Block Four Flashcards
What is a function notation
input value (usally x) then applies a rule to create an output value.
e.g the function y= 3x-1 has an input of x and output of y
what do all these mean
f(x) = 3x -1
f = function
x= input
3x-1 = rule
How to evaluate a function
when evaluating a function you must substitute a value for x and solve the equation from there
f(-2) = 2(-2) -1
= -4 -1
= -5
How to find the input of a function
- you just work backwards and find the imput value
-this is basically solving an equation question - pay attention to the later used in the question
What is the formula to find a y- intercept
y = mx + c
in this equation m is the gradient
and c is the y- intercept that means the line crosses the y axis at (0,C)
What is the equation of a line through two points
y - b = m(x - a )
how to find the gradient and y- intercept from an equation
if a straight line equation is in the form y= mx+c
if it is not written like this then you need to rearrange to y = mx+c
Equations of parallel lines
y= mx+c
you must remember that parallel lines have an equal gradient
formula volume of a cuboid
V = L x B x H
formula volume of a prism
V = AH
Formula Volume of a cylinder
V = 3.14 x radius squared x h
Formula Volume of a pyramid
V = 1/3 of ( area of base ) x H
V = 1/3 AH
Formula Volume of a cone
1/3 x 3.14 x radius squared x H
what is a composite shape
large shape with a smaller shape cut away
how to solve the volume of a composite shape
calculate the volume of the total shape and then calculate the volume of the smaller shape and take them away
Formula Volume of a sphere
V= 4/3 x 3.14 x radius cubed
Volume of a semi sphere
V= 1/2 of ( 4/3 x 3.14 x radius cubed )
how to find the height from volume
- changing the subject
H = v / 3.14 x radius cubed
how to find the missing radius
change the subject
- R = cubed root ( 3V / 4x 3.14 )
How to find the volume of a composite shape
Can be calculated by adding the volumes of the two individual shapes together
e.g Vcone + Vhemi
How to solve equations with a bracket
begin by expanding the brackets and collect like terms
How to solve an equation with fractions
remove the fraction by multiplying all terms by the denominator
if it involves more than one fraction you should multiply by the LCM of all denominators
how to solve inequalities
- it is the same rules that apply
- if you multiply or divide by a negitive number change the direction of the inequality
V of a cuboid
L x B x h
V of a prism
A x h
V of cylinder
pi x r x r x h
V of a pyramid
1/3 x pi x A x h
V of cone
1/3 x pi x r x r x h
V of sphere
4/3 x pi x r 3
V of hemi sphere
1/2 of 4/3 x pi x r 3
