Core 2 Flashcards
Equations coefficients
eg verify that 3x+2 is a factor of 15x^2+x-6
Sub in x=-2/3 =0
15x^2+x-6=(3x+2)(Ax+B)=3Ax^2+3Bx+2Ax+2B
15=3A A=5;,2B=-6 B=-3; 3B+2A=1
(3x+2)(5x-3)
Finding factors
eg 6x^2-7x-10
Use -10 so +/-1 +/-10 +/-2 +/-5
Then sub in for x and if it = 0 it is a factor along with the other one in the pair (eg +2, -5)
Then (6x+5)(x-2) so x=-5/6 or 2
If the number subbed in does not come out at 0 then the number obtained is the remainder
Finding the quotient remainder
eg 20x^3-x^2-4x-7 = (4x+3)(Ax^2+Bx+C) +R
A=5; B=-4; C=2 R=remainder=-13
Quotient = 5x^2-4x+2
Logs
Y=b^x
X=logby
Log nroot p
Logp/n
Sigma2r
2Sigmar
Geometric 20th term
Ar^19
As n tends to infinity, x^n gets smaller so sn tends
towards 10
The series converges to 10
When calculating area to the y axis
Make x=
Infinite integral
eg y=1/x^2
Infinity = s
As s tends to infinity
1/-s tends to 0
So 0-(-1)=1
Improper integral
eg 1/3rtx
R=0
As r tends to 0
3/2 xr tends to 0
3 ordinals
2 trapeziums = 2 intervals
Area of a triangle
1/2abSinC
Sine rule
To find angle given two sides and an angle
SinA/a=SinB/b
To find a side given two angles and a side
a/SinA=b/SinB
Cosines rule
To find third side when given two sides and angle between
a^2=b^2+c^2-2bcCosA
To find angle given three sides
CosA=b^2+c^2-a^2/2bc
