PURE YEAR 1 Flashcards by hannah king

what is a^m x a^n

a^(m+n)

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what is (a^m)^n

a^mn

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what is a^m / a^n

a^(m-n)

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what is (ab)^n

a^n b^n

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what is a^(1/m)

m root a

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what is a^-m

1/a^m

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what is a^(n/m)

m root a^n

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what is a^0

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simplify sqrt(ab)

sqrt(a) x sqrt(b)

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simplify sqrt(a/b)

sqrt(a)/sqrt(b)

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what is the domain

the set of possible inputs for a function

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what is the range

the set of possible outputs of a function

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what are the roots for a function

the values of x for which f(x)=0

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how to find turning point of a quadratic graph

complete the square
f(x)= a(x+p)^2 +q
turning point (-p, q)

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different cases of discriminants

b^2-4ac
if >0, 2 roots
if =0, 1 root
if <0, 0 roots

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when is an inequality represented with a dotted line

if y>f(x) or y<f(x), the curve y=f(x) is not included in the region and is represented by a dotted line

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when is an inequality represented with a solid line

if y≥f(x) or y≤f(x), the curve y=f(x) is included in the region and is represented by a solid line

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where do the graphs y=k/x and y=k/x^2 have asymptotes

x=0
y=0

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y=-f(x) transformation description

reflection of y=f(x) in x-axis

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y=f(-x) transformation description

reflection of y=f(x) in y-axis

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gradient formula

m= (y2-y1)/(x2-x1)

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product of gradients of perpendicular lines

-1

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equation of distance between 2 points

d= sqrt((x2-x1)^2 + (y2-y1)^2)

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when are 2 quantities said to be in direct proportion
what is the graph of these quantities

when they increase at the same rate
a straight line through the origin

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midpoint of a line segment equation

(x1+x2)/2, (y1+y2)/2

what is the perpendicular bisector of line segment AB

straight line perpendicular to AB that passes through midpoint of AB

equation of circle w centre 0,0

x^2 + y^2 = r^2

equation of circle w centre (a,b)

(x-a)^2 + (y-b)^2 = r^2

tangent to circle property

perpendicular to radius at point of intersection

perpendicular bisector of a chord property

goes through centre of circle

property of right angle in circle

if angle PRQ=90 then R lies on circle w diameter PQ angle in semicircle is always a right angle

how to find centre of a circle given any 3 points

find the equations of the perpendicular bisectors of 2 different chords find coordinates of intersection of the perpendicular bisectors

factor theorem of polynomials

if f(p)=0, then (x-p) is a factor of f(x)

3 methods of proof

deduction exhaustion counter-example

cosine rule w a^2 as subject

a^2= b^2 + c^2 - 2bc cosA

cosine rule w A as subject

A= cos^-1 ( (b^2 + c^2 - a^2)/2bc )

sine rule

sinA/ a = sinB/ b (or reciprocal)

sin(x) is same as what

sin (180-x)

area of triangle

1/2 ab sinC

how often does y=sin(x) repeat

every 360 degrees

where does y=sin(x) cross x-axis

-180 0 180 360

how often does y=cos(x) repeat

every 360 degrees

where does y=cos(x) cross x-axis

-90 90 270 450

how often does y=tan(x) repeat

every 180 degrees

where does y=tan(x) cross x-axis

-180 0 180 360

where are asymptotes of y=tan(x)

-90 90 270

if vectors PQ=RS what is to say

equal in length parallel

if vectors AB=-BA:

AB is equal in length, parallel and in opposite direction to BA

triangle law for vector addition

AB + BC = AC is AB=a, BC=b, AC=c, a + b = c

what does adding vectors PQ and QP give

the zero vector 0

what can any vector parallel to vector a be written as

λa λ is a non-zero scalar

how to multiply a column vector by a scalar

multiply each component by the scalar λ(p q)= (λp λq)

how to add 2 column vectors

add the x- components tgt add the y- components tgt

how is the magnitude of vector xi + yj given

sqrt(x^2 + y^2)

what is a unit vector in the direction of a

a / |a| (a over magnitude of a)

equation for differentiating from first principles

f'(x)= lim h->0 (f(x+h)-f(x)) / h

derivative of x^n

n x^(n-1)

derivative of ax^n

an x^(n-1)

when is a function said to be increasing

if, on an interval, f'(x)>0

when is a function said to be decreasing

if, on an interval, f'(x)<0

local maximum?

f'(x)=0 f''(x)<0

local minimum?

f'(x)=0 f''(x)>0

derivative of e^x

e^x

derivative of e^kx

ke^kx

what is loga n = x equivalent to

a^x=n

loga x + loga y =

loga xy

loga x - loga y =

loga (x/y)

loga (x^k) =

k loga x

loga (1/x) =

-loga x

loga a =

log a 1=

what is the graph of y= lnx a reflection of

the graph y=e^x in the line y=x

e^lnx =

ln (e^x) = x

if y= a x^n , what is graph of log y against log x

straight line gradient n vertical intercept log a

if y= a b^x , what is the graph of log y against log x

straight line gradient log b vertical intercept log a