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Maths - Core 1

Revision notes for the OCR MEI exam (Which I am taking on the 13th of January 2012)
by

Luke Storry

on 13 January 2012

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Transcript of Maths - Core 1

Core 1
Curves & Translations
Quadratics
Co-ordinate Geometry
by Luke Storry 2011
https://portal.exe-coll.ac.uk/courses/mas/maths/asm/01d/Specification/MEI%20Core%20Maths%201%20Specification.pdf
For 13th Jan 2012 Exam
Specification:
Revision Notes
Polynomials
Uncertainty
Indices
d > 0 -> 2 distinct roots
d = 0 -> 2 equal roots (aka just 1)
d < 0 -> 0 real roots
Gradients
Distances
A
B
Dx
Dy
using pythagoras,
Straight Lines
Equation
perpendicular gradients have a product of -1, so
Circles
if (a,b) is the origin and (x,y) is a point on the circle, then:
To find origin from three points, find equation of two lines through those points, then the perp.bisectors will intersect on the origin
Parallel lines have EQUAL gradients; only 'C' changes
to find points of intersection (or if there are any) just do a simulatanious equation with them, to see if any values meet both.
Order of Polynomials
is the highest power of x in it.
eg quadrilaterals are 2nd order, and cubics are 3rd
let
be any polynomial
function of x
F(x)
Factor Theorem
f(a) =0 <=> (x-a) is a factor of f(x)
f(a/b) = 0 <=> (bx-a) is a factor of f(x)
Remainder Theorem
when
f(x)
is divided by
(x-a)
, the remainder is
f(a)
Solving
& sketching the graph
1) factorise (divide) down to roots
2) draw curve
3) draw x axis through it at appropriate place
4) mark on roots
5) draw y axis through ti at appropriate place
Operations
+&-
x
just do the coefficients
Box method
/
reverse box plot
Binomial Expansions
nCr w/o calc
- NEED TO KNOW!!
where
Quadratic
has vertex
line of symmetry
y intercept
( -p , q )
x = -p
( 0 , c )
f(x) = ax^3 + bx^2 + cx + d
Cubic
Completed square
A
translation
of a function may be given by:
Translations
f(x - t) + s
this is given by the vector
t
s
()
horizontal (x)
vertical (y)
can be solved like linear equations,
Linear Inequalities
Solve by drawing it!
Quadratic Inequalities
except that when multiplied or divided by a negative, the sign reverses
then identify the part(s) of the x axis that complies with the equation.
if the denominator of a fraction is sqrt{b},
multiply top and bottom by sqrt{b}
Rationalising Denominators
if the denominator is (a + sqrt{b}), then
multiply top and bottom by (a - sqrt{b})
look for square factors
Simplifying square roots
Positive "a" (x coefficient)
means a smily face,
and visa versa
Smily / Frowny
vertex (aka turning point) is also at
x= -b/2a
Logic
-1/grad = perp. grad
Basically, if no remainder, it must be a factor
eg. 7C4
= 7! /(4! 3!)
=> implies
<= is implied by
<=> both^ (equivilant to)
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