Clearview Regional High School District
Summer Assignment Coversheet
Course
Teacher(s)
Due Date
Grade
Category/Weight
for Q1
Common Core
and/or NJ Core
Curriculum
Content
Standards
covered
Honors Calculus
M. Zayicek
September 4th
2 Homework Grades
Quiz on material (September 8th - 12th)
Description of
Assignment
Summer Work specifically meant to review of Algebra II and Pre-Calculus
Skills – specific topics include:
I. Algebra:
A. Exponents (operations with integer, rational (fractional), and negative
exponents)
B. Factoring (GCF, trinomials, difference of squares and cubes, sum of
cubes, grouping)
C Rationalizing (numerator and denominator)
D. Simplifying rational expressions
E. Solving algebraic equations (linear, quadratic, rational and radical
functions)
F. Interval Notation
II. Graphing and Functions
A. Lines (intercepts, slopes, write equations using slope intercept form,
parallel, perpendicular)
B. Functions (definition, notation)
C. Symmetry
D. Asymptotes
III. Trigonometry
A. Unit Circle (definition of functions, angles in radians and degrees)
B. Use of Pythagorean Identities and formulas to simplify expressions
and prove identities
C. Solve equations
F-IF: Interpreting Functions ~ Understand concept of function and use function notation;
Interpret functions that arise in applications in terms of the context.; Analyze functions using
different representations.
F-IF-8a: Use process of factoring and completing the square in a quadratic function to show
zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
A-SSE-3a: Factor a quadratic expression to reveal the zeros of the function it defines.
A-REI.4: Solve quadratic equations in one variable.
A-APR.7: Understand that rational expressions form a system analogous to the rational
numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational
expression; add, subtract, multiply, and divide rational expressions.
A-SSE.3c: Use the properties of exponents to transform expressions for exponential functions.
F-TF.8: Prove the Pythagorean identity sin2(?) + cos2(?) = 1 and use it to calculate
trigonometric ratios.
F-TF: Trigonometric Functions
F-IF.6: Calculate and interpret the average rate of change of a function (presented symbolically
or as a table) over a specified interval.
Purpose of
Assignment
Specific
Expectations
Where to Locate
Assignment
Helpful
Resource(s)
To review the prerequisite skills necessary to be successful in Calculus.
Students should show all work necessary to complete each problem.
Credit will not be given for answers that do not show sufficient work.
District Website
Algebra 1, 2 and Pre-Calculus notes from previous courses
The Virtual Mathlab:
Offers free online tutorials for Intermediate Algebra, College Algebra and also for the
Accuplacer and the GRE assessments. It hosts many high-quality video tutorials on these
subjects. http://www.wtamu.edu/academic/anns/mps/math/mathlab/
Math.com:
A basic math resource for high school math subjects that includes definitions, examples and
some games. http://www.math.com/
Purple Math:
A website that hosts detailed tutorials for algebra concepts that range from beginning to
advanced. http://www.purplemath.com/
SOS Mathematics:
Detailed tutorials on high school math concepts from Pre-Algebra to Calculus.
http://www.sosmath.com/index.html
Algebra Help:
An algebra support website that explains common algebra concepts and provides practice
templates that grades the student’s work. http://www.algebrahelp.com
Dept.
Coordinator
Signature
Dear Calculus Student,
You have elected to take Honors Calculus next year. This will be a challenging and rewarding course that
will provide you with a strong foundation in limits, differential calculus and its applications, and integral
calculus and its applications. As an upper level mathematics course, grades will be calculated using the
60% tests, 30% quizzes, and 10% homework method.
All students enrolled in Calculus must use a graphing calculator. While we urge you to have one of your
own, some will be available for use in class. However, these calculators must remain in the classroom and
will not be available for borrowing purposes. We will be using the TI-84 Plus edition calculator during
instruction. This is an expensive tool, but one that you will use for many years.
For this course to be most meaningful and for you to be most successful, you must have a strong
background in Algebra, Geometry and Trigonometry. Attached is a packet of problems that you should
be able to complete. This work will review and sharpen your skills to better prepare you for this course.
These problems represent an overview, but certainly do not cover all of the pre-requisite skills needed.
This packet will be checked for completion on the first day of school and will count as two homework
grades. Accuracy is recommended as you will take a quiz on these prerequisite skills during the first full
week of school. The pre-requisite material will not be re-taught, though there will be an opportunity for
you to ask questions during the first few days of school prior to taking the quiz.
Have a safe and fun-filled summer. See you in September.
Mrs. M. Zayicek
Clearview Regional High School
Honors Calculus
Summer Packet
Name: _________________________________________________
1. This completed packet will be collected on the first day of school. It will count as
your first two homework grades.
2. For credit, all work must be shown in the packet OR on separate paper attached to
packet.
3. All problems should be completed without the use of a calculator.
Topics Include:
I. Algebra:
A. Exponents (operations with integer, rational (fractional), and negative exponents)
B. Factoring (GCF, trinomials, difference of squares and cubes, sum of cubes, grouping)
C Rationalizing (numerator and denominator)
D. Simplifying rational expressions
E. Solving algebraic equations (linear, quadratic, rational and radical functions)
F. Interval Notation
II. Graphing and Functions
A. Lines (intercepts, slopes, write equations using slope intercept form, parallel,
perpendicular)
B. Functions (definition, notation)
C. Symmetry
D. Asymptotes
III. Trigonometry
A. Unit Circle (definition of functions, angles in radians and degrees)
B. Use of Pythagorean Identities and formulas to simplify expressions and prove
identities
C Solve equations
Solve for x:
1.
3(x - 4) + 7x = 4 – (x + 3)
2. x -
5
2
3. x
=6
3
2
=0
x
4. y = 6x – 3
Simplify. Answers must be expressed using only positive exponents.
5.
x4
2
x  3x  4
6.
x3  8
x2
7.
5 x
x 2  25
8.
x 2 y 5
x 7 y 8
11. (6x + 2)(3x –5)
 13
 2x
14.  2
 y3

10.
x 3  6 x 2  5x  4
x
12. (2x + 1)2
13.
x
1

x 1 x  2
2
2
15. x
10
x5
16.
1
1

xh x
9.





3
5x 9 y 7 z
25 x 5 y 10 z
Using slope/intercept ( y  mx  b ) form of the equation of a line, write an equation for the
lines described. SHOW ALL WORK.
17. with slope -2, containing the point (3, 4)
18.
containing the points (1, -3) and (-5, 2)
19.
parallel to 2x – 3y = 7 and passes through (5,1)
20.
perpendicular to the line in problem #17 a, containing the point (3, 4)
3
21. Confirm that 4 2  8
22. Confirm that 32
2
5

1
4
Let f(x) = -x2 - 1 , find:
23. f(5)
24. f(-3)
25. find f(a + b)
Factor completely:
26. 6x2 – 5x – 4
27. 3x2y7z – 6x3y5
28. 12x2 + 2x – 24
29. x2 – 25
Find the roots:
30. x2 – 2x – 2 = 0
31. x2 – 15x = 54
32. -x2 + 4x – 5 = 0
33. Find the ordered pairs of the x-intercept and y-intercepts of the line 5x – 7y = 10.
Interval Notation
34. Complete the table with the appropriate notation or graph.
Inequality
Interval
Notation
Notation
-2 < x < 4
(-1, 7]
Graph
Fill in the blanks to complete the Trigonometric Pythagorean Identities.
35. sin 2 x + cos 2x = _______ 36. 1 + tan2x = ________
37. cot2x + 1 = ___________
38. Prove the identity (cscx)(secx) – cotx = tanx
Determine all vertical asymptotes for each function.
39. f ( x) 
1
x2
40. f ( x) 
x2
x2  4
41. f ( x) 
Determine all horizontal asymptotes for each function.
42. f ( x) 
x 2  2x  1
x3  x  7
43. f ( x) 
5x 3  2 x 2  8
4 x  3x 3  5
2 x
x (1  x)
2