Honors Calculus Summer Assignment

Back by popular demand

Pinkston 2015

Possible online Resources if you don’t remember or know how to do a problem.

You have chosen to take Honors Calculus, an accelerated course. You are expected to have a strong mathematical background and be willing to work hard all year long.

The first chapter of the textbook is referred to as Chapter zero. Chapter zero is a detailed review of Algebra II and Pre-Calculus topics. Instead of using class time to discuss these topics, I am assigning problems to you for the summer!  In the past, I copied Chapter zero, and the first few sections of Chapter one. This year, I have decided to compile various problems from multiple sites. Your textbook: Calculus (an applied approach) Larson: Houghton Mifflin

(7th edition)

DIRECTIONS:

You are to complete all the following problems contained in this packet.
You must show all of your work in the space provided in the packet. (If you need to use a separate sheet of paper, be sure to use a separate sheet for ALL PROBLEMS, clearly identify the page number/problem number, and attach the work to the packet.)
Be sure all problems are neatly organized and all writing is legible.
This assignment will be worth 30-50 total points. I strongly suggest that you pace yourself and do not wait until the last two weeks of summer to begin working. If you spread out your work sessions, you are more likely to retain the information better.
Once again, this assignment is due, completed with quality, on the FIRST DAY that all students attend school (grades 9-12) and our class period meets. You will hand it in that day.

On the FIRST DAY OF SCHOOL, I will collect the assignment and grade it for completion only. I will then hand back the assignment (the next class period?) and we will take (45 – 90 minutes), oneclass, to discuss the problems that were the most challenging. (NOT EVERY SINGLE PROBLEM). You will then have a test on the Summer Assignment. I will notify you of the date. On the day of the test, I will collect your summer assignment again and select random problems to grade. This time, I will be looking for the correct solutions. Please show as much work as possible when necessary. Just a list of all answers will not be acceptable. Turning the assignment in late will not be acceptable. There will be severe late penalties. 

Supplies:

It is strongly suggested that you purchase a graphing calculator for the upcoming year. Check your local office supply store/on line. There are several on the market, however, the Texas Instruments: TI –84 and TI-84plus“family” of calculators are the preferred choice here at Brandywine. A few calculators that may NOT be used on tests and quizzes are the TI-Nspire CAS, TI – 89 and the TI-92 (Or any Casio, Hewlett-Packard, etc. equivalent).

Please purchase a three – ring binder, 2.5 to 3 inch. A one- inch binder will not be large enough to last throughout the entire school year. Your notebook will be graded. Information on requirements will be distributed at the beginning of the school year.

I may check my school email every 2-3 weeks during the summer in case you have any concerns: (Please forgive any typos.)

Have a wonderful summer and I will see you at the end of August! Miss Pinkston 

Summer Assignment Problems:

Simplifying Radicals

An expression under a radical sign is in simplest radical form when:

1)there is no integer under the radical sign with a perfect square factor,

2)there are no fractions under the radical sign,

3) there are no radicals in the denominator

Express the following in simplest radical form.

1) 2) 3) 4) 5)

Misc

1)Determine the domain, range and the zeros of:.

Domain: ______

Range: ______

Zeros: ______

Properties of Exponents – Complete the example problems.

Property / Example
Product of Powers / am an = am + n / x4 x2 =
Power of a Power / (am)n = amn / (x4)2 =
Power of a Product / (ab)m = ambm / (2x)3 =
Negative Power / a-n = (a0) / x-3 =
Zero Power / a0 = 1 (a0) / 40 = 1
Quotient of Powers / = am – n (a0) / =
Power of Quotient / = (b0) / =

Simplify each expression. Answers should be written using positive exponents.

1)g5 g11 ______2)(b6)3 ______

3)w-7 ______4) ______

5)(3x7)(-5x-3) ______6)(-4a-5b0c)2 ______

7) ______8) ______

9)Simplify . Express your answer using a single radical.

Misc

1)Factor completely.

2) Find the equation of the line through and in point slope form.

3) A taxicab company charges each person a flat fee of $1.85 plus an additional $.40 per quarter mile.

A. Write a formula to find the cost for each fare.

B. Use the formula to find the cost for 1 person to travel 8 mi.

4) Find the dimensions of the rectangle given the area = 164 sq. ft.

5) Three sides of a fence and an existing wall form a rectangular enclosure. The total length of a fence used for the three sides is 240 ft. Let be the length of two sides perpendicular to the wall as shown. Write an equation of area of the enclosure as a function of the length of the rectangular area as shown in the above figure. The find value(s) of for which the area is 5500 .

6)Let and . Compute , state its domain in interval notation.

: ______

Domain: ______

7)Let. Find , the inverse of .

8)Which of the following could represent a complete graph of , where is a real number?

A.B.C.D.

9)Find a degree 3 polynomial with zeros -2, 1, and 5 and going through the point.

10)The number of elk after years in a state park is modeled by the function .

a)What was the initial population of elk? (Time t =0)

b) When will the number of elk by 750?

11)Arturo invests $2700 in a savings account that pay 9% interest, compounded quarterly. If there are no other transactions, when will his balance reach $4550?

12)Solve the inequality:.

A. B. C. D.

Trigonometry

1)Fill in the table. Answers should be exact (Radical form where appropriate.) No decimals.

Degree / Radians / SINE / COS / TAN / CSC / SEC / COT
0
30
45
60
90
120
135
150
180
210
225
240
270
300
315
330
360

2)Without using a calculator, find the exact value of . Justify your answer.

3)Simplify

A. B.

C.D.

4) Find the exact value of each without the use of a calculator.

5)Find the perimeter of a slice of cheesecake if the radius of the cheesecake is 8 inches.

6)Two students are 180 feet apart on opposite sides of a telephone pole. The angles of elevation from the students to the top of the pole are and . Find the height of the telephone pole.

7)Solve the equation algebraically.

8)Find all the exact solutions to on the interval .

Misc

1)Transform y = -3x2 – 24x + 11 to vertex form by completing the square.

2)Use polynomial long division to rewrite the expression

3)Graph the piecewise function.

4)For the function graphed answer the following

A. B.

C. D.

5)Give that. Find the asymptotes and the domain of the function.

Domain: ______

Vertical Asymptote(s): ______

Horizontal Asymptote(s): ______

6)Use a graphing calculator to approximate all of the function’s real zeros. Round your results to four decimal places.

7)Each of the lines shown below passes through (2, 1) and forms a triangle with the axes. Which of these three triangles has the least area?

8)Factor to solve the inequality. Write your answer in interval notation.

9)Simplify the expression and determine where the expression is positive.

10)Use algebra to find the exact solution to x4 – 5x2 + 3 = 0. Show all work.

11)Find the value of k if the line joining (4, k) and (6, 8) and the line joining( – 1, 4) and (0, 8) are:

a.parallel

b. perpendicular

12)Write an equation of the perpendicular bisector(intersects at the midpoint) of the segment joining (0, 3) and ( – 4, 5).

13)Maria Correia’s new car costs $280 per month for car payments and insurance. She estimates that gas and maintenance cost $0.15 per mile.

a) Express her total monthly cost as a function of the miles driven during the month.

b) What is the slope of the graph of the cost function?

14)Simplify

15)Solve by whichever method seems easiest. Be sure to check for extraneous roots.

16)is parallel to . Find the value of x.

17)Find an equation of the quadratic function described.

a)Its graph is a parabola with x-intercepts 2 and – 1 and y-intercept 6.

b) Its graph is a parabola with vertex (4, 8) and passing through the origin.

18)A stone is thrown with an upward velocity of 14 m/s from a cliff 30 m high.

a) Find its height above the ground t seconds later.

b) When will the stone reach its highest elevation?

c)When will the stone hit the ground?

19)Solve and graph.

20) Solve for x.

51a)

51b.

51c)

21)Complete the square (twice) to write the equation in center-radius form. Give the center and radius. Center:

Radius:

22)State the domain and range of the function. Then graph the function.

Domain:

Range:

23) Give the domain and the range of the function. Then graph the function.

Domain:

Range:

24)Complete each of the following:

A)Point-Slope formula:______

B)Slope-intercept form:______

C)Standard form:______

Operations With Polynomials (Algebra I)

To add or subtract polynomials, just combine like terms.

To multiply polynomials, multiply the numerical coefficients and apply the rules for exponents for variables.

Perform the indicated operations and simplify:

1) (7x2 + 4x - 3) - (-5x2 - 3x + 2)2) (7x - 3)(3x + 7)

3) (4x + 5)(5x + 4)4) (n2 + 5n + 3) + (2n2 + 8n + 8)

5) (5x2 - 4) – 2(3x2 + 8x + 4)6) -2x(5x + 11)

7) (2m + 6)(2m + 6)8) (5x – 6)2

9) 10)

Factoring is forever!

Factor each of the following polynomial expressions (completely) over the set of integers.

1)2)3)

4)5)6)

Factor!

7)8)9)

10)11)12)

Solving systems of Equations

Solve each system of equations by either the substitution method or the linear combination (addition/ subtraction) method. Write your answer as an ordered pair.

1) y = 2x + 4 2) 2x + 3y = 6

-3x + y = - 9 -3x + 2y = 17

3) x – 2y = 5 4) 3x + 7y = -1

3x – 5y = 8 6x + 7y = 0

Solving Linear Inequalities

4) or