JMAP REGENTS BY PERFORMANCE INDICATOR: TOPIC

Transcription

1 JMAP REGENTS BY PERFORMANCE INDICATOR: TOPIC NY Algebra /Trigonometry Regents Exam Questions from Fall 009 to June 0 Sorted by PI: Topic Dear Sir I have to acknolege the reciept of your favor of May. in which you mention that you have finished the 6. first books of Euclid, plane trigonometry, surveying & algebra and ask whether I think a further pursuit of that branch of science would be useful to you. there are some propositions in the latter books of Euclid, & some of Archimedes, which are useful, & I have no doubt you have been made acquainted with them. trigonometry, so far as this, is most valuable to every man, there is scarcely a day in which he will not resort to it for some of the purposes of common life. the science of calculation also is indispensible as far as the extraction of the square & cube roots; Algebra as far as the quadratic equation & the use of logarithms are often of value in ordinary cases: but all beyond these is but a luxury; a delicious luxury indeed; but not to be indulged in by one who is to have a profession to follow for his subsistence. in this light I view the conic sections, curves of the higher orders, perhaps even spherical trigonometry, Algebraical operations beyond the d dimension, and fluxions. Letter from Thomas Jefferson to William G. Munford, Monticello, June 8, 799.

2 TABLE OF CONTENTS TOPIC PI: SUBTOPIC QUESTION NUMBER GRAPHS AND STATISTICS PROBABILITY ABSOLUTE VALUE QUADRATICS A.S.-: Analysis of Data A.S.: Average Known with Missing Data A.S.: Dispersion...9- A.S.6-7: Regression...-9 A.S.8: Correlation Coefficient...0- A.S.5: Normal Distributions A.S.0: Permutations...-6 A.S.: Combinations A.S.9: Differentiating Permutations and Combinations...- A.S.: Sample Space... 5 A.S.: Geometric Probability... 6 A.S.5: Binomial Probability A.A.: Absolute Value Equations and Equalities A.A.0-: Roots of Quadratics A.A.7: Factoring Polynomials A.A.7: Factoring the Difference of Perfect Squares... 7 A.A.7: Factoring by Grouping A.A.5: Quadratic Formula A.A.: Using the Discriminant A.A.: Completing the Square A.A.: Quadratic Inequalities SYSTEMS A.A.: Quadratic-Linear Systems POWERS A.N.: Operations with Polynomials A.N., A.8-9: Negative and Fractional Exponents A.A.: Evaluating Exponential Expressions A.A.8: Evaluating Logarithmic Expressions A.A.5: Graphing Exponential Functions... - A.A.5: Graphing Logarithmic Functions A.A.9: Properties of Logarithms A.A.8: Logarithmic Equations A.A.6, 7: Exponential Equations A.A.6: Binomial Expansions A.A.6, 50: Solving Polynomial Equations i

3 RADICALS RATIONALS FUNCTIONS SEQUENCES AND SERIES TRIGONOMETRY A.N.: Operations with Irrational Expressions... 5 A.A.: Simplifying Radicals A.N., A.: Operations with Radicals A.N.5, A.5: Rationalizing Denominators A.A.: Solving Radicals A.A.0-: Exponents as Radicals A.N.6: Square Roots of Negative Numbers... 7 A.N.7: Imaginary Numbers A.N.8: Conjugates of Complex Numbers A.N.9: Multiplication and Division of Complex Numbers A.A.6: Multiplication and Division of Rationals A.A.6: Addition and Subtraction of Rationals A.A.: Solving Rationals A.A.7: Complex Fractions A.A.5: Inverse Variation A.A.0-: Functional Notation A.A.5: Families of Functions... 0 A.A.6: Properties of Graphs of Functions and Relations... 0 A.A.5: Identifying the Equation of a Graph A.A.8, : Defining Functions A.A.9, 5: Domain and Range A.A.: Compositions of Functions A.A.: Inverse of Functions A.A.6: Transformations with Functions and Relations A.A.9-: Sequences... - A.N.0, A.: Sigma Notation A.A.5: Series A.A.55: Trigonometric Ratios A.M.-: Radian Measure A.A.60: Unit Circle A.A.60: Finding the Terminal Side of an Angle... 7 A.A.6, 66: Determining Trigonometric Functions A.A.6: Using Inverse Trigonometric Functions A.A.57: Reference Angles... 8 A.A.6: Arc Length A.A.58-59: Cofunction/Reciprocal Trigonometric Functions A.A.67: Proving Trigonometric Identities A.A.76: Angle Sum and Difference Identities ii

4 A.A.77: Double and Half Angle Identities A.A.68: Trigonometric Equations A.A.69: Properties of Trigonometric Functions... - A.A.7: Identifying the Equation of a Trigonometric Graph A.A.65, 70-7: Graphing Trigonometric Functions A.A.6: Domain and Range... - A.A.7: Using Trigonometry to Find Area A.A.7: Law of Sines A.A.75: Law of Sines - The Ambiguous Case A.A.7: Law of Cosines... - A.A.7: Vectors CONICS A.A.7, 9: Equations of Circles iii

5 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic GRAPHS AND STATISTICS A.S.-: ANALYSIS OF DATA Which task is not a component of an observational study? The researcher decides who will make up the sample. The researcher analyzes the data received from the sample. The researcher gathers data from the sample, using surveys or taking measurements. The researcher divides the sample into two groups, with one group acting as a control group. A doctor wants to test the effectiveness of a new drug on her patients. She separates her sample of patients into two groups and administers the drug to only one of these groups. She then compares the results. Which type of study best describes this situation? census survey observation controlled experiment A market research firm needs to collect data on viewer preferences for local news programming in Buffalo. Which method of data collection is most appropriate? census survey observation controlled experiment Howard collected fish eggs from a pond behind his house so he could determine whether sunlight had an effect on how many of the eggs hatched. After he collected the eggs, he divided them into two tanks. He put both tanks outside near the pond, and he covered one of the tanks with a box to block out all sunlight. State whether Howard's investigation was an example of a controlled experiment, an observation, or a survey. Justify your response. 5 A survey completed at a large university asked,000 students to estimate the average number of hours they spend studying each week. Every tenth student entering the library was surveyed. The data showed that the mean number of hours that students spend studying was 5.7 per week. Which characteristic of the survey could create a bias in the results? the size of the sample the size of the population the method of analyzing the data the method of choosing the students who were surveyed 6 The yearbook staff has designed a survey to learn student opinions on how the yearbook could be improved for this year. If they want to distribute this survey to 00 students and obtain the most reliable data, they should survey every third student sent to the office every third student to enter the library every third student to enter the gym for the basketball game every third student arriving at school in the morning A.S.: AVERAGE KNOWN WITH MISSING DATA 7 The number of minutes students took to complete a quiz is summarized in the table below. If the mean number of minutes was 7, which equation could be used to calculate the value of x?

6 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic 8 The table below displays the results of a survey regarding the number of pets each student in a class has. The average number of pets per student in this class is. The scores of one class on the Unit mathematics test are shown in the table below. What is the value of k for this table? 9 8 A.S.: DISPERSION 9 The table below shows the first-quarter averages for Mr. Harper s statistics class. Find the population standard deviation of these scores, to the nearest tenth. During a particular month, a local company surveyed all its employees to determine their travel times to work, in minutes. The data for all 5 employees are shown below Determine the number of employees whose travel time is within one standard deviation of the mean. What is the population variance for this set of data? Ten teams competed in a cheerleading competition at a local high school. Their scores were 9, 8, 9, 7, 5, 0,, 8, 7, and 8. How many scores are within one population standard deviation from the mean? For these data, what is the interquartile range? 0 The heights, in inches, of 0 high school varsity basketball players are 78, 79, 79, 7, 75, 7, 7, 7, 8, and 7. Find the interquartile range of this data set.

7 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic A.S.6-7: REGRESSION Samantha constructs the scatter plot below from a set of data. 5 The table below shows the number of new stores in a coffee shop chain that opened during the years 986 through 99. Based on her scatter plot, which regression model would be most appropriate? exponential linear logarithmic power Using to represent the year 986 and y to represent the number of new stores, write the exponential regression equation for these data. Round all values to the nearest thousandth. 6 A cup of soup is left on a countertop to cool. The table below gives the temperatures, in degrees Fahrenheit, of the soup recorded over a 0-minute period. Write an exponential regression equation for the data, rounding all values to the nearest thousandth.

8 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic 7 A population of single-celled organisms was grown in a Petri dish over a period of 6 hours. The number of organisms at a given time is recorded in the table below. 9 The table below shows the results of an experiment involving the growth of bacteria. Write a power regression equation for this set of data, rounding all values to three decimal places. Using this equation, predict the bacteria s growth, to the nearest integer, after 5 minutes. A.S.8: CORRELATION COEFFICIENT 0 Which value of r represents data with a strong negative linear correlation between two variables? Determine the exponential regression equation model for these data, rounding all values to the nearest ten-thousandth. Using this equation, predict the number of single-celled organisms, to the nearest whole number, at the end of the 8th hour. 8 The data collected by a biologist showing the growth of a colony of bacteria at the end of each hour are displayed in the table below. Which calculator output shows the strongest linear relationship between x and y? Write an exponential regression equation to model these data. Round all values to the nearest thousandth. Assuming this trend continues, use this equation to estimate, to the nearest ten, the number of bacteria in the colony at the end of 7 hours.

9 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic As shown in the table below, a person s target heart rate during exercise changes as the person gets older. Which value represents the linear correlation coefficient, rounded to the nearest thousandth, between a person s age, in years, and that person s target heart rate, in beats per minute? The relationship between t, a student s test scores, and d, the student s success in college, is modeled by the equation. Based on this linear regression model, the correlation coefficient could be between and 0 between 0 and equal to equal to 0 Which value of r represents data with a strong positive linear correlation between two variables? A.S.5: NORMAL DISTRIBUTIONS 5 The lengths of 00 pipes have a normal distribution with a mean of 0. inches and a standard deviation of 0. inch. If one of the pipes measures exactly 0. inches, its length lies below the 6 th percentile between the 50 th and 8 th percentiles between the 6 th and 50 th percentiles above the 8 th percentile 6 In a certain high school, a survey revealed the mean amount of bottled water consumed by students each day was 5 bottles with a standard deviation of bottles. Assuming the survey represented a normal distribution, what is the range of the number of bottled waters that approximately 68.% of the students drink? 7 An amateur bowler calculated his bowling average for the season. If the data are normally distributed, about how many of his 50 games were within one standard deviation of the mean? If the amount of time students work in any given week is normally distributed with a mean of 0 hours per week and a standard deviation of hours, what is the probability a student works between 8 and hours per week?.% 8.% 5.% 68.% 5

10 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic 9 Assume that the ages of first-year college students are normally distributed with a mean of 9 years and standard deviation of year. To the nearest integer, find the percentage of first-year college students who are between the ages of 8 years and 0 years, inclusive. To the nearest integer, find the percentage of first-year college students who are 0 years old or older. 0 In a study of 8 video game players, the researchers found that the ages of these players were normally distributed, with a mean age of 7 years and a standard deviation of years. Determine if there were 5 video game players in this study over the age of 0. Justify your answer. PROBABILITY A.S.0: PERMUTATIONS A four-digit serial number is to be created from the digits 0 through 9. How many of these serial numbers can be created if 0 can not be the first digit, no digit may be repeated, and the last digit must be 5? 8 50,0,50 How many different six-letter arrangements can be made using the letters of the word TATTOO? Which formula can be used to determine the total number of different eight-letter arrangements that can be formed using the letters in the word DEADLINE? Find the total number of different twelve-letter arrangements that can be formed using the letters in the word PENNSYLVANIA. 5 Find the number of possible different 0-letter arrangements using the letters of the word STATISTICS. 6 The letters of any word can be rearranged. Carol believes that the number of different 9-letter arrangements of the word TENNESSEE is greater than the number of different 7-letter arrangements of the word VERMONT. Is she correct? Justify your answer. A.S.: COMBINATIONS 7 The principal would like to assemble a committee of 8 students from the 5-member student council. How many different committees can be chosen? 0 6,5,,00 59,59,00 8 Ms. Bell's mathematics class consists of sophomores, 0 juniors, and 5 seniors. How many different ways can Ms. Bell create a four-member committee of juniors if each junior has an equal chance of being selected? 0,876 5,00 9,0 9 If order does not matter, which selection of students would produce the most possible committees? 5 out of 5 5 out of 5 0 out of 5 5 out of 5 0 A blood bank needs twenty people to help with a blood drive. Twenty-five people have volunteered. Find how many different groups of twenty can be formed from the twenty-five volunteers. 6

11 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic A.S.9: DIFFERENTIATING BETWEEN PERMUTATIONS AND COMBINATIONS Twenty different cameras will be assigned to several boxes. Three cameras will be randomly selected and assigned to box A. Which expression can be used to calculate the number of ways that three cameras can be assigned to box A? Three marbles are to be drawn at random, without replacement, from a bag containing 5 red marbles, 0 blue marbles, and 5 white marbles. Which expression can be used to calculate the probability of drawing red marbles and white marble from the bag? Which problem involves evaluating? How many different four-digit ID numbers can be formed using,,,, 5, and 6 without repetition? How many different subcommittees of four can be chosen from a committee having six members? How many different outfits can be made using six shirts and four pairs of pants? How many different ways can one boy and one girl be selected from a group of four boys and six girls? A.S.: SAMPLE SPACE 5 A committee of 5 members is to be randomly selected from a group of 9 teachers and 0 students. Determine how many different committees can be formed if members must be teachers and members must be students. There are eight people in a tennis club. Which expression can be used to find the number of different ways they can place first, second, and third in a tournament? 7

12 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic A.S.: GEOMETRIC PROBABILITY 6 A dartboard is shown in the diagram below. The two lines intersect at the center of the circle, and the central angle in sector measures. 8 A study finds that 80% of the local high school students text while doing homework. Ten students are selected at random from the local high school. Which expression would be part of the process used to determine the probability that, at most, 7 of the 0 students text while doing homework? If darts thrown at this board are equally likely to land anywhere on the board, what is the probability that a dart that hits the board will land in either sector or sector? A.S.5: BINOMIAL PROBABILITY 7 A spinner is divided into eight equal sections. Five sections are red and three are green. If the spinner is spun three times, what is the probability that it lands on red exactly twice? 9 On a multiple-choice test, Abby randomly guesses on all seven questions. Each question has four choices. Find the probability, to the nearest thousandth, that Abby gets exactly three questions correct. 50 The probability that the Stormville Sluggers will win a baseball game is. Determine the probability, to the nearest thousandth, that the Stormville Sluggers will win at least 6 of their next 8 games. 5 The probability that a professional baseball player will get a hit is. Calculate the exact probability that he will get at least hits in 5 attempts. 5 The members of a men s club have a choice of wearing black or red vests to their club meetings. A study done over a period of many years determined that the percentage of black vests worn is 60%. If there are 0 men at a club meeting on a given night, what is the probability, to the nearest thousandth, that at least 8 of the vests worn will be black? 8

13 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic 5 A study shows that 5% of the fish caught in a local lake had high levels of mercury. Suppose that 0 fish were caught from this lake. Find, to the nearest tenth of a percent, the probability that at least 8 of the 0 fish caught did not contain high levels of mercury. ABSOLUTE VALUE A.A.: ABSOLUTE VALUE EQUATIONS AND INEQUALITIES 5 What is the solution set of the equation? 57 What is the graph of the solution set of? 58 Graph the inequality for x. Graph the solution on the line below. 59 Determine the solution of the inequality. [The use of the grid below is optional.] 55 Which graph represents the solution set of? 56 Which graph represents the solution set of? 9

14 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic QUADRATICS A.A.0-: ROOTS OF QUADRATICS 60 What are the sum and product of the roots of the equation? 6 Find the sum and product of the roots of the equation. 6 Determine the sum and the product of the roots of. 6 Determine the sum and the product of the roots of the equation. 6 For which equation does the sum of the roots equal and the product of the roots equal? 65 For which equation does the sum of the roots equal and the product of the roots equal? 66 Which equation has roots with the sum equal to and the product equal to? 67 Write a quadratic equation such that the sum of its roots is 6 and the product of its roots is. A.A.7: FACTORING POLYNOMIALS 68 Factored completely, the expression is equivalent to 69 Factored completely, the expression is equivalent to 70 Factor completely: A.A.7: FACTORING THE DIFFERENCE OF PERFECT SQUARES 7 Factor the expression completely. A.A.7: FACTORING BY GROUPING 7 When factored completely, equals 0

15 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic 7 When factored completely, the expression is equivalent to A.A.5: QUADRATIC FORMULA 7 The roots of the equation are and and 75 The solutions of the equation are 76 Solve the equation and express the answer in simplest radical form. A.A.: USING THE DISCRIMINANT 79 The discriminant of a quadratic equation is. The roots are imaginary real, rational, and equal real, rational, and unequal real, irrational, and unequal 80 Use the discriminant to determine all values of k that would result in the equation having equal roots. A.A.: COMPLETING THE SQUARE 8 Brian correctly used a method of completing the square to solve the equation. Brian s first step was to rewrite the equation as. He then added a number to both sides of the equation. Which number did he add? 9 8 If is solved by completing the square, an intermediate step would be 8 Solve by completing the square, expressing the result in simplest radical form. 77 The roots of the equation are imaginary real, rational, and equal real, rational, and unequal real, irrational, and unequal 78 The roots of the equation are imaginary real and irrational real, rational, and equal real, rational, and unequal

16 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic A.A.: QUADRATIC INEQUALITIES 8 Which graph best represents the inequality? 85 The solution set of the inequality is 86 Find the solution of the inequality, algebraically. SYSTEMS A.A.: QUADRATIC-LINEAR SYSTEMS 87 Which values of x are in the solution set of the following system of equations? 88 Which ordered pair is in the solution set of the system of equations shown below? 89 Which ordered pair is a solution of the system of equations shown below? 90 Solve the following systems of equations algebraically:

17 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic POWERS A.N.: OPERATIONS WITH POLYNOMIALS 95 Express as a trinomial. 9 When is subtracted from 96 Express the product of and, the difference is as a trinomial. A.N., A.8-9: NEGATIVE AND FRACTIONAL EXPONENTS 97 If and, what is the value of the 9 When is subtracted from, the difference is 9 What is the product of and? 9 What is the product of and? expression? 98 If n is a negative integer, then which statement is always true? 99 Which expression is equivalent to?

18 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic 00 When simplified, the expression is equivalent to 0 The expression is equivalent to 0 Which expression is equivalent to? 0 Which expression is equivalent to? 0 Simplify the expression and write the answer using only positive exponents. 05 When is divided by, the quotient is 06 When is divided by, the quotient equals A.A.: EVALUATING EXPONENTIAL EXPRESSIONS 07 Evaluate when and. 08 Matt places $,00 in an investment account earning an annual rate of 6.5%, compounded continuously. Using the formula, where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, that Matt will have in the account after 0 years. 09 The formula for continuously compounded interest is, where A is the amount of money in the account, P is the initial investment, r is the interest rate, and t is the time in years. Using the formula, determine, to the nearest dollar, the amount in the account after 8 years if $750 is invested at an annual rate of %.

19 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic A.A.8: EVALUATING LOGARITHMIC EXPRESSIONS 0 The expression is equivalent to 8 A.A.5: GRAPHING EXPONENTIAL FUNCTIONS The graph of the equation has an asymptote. On the grid below, sketch the graph of and write the equation of this asymptote. The expression is equivalent to 5

20 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic On the axes below, for, graph. A.A.5: GRAPHING LOGARITHMIC FUNCTIONS 5 If a function is defined by the equation, which graph represents the inverse of this function? What is the equation of the graph shown below? 6

21 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic 6 Which graph represents the function? 8 If, then can be represented by 9 If, then expressed in terms of is equivalent to 0 The expression is equivalent to If, then the value of x is A.A.9: PROPERTIES OF LOGARITHMS 7 The expression is equivalent to 7

22 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic If and, the expression is equivalent to A.A.8: LOGARITHMIC EQUATIONS What is the value of x in the equation? ,0 What is the solution of the equation? If and, find the numerical value of, in simplest form. 6 Solve algebraically for all values of x: 7 Solve algebraically for x: 8 Solve algebraically for x: 9 The temperature, T, of a given cup of hot chocolate after it has been cooling for t minutes can best be modeled by the function below, where is the temperature of the room and k is a constant. A cup of hot chocolate is placed in a room that has a temperature of 68. After minutes, the temperature of the hot chocolate is 50. Compute the value of k to the nearest thousandth. [Only an algebraic solution can receive full credit.] Using this value of k, find the temperature, T, of this cup of hot chocolate if it has been sitting in this room for a total of 0 minutes. Express your answer to the nearest degree. [Only an algebraic solution can receive full credit.] A.A.6, 7: EXPONENTIAL EQUATIONS 0 A population of rabbits doubles every 60 days according to the formula, where P is the population of rabbits on day t. What is the value of t when the population is 0? Susie invests $500 in an account that is compounded continuously at an annual interest rate of 5%, according to the formula, where A is the amount accrued, P is the principal, r is the rate of interest, and t is the time, in years. Approximately how many years will it take for Susie s money to double? The number of bacteria present in a Petri dish can be modeled by the function, where N is the number of bacteria present in the Petri dish after t hours. Using this model, determine, to the nearest hundredth, the number of hours it will take for N to reach 0,700. 8

23 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic Akeem invests $5,000 in an account that pays.75% annual interest compounded continuously. Using the formula, where the amount in the account after t years, principal invested, and the annual interest rate, how many years, to the nearest tenth, will it take for Akeem s investment to triple? The solution set of is 5 The value of x in the equation is 5 6 Which value of k satisfies the equation? 7 What is the value of x in the equation? 8 Solve algebraically for all values of x: 9 Solve algebraically for x: A.A.6: BINOMIAL EXPANSIONS 0 What is the coefficient of the fourth term in the expansion of? 6 5,76 Which expression represents the third term in the expansion of? What is the fourth term in the expansion of? What is the fourth term in the binomial expansion? What is the middle term in the expansion of? 9

24 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic 5 Write the binomial expansion of as a polynomial in simplest form. 5 The graph of is shown below. A.A.6, 50: SOLVING POLYNOMIAL EQUATIONS 6 Which values of x are solutions of the equation? 7 What is the solution set of the equation? 8 Solve algebraically for all values of x: 9 Solve the equation algebraically for all values of x. Which set lists all the real solutions of? 50 How many negative solutions to the equation exist? 0 0

25 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic 5 The graph of is shown below. 55 Express in simplest form: A.N., A.: OPERATIONS WITH RADICALS 56 The sum of and, expressed in simplest radical form, is 57 Express in simplest radical form. What is the product of the roots of the equation 6? RADICALS A.N.: OPERATIONS WITH IRRATIONAL EXPRESSIONS 5 The product of and is A.A.: SIMPLIFYING RADICALS 58 The expression is equivalent to 59 Express in simplest radical form. A.N.5, A.5: RATIONALIZING DENOMINATORS 60 Which expression is equivalent to? 5 The expression is equivalent to

26 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic 6 The expression is equivalent to 6 Express with a rational denominator, in simplest radical form. 6 The fraction is equivalent to 6 The expression is equivalent to 65 Expressed with a rational denominator and in simplest form, is A.A.: SOLVING RADICALS 66 The solution set of is 67 What is the solution set for the equation? 68 The solution set of the equation is 69 Solve algebraically for x: 70 Solve algebraically for x:

27 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic A.A.0-: EXPONENTS AS RADICALS 7 The expression is equivalent to 7 The expression is equivalent to A.N.7: IMAGINARY NUMBERS 75 The product of and is equivalent to 76 The expression is equivalent to 77 Determine the value of n in simplest form: 7 The expression is equivalent to A.N.6: SQUARE ROOTS OF NEGATIVE NUMBERS 7 In simplest form, is equivalent to A.N.8: CONJUGATES OF COMPLEX NUMBERS 78 What is the conjugate of? 79 The conjugate of is 80 What is the conjugate of? 8 The conjugate of the complex expression is

28 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic A.N.9: MULTIPLICATION AND DIVISION OF COMPLEX NUMBERS 8 The expression is equivalent to 8 The expression is equivalent to 0 8 If,, and, the expression equals RATIONALS A.A.6: MULTIPLICATION AND DIVISION OF RATIONALS 85 Perform the indicated operations and simplify completely: A.A.6: ADDITION AND SUBTRACTION OF RATIONALS 87 Expressed in simplest form, is equivalent to A.A.: SOLVING RATIONALS 88 Solve for x: 89 Solve algebraically for x: 90 Solve the equation below algebraically, and express the result in simplest radical form: A.A.7: COMPLEX FRACTIONS 86 Express in simplest form: 9 Written in simplest form, the expression is equivalent to

29 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic 9 The simplest form of is 9 Express in simplest form: A.A.5: INVERSE VARIATION 9 If p varies inversely as q, and when, what is the value of p when? The quantities p and q vary inversely. If when, and when, then x equals and 5 and 97 For a given set of rectangles, the length is inversely proportional to the width. In one of these rectangles, the length is and the width is 6. For this set of rectangles, calculate the width of a rectangle whose length is 9. FUNCTIONS A.A.0-: FUNCTIONAL NOTATION 98 The equation may be rewritten as 99 If, what is the value of? 00 If, express in simplest form. 96 The points,, and lie on the graph of a function. If y is inversely proportional to the square of x, what is the value of d? 7 5

30 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic A.A.5: FAMILIES OF FUNCTIONS 0 On January, a share of a certain stock cost $80. Each month thereafter, the cost of a share of this stock decreased by one-third. If x represents the time, in months, and y represents the cost of the stock, in dollars, which graph best represents the cost of a share over the following 5 months? A.A.5: PROPERTIES OF GRAPHS OF FUNCTIONS AND RELATIONS 0 Which statement about the graph of the equation is not true? It is asymptotic to the x-axis. The domain is the set of all real numbers. It lies in Quadrants I and II. It passes through the point. A.A.5: IDENTIFYING THE EQUATION OF A GRAPH 0 Four points on the graph of the function are shown below. Which equation represents? 0 Which equation is represented by the graph below? 6

31 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic A.A.8, : DEFINING FUNCTIONS 06 Which graph does not represent a function? 05 Which graph does not represent a function? 7

32 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic 07 Which graph represents a relation that is not a function? 09 Given the relation, which value of k will result in the relation not being a function? 0 Which graph represents a one-to-one function? 08 Which relation is not a function? 8

33 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic Which diagram represents a relation that is both one-to-one and onto? Which function is one-to-one? Which function is one-to-one? A.A.9, 5: DOMAIN AND RANGE 5 What is the domain of the function? 6 What is the range of? 7 What is the range of? 8 If, what are its domain and range? domain: ; range: domain: ; range: domain: ; range: domain: ; range: Which function is not one-to-one? 9

34 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic 9 What is the domain of the function shown below? What are the domain and the range of the function shown in the graph below? 0 What is the range of the function shown below? The graph below represents the function. State the domain and range of this function. 0

35 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic A.A.: COMPOSITIONS OF FUNCTIONS 9 If, find. If and, what is the value of?.5 6 If and, then is equal to 5 If and, then is equal to 6 Which expression is equivalent to, given,, and? 7 If and, determine the value of. A.A.: INVERSE OF FUNCTIONS 8 Which two functions are inverse functions of each other? and and and and

36 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic A.A.6: TRANSFORMATIONS WITH FUNCTIONS AND RELATIONS 0 The graph below shows the function. The minimum point on the graph of the equation is. What is the minimum point on the graph of the equation? SEQUENCES AND SERIES A.A.9-: SEQUENCES Which graph represents the function? What is the formula for the nth term of the sequence? What is a formula for the nth term of sequence B shown below? A sequence has the following terms:,,,. Which formula represents the nth term in the sequence?

37 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic 5 What is the common difference of the arithmetic sequence? 9 6 Which arithmetic sequence has a common difference of? 7 What is the common ratio of the geometric sequence shown below? 0 What is the fifteenth term of the sequence? 8,90 7,680 What is the fifteenth term of the geometric sequence? Find the first four terms of the recursive sequence defined below. 8 What is the common ratio of the sequence 9 What is the common ratio of the geometric sequence whose first term is 7 and fourth term is 6?? Find the third term in the recursive sequence, where. A.N.0, A.: SIGMA NOTATION The value of the expression is The expression is equal to

38 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic 6 The value of the expression is 6 7 Evaluate: 8 Evaluate: 9 Which summation represents? 5 Express the sum using sigma notation. A.A.5: SERIES 5 The sum of the first eight terms of the series is 5 What is the sum of the first 9 terms of the sequence? An auditorium has rows of seats. The first row has 8 seats, and each succeeding row has two more seats than the previous row. How many seats are in the auditorium? Determine the sum of the first twenty terms of the sequence whose first five terms are 5,,,,. 50 Mrs. Hill asked her students to express the sum using sigma notation. Four different student answers were given. Which student answer is correct?

39 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic TRIGONOMETRY A.A.55: TRIGONOMETRIC RATIOS 58 Which ratio represents in the diagram below? 56 In the diagram below of right triangle KTW,,, and. What is the measure of, to the nearest minute? 59 In the diagram below of right triangle JTM,,, and. 57 In the right triangle shown below, what is the measure of angle S, to the nearest minute? What is the value of? 5

40 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic 60 In the diagram below, the length of which line segment is equal to the exact value of? 6 What is the number of degrees in an angle whose radian measure is? What is the number of degrees in an angle whose measure is radians? A.M.-: RADIAN MEASURE 6 What is the radian measure of the smaller angle formed by the hands of a clock at 7 o clock? 6 What is the radian measure of an angle whose measure is? What is the number of degrees in an angle whose radian measure is? Find, to the nearest tenth, the radian measure of 6º. 67 Find, to the nearest minute, the angle whose measure is.5 radians. 68 Find, to the nearest tenth of a degree, the angle whose measure is.5 radians. 69 Convert radians to degrees and express the answer to the nearest minute. 6

41 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic A.A.60: UNIT CIRCLE 70 In which graph is coterminal with an angle of? 7 If, which diagram represents drawn in standard position? 7

42 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic 7 On the unit circle shown in the diagram below, sketch an angle, in standard position, whose degree measure is 0 and find the exact value of. 77 The value of to the nearest ten-thousandth is 78 The value of rounded to four decimal places is Which expression, when rounded to three decimal places, is equal to? A.A.60: FINDING THE TERMINAL SIDE OF AN ANGLE 7 An angle, P, drawn in standard position, terminates in Quadrant II if and and and and A.A.56, 6, 66: DETERMINING TRIGONOMETRIC FUNCTIONS 7 In the interval, is undefined when x equals 0º and 90º 90º and 80º 80º and 70º 90º and 70º 75 Express the product of cos 0 and sin 5 in simplest radical form. 76 If is an angle in standard position and its terminal side passes through the point, find the exact value of. A.A.6: USING INVERSE TRIGONOMETRIC FUNCTIONS 80 What is the principal value of? 8 If, then 8

43 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic 8 If, then k is 8 In the diagram below of a unit circle, the ordered A.A.6: ARC LENGTH 85 A circle has a radius of inches. In inches, what is the length of the arc intercepted by a central angle of radians? 8 pair the terminal side of represents the point where intersects the unit circle. 86 A circle is drawn to represent a pizza with a inch diameter. The circle is cut into eight congruent pieces. What is the length of the outer edge of any one piece of this circle? A.A.58-59: COFUNCTION AND RECIPROCAL TRIGONOMETRIC FUNCTIONS 87 If is acute and, then What is? A.A.57: REFERENCE ANGLES 8 Expressed as a function of a positive acute angle, is equal to 88 The expression is equivalent to 89 Express, in terms of. 9

44 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic 90 Express as a single trigonometric function, in simplest form, for all values of x for which it is defined. 9 If, find the smallest positive value of a, in degrees. 9 Express the exact value of, with a rational denominator. A.A.67: PROVING TRIGONOMETRIC IDENTITIES 9 Which expression always equals? 9 Starting with, derive the formula. A.A.76: ANGLE SUM AND DIFFERENCE IDENTITIES 95 The expression is equivalent to 96 Given angle A in Quadrant I with and 97 If and and angles A and B are in Quadrant I, find the value of. 98 Express as a single fraction the exact value of. 99 The value of is equivalent to 00 The expression is equivalent to A.A.77: DOUBLE AND HALF ANGLE IDENTITIES 0 The expression is equivalent to 0 If where, what is the value of? angle B in Quadrant II with value of?, what is the 0

45 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic 0 If, what is the value of? 0 What is a positive value of, when? A.A.68: TRIGONOMETRIC EQUATIONS 05 What is the solution set for in the interval? 06 What are the values of in the interval that satisfy the equation? 60º, 0º 7º, 5º 7º, 08º, 5º, 88º 60º, 0º, 0º, 00º 09 Find, algebraically, the measure of the obtuse angle, to the nearest degree, that satisfies the equation. 0 Find all values of in the interval that satisfy the equation. A.A.69: PROPERTIES OF TRIGONOMETRIC FUNCTIONS What is the period of the function? What is the period of the function? 07 What is the solution set of the equation when? 08 Solve the equation algebraically for all values of C in the interval.

46 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic A.A.7: IDENTIFYING THE EQUATION OF A TRIGONOMETRIC GRAPH 5 Which equation is graphed in the diagram below? Which equation is represented by the graph below? Which equation represents the graph below? 6 Write an equation for the graph of the trigonometric function shown below.

47 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic A.A.65, 70-7: GRAPHING TRIGONOMETRIC FUNCTIONS 8 Which graph represents the equation? 7 Which graph shows?

48 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic 9 Which graph represents one complete cycle of the equation? 0 Which equation is represented by the graph below? Which equation is sketched in the diagram below?

49 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic Which is a graph of? The function is defined in such a way that is a function. What can be the domain of? A.A.7: USING TRIGONOMETRY TO FIND AREA A.A.6: DOMAIN AND RANGE In which interval of is the inverse also a function? 5 In,,, and. What is the area of to the nearest square inch? A ranch in the Australian Outback is shaped like triangle ACE, with,, and miles. Find the area of the ranch, to the nearest square mile. 7 The area of triangle ABC is. If and , the length of is approximately 8 In parallelogram BFLO,,, and. If diagonal is drawn, what is the area of?

50 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic 9 The sides of a parallelogram measure 0 cm and 8 cm. One angle of the parallelogram measures 6 degrees. What is the area of the parallelogram, to the nearest square centimeter? As shown in the diagram below, fire-tracking station A is 00 miles due west of fire-tracking station B. A forest fire is spotted at F, on a bearing 7 northeast of station A and 5 northeast of station B. Determine, to the nearest tenth of a mile, the distance the fire is from both station A and station B. [N represents due north.] 0 Two sides of a parallelogram are feet and 0 feet. The measure of the angle between these sides is. Find the area of the parallelogram, to the nearest square foot. The two sides and included angle of a parallelogram are 8,, and 60. Find its exact area in simplest form. A.A.7: LAW OF SINES In, p equals The diagram below shows the plans for a cell phone tower. A guy wire attached to the top of the tower makes an angle of 65 degrees with the ground. From a point on the ground 00 feet from the end of the guy wire, the angle of elevation to the top of the tower is degrees. Find the height of the tower, to the nearest foot. 5 In,,, and. Find the measures of the missing angles and side of. Round each measure to the nearest tenth. A.A.75: LAW OF SINES-THE AMBIGUOUS CASE 6 In,,, and. What are the two possible values for, to the nearest tenth? 7.7 and and and and How many distinct triangles can be formed if,, and? 0 8 Given with,, and, what type of triangle can be drawn? an acute triangle, only an obtuse triangle, only both an acute triangle and an obtuse triangle neither an acute triangle nor an obtuse triangle 6

51 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic 9 In, and. Two distinct triangles can be constructed if the measure of angle M is In,,, and. The measure of? must be between 0 and 90 must equal 90 must be between 90 and 80 is ambiguous A.A.7: LAW OF COSINES In,,, and, as shown in the diagram below. What is the, to the nearest degree? A.A.7: VECTORS Two forces of 5 newtons and 85 newtons acting on a body form an angle of 55. Find the magnitude of the resultant force, to the nearest hundredth of a newton. Find the measure, to the nearest degree, of the angle formed between the resultant and the larger force. 5 The measures of the angles between the resultant and two applied forces are 60 and 5, and the magnitude of the resultant is 7 pounds. Find, to the nearest pound, the magnitude of each applied force. CONICS A.A.7, 9: EQUATIONS OF CIRCLES 6 The equation is equivalent to 7 Write an equation of the circle shown in the diagram below In,,, and. What is? In a triangle, two sides that measure 6 cm and 0 cm form an angle that measures. Find, to the nearest degree, the measure of the smallest angle in the triangle. 7

52 Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic 8 Which equation represents the circle shown in the graph below that passes through the point? 50 Write an equation of the circle shown in the graph below. 5 A circle shown in the diagram below has a center of and passes through point. 9 Which equation is represented by the graph below? Write an equation that represents the circle. 8

53 ID: A Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic Answer Section ANS: PTS: REF: 07a STA: A.S. TOP: Analysis of Data ANS: PTS: REF: 060a STA: A.S. TOP: Analysis of Data ANS: PTS: REF: 060a STA: A.S. TOP: Analysis of Data ANS: Controlled experiment because Howard is comparing the results obtained from an experimental sample against a control sample. PTS: REF: 0800a STA: A.S. TOP: Analysis of Data 5 ANS: Students entering the library are more likely to spend more time studying, creating bias. PTS: REF: fall090a STA: A.S. TOP: Analysis of Data 6 ANS: PTS: REF: 00a STA: A.S. TOP: Analysis of Data 7 ANS: PTS: REF: 06a STA: A.S. TOP: Average Known with Missing Data 8 ANS: PTS: REF: 06a STA: A.S. TOP: Average Known with Missing Data 9 ANS: PTS: REF: fall09a STA: A.S. TOP: Dispersion KEY: range, quartiles, interquartile range, variance

54 ID: A 0 ANS: Ordered, the heights are 7, 7, 7, 7, 7, 75, 78, 79, 79, 8. and.. PTS: REF: 0a STA: A.S. TOP: Dispersion KEY: range, quartiles, interquartile range, variance ANS: 7. PTS: REF: 0609a STA: A.S. TOP: Dispersion KEY: basic, group frequency distributions ANS:. There are 8 scores between 5. and 5.9. PTS: REF: 067a STA: A.S. TOP: Dispersion KEY: advanced ANS:. 6 scores are within a population standard deviation of the mean. PTS: REF: 068a STA: A.S. TOP: Dispersion KEY: advanced ANS: PTS: REF: 067a STA: A.S.6 TOP: Regression 5 ANS: PTS: REF: 080a STA: A.S.7 TOP: Exponential Regression 6 ANS: PTS: REF: 06a STA: A.S.7 TOP: Exponential Regression 7 ANS:. PTS: REF: 08a STA: A.S.7 TOP: Exponential Regression 8 ANS:. PTS: REF: 07a STA: A.S.7 TOP: Exponential Regression 9 ANS:,,009. PTS: REF: fall098a STA: A.S.7 TOP: Power Regression 0 ANS: PTS: REF: 060a STA: A.S.8 TOP: Correlation Coefficient

55 ID: A ANS: () shows the strongest linear relationship, but if,. The Regents announced that a correct solution was not provided for this question and all students should be awarded credit. PTS: REF: 0a STA: A.S.8 TOP: Correlation Coefficient ANS:. PTS: REF: 065a STA: A.S.8 TOP: Correlation Coefficient ANS: Since the coefficient of is greater than 0,. PTS: REF: 00a STA: A.S.8 TOP: Correlation Coefficient ANS: PTS: REF: 066a STA: A.S.8 TOP: Correlation Coefficient 5 ANS: PTS: REF: fall095a STA: A.S.5 TOP: Normal Distributions KEY: interval 6 ANS: PTS: REF: 007a STA: A.S.5 TOP: Normal Distributions KEY: interval 7 ANS: PTS: REF: 080a STA: A.S.5 TOP: Normal Distributions KEY: predict

56 ID: A 8 ANS: PTS: REF: 0a STA: A.S.5 TOP: Normal Distributions KEY: probability 9 ANS: 68% of the students are within one standard deviation of the mean. 6% of the students are more than one standard deviation above the mean. PTS: REF: 0a STA: A.S.5 TOP: Normal Distributions KEY: percent 0 ANS: no. over 0 is more than standard deviation above the mean. PTS: REF: 069a STA: A.S.5 TOP: Normal Distributions KEY: predict ANS:. The first digit cannot be 0 or 5. The second digit cannot be 5 or the same as the first digit. The third digit cannot be 5 or the same as the first or second digit. PTS: REF: 05a STA: A.S.0 TOP: Permutations ANS: PTS: REF: 0a STA: A.S.0 TOP: Permutations ANS: PTS: REF: fall095a STA: A.S.0 TOP: Permutations ANS: 9,96,800. PTS: REF: 0805a STA: A.S.0 TOP: Permutations 5 ANS: PTS: REF: 060a STA: A.S.0 TOP: Permutations 6 ANS: No. TENNESSEE:. VERMONT: PTS: REF: 0608a STA: A.S.0 TOP: Permutations 7 ANS: PTS: REF: 080a STA: A.S. TOP: Combinations

57 ID: A 8 ANS: PTS: REF: 06a STA: A.S. TOP: Combinations 9 ANS:... PTS: REF: 067a STA: A.S. TOP: Combinations 0 ANS: PTS: REF: 0a STA: A.S. TOP: Combinations ANS: PTS: REF: 06007a STA: A.S.9 TOP: Differentiating Permutations and Combinations ANS: PTS: REF: 07a STA: A.S.9 TOP: Differentiating Permutations and Combinations ANS: PTS: REF: 00a STA: A.S.9 TOP: Differentiating Permutations and Combinations ANS: PTS: REF: 067a STA: A.S.9 TOP: Differentiating Permutations and Combinations 5 ANS:,00. PTS: REF: fall095a STA: A.S. TOP: Sample Space 6 ANS: PTS: REF: 008a STA: A.S. TOP: Geometric Probability 5

58 ID: A 7 ANS: PTS: REF: 0a STA: A.S.5 TOP: Binomial Probability KEY: spinner 8 ANS: PTS: REF: 06a STA: A.S.5 TOP: Binomial Probability KEY: modeling 9 ANS: PTS: REF: 065a STA: A.S.5 TOP: Binomial Probability KEY: exactly 50 ANS: PTS: REF: 08a STA: A.S.5 TOP: Binomial Probability KEY: at least or at most 5 ANS:. PTS: REF: 068a STA: A.S.5 TOP: Binomial Probability KEY: at least or at most 5 ANS: PTS: REF: 0606a STA: A.S.5 TOP: Binomial Probability KEY: at least or at most 5 ANS: 6.%. PTS: REF: 0808a STA: A.S.5 TOP: Binomial Probability KEY: at least or at most 6

59 ID: A 5 ANS:.. PTS: REF: 006a STA: A.A. TOP: Absolute Value Equations 55 ANS: PTS: REF: fall0905a STA: A.A. TOP: Absolute Value Inequalities KEY: graph 56 ANS: or PTS: REF: 0609a STA: A.A. TOP: Absolute Value Inequalities KEY: graph 57 ANS:. PTS: REF: 0607a STA: A.A. TOP: Absolute Value Inequalities KEY: graph 58 ANS:. PTS: REF: 067a STA: A.A. TOP: Absolute Value Inequalities KEY: graph 7

60 ID: A 59 ANS: or PTS: REF: 0a STA: A.A. TOP: Absolute Value Inequalities KEY: graph 60 ANS: sum:. product: PTS: REF: 009a STA: A.A.0 TOP: Roots of Quadratics 6 ANS: Sum. Product PTS: REF: 0600a STA: A.A.0 TOP: Roots of Quadratics 6 ANS:. Sum. Product PTS: REF: 09a STA: A.A.0 TOP: Roots of Quadratics 6 ANS: Sum. Product PTS: REF: 068a STA: A.A.0 TOP: Roots of Quadratics 6 ANS:. PTS: REF: fall09a STA: A.A. TOP: Roots of Quadratics KEY: basic 65 ANS:. PTS: REF: 0a STA: A.A. TOP: Roots of Quadratics KEY: basic 66 ANS: sum of the roots,. product of the roots, PTS: REF: 0608a STA: A.A. TOP: Roots of Quadratics KEY: basic 8

61 ID: A 67 ANS:,.. If then and PTS: REF: 060a STA: A.A. TOP: Roots of Quadratics KEY: basic 68 ANS: PTS: REF: fall097a STA: A.A.7 TOP: Factoring Polynomials KEY: single variable 69 ANS: PTS: REF: 06008a STA: A.A.7 TOP: Factoring Polynomials KEY: single variable 70 ANS: PTS: REF: 0808a STA: A.A.7 TOP: Factoring Polynomials KEY: multiple variables 7 ANS: PTS: REF: 06a STA: A.A.7 TOP: Factoring the Difference of Perfect Squares 7 ANS: KEY: binomial PTS: REF: 06a STA: A.A.7 TOP: Factoring by Grouping 7 ANS: PTS: REF: 07a STA: A.A.7 TOP: Factoring by Grouping 9

62 ID: A 7 ANS: PTS: REF: 08009a STA: A.A.5 TOP: Quadratic Formula 75 ANS: PTS: REF: 06009a STA: A.A.5 TOP: Quadratic Formula 76 ANS: PTS: REF: 0a STA: A.A.5 TOP: Quadratics with Irrational Solutions 77 ANS: PTS: REF: 0806a STA: A.A. TOP: Using the Discriminant KEY: determine nature of roots given equation 78 ANS: PTS: REF: 00a STA: A.A. TOP: Using the Discriminant KEY: determine nature of roots given equation 79 ANS: PTS: REF: 0a STA: A.A. TOP: Using the Discriminant KEY: determine nature of roots given equation 80 ANS: PTS: REF: 0608a STA: A.A. TOP: Using the Discriminant KEY: determine equation given nature of roots 8 ANS: PTS: REF: 06a STA: A.A. TOP: Completing the Square 0

63 ID: A 8 ANS: PTS: REF: 06a STA: A.A. TOP: Completing the Square 8 ANS:. PTS: REF: fall096a STA: A.A. TOP: Completing the Square 8 ANS: PTS: REF: 0607a STA: A.A. TOP: Quadratic Inequalities KEY: two variables 85 ANS: PTS: REF: 05a STA: A.A. TOP: Quadratic Inequalities KEY: one variable 86 ANS: or.. or PTS: REF: 08a STA: A.A. TOP: Quadratic Inequalities KEY: one variable

64 ID: A 87 ANS: PTS: REF: 0805a STA: A.A. TOP: Quadratic-Linear Systems KEY: equations 88 ANS:.. PTS: REF: 06a STA: A.A. TOP: Quadratic-Linear Systems KEY: equations 89 ANS:. PTS: REF: 00a STA: A.A. TOP: Quadratic-Linear Systems KEY: equations

65 ID: A 90 ANS:.. PTS: 6 REF: 069a STA: A.A. TOP: Quadratic-Linear Systems KEY: equations 9 ANS: PTS: REF: 0a STA: A.N. TOP: Operations with Polynomials 9 ANS: PTS: REF: 0a STA: A.N. TOP: Operations with Polynomials 9 ANS: The binomials are conjugates, so use FL. PTS: REF: 006a STA: A.N. TOP: Operations with Polynomials 9 ANS: The binomials are conjugates, so use FL. PTS: REF: 060a STA: A.N. TOP: Operations with Polynomials 95 ANS:. PTS: REF: 080a STA: A.N. TOP: Operations with Polynomials 96 ANS:. PTS: REF: 068a STA: A.N. TOP: Operations with Polynomials 97 ANS: PTS: REF: 0600a STA: A.N. TOP: Negative and Fractional Exponents

66 ID: A 98 ANS:. Flip sign when multiplying each side of the inequality by n, since a negative number. PTS: REF: 06a STA: A.N. TOP: Negative and Fractional Exponents 99 ANS: PTS: REF: 006a STA: A.A.8 TOP: Negative and Fractional Exponents 00 ANS: PTS: REF: 080a STA: A.A.8 TOP: Negative and Fractional Exponents 0 ANS: PTS: REF: fall09a STA: A.A.9 TOP: Negative and Fractional Exponents 0 ANS: PTS: REF: 060a STA: A.A.9 TOP: Negative Exponents 0 ANS: PTS: REF: 06a STA: A.A.9 TOP: Negative Exponents 0 ANS:. PTS: REF: 06a STA: A.A.9 TOP: Negative Exponents 05 ANS: PTS: REF: 0808a STA: A.A.9 TOP: Negative Exponents 06 ANS: PTS: REF: 0a STA: A.A.9 TOP: Negative Exponents 07 ANS: PTS: REF: 06a STA: A.A. TOP: Evaluating Exponential Expressions

67 ID: A 08 ANS:, PTS: REF: fall09a STA: A.A. TOP: Evaluating Exponential Expressions 09 ANS: PTS: REF: 069a STA: A.A. TOP: Evaluating Exponential Expressions 0 ANS: PTS: REF: fall0909a STA: A.A.8 TOP: Evaluating Logarithmic Expressions ANS: PTS: REF: 0a STA: A.A.8 TOP: Evaluating Logarithmic Expressions ANS: PTS: REF: 060a STA: A.A.5 TOP: Graphing Exponential Functions 5

68 ID: A ANS: PTS: REF: 0a STA: A.A.5 TOP: Graphing Exponential Functions ANS: PTS: REF: 00a STA: A.A.5 TOP: Graphing Exponential Functions 5 ANS: PTS: REF: fall096a STA: A.A.5 TOP: Graphing Logarithmic Functions 6 ANS: PTS: REF: 06a STA: A.A.5 TOP: Graphing Logarithmic Functions 7 ANS: PTS: REF: 06a STA: A.A.9 TOP: Properties of Logarithms KEY: splitting logs 8 ANS: PTS: REF: 060a STA: A.A.9 TOP: Properties of Logarithms KEY: splitting logs 9 ANS: PTS: REF: 0a STA: A.A.9 TOP: Properties of Logarithms KEY: splitting logs 0 ANS: PTS: REF: 0600a STA: A.A.9 TOP: Properties of Logarithms 6

69 ID: A ANS: PTS: REF: 0607a STA: A.A.9 TOP: Properties of Logarithms KEY: antilogarithms ANS: PTS: REF: 06a STA: A.A.9 TOP: Properties of Logarithms KEY: expressing logs algebraically ANS: PTS: REF: 0606a STA: A.A.8 TOP: Logarithmic Equations KEY: basic ANS: PTS: REF: fall09a STA: A.A.8 TOP: Logarithmic Equations KEY: advanced 5 ANS: PTS: REF: 07a STA: A.A.8 TOP: Logarithmic Equations KEY: advanced 7

70 ID: A 6 ANS: PTS: REF: 06a STA: A.A.8 TOP: Logarithmic Equations KEY: basic 7 ANS: PTS: 6 REF: 0809a STA: A.A.8 TOP: Logarithmic Equations KEY: basic 8 ANS: PTS: REF: 069a STA: A.A.8 TOP: Logarithmic Equations KEY: advanced 8

71 ID: A 9 ANS:.. PTS: 6 REF: 09a STA: A.A.8 TOP: Logarithmic Equations KEY: advanced 0 ANS: PTS: REF: 005a STA: A.A.6 TOP: Exponential Growth ANS: PTS: REF: 06a STA: A.A.6 TOP: Exponential Growth ANS: PTS: REF: 0a STA: A.A.6 TOP: Exponential Growth 9

72 ID: A ANS: PTS: REF: 067a STA: A.A.6 TOP: Exponential Growth ANS:. PTS: REF: 0605a STA: A.A.7 TOP: Exponential Equations KEY: common base shown 5 ANS:. PTS: REF: 0605a STA: A.A.7 TOP: Exponential Equations KEY: common base not shown 0

73 ID: A 6 ANS:. PTS: REF: 009a STA: A.A.7 TOP: Exponential Equations KEY: common base not shown 7 ANS:. PTS: REF: 08008a STA: A.A.7 TOP: Exponential Equations KEY: common base not shown 8 ANS: PTS: 6 REF: 069a STA: A.A.7 TOP: Exponential Equations KEY: common base not shown

74 ID: A 9 ANS: PTS: REF: 08a STA: A.A.7 TOP: Exponential Equations KEY: common base not shown 0 ANS: PTS: REF: 066a STA: A.A.6 TOP: Binomial Expansions ANS: PTS: REF: 05a STA: A.A.6 TOP: Binomial Expansions ANS: PTS: REF: fall099a STA: A.A.6 TOP: Binomial Expansions ANS: PTS: REF: 008a STA: A.A.6 TOP: Binomial Expansions ANS: PTS: REF: 065a STA: A.A.6 TOP: Binomial Expansions 5 ANS: PTS: REF: 06a STA: A.A.6 TOP: Binomial Expansions 6 ANS: PTS: REF: 00a STA: A.A.6 TOP: Solving Polynomial Equations

75 ID: A 7 ANS: PTS: REF: 06a STA: A.A.6 TOP: Solving Polynomial Equations 8 ANS: PTS: 6 REF: 069a STA: A.A.6 TOP: Solving Polynomial Equations 9 ANS:. PTS: REF: fall097a STA: A.A.6 TOP: Solving Polynomial Equations 50 ANS: PTS: REF: 06a STA: A.A.50 TOP: Solving Polynomial Equations 5 ANS: PTS: REF: 06005a STA: A.A.50 TOP: Solving Polynomial Equations 5 ANS: The roots are. PTS: REF: 080a STA: A.A.50 TOP: Solving Polynomial Equations

76 ID: A 5 ANS: PTS: REF: 0800a STA: A.N. TOP: Operations with Irrational Expressions KEY: without variables index = 5 ANS: PTS: REF: 060a STA: A.A. TOP: Simplifying Radicals KEY: index > 55 ANS: PTS: REF: 0a STA: A.A. TOP: Simplifying Radicals KEY: index > 56 ANS: PTS: REF: 09a STA: A.N. TOP: Operations with Radicals 57 ANS: PTS: REF: 060a STA: A.N. TOP: Operations with Radicals 58 ANS: PTS: REF: fall098a STA: A.A. TOP: Operations with Radicals KEY: with variables index = 59 ANS: PTS: REF: 0a STA: A.A. TOP: Operations with Radicals KEY: with variables index = 60 ANS: PTS: REF: 060a STA: A.N.5 TOP: Rationalizing Denominators

77 ID: A 6 ANS: PTS: REF: 066a STA: A.N.5 TOP: Rationalizing Denominators 6 ANS:. PTS: REF: fall098a STA: A.N.5 TOP: Rationalizing Denominators 6 ANS: PTS: REF: 0809a STA: A.A.5 TOP: Rationalizing Denominators KEY: index = 6 ANS: PTS: REF: 0a STA: A.A.5 TOP: Rationalizing Denominators KEY: index = 65 ANS: PTS: REF: 065a STA: A.A.5 TOP: Rationalizing Denominators KEY: index = 66 ANS:. is an extraneous solution. PTS: REF: 06a STA: A.A. TOP: Solving Radicals KEY: extraneous solutions 5

78 ID: A 67 ANS:. shows an extraneous solution. PTS: REF: 06a STA: A.A. TOP: Solving Radicals KEY: extraneous solutions 68 ANS: PTS: REF: 0608a STA: A.A. TOP: Solving Radicals KEY: extraneous solutions 69 ANS: 7. PTS: REF: 09a STA: A.A. TOP: Solving Radicals KEY: basic 70 ANS: PTS: 6 REF: 09a STA: A.A. TOP: Solving Radicals KEY: extraneous solutions 7 ANS: PTS: REF: 08a STA: A.A.0 TOP: Fractional Exponents as Radicals 7 ANS: PTS: REF: 060a STA: A.A.0 TOP: Fractional Exponents as Radicals 6

79 ID: A 7 ANS: PTS: REF: 0607a STA: A.A. TOP: Radicals as Fractional Exponents 7 ANS: PTS: REF: 06006a STA: A.N.6 TOP: Square Roots of Negative Numbers 75 ANS: PTS: REF: 0609a STA: A.N.7 TOP: Imaginary Numbers 76 ANS: PTS: REF: 0800a STA: A.N.7 TOP: Imaginary Numbers 77 ANS: PTS: REF: 068a STA: A.N.7 TOP: Imaginary Numbers 78 ANS: PTS: REF: 080a STA: A.N.8 TOP: Conjugates of Complex Numbers 79 ANS: PTS: REF: 0a STA: A.N.8 TOP: Conjugates of Complex Numbers 80 ANS: PTS: REF: 0a STA: A.N.8 TOP: Conjugates of Complex Numbers 8 ANS: PTS: REF: 069a STA: A.N.8 TOP: Conjugates of Complex Numbers 7

80 ID: A Algebra /Trigonometry Regents Exam Questions by Performance Indicator: Topic Answer Section 8 ANS: PTS: REF: fall090a STA: A.N.9 TOP: Multiplication and Division of Complex Numbers 8 ANS: PTS: REF: 07a STA: A.N.9 TOP: Multiplication and Division of Complex Numbers 8 ANS: PTS: REF: 069a STA: A.N.9 TOP: Multiplication and Division of Complex Numbers 85 ANS:. PTS: 6 REF: 09a STA: A.A.6 TOP: Multiplication and Division of Rationals KEY: division 86 ANS: PTS: REF: 066a STA: A.A.6 TOP: Multiplication and Division of Rationals KEY: division

81 ID: A 87 ANS: PTS: REF: 05a STA: A.A.6 TOP: Addition and Subtraction of Rationals 88 ANS: no solution. PTS: REF: fall090a STA: A.A. TOP: Solving Rationals KEY: rational solutions 89 ANS: PTS: REF: 0806a STA: A.A. TOP: Solving Rationals KEY: rational solutions 90 ANS:. PTS: REF: 066a STA: A.A. TOP: Solving Rationals KEY: irrational and complex solutions

82 ID: A 9 ANS: PTS: REF: fall090a STA: A.A.7 TOP: Complex Fractions 9 ANS: PTS: REF: 0605a STA: A.A.7 TOP: Complex Fractions 9 ANS: PTS: REF: 0605a STA: A.A.7 TOP: Complex Fractions 9 ANS: PTS: REF: 06a STA: A.A.5 TOP: Inverse Variation 95 ANS: PTS: REF: 0a STA: A.A.5 TOP: Inverse Variation

83 ID: A 96 ANS:. PTS: REF: 060a STA: A.A.5 TOP: Inverse Variation 97 ANS: PTS: REF: 00a STA: A.A.5 TOP: Inverse Variation 98 ANS: PTS: REF: fall097a STA: A.A.0 TOP: Functional Notation 99 ANS: PTS: REF: 060a STA: A.A. TOP: Functional Notation 00 ANS: PTS: REF: 06a STA: A.A. TOP: Functional Notation 0 ANS: PTS: REF: 09a STA: A.A.5 TOP: Families of Functions 0 ANS: PTS: REF: 09a STA: A.A.5 TOP: Properties of Graphs of Functions and Relations 0 ANS: PTS: REF: 0600a STA: A.A.5 TOP: Identifying the Equation of a Graph 0 ANS: PTS: REF: 0608a STA: A.A.5 TOP: Identifying the Equation of a Graph 05 ANS: PTS: REF: fall0908a STA: A.A.8 TOP: Defining Functions KEY: graphs 06 ANS: PTS: REF: 00a STA: A.A.8 TOP: Defining Functions KEY: graphs 07 ANS: PTS: REF: 06a STA: A.A.8 TOP: Defining Functions KEY: graphs 08 ANS: PTS: REF: 060a STA: A.A.8 TOP: Defining Functions

84 ID: A 09 ANS: PTS: REF: 005a STA: A.A.8 TOP: Defining Functions KEY: graphs 0 ANS: () and () fail the horizontal line test and are not one-to-one. Not every element of the range corresponds to only one element of the domain. () fails the vertical line test and is not a function. Not every element of the domain corresponds to only one element of the range. PTS: REF: 0800a STA: A.A. TOP: Defining Functions ANS: PTS: REF: 060a STA: A.A. TOP: Defining Functions ANS: PTS: REF: 05a STA: A.A. TOP: Defining Functions ANS: PTS: REF: 068a STA: A.A. TOP: Defining Functions ANS: () fails the horizontal line test. Not every element of the range corresponds to only one element of the domain. PTS: REF: fall0906a STA: A.A. TOP: Defining Functions 5 ANS: PTS: REF: fall09a STA: A.A.9 TOP: Domain and Range KEY: real domain 6 ANS: PTS: REF: 06a STA: A.A.9 TOP: Domain and Range KEY: real domain 7 ANS: PTS: REF: 0a STA: A.A.9 TOP: Domain and Range KEY: real domain 8 ANS: PTS: REF: 0a STA: A.A.9 TOP: Domain and Range KEY: real domain 9 ANS: PTS: REF: 060a STA: A.A.5 TOP: Domain and Range 0 ANS: PTS: REF: 0608ge STA: A.A.5 TOP: Domain and Range ANS: PTS: REF: 0800a STA: A.A.5 TOP: Domain and Range ANS: D:. R: PTS: REF: 0a STA: A.A.5 TOP: Domain and Range ANS:. PTS: REF: fall090a STA: A.A. TOP: Compositions of Functions KEY: numbers 5

85 ID: A ANS:. PTS: REF: 00a STA: A.A. TOP: Compositions of Functions KEY: numbers 5 ANS: PTS: REF: 009a STA: A.A. TOP: Compositions of Functions KEY: variables 6 ANS: PTS: REF: 066a STA: A.A. TOP: Compositions of Functions KEY: variables 7 ANS: 7... PTS: REF: 065a STA: A.A. TOP: Compositions of Functions KEY: numbers 8 ANS: PTS: REF: 0807a STA: A.A. TOP: Inverse of Functions KEY: equations 9 ANS:. is not a function. PTS: REF: 06a STA: A.A. TOP: Inverse of Functions KEY: equations 0 ANS: PTS: REF: fall096a STA: A.A.6 TOP: Transformations with Functions and Relations ANS: PTS: REF: 080a STA: A.A.6 TOP: Transformations with Functions and Relations ANS: PTS: REF: 0606a STA: A.A.9 TOP: Sequences ANS: common difference is. PTS: REF: 080a STA: A.A.9 TOP: Sequences 6

86 ID: A ANS: PTS: REF: 07a STA: A.A.9 TOP: Sequences 5 ANS: PTS: REF: 0600a STA: A.A.0 TOP: Sequences 6 ANS: PTS: REF: 00a STA: A.A.0 TOP: Sequences 7 ANS: PTS: REF: 00a STA: A.A. TOP: Sequences 8 ANS: PTS: REF: 066a STA: A.A. TOP: Sequences 9 ANS: PTS: REF: 0805a STA: A.A. TOP: Sequences 0 ANS: PTS: REF: 005a STA: A.A. TOP: Sequences ANS: PTS: REF: 0609a STA: A.A. TOP: Sequences ANS: PTS: REF: fall09a STA: A.A. TOP: Recursive Sequences 7

87 ID: A ANS:... PTS: REF: 06a STA: A.A. TOP: Recursive Sequences ANS: n 5 PTS: REF: 068a STA: A.N.0 TOP: Sigma Notation KEY: basic 5 ANS: PTS: REF: 065a STA: A.N.0 TOP: Sigma Notation KEY: basic 6 ANS: n 0 PTS: REF: fall09a STA: A.N.0 TOP: Sigma Notation KEY: basic 7 ANS: 0. PTS: REF: 0a STA: A.N.0 TOP: Sigma Notation KEY: basic 8 ANS:. PTS: REF: 00a STA: A.N.0 TOP: Sigma Notation KEY: basic 9 ANS: PTS: REF: 0605a STA: A.A. TOP: Sigma Notation 50 ANS: PTS: REF: 0605a STA: A.A. TOP: Sigma Notation 8

88 ID: A 5 ANS: PTS: REF: 0809a STA: A.A. TOP: Sigma Notation 5 ANS: PTS: REF: 060a STA: A.A.5 TOP: Summations KEY: geometric 5 ANS: PTS: REF: 00a STA: A.A.5 TOP: Summations KEY: arithmetic 5 ANS: PTS: REF: 060a STA: A.A.5 TOP: Series KEY: arithmetic 55 ANS:. PTS: REF: 08a STA: A.A.5 TOP: Summations KEY: arithmetic 56 ANS: PTS: REF: 060a STA: A.A.55 TOP: Trigonometric Ratios 9

89 ID: A 57 ANS: PTS: REF: 06a STA: A.A.55 TOP: Trigonometric Ratios 58 ANS: PTS: REF: 0800a STA: A.A.55 TOP: Trigonometric Ratios 59 ANS:. PTS: REF: 00a STA: A.A.55 TOP: Trigonometric Ratios 60 ANS: PTS: REF: 05a STA: A.A.55 TOP: Trigonometric Ratios 6 ANS: PTS: REF: 065a STA: A.M. TOP: Radian Measure 6 ANS: PTS: REF: 0800a STA: A.M. TOP: Radian Measure KEY: radians 6 ANS: PTS: REF: 0600a STA: A.M. TOP: Radian Measure KEY: degrees 6 ANS: PTS: REF: 00a STA: A.M. TOP: Radian Measure KEY: degrees 0

90 ID: A 65 ANS: PTS: REF: 060a STA: A.M. TOP: Radian Measure KEY: degrees 66 ANS: PTS: REF: 06a STA: A.M. TOP: Radian Measure KEY: radians 67 ANS: 97º0.. PTS: REF: fall09a STA: A.M. TOP: Radian Measure KEY: degrees 68 ANS: PTS: REF: 09a STA: A.M. TOP: Radian Measure KEY: degrees 69 ANS:. PTS: REF: 05a STA: A.M. TOP: Radian Measure KEY: degrees 70 ANS: PTS: REF: 08005a STA: A.A.60 TOP: Unit Circle 7 ANS: PTS: REF: 0606a STA: A.A.60 TOP: Unit Circle

91 ID: A 7 ANS: PTS: REF: 060a STA: A.A.60 TOP: Unit Circle 7 ANS: If,. If and, PTS: REF: 060a STA: A.A.60 TOP: Finding the Terminal Side of an Angle 7 ANS: PTS: REF: 0a STA: A.A.56 TOP: Determining Trigonometric Functions KEY: degrees, common angles 75 ANS: PTS: REF: 06a STA: A.A.56 TOP: Determining Trigonometric Functions KEY: degrees, common angles 76 ANS:... PTS: REF: fall09a STA: A.A.6 TOP: Determining Trigonometric Functions 77 ANS: PTS: REF: 065a STA: A.A.66 TOP: Determining Trigonometric Functions

92 ID: A 78 ANS: PTS: REF: 067a STA: A.A.66 TOP: Determining Trigonometric Functions 79 ANS: PTS: REF: 00a STA: A.A.66 TOP: Determining Trigonometric Functions 80 ANS: PTS: REF: 08007a STA: A.A.6 TOP: Using Inverse Trigonometric Functions KEY: basic 8 ANS: PTS: REF: 0a STA: A.A.6 TOP: Using Inverse Trigonometric Functions KEY: advanced 8 ANS:. PTS: REF: 06a STA: A.A.6 TOP: Using Inverse Trigonometric Functions KEY: advanced 8 ANS: PTS: REF: 00a STA: A.A.6 TOP: Using Inverse Trigonometric Functions KEY: unit circle 8 ANS: PTS: REF: 060a STA: A.A.57 TOP: Reference Angles 85 ANS: PTS: REF: fall09a STA: A.A.6 TOP: Arc Length KEY: arc length 86 ANS: PTS: REF: 06a STA: A.A.6 TOP: Arc Length KEY: arc length

93 ID: A 87 ANS: Cofunctions tangent and cotangent are complementary PTS: REF: 060a STA: A.A.58 TOP: Cofunction Trigonometric Relationships 88 ANS: PTS: REF: 06a STA: A.A.58 TOP: Reciprocal Trigonometric Relationships 89 ANS: PTS: REF: 060a STA: A.A.58 TOP: Reciprocal Trigonometric Relationships 90 ANS: PTS: REF: 06a STA: A.A.58 TOP: Reciprocal Trigonometric Relationships 9 ANS: PTS: REF: 00a STA: A.A.58 TOP: Cofunction Trigonometric Relationships 9 ANS:. If, then PTS: REF: 05a STA: A.A.59 TOP: Reciprocal Trigonometric Relationships 9 ANS: PTS: REF: 008a STA: A.A.67 TOP: Proving Trigonometric Identities 9 ANS: PTS: REF: 05a STA: A.A.67 TOP: Proving Trigonometric Identities 95 ANS: PTS: REF: fall090a STA: A.A.76 TOP: Angle Sum and Difference Identities KEY: simplifying

94 ID: A 96 ANS: PTS: REF: 0a STA: A.A.76 TOP: Angle Sum and Difference Identities KEY: evaluating 97 ANS: PTS: REF: 0807a STA: A.A.76 TOP: Angle Sum and Difference Identities KEY: evaluating 98 ANS: PTS: REF: 066a STA: A.A.76 TOP: Angle Sum and Difference Identities KEY: evaluating 99 ANS: PTS: REF: 08a STA: A.A.76 TOP: Angle Sum and Difference Identities KEY: identities 00 ANS: PTS: REF: 0609a STA: A.A.76 TOP: Angle Sum and Difference Identities KEY: identities 5

95 ID: A 0 ANS: PTS: REF: 060a STA: A.A.77 TOP: Double Angle Identities KEY: simplifying 0 ANS: PTS: REF: 007a STA: A.A.77 TOP: Double Angle Identities KEY: evaluating 0 ANS: PTS: REF: 0a STA: A.A.77 TOP: Double Angle Identities KEY: evaluating 0 ANS: If, then.. PTS: REF: 060a STA: A.A.77 TOP: Half Angle Identities 05 ANS: PTS: REF: 060a STA: A.A.68 TOP: Trigonometric Equations KEY: basic 6

96 ID: A 06 ANS:.. PTS: REF: fall090a STA: A.A.68 TOP: Trigonometric Equations KEY: basic 07 ANS: PTS: REF: 0a STA: A.A.68 TOP: Trigonometric Equations KEY: reciprocal functions 08 ANS: 5, 5 PTS: REF: 080a STA: A.A.68 TOP: Trigonometric Equations KEY: basic 09 ANS: PTS: REF: 06a STA: A.A.68 TOP: Trigonometric Equations KEY: reciprocal functions 7

97 ID: A 0 ANS: 0, 60, 80, 00. PTS: REF: 0607a STA: A.A.68 TOP: Trigonometric Equations KEY: double angle identities ANS: PTS: REF: 06a STA: A.A.69 TOP: Properties of Graphs of Trigonometric Functions ANS: KEY: period PTS: REF: 0607a STA: A.A.69 TOP: Properties of Graphs of Trigonometric Functions KEY: period ANS: PTS: REF: 00a STA: A.A.7 TOP: Identifying the Equation of a Trigonometric Graph ANS: PTS: REF: 0606a STA: A.A.7 TOP: Identifying the Equation of a Trigonometric Graph 5 ANS: PTS: REF: 07a STA: A.A.7 TOP: Identifying the Equation of a Trigonometric Graph 6 ANS:. The period of the function is, the amplitude is and it is reflected over the x-axis. PTS: REF: 065a STA: A.A.7 TOP: Identifying the Equation of a Trigonometric Graph 7 ANS: PTS: REF: 069a STA: A.A.65 TOP: Graphing Trigonometric Functions 8

98 ID: A 8 ANS: PTS: REF: fall09a STA: A.A.65 TOP: Graphing Trigonometric Functions 9 ANS: PTS: REF: 0806a STA: A.A.70 TOP: Graphing Trigonometric Functions KEY: recognize 0 ANS: PTS: REF: 0600a STA: A.A.7 TOP: Graphing Trigonometric Functions ANS: PTS: REF: 0a STA: A.A.7 TOP: Graphing Trigonometric Functions ANS: PTS: REF: 007a STA: A.A.7 TOP: Graphing Trigonometric Functions ANS: PTS: REF: 06a STA: A.A.6 TOP: Domain and Range ANS: PTS: REF: 060a STA: A.A.6 TOP: Domain and Range 5 ANS: PTS: REF: fall0907a STA: A.A.7 TOP: Using Trigonometry to Find Area KEY: basic 9