Maths Flashcards
(17 cards)
What do these letters mean in maths:
N
Z
R
Q
N means all natural numbers so starts from zero and goes to infinity
Z means a set of all integers ( zero, all positive and all negative whole numbers)
R means all real numbers, all fractions, decimals, integers and whole numbers.
Q means a set of rational numbers.
What is a rational number?
A rational number is a number which can be expressed as a fractional p/q where p and q are integers and q is not zero
Why can’t you divide by sin theta or cos theta or any variable?
Whenever you divide by a variable you are assuming that the variable is to equal to zero because this is not a valid mathematical operation dividing by zero. Therefore is you do divide by a variable you must first find the solution of variable=zero. You should add this too all of your other solutions at the end.
What does proof by exhaustion mean?
Write all possible combinations in the set of numbers which they give you to show that it is not possible.
When given two parametric equations and a cartesian how should you show that the two parametric equations satisfy the cartesian?
You should substitute the expressions of both parametric equations into the cartesian and show that they equal what is written.
Sub in parametric equations into cartesian to show they satisfy the cartesian.
How do you integrate lnx?
By parts (1)(lnx).
when sin x=0 (or cosX=0) аnd range is 0<x<180 what do you need to be careful of?
The theta solutions of 0 and 180 degrees are not valid solutions because they are not in the range. <x< really be careful, check at end of trig questions that you/re answers satisfy (are in) the required range.
When using discriminant in questions with x and k and given a circle equation and a line equation where should you sub this line equation in a what should your discriminant look like?
Even though you rearrange the x^2 + y^2 +10x… equation into circle equation format (x-a)^2 + (y-b)^2 … you should sub in the line equation e.g. y=3x+K into the original equation.
When you rearrange this, expand and want to use the discriminant the coefficient of x should be as unsimplified as possible, once x should be factored out you must leave everything else in. Now you use the discriminant.
What year is the total profit of this geometric sequence greater than X (e.g. 65000), watch out for?
Geometric sequence is n-1, watch out for this.
3 Things you must say to show root alpha is in a given interval.
- There is a root because there is a sign change
- Function used if continuous (must specify what function you used.)
-Root alpha = 0.3410
Why do we use the iteration formula then minus xn+1 and equal it to zero?
e.g.
2xn^2 + 4xn+ 5= Xn+1
rearrange to
2xn^2 +4xn +5 -Xn+1= 0 because after a certain n value all Xn+1 values after are the same so if subtract expression which gives Xn+1 from Xn+1 then will give zero because they are equal.
When do you use cosine and sine rule?
Cosine Rule used when you have 3 sides and want to find an angle and when you have two sides and an angle opposite the missing side.
Note: The ‘a’ doesn’t have to be the longest side in the triangle. Cos A must be the opposite angle to it but a itself does not have to be the longest side in the triangle. As long as Cos A is opposite a any side can be a.
Sine rule when you have two angles and a side and want to find an angle, or two sides an an angle and want to find an angle.
A=1/2 ab(sinC)
a and b can be any sides of the triangle. As longs as sinC is opposite to side c then can use this. No specific side has to be a, b or c.
lne^x = e^lnx=
x.
if lne^4x then = e^ln4x = 4x.
How can you make the area given by the trapezium rule more accurate?
-Use more trapezia
-Decrease the width of the trapezia
Why does a function not have an inverse?
It is a many-to-one function or it’s inverse will be a one-to-many function.
When using coded data and it asks you to find the mean what must you do?
if code is y= x -1100 then mean of y (y bar) = x bar -1100
