# C2

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If (x-a) is a factor of f(x)
f(a)=0
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if (ax-b) is a factor of f(x)
f(b/a)=0
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If f(x) is divided by (x-a)
the remainder is f(a)
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If f(x) is divided by (ax-b)
the remainder is f(b/a)
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cosine rule
a²-b²+c²-2bc(cosA)
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sine area of a triangle
(1/2)absinC
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area of a sector
(1/2)(r²)theta
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length of an arc
r*theta
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area of a segment
(1/2)(r²)(theta-sin(theta))
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all exponential functions
pass through (0.1) and have asymptote y=0
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logₐBC=logₐB+ logₐC
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log subtraction rule
logₐ(B/C)=logₐB- logₐC
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logₐBⁿ=nlogₐB
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logₐa=
1
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logₐ1=
0
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logₐ(1/x)=
-logₐx
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equation of a circle center (a,b) radius r
(x-a)²+(x-b)²=r²
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uncompleted square of circle equation
x²+y²+2gx+2fy+c=0
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nth term of a geometric series
arⁿ⁻1
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Sn=
[a(1-rⁿ)]/[1-r]
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Sn proof
Sn=a+ar+ar²+...+arⁿ⁻¹..............rSn=ar+ar²+ar³+...+arⁿ.............. Sn-rSn = a-arⁿ..............Sn(1-r)=a-arⁿ..............Sn= (a-arⁿ)/1-r
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If r is between -1 and 1, s(infinity) is
a/1-r
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describe y=sin(x)
period of 360°. symmetrical around 90°. pos-90-neg-180
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describe y=cos(x)
period of 360°. symmetrical around 0°.
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describe y=tan(x)
period of 180°. asymptotes at theta=90°(2n+1)
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what is the sv when cos(x)=c
±cos⁻¹(c)+360n
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what is the sv when sin(x)=s
(-1)ⁿsin⁻¹(s)+180n
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what is the sv when tan(x)=t
tan⁻¹(t)+180n
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at what point on a curve is there a stationary point?
when f'(x)=0
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when is a curve increasing?
when f'(x)>0
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when is a curve decreasing?
when f'(x)
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when is a stationary point a maximum?
when f''(x)
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when is a stationary point a minimum?
when f''(x)>0
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trig identities
tan(x)=(sin(x))/(tan(x)) and cos²(x)+sin²(x)=1
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area beneath a curve equation
integrate f(b)-f(a)
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area between two curves equation
integrate (t(x)-b(x))
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trapezium rule
for n equal intervals, of width h, A=(h/2)(Y₀+Yₓ+2(Y₁+Y₂+...+Yₓ₋₁))
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area of a trapezium
(h/2)(a+b)
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how to convert degrees to radians?
multiply by pi/180
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how to convert radians to degrees?
multiply by 180/pi
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## Other cards in this set

### Card 2

#### Front

if (ax-b) is a factor of f(x)

f(b/a)=0

### Card 3

#### Front

If f(x) is divided by (x-a)

### Card 4

#### Front

If f(x) is divided by (ax-b)

cosine rule