Maths Flashcards
How do you test if something has an inverse function?
Horizontal line test
Set builder notation?
the one with the wavy brackets {x: x>7}
Interval notation?
[ = or equal to ( = than
What is I(x)?
The identify function, it leaves X unchanged. So goes through the function and then the inverse.
f(x) + k?
Translates y upwards
f(x) - k?
Translated y downwards
f(x+k)?
Translates x to the left
f(x-k)?
Translates x to the right
-f(x)?
Reflection in the x
f(-x)?
Reflection in the y
f(qx)?
stretches or compresses horizontally of a factor 1/q
pf(x)?
stretches or compresses vertically of a factor of q
How do you test if something is a function?
Vertical line test
How do you complete the square?
You put it in without changing the signs at all!!!!!!!
It is if you want the vertex that you change the one inside!
What is the log change of base formula?
logb(a) = logc(a)/logc(b)
What is a inflexion point?
One where the concavity changes.
What is variance?
STANDARD DEVIATION SQUARED
What is a residual?
A residual is the vertical distance between a data point and the regression line.
What is sin45?
1/square root of 2 REMEMBER 1,1, SQUARE ROOT 2 TRIANGLE FOR 45 DEGREES
What is cos45
1/square root of 2 REMEMBER 1,1, SQUARE ROOT 2 TRIANGLE FOR 45 DEGREES
What is tan45?
1 REMEMBER 1,1, SQUARE ROOT 2 TRIANGLE FOR 45 DEGREES
What is sin30?
1/2 REMEMBER 1, SQUAREROOT 3 , 2 TRIANGLE
What is sin60?
squareroot3/2 REMEMBER 1, SQUAREROOT 3 , 2 TRIANGLE
What is cos30?
squareroot3/2 REMEMBER 1, SQUAREROOT 3 , 2 TRIANGLE
What is cos60?
1/2 REMEMBER 1, SQUAREROOT 3 , 2 TRIANGLE
What is tan30?
1/squareroot3 REMEMBER 1, SQUAREROOT 3 , 2 TRIANGLE
What is tan60?
squareroot3/1 REMEMBER 1, SQUAREROOT 3 , 2 TRIANGLE
In the unit circle which is x and which is y?
cos is x
sin is y
How do you convert from degrees to radians?
degrees x pi/180
How do you convert from radians to degrees?
radians x 180/pi
What do you need to know about the unit circle?
sin0 = sin(180-0) cos0 = cos(-0) tan0 = tan(180 + 0)
How do you find the period of a trig function?
Divide it by 2pi!
How do you write cast?
c a s t - starts in the bottom right hand corner and goes clockwise.
What do you have to be careful with with tan and the unit circle?
If it is tanx= squareroot of 3
THEN IT CAN BE PLUS OR MINUS ANY OF THE VALUES.
SO THERE ARE LOADS OF VALUES
What is sin2x?
It is a horizontal stretch of 1/2 and so you multiply every x value by 1/2.
Differentiate tan(3x)?
3/cos^2(3x) DO NOT FORGET TIMES BY THE POWER
How do you integrate cos(4x-6)
-1/4sin(4x-6) IS JUST A RULE JUST ACCEPT IT
What is the difference between the product rule and the chain rule?
BOTH TO DIFFERENTIATE
The chain rule is used if you are multiplying a number. You use the product rule if you are multiplying a function by a function.
e.g.
4(sin(4x)^2 - CHAIN RULE
(4x + 2)(sin(4x)^2 - PRODUCT RULE
