Core 1 Flashcards
How do you find the intersection of 2 lines?
Using simultaneous equations
What happens if y2-y1=0?
Horizontal line, so y=…
What happens if x2-x1=0?
Vertical line, so x=
What’s the order of a polynomial?
The biggest power in the expression
How do you know if a polynomial has an odd or an even function?
Look at the order, if it’s odd then odd, if it’s even then even
In an odd function, f(a)=…
-f(a)
In an even function, f(a)=…
f(-a)
When multiplying functions, which way do you work from?
Right to left
What’s general form?
y=a(x-b)(x-c)
Turning point or vertex of y=(x-a)^2+b
(a,b)
Line of symmetry of y=(x-a)^2+b
x=a
How many solutions?
Discriminant > 0
2 real solutions
How many solutions?
Discriminant < 0
0 real solutions
How many solutions?
Discriminant = 0
1 real solution
When can you transform an equation into a quadratic?
When the larger power is double the smaller power
When does an equality sign flip?
When you multiply or divide by a negative
What does differentiation tell you?
Rate of change
What’s the normal perpendicular to?
The tangent
What’s the gradient at a maximum and minimum point?
0
What does the second derivative tell you?
Rate of change of the gradient
What type of stationary point is this?
Second derivative > 0
Minimum point
What type of stationary point is this?
Second derivative < 0
Maximum point
What type of stationary point is this?
Second derivative = 0
Probably point of inflection, need to use table method to check
Equation of a circle
(x-a)^2 + (y-b)^2 = r^2
What angle does a tangent meet a radius at?
Right angle
If a radius bisects a chord then they are…
Perpendicular
What’s the angle in a semi circle?
Right angle
What transformation is this?
y=f(x)+k
Translation of k in the y direction
What transformation is this?
y=f(x+k)
Translation of -k in the x direction
What transformation is this?
y=kf(x)
Stretch factor k in the y direction
What transformation is this?
y=f(kx)
Stretch factor 1/k in the x direction
What transformation is this?
y=-f(x)
Reflection in the x axis
What transformation is this?
y=f(-x)
Reflection in the y axis
