AP Calculus BC Summer Preparation Packet

AP Calculus BC Summer Preparation Packet

AP Calculus BC is designed for high school students preparing for the Advanced Placement exam. This summer preparation packet reviews essential algebra and pre-calculus skills, ensuring students are ready for the rigorous curriculum. It includes exercises on slope calculations, distance between points, and polynomial functions. Students will also explore calculus concepts through problems and graphing exercises. Completing this packet is crucial for success in the upcoming school year and the AP exam in May.

Key Points

  • Reviews prerequisite algebra and pre-calculus skills for AP Calculus BC.
  • Includes exercises on finding slopes, distances, and equations of lines.
  • Covers polynomial functions and their properties, including roots and vertices.
  • Prepares students for the Chapter 1 Test at the beginning of the school year.
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AP Calculus BC
My Dear and Stellar Honors Pre-Calculus Student,
Next September, we hope to hit the ground running beginning on the first day! Therefore,
it is our distinct pleasure to present you this packet of summer fun. This packet is
intended to prepare you for the course by:
• Reviewing prerequisite algebra and pre-calculus skills.
• Covering Chapter 1 of the calculus textbook. (With the amount of curriculum to be
covered before the AP Exam in May, we need to cover this review chapter before
the school year.)
It is due on the first day of school and worth 20 points in the homework category. At
the end of the first week of school, there will be the Chapter 1 Test assessing you on this
review content.
You might need to look up an occasional formula or definition—taking shortcuts with
this packet won’t benefit you in the Fall! Questions marked with an asterisk (*) should
be solvable without having to rely on a graphing calculator. Use your resources
(friends, internet, etc.) if necessary. If there is anything in this packet you don’t know
how to do, make sure you learn it before the first day of school!
It is also suggested that you watch the original Star Wars trilogy and Monty Python’s
Search For the Holy Grail sometime this summer so that your education can be
considered somewhat complete. You’ll miss a lot of references if you come to class
without having watched them.
Have a relaxing and enjoyable summer!
Mr. Haugh and Mr. Kemp
Show all work in the space provided. Put final answers on the lines on the right side, if applicable.
*1. Find the slope of the line 3x + 2y = 4 ____________
*2. Given the points (1, 2) & (-3, 0)
a. Find the exact distance between the points ____________
b. Find the equation of the line that passes through the two points __________________
(in both slope-intercept AND point-slope form)
__________________
c. Find the equation of the line normal (perpendicular) to the segment joining the two points at the
segment’s midpoint.
y = __________________
3. Let
463)(
2
−−= xxxf
, and let
1
2
)( +=
x
xg
. Use a graphing calculator to determine the following:
a. The roots of the parabola ____________
b. The vertex of the parabola ____________
c. The point(s) of intersection of the two graphs ____________
*4. Find the exact, fully reduced solutions to the equation 

____________
*5. Sketch a graph of
65
2
−+= xxy
. Find and label roots, vertex, and y-intercept. What is the
equation of the parabola in vertex form?
*6. Use whatever means available (except a calculator) to find the exact roots of the function
472
23
+−+= xxxy
. (Try Synthetic Division &/or Factoring?)
__________________
*7. Find the solutions to the following: | x + 2 | - 1 < 4. __________________
*8. Sketch a graph of y = | x – 1 |
*9. State the domain and range of the function
4)(
2
+= xxf
. D: _________
R: _________
*10. Let
,)(
2
xxf =
and let
1)( += xxg
, and let
1)( += xxh
. Does h(x) = f(g(x)), or does h(x) =
g(f(x)), (or neither?) What is h(f(g(x)))?
____________
h(f(g(x))) = ____________
*11. Let
12
1
)(
+
=
x
xf
. Find
. ____________
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End of Document
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Faqs of AP Calculus BC Summer Preparation Packet
What topics are covered in the AP Calculus BC summer packet?
The summer packet covers essential topics such as algebraic skills, slope calculations from linear equations, and the distance formula between points. It also includes exercises on polynomial functions, their roots, and how to find the vertex of parabolas. Students will engage with both theoretical concepts and practical applications to prepare for the AP exam.
How does the summer packet prepare students for the AP Calculus exam?
The packet is designed to reinforce foundational skills necessary for success in AP Calculus BC. By reviewing algebra and pre-calculus concepts, students will build confidence and proficiency in key areas such as functions, limits, and derivatives. Completing the packet ensures that students are well-prepared for the fast-paced curriculum and the Chapter 1 Test that occurs in the first week of school.
What types of problems can students expect in the summer packet?
Students will encounter a variety of problems including finding slopes of lines, calculating distances between points, and deriving equations in both slope-intercept and point-slope forms. The packet also includes polynomial equations and requires students to sketch graphs, identify roots, and determine vertex forms. These exercises are designed to solidify understanding and application of calculus concepts.
What is the significance of completing the summer packet?
Completing the summer packet is crucial for students entering AP Calculus BC as it lays the groundwork for the entire course. It helps identify areas where students may need additional practice and ensures they are familiar with the material before the school year begins. This preparation is essential for achieving a high score on the AP exam in May.