MAT251 Calculus 1
Unit 3 Test: 3.7-3.11
Prof. OShea
Name_
Spring 2016
Part I: No Calculator
Answers must be supported with work.
1-6 Find the derivative of the following. ( 5 pts each)
1.
3.
5.
y sin 2 (4 x 1)
1
e
5x
y tan 1 x
4.
y x
y sec
2.
6.
y 7 0.5
North Shore Community College
Department of Sciences and Mathematics
MAT251 Calculus I Syllabus Spring 2016
Instructor: Anne E. OShea
Ofce: LE306 Phone: 781-593-6722 x 6264
Email: [email protected]
Ofce Hours: MW 12:00-1:00, Tu 11:00-12:00 Th 8:25 9:2
Mat251 Calculus 1
Final Exam Review Units 1-3
*Final Exam will include material from Unit 4
#1-4 Find the natural domain of the following functions. For numbers 1 3 leave your answer
in interval notation or set notation.
1
1. f ( x)
x 5
2
2. g ( x) ln x
Mat 251 Calculus 1
Unit 1 Test
Prof. Anne OShea
Name_
Spring 2016
PART I: NO CALCULATOR
Show work for all problems other than number 1. All problems are worth 4 points unless otherwise
indicated.
1 a. To evaluate the average rate of change of a function o
Class Problems: Average vs. Instantaneous Rates of Change
1. A ball is dropped from a height of 110 feet, its height s at time t is given by the
2
position function s 16t 110 , where s is measured in feet and it is measured
in seconds. Find the average ve
MAT251 Calculus 1
Unit 2 Test: 3.1 3.5
Prof. OShea
Name_
Spring 2016
All answers should be supported with work.
1. A C Match the graph of the derivative with the original function.
four derivative graphs below in the appropriate space. ( 6 pts)
A _
B _
Wr
Graphing Functions
a) Graph the following functions by hand on graph paper. b) At least three ordered pairs should be
correct. Check your answer with a graphing calculator. c) State the domain of each.
1. f ( x) 2
12. f ( x ) log x
2. f ( x) x
13. f ( x )
Hypothesis Testing for a Population Proportion Example Of 880 randomly selected drivers, 56% admitted that they run red lights. Test the claim that the majority (more than half) of all Americans run red lights. Use the traditional method, P-value met
Sketching Normal Areas on the Calculator It is strongly suggested that when solving problems based on the normal distribution it is a good strategy to sketch the curve and shade the area corresponding to what is desired. TI calculators can be used to
Continuity Correction for the Normal Approximation to the Binomial Distribution
Binomial P( X = a) P( X a) P( X > a) P( X a) P( X < a) Normal P (a - 0.5 < X < a + 0.5) P ( X > a - 0.5) P ( X > a + 0.5) P ( X < a + 0.5) P ( X < a - 0.5)
For all cas
7-5 Testing a Claim about a Mean: Not Known
Assumptions
1. The sample is a simple random sample. 2. The population standard deviation, , is NOT known. 3. Either or both of these conditions is satisfied: The population is normally distributed or n >
7-4 Testing a Claim about a Mean: Known
Assumptions
1. The sample is a simple random sample. 2. The population standard deviation, , is known. 3. Either or both of these conditions is satisfied: The population is normally distributed or n > 30 . Te
7-3 Testing a Claim About a Proportion
Testing Claims About a Population Proportion p Assumptions
1. The sample observations are a simple random sample. 2. The conditions for a binomial distribution are satisfied. 3. The conditions np 5 and nq 5 ar
7-2 Basics of Hypothesis Testing
Definitions
In statistics, a hypothesis is a claim or statement about a property of a population. A hypothesis test (or test of significance) is a standard procedure for testing a claim about a property of a populatio
6-4 Estimating a Population Mean: Not Known
In this case, we also wish to estimate the population mean, .
Assumptions
1. The sample is a simple random sample. 2. Either or both of these conditions are satisfied: The population is normally distribu
6-3 Estimating a Population Mean: Known
In this case, we wish to estimate the population mean, .
Assumptions
1. The sample is a simple random sample. 2. The value of the population standard deviation, , is known. 3. Either or both of these condit
6-2 Estimating a Population Proportion
Two major applications of inferential statistics involve use of sample data to 1. estimate the value of a population parameter, and 2. test some claim (or hypothesis) about a population. In this section we will
5-6 Normal as Approximation to Binomial
Objectives: Students will be able to: Use the normal probability distribution to approximate binomial probabilities.
Requirements for a Binomial Distribution
Recall that: The procedure must have a fixed numb
5-5 The Central Limit Theorem
Objectives: Students will be able to: Learn about and apply the Central Limit Theorem to solving problems involving the distribution of an original population and the distribution of sample means. The Central Limit Theo
5-4 Sampling Distributions and Estimators
Objectives: Students will be able to: Define the sampling distribution of a statistic; Learn basic principles about the sampling distribution of sample means and the sampling distribution of sample proporti
5-3 Applications of Normal Distributions
Objectives: Students will be able to: Solve Normal Distribution application problems. Recall that the Standard Normal Distribution has a mean of 0 and standard deviation 1. Also recall The Empirical Rule. Abo
5-2 The Standard Normal Distribution
Objectives: Students will be able to: Calculate probabilities under the standard normal curve. The ideas in this section serve as important groundwork for the remaining content in this course. Recall that a discr
4-4 Mean, Variance, and Standard Deviation for Binomial Distributions
Objectives: Students will be able to: Calculate the mean, variance, and standard deviation for a binomial distribution.
For Binomial Distributions Mean = np
Variance Standard De
4-3 Binomial Distributions
Objectives: Students will be able to: Define binomial probability distribution; Calculate binomial probabilities; and Solve application problems involving binomial probabilities.
Definition
A binomial probability distri
4-2 Random Variables
Objectives: Students will be able to: Define Random Variable, Probability Distribution, Discrete or Continuous Random Variable; Calculate Mean, Variance, and Standard Deviation of Random Variables; Identify unusual results wit
2-6 Measures of Relative Standing
Objectives: Students will be able to Compute z-scores, quartiles, and percentiles for a data set; Use z-scores to interpret usual and unusual data values; Interpret and understand standard deviation.
Standard Sco
2-5 Measures of Variation
Objectives: Students will be able to Compute the range, variation, and standard deviation for a set of data; Use the coefficient of variation to compare variation in different populations; Interpret and understand standar
2-4 Measures of Center
Objectives: Students will be able to: Compute measures of center such as mean, median, mode, midrange for a set of data. Problem (page 65, #8) The blood alcohol concentrations of a sample of drivers involved in fatal crashes a
2-3 Visualizing Data
Objectives: Students will be able to: Construct a Histogram, Relative Frequency Histogram, Frequency Polygon, or Ogive given a frequency distribution. Construct a Dot Plot or Stem-and-Leaf Plot for a set of numerical data. Con