Summer AP Calculus Assignment for AP Calculus -AB Students-To-Be - Review Packet - Complete and Turn In

Sep 30, 2026

Summer AP Calculus assignment packet for students entering AP Calculus -AB, focused on reviewing prerequisite college-level concepts and practicing core skills required for success. The materials cover rules of exponents including fractional and negative exponents, simplifying expressions with rational and power properties, linear functions with various line forms, domain and range in interval notation, function composition, polynomial factoring, solving quadratics, rational functions with asymptotes and complex fractions, and intercepts and intersection problems. A test on this reviewed content is scheduled for the second class day.

LanguageEnglish

CategoryExam

FormatPDF

Pages15

Reading Time38 min

AccessFree to download

Rules of exponents

Linear functions

Functions (domain/range, composition)

Polynomials and factoring

Rational functions

Intercepts and points of intersection

# Summer AP Calculus Assignment for AP Calculus -AB Students-To-Be The purpose of this assignment is to review the concepts and practice the skillsnecessary for success in AP Calculus.Every topic in this review has been covered inyour previous math courses.You will be expected to be able to do all of this packetwhen your AP Calculus course begins in September. The AP Calculus curriculum is taught at a college level and a brisk pace so there islittle time for review of this material.I suggest you start work on this packet inAugust as it must be completed and turned in on the first day of class.During thesecond class you will be tested on the material reviewed in this summer packet.The test will represent the first major grade of the first quarter. If you need to contact me please email at minnes@mvyps.orq. Mr.Innes | Rules of exponents
Power of a Power Property
Fractional Exponents
Product of Powers Property
am。a"=am+n
Quotient of Powers Property
(①"
Negative Exponent Property
a≠0
a≠0 | | --- | Negative Exponents.Simplify each expression a)x-2y³ b ⑦ Multiplying with exponents.Simplify without the use of a calculator a)x²y³·x-⁷y⁵ C b) Fractional Exponents.Evaluate each WITHOUT the use of a calculator. a)(273b)(25) c)(8)d)(9) | Linear Functions
Writing equations of lines
Slope intercept form:y=mx+b
Vertical line:x=c(slope is undefined)
Point-slope form:y-y₁=m(x-x₁)
Horizontal line:y=c(slope is O) | | --- | a)Use slope-intercept form to find the equation of the line having a slope of 3 and a y-intercept of 5. b)Determine the equation of a line passing through the point(5,-3)with an undefined slope. c)Determine the equation of a line passing through the point(-4,2)with a slope of 0. d)Use point-slope form to find the equation of a line passing through the point(6,5)with a slope e)Find the equation of a line passing through the point(2,8)and parallel to the line f)Find the equation of a line perpendicular to the y-axis passing through the point(4,7). g)Find the equation of a line passing through the points(-3,6)and(1,2). h)Find the equation of the line that is perpendicular to the line 2x+3y-8=0 at the point(1,2). i)The line with slope 5 that passes through the point(-1,3)intersects the x axis at a point.What are thecoordinates of this point? ## Functions: Domain/Range-Find the domain and range of the following functions.You should be able to completeWITHOUT the aid of a calculator.Leave answers in interval notation.(33 is written as(3,∞)) b)f(x)=-√x+3 a)f(x)=x²-5 c)f(x)=3sinx e)f(x)=|x-3| d) | To evaluate a function for a given value,simply plug the value into the function forx.
(f.og)(x)=f(g(x))OR f[g(x)]read “fofg ofx”Means to plug the inside function(in this cas
Recall:
g(x))in for x in the outside function(in this case,f(x)).
Example:Given f(x)=2x²+1 and g(x)=x-4 find f(g(x).
f(g(x))=f(x-4)
=2(x-4)²+1
=2(x²-8x+16)+1
=2x²-16x+32+1
f(g(x))=2x²-16x+33 | | --- | ### a)Given f(x)=2x²+4x and g(x)=x-3,find each: i)(f+g)(x) iii)f(g(2)) ### b)Given the table of values,find each: | x | f(x) | g(x) | h(x) | | --- | --- | --- | --- | | 2 | 3 | 5 | 8 | | 5 | 1 | 3 | 1 | | 8 | 7 | 2 | 9 | i)f-h)(8) iii)f(g(h(2)) ii)(fg)(x) iv)g(f(2)) ii)f(g(2)) ### c)Findfor the given function f: ii)f(x)=x²-1i)f(x)=9x+3 Polynomials Factoring -Factor each of the following completely. a)a²-b² b)a³-b³ c)8x³+y³ d)4x²-21x-18 e)2x²+x-3 f)3x²+6x³-9x g)(x+1)³(4x-9)-(16x+9)(x+1)² h)(x-1)³(2x-3)-(2x+12)(x-1)² Solving quadratics-Find the value(s)of x.Round to three decimals places if necessary. b)x²+2x+1=15c)7x²-9x+1=0a)x²+11x+18=0 e)x²-10x+25=0f)x²+3x+7=0d)(x+2)²=36 ## Rational Functions Multiplying and Dividing-Multiply or divide as indicated.Express a

FAQs

What is the main purpose of the summer AP Calculus -AB assignment packet?

It is designed to review key calculus concepts and practice essential skills needed for success when the AP Calculus course begins.

When do students need to complete and submit the packet?

Students are expected to start in August, complete it, and turn it in on the first day of class. A test on the reviewed material occurs during the second class.

What topics are included in the packet?

The packet includes exponents rules, linear functions and equations of lines, functions (domain/range and evaluation), function composition, polynomials (factoring and solving quadratics), rational functions (including asymptotes), and intercepts and points of intersection.

Sep 30, 2026

Upload by Lucas Martin