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IB Maths HL
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Gravity
Review of important formulas
Terms in this set (50)
General term for an arithmetic sequence.
Un=U1+(n-1)d
Proof of an arithmetic sequence.
Un+1-Un=d
Common ratio.
(Un+1)/Un=r
General term for a geometric sequence.
Un=U1*r^n-1
Compound interest formula.
Un+1=U1*r^n
Formula for sum of arithmetic series.
Sn=(n/2)(U1+Un)
Formula for sum of arithmetic series. (If you don't know the last term.)
Sn=(n/2)(2U1+(n-1)d)
Formula for sum of a geometric series.
Sn=((U1)(1-r^n))/1-r
Formula for sum of an infinite geometric series.
S=(U1)/(1-r)
(a^m)*(a^n)=?
a^(m+n)
(a^m)/(a^n)=?
a^(m-n)
(a^m)^n=?
a^(m*n)
(a*b)^m=?
(a^m)*(b^m)
(a/b)^m=?
(a^m)/(b^m)
a^0=?
1
a^(-m)=?
1/(a^m)
(a+b)^2=?
a^2+2ab+b^2
(a-b)^2=?
a^2-2ab+b^2
(a+b)(a-b)=?
(a^2)-(b^2)
nPr=? (Permutation formula)
n!/(n-r)!
nCr=? (Combination formula)
n!/((r!)(n-r)!)
Formula for the (r+1)th of a Binomial Expansion
nCr(a^(n-r))(b^r)
If a horizontal line drawn through a function intersects it ____, it is a one-to-one function.
once
If a horizontal line drawn through a function intersects it ____ _____ _____, it is a many-to-one function.
more than once
If a vertical line drawn through a relationship intersects it once only, then it is called a _______.
function
_____ _______ _______ functions do NOT have inverses.
Many-to-one
The formula for a general reciprocal function is:
y=((a)/(x-h))+k
To find a function's inverse, swap the _____ and write in terms of y.
variables
In the equation y=a^x, if a is negative, the equation is reflected about the ____ axis.
x
In the equation y=a^x, if x is negative, the equation is reflected about the ____ axis.
y
The general exponential equation is y=n*(a^(x+h))+k, where k controls the _______ asymptote.
horizontal
The general exponential equation is y=n*(a^(x+h))+k, where -h controls the _______ asymptote.
vertical
log(base b)(b^x)=___
x
'ln' represents the ______ _________.
natural logarithm
The polynomial form of a quadratic is: ______________.
y=ax^2+bx+c
The T.P form of a quadratic is: ___________________.
y=a(x-h)^2+k
The discriminant of a quadratic is:
b^2-4(a)(c)
If solving for two real distinct roots, the discriminant must be _ 0.
>
If solving for two real roots, the discriminant must be _ 0.
≥
If solving for two identical real roots, the discriminant must _ 0.
=
If solving for no real roots, the discriminant must _ 0
<
To find the x-coordinate of a quadratic turning point, use the formula:
x=-b/2a
The sum of a quadratic's roots equals:
-b/a
The product of a quadratic's roots equals:
c/a
Positive definite quadratics have no _____ values.
negative
Negative definite quadratics have no _____ values.
positive
∫ sin(ax+b) dx
-1/a cos(ax+b) + c
∫ cos(ax+b) dx
1/a sin(ax+b) + c
∫ sec^2(ax+b) dx
1/a tan(ax+b) + c
∫ e^(ax+b) dx
1/a e^(ax+b) +c
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