Pure Maths Flashcards
What are the 6 index laws?
a^m x a^n = a^m+n
a^m / a^n = a^m-n
(a^m)^n = a^mn
a^m/n = ( n root a)^m
a^-n = 1/a^n
a^0 = 1
What can you find from CTS?
Minimum point, y intercept, solutions to quadratics
What does the discriminant find, explain?
It tells us how many roots
Discriminant> 0 means 2 roots
Discriminant< 0 means no roots
Discriminant= 0 means 1 root
What are all the equations for coordinate geometry?
1) midpoint- (( x1+x2)/2, (y1+y2)/2)
2) gradient- (y2-y1) / (x2-x1)
3) distance- root ( (x2-x1)^2 + (y2-y1)^2)
4) line equation- y-y1=m(x-x1)
5) perp gradient - negative reciprocal
What happens to an inequality when u multiply by -1?
Your flip the inequality
> turns into <
Explain how f(x) is transformed?
When the transformation is outside the bracket it affects the y
And if the transformation is in the bracket it affects the x in the opposite way
What is the equation of the circle and what do you use to find it?
(X+a)^2 + (Y+a)^2 = r^2
Use need to use CTS
How do you find the tangent to a circle?
You use the centre and point where circle and tangent intersect, finding its gradient.
Use negative reciprocal gradient and put into line equation to find tangent
When subbing a value into a function and it equals zero what does that mean?
The (x + the opposite) is a factor
f(2)=0 therefore (x-2) is a factor
Explain what it means when a function is increasing or decreasing?
Increasing- dy/dx > 0
Decreasing- dy/dx < 0
What is the equation for differentiation from first principles?
f(x+h)-f(x) all over h
What are all the trig equations and identities?
Area= 1/2 ABsinC
Sin rule- a/sinA = b/sinB
Cosine rule- a^2 = a^2 + b^2 - 2bcCosa
Tan x = sin x/ cos x
Sin^2 + cos^2 = 1
What are the max and min values for sin cos and tan graphs?
Sin= -1 to 1
Cos= -1 to 1
Tan= undefined/ infinity
What does e^kx differentiate to?
Ke^kx
What does e^x graph look like?
Intercepts y axis at 1
Tends towards zero ( asymptote at zero)
