AP Precalculus Exam Prep EXAM UPDATED VERSION
QUESTIONS AND CORRECT ANSWERS LATEST
UPDATE THIS YEAR
When does a rational function have an oblique asymptote?
⋅ When the degree of the poly in the numerator is greater than the degree of the poly in the
denominator
⋅ use division [reverse box] to calculate oblique asymptote
Where does a rational function have a hole?
⋅ When a factor cancels in the numerator and denominator (unless covered by a V.A. --> factor still
remains in denominator)
⋅Let f(x) be a polynomial in numerator and g(x) be polynomial in denominator. Hole occurs at x = a if a is
a zero of BOTH f(x) and g(x)
Where does a function have a V.A.?
⋅ When a factor is a zero of the denominator after canceling
⋅Let f(x) be a polynomial in numerator and g(x) be polynomial in denominator. VA occurs at x = a if a is a
zero of only g(x) [after canceling]
Standard form of arithmetic sequence
an=ak+d(n-k) where (k, ak) is any ordered pair in the sequence
Standard form of geometric sequence
1
,gn=gk⋅ r^n-k where (k, gk) is any ordered pair in the sequence
Exponential decay in y=a⋅b^x
⋅ When 0<|b|<1 , a>0
⋅ As inputs increase, outputs move toward x-axis
Exponential growth in y=a⋅b^x
⋅ When |b| > 1 , a> 0
⋅ As inputs increase, outputs moving away from x-axis
log (x) + log (y) =
= log (xy)
n*log( x) =
log (x^n)
log(x) - log(y) =
log (x/y)
log_a (x)
--------- =
log_a (y)
log_y (x)
Period of sin or cos function
2
,2π/b
Arc length (s)
rθ, theta in radians
Range of y=arcsin(x)
[-π/2, π/2]
Range of y=arccosx
[0, π]
Range of y=arctanx
[-π/2, π/2]
What is error?
Predicted - Actual (EPA)
Period vs frequency in a trig function
⋅ Period is length required for one full cycle of outputs
⋅ Frequency is reciprocal of period
⋅ Frequency is how many cycles per unit of time
The a in g(x)=a⋅f (b(x-h))+k
Vertical dilation by a factor of a
Reflection over x-axis if a <0
3
, The h in g(x)=a⋅f (b(x-h))±k
Horizontal translation
Left when x+h, Right when x-h
The k in g(x)=a⋅f (b(x±h))+k
vertical translation
Up when k>0, Down when k<0
The b in g(x)=a⋅f (b(x±h))+k
Horizontal dilation by a factor of 1/b
Reflection over y-axis if b<0
Average Rate of Change Formula
f(b)-f(a)
---------
b-a
Where is a function positive/negative?
⋅Positive-when the y-coordinates are above
the x-axis [ positive]
⋅Negative when the y-coordinates are below
the x-axis [negative]
What defines an increasing/decreasing
function?
4
QUESTIONS AND CORRECT ANSWERS LATEST
UPDATE THIS YEAR
When does a rational function have an oblique asymptote?
⋅ When the degree of the poly in the numerator is greater than the degree of the poly in the
denominator
⋅ use division [reverse box] to calculate oblique asymptote
Where does a rational function have a hole?
⋅ When a factor cancels in the numerator and denominator (unless covered by a V.A. --> factor still
remains in denominator)
⋅Let f(x) be a polynomial in numerator and g(x) be polynomial in denominator. Hole occurs at x = a if a is
a zero of BOTH f(x) and g(x)
Where does a function have a V.A.?
⋅ When a factor is a zero of the denominator after canceling
⋅Let f(x) be a polynomial in numerator and g(x) be polynomial in denominator. VA occurs at x = a if a is a
zero of only g(x) [after canceling]
Standard form of arithmetic sequence
an=ak+d(n-k) where (k, ak) is any ordered pair in the sequence
Standard form of geometric sequence
1
,gn=gk⋅ r^n-k where (k, gk) is any ordered pair in the sequence
Exponential decay in y=a⋅b^x
⋅ When 0<|b|<1 , a>0
⋅ As inputs increase, outputs move toward x-axis
Exponential growth in y=a⋅b^x
⋅ When |b| > 1 , a> 0
⋅ As inputs increase, outputs moving away from x-axis
log (x) + log (y) =
= log (xy)
n*log( x) =
log (x^n)
log(x) - log(y) =
log (x/y)
log_a (x)
--------- =
log_a (y)
log_y (x)
Period of sin or cos function
2
,2π/b
Arc length (s)
rθ, theta in radians
Range of y=arcsin(x)
[-π/2, π/2]
Range of y=arccosx
[0, π]
Range of y=arctanx
[-π/2, π/2]
What is error?
Predicted - Actual (EPA)
Period vs frequency in a trig function
⋅ Period is length required for one full cycle of outputs
⋅ Frequency is reciprocal of period
⋅ Frequency is how many cycles per unit of time
The a in g(x)=a⋅f (b(x-h))+k
Vertical dilation by a factor of a
Reflection over x-axis if a <0
3
, The h in g(x)=a⋅f (b(x-h))±k
Horizontal translation
Left when x+h, Right when x-h
The k in g(x)=a⋅f (b(x±h))+k
vertical translation
Up when k>0, Down when k<0
The b in g(x)=a⋅f (b(x±h))+k
Horizontal dilation by a factor of 1/b
Reflection over y-axis if b<0
Average Rate of Change Formula
f(b)-f(a)
---------
b-a
Where is a function positive/negative?
⋅Positive-when the y-coordinates are above
the x-axis [ positive]
⋅Negative when the y-coordinates are below
the x-axis [negative]
What defines an increasing/decreasing
function?
4
