AP CALCULUS BC TEST PAPER QUESTIONS AND SOLUTIONS 2026 ALREADY PASSED

AP CALCULUS BC TEST PAPER QUESTIONS
AND SOLUTIONS 2026 ALREADY PASSED



◍ If the graph of a function shows a hole or open-circle point, then...
Answer: the function does not exist there


◍ What should you do when asked to find the limit of a composite
function?
ex) limit as x approaches a of f(g(x)) Answer: Find the limit as x
approaches A of g(x). Let that limit value equal B.
Then, find the limit as x approaches B of f(x)


◍ What should you do when asked to find the limit of a compound
function?
ex) limit as x approaches 1 of [ f(x) + g(x) ] Answer: Find both the
left and right hand limits of both functions
ex) you will need the left-hand limits of f(x) and g(x), then add them
together to find the left compound limit
THEN, find the right-hand limits of f(x) and g(x) and add them
together to find the right compound limit.
(IF the right compound limit does not equal the left compound limit,
the limit DNE.)


◍ What are the rules for finding limits at infinity of rational
functions? Answer: Look at the degree of the numerator and degree of

,the denominator. (Let the degree of the numerator = N and the degree
of the denominator = D)
- If N = D, the limit is a ratio of the leading coefficients
- If N < D (or D > N), the limit is zero
- If N > D, the limit DNE


◍ What are the rules for determining limits at infinity of non-rational
functions? Answer: Look at the degree and the sign of the leading
coefficient to determine end behavior!
- For even positive end behavior, the limit as x approaches both
infinities is positive infinity.
- For even negative end behavior, the limit as x approaches both
infinities is negative infinity
- For odd positive end behavior, the limit as x approaches negative
infinity is negative infinity. The limit as x approaches positive infinity
is positive infinity.
- For odd negative end behavior, the limit as x approaches negative
infinity is positive infinity. The limit as x approaches positive infinity
is negative infinity.


◍ If the numerator or denominator has a radical, what should you do?
Answer: Remember that square roots can be positive or negative!
ex) square root of 4 can be 2 or -2
Determine whether to use the positive or negative root by which
infinity x is approaching:
- if x approaches positive infinity, use the positive root
- if x approaches negative infinity, use the negative root

, ◍ What do you do to find the limits at a horizontal asymptote?
Answer: Use the same rules as limits at infinity, because you will be
taking the limit as x approaches both positive and negative infinity.
(If there is a radical, remember to include the positive and negative
root, because you are approaching both infinities)


◍ What are the rules for absolute value functions as piecewise
functions? Answer: Recall that the absolute value of x is a piecewise
function
- If x > 0, then f(x) = x. If x < 0, then f(x) = -x
|x| / x is also piecewise:
- If x > 0, then |x| / x = 1.
- If x < 0, then |x| / x = -1.
Therefore, the limit of an absolute value function will always be 1 or -
1, unless being multiplied/divided by a factor.


◍ What are the steps to finding the limit of an absolute value
function? Answer: 1) Factor out any numbers being multiplied or
divided
2) If you aren't being asked for a one-sided limit, separate the limit
into left- and right-hand limits and solve
3) For a left-hand limit, plug in a number slightly less than what x is
approaching. For a right-hand limit, plug in a number slightly greater
than what x is approaching.
4) Multiply by the factor (if applicable).