Introduction to Statistics and Calculus

Summer Assignment

Enclosed you will find two parts to this Assignment. Part 1 consists of Pre‐Requisite Skills Practice that review concepts

learned in Pre‐Calculus and Algebra 2. These concepts are essential to your understanding of Calculus. You are

expected to complete all exercises contained in this packet, showing all work when necessary. Part 2 consists of a project involving an application to real‐life. You will discover that examples for all of the questions can be found through a basic search however there are free internet sites that you can use that will offer full instruction on the various mathematical concepts. An excellent source is khanacademy.com which covers many academic areas. Included on the next page is a table containing Khan Academy links on how to complete each type of question.

This assignment will be collected on the first day of class. Any student who does not have the assignment will be given one by the teacher. The teacher will inform the parent/guardian of the missing assignment and that there is an opportunity for the child to complete it. Late projects will lose 10 points each day.  Summer assignments will
be graded as a quiz. 

This quiz grade will consist of 20% completion and

80% accuracy. Completion is defined as having all work shown in the space provided to receive full credit, and a parent/guardian signature.
Any student who registers as a new attendee of Teaneck High School after August 15th will have an extra week to complete the summer assignment.

Student Name: __________________________________________________________________________________

Parent/Guardian Signature: ________________________________________________________________________

Parent/Guardian Name (Please print): _______________________________________________________________

Pre‐Requisite Skills Practice References

Question
	Topic
	Link (At KhanAcademy.org, under math, unless specified)
	
1
	Graphing Linear Equations
	http://www.khanacademy.org/math/algebra/linear‐equations‐and‐ inequalitie/v/linear‐equations‐in‐standard‐form
Algebra ÆGraphing linear equations and inequalities ÆLinear Equations in Standard Form
	
2
	Graphing Quadratic Equations
	http://www.khanacademy.org/math/algebra/quadtratics/v/graphing‐a‐ quadratic‐function
Algebra ÆQuadratics ÆGraphing a Quadratic Function
	
5 – 8
	Evaluating Functions
	http://www.khanacademy.org/math/algebra/algebra‐functions/v/evaluating‐ functions
Algebra ÆFunctions ÆEvaluating Functions
	
9 ‐ 10
	Compound Interest Functions
	http://www.khanacademy.org/math/precalculus/v/interest‐‐part‐2 Precalculus ÆInterest (Part 2) – (You may want to watch this whole series to better understand compound interest.)
	
11 ‐ 13
	Domain and Range
	http://www.khanacademy.org/math/algebra/ck12‐algebra‐1/v/domain‐and‐ range‐of‐a‐function
Math ÆAlgebra Æck12.org Algebra 1 Examples ÆDomain and Range of a Function
	
14 ‐ 15
	Writing Linear Equations
	http://www.khanacademy.org/math/algebra/linear‐equations‐and‐ inequalitie/v/linear‐equations‐in‐slope‐intercept‐form
Algebra ÆGraphing linear equations and inequalities ÆLinear Equations in Slope Intercept Form
	
16 ‐ 17
	Solve a Quadratic Equation using the Quadratic Formula
	http://www.khanacademy.org/math/algebra/quadtratics/v/quadratic‐equation‐ part‐2
Algebra ÆQuadratics ÆQuadratic Equation Part 2
	
18 – 20
	Rewrite radical expressions with rational exponents
	http://www.khanacademy.org/math/algebra/exponents‐radicals/v/zero‐‐ negative‐‐and‐fractional‐exponents
Algebra ÆExponents and Radicals ÆZero, Negative and Fractional Exponents
	
21 ‐ 23
	Evaluate expressions with rational exponents
	http://www.khanacademy.org/math/algebra/exponents‐radicals/v/level‐3‐ exponents
Algebra ÆExponents and Radicals ÆLevel 3 Exponents
	
24 ‐ 25
	Supply and Demand/Break Even points
	http://www.khanacademy.org/math/algebra/systems‐of‐eq‐and‐ineq
Algebra ÆSystems of Equations and Inequalities, select any method to help you solve these problems.

Project Portion Reference

Compound Interest

https://www.khanacademy.org/math/trigonometry/exponential_and_logarithmic_func/continuous_compoundi ng/v/introduction‐to‐interest
Trigonmoetry ÆExponential and Logarithmic functions ÆContinuous compounding and e

Graphing Piecewise Functions

http://www.purplemath.com/modules/graphing3.htm
Purplemath.com, Select Lessons Index on right‐hand side, Under Beginning Algebra topics, select graphing overview, then select Polynomials, radicals, rationals,& piecewise

Grading Rubric:

Part 1: Pre‐Requisite Skills Review (75 points total)

Correct Answers with work shown: 2 points x 25 = 50 points maximum

Completed with work shown: 1 point x 25 = 25 points maximum

Part 2: Project (115 points)

Showed calculations for all savings plans and graphed all functions: 15 points

Correctly calculated for each savings plan: 3 x 15 = 45 points maximum

Correctly graphed each function: 3 x 15 = 45 points maximum

Answered Final question with explanation: 10 points

Parent/Guardian Signature: (10 points)

Total Points: Part 1 (75) + Part 2 (115) + Parent/Guardian Signature (10) = 200

Name__________________________________________________________ Introduction to Statistics and Calculus

Date: _______________ Summer Assignment

Graphing Functions: Linear, and Quadratic. 1) 3y - 18x = -6
y 10

5

-10	-5	5	10      x

-5

-10

2) y = x2 + 4

y 10

5

-10	-5	5	10      x

-5

-10

Interpreting Graphs

3) The population of a formerly endangered mouse is now on the rise. The population, N, over the last 8 years can be represented with the following graph.

When was the mice population the lowest?

1

4) The following graph shows the stock price of a new internet company over the first 18 months after the initial public offering of its stock.

	y

		

		

		

80

70

60

50

Stock Price     40 (in dollars)     30

20

10

2      4      6      8     10 12 14 16 18 x

Month
What was the stock price to the nearest dollar in the fourteenth month?

Evaluate the function.

5) Find f(-5.2) when f(x) = -2x + 0.90.

6) Find f(k - 1) when f(x) = 2x2 + 2x + 2.

7) The number of people present at a stadium for a big rock concert can be estimated with the following function:

y = 13252x0.79 + 0.42x + 102,

where y is the number of people present and x is the amount of time after 3:00 P.M. on the day of the concert. Predict the number of people present at 7:00PM.

8) A cellular phone company determines a monthly bill from the x number of minutes of usage. The amount of the bill, B(x), (in dollars) is given by the function:

B(x) = 29.87 + 0.12x.

Determine the bill of a customer who uses her cellular phone 32.00 minutes during the month.

Compund Interest.

9) Suppose $4000 is invested at 7%. How much is in the account at the end of 1 year, if interest is compounded hourly?

10) Joan wants to start an annuity that will have $260,000 in it when she retires in 21 years. How much should she initially invest in her annuity to do this if the interest is 6% compounded annually?

2

State the domain and the range for the functions in Numbers 11 - 13 and write them in set notation. Example: {x| 3 < x < 12}.

11)

y 10

8 6 4 2

-
-10 -8 -6 -4 -22	2     4     6     8 10      x -4
-6 -8 -10

12)

10
	y

-10

-10
	10      x

13) The following graph approximates the number y, in thousands, of graduates from nursing schools in the U. S. since 1985(Source: Statistical abstract of the US). The equation of this graph is the function given by
y = -0.036t4 + 0.605t3 - 1.87t2 - 4.67t + 82.5

	y

(13.1, 0)

		

		

									

105

1000's of nursing graduates
90

75

60

45

30

15

2	 4	6	8	10	12	14 x years since 1985
Use the graph to approximate the domain and range of the function and write in set notation.

3

Find an equation of the line:

14) with m = -9, containing (1, -9).

15) (-7, 9) and (-3, 4)

Solving Quadratics.

16) x2 + 3x - 9 = 0

17) x2 + 8x = 3

Convert to an expression with a rational exponent. 18) 10 b3

b
19) 31 9

20)

1 s6

Evaluate the expression. 21) 811/4

22) 644/3

23) 324/5

Find the equilibrium point for the supply and demand curves. Round answers to two decimal places. 24) D(p) = 900 - 20p, S(p) = 280 + 10p

Quantity (q)

1000 900 800 700 600 500 400 300 200
100

S

D

10	20	30	40	50

Price (p)

4

25) D(p) = 10 - p, S(p) =	p + 6

9

8

7

6

Quantity (q)      5 4

3

2

1

S

1     2     3     4     5     6     7     8     9	D

Price (p)

5

Part 2: Project

You have just graduated from eighth grade and after your graduation party your Great Aunt Millie tells you she has a special gift for you. Each year, for the next four years she will give $2000.00 on June 30. This means you will receive $2000 on the following dates:

•	June 30, 2015 •	June 30, 2016 •	June 30, 2017 •	June 30, 2018

Your Aunt makes one stipulation to her gift: You must invest the money in a savings account so that you will have the money to help pay for college.

After doing some research you find that the following interest rates for three banks in your area:

•	Bank of America – 0.05%, compounded daily •	TD Bank – 0.125 %, compounded monthly
•	Hudson City Savings – 0.25%, compounded quarterly

Step 1: Calculate the amount of money that would be in the accounts at the end of each year (July 1 to June 30). Remember that you are making a deposit every July 1 of $2000.00.

Step 2: Graph each of the functions on the same graph.

Which account would be the best one to invest in and why?