) + a
transform a graph
Moves it upwards by a
(a units in the direction of the positive y- axis)
How does
y = f(x) - a
transform a graph
Moves it downwards by a
(a units in the direction of the negative y- axis)
How does
y = f(x + a)
transform a graph
Moves it left by a
(a units in the direction of the negative x-axis)
How does
y = f(x - a)
transform a graph
Moves it right by a
(a units in the direction of the positive x-axis)
How does
y = af(x)
transform a graph
stretches the graph by scale factor a in the vertical direction.
How does
y = f(ax)
transform a graph
stretches the graph by scale factor 1/a in the horizontal direction.
How does
y = -f(x)
transform a graph
Reflects in the x-axis
How does
y = f(-x)
transform a graph
Reflects in the y-axis
What is the equation of a circle with a centre (0,0)
r² = x² + y²
What is the equation of a circle with a centre (a,b)
r² = (x - a)² + (y - b)²
How to find the equation for a circle
complete the square
Tangent of a circle
Perpendicular to radius of circle
perpendicular bisector of a chord
goes through the centre of the circle
How to find the area of a non right angled triangle
1/2abSinC
Cosine rule (non right angled triangles)
a² = b² + c² - 2bcCosA
Sine rule (non right angled triangles)
SinA/a = SinB/b
how are sin and cos related
sin²x + cos²x = 1
How to find the turning point of a function
use the first derivative and solve it set to zero
How to determine if the turning point of a function is maximum of minimum
Insert the solution from the first derivative into the second derivative of the function.
What will the output from the second derivative be if the turning point is a maximum?
it is less than zero
What will the output from the second derivative be if the turning point is a minimum?
it is more than zero
How to find area under a curve
integration
logarithm power law when k = -1
loga(1/x) = loga(x^-1) =
-loga(x)
How to find area of a sector of a circle where r is the radius of the circle and O is the angle in radians contained by the sector
A = 1/2 x r² x O
How to find the arc length of a sector of a circle where r is the radius of the circle and O is the angle in radians contained by the sector
L = rO
