REVIEW FOR FINAL 2ND SEMESTER

Transcription

1 REVIEW FOR FINL 2N SEMESTER Multiple hoice Identify the choice that best completes the statement or answers the question. Simplify the given expression. ssume that no variable equals b. d. Simplify the given expression b. d. b. d. 4. b. d. 5. b. d. 6.

2 b. d. 7. Simplify the expression using long division. a. quotient and remainder 16 c. quotient and remainder 32 b. quotient and remainder 0 d. quotient and remainder a. quotient and remainder 26 c. quotient and remainder 14 b. quotient and remainder 4 d. quotient and remainder Find and for the function. a. 6,555; 12,255 c. 6,584; 12,280 b. 6,585; 12,279 d. 185; 221 For the given graph, a. describe the end behavior, b. determine whether it represents an odd-degree or even-degree polynomial function, and c. state the number of real zeros f(x) x a. The end behavior of the graph is as and as. It is an odd-degree polynomial function. The function has three real zeros. b. The end behavior of the graph is as and as. It is an odd-degree polynomial function. The function has three real zeros. c. The end behavior of the graph is as and as. It is an odd-degree polynomial function. The function has four real zeros. d. The end behavior of the graph is as and as. It is an even-degree polynomial function. The function has three real zeros.

3 f(x) x a. The end behavior of the graph is as and as. It is an even-degree polynomial function. The function has two real zeros. b. The end behavior of the graph is as and as. It is an odd-degree polynomial function. The function has two real zeros. c. The end behavior of the graph is as and as. It is an even-degree polynomial function. The function has three real zeros. d. The end behavior of the graph is as and as. It is an even-degree polynomial function. The function has two real zeros. 30 f(x) x a. The end behavior of the graph is as and as. It is an odd-degree polynomial function. The function has three real zeros. b. The end behavior of the graph is as and as. It is an odd-degree polynomial function. The function has four real zeros.

4 c. The end behavior of the graph is as and as. It is an even-degree polynomial function. The function has three real zeros. d. The end behavior of the graph is as and as. It is an odd-degree polynomial function. The function has three real zeros. 13. Graph the function by making a table of values. a. f(x) c. f(x) x x b. f(x) d f(x) x x Graph the function by making a table of values.

5 a. f(x) c f(x) x x b. f(x) d f(x) x x For the given function, determine consecutive values of x between which each real zero is located. 15. a. There is a zero between x = 0 and x = 1. b. There is a zero between x = 0 and x = 1. c. There are zeros between x = 1 and x = 0, x = 0 and x = 1. d. There are zeros between x = 2 and x = 3, x = 1 and x = 2, x = 1 and x = 2, x = 1 and x = 2, x = 2 and x = 3. Estimate the x-coordinates at which the relative maxima and relative minima occur for the function. 16. a. The relative maximum is at, and the relative minimum is at. b. The relative maximum is at, and the relative minimum is at. c. The relative maximum is at, and the relative minimum is at. d. The relative maximum is at, and the relative minimum is at. Factor the polynomial completely. 17.

6 18. b. d. b. d. Solve the given equation. State the number and type of roots. 19. a. The equation has two real roots, and 4. b. The equation has two real roots, and 4. c. The equation has two real roots, 2 and 4. d. The equation has two real roots, 2 and a. The equation has two real roots, and 10. b. The equation has two real roots, 1 and 10. c. The equation has two real roots, 1 and 10. d. The equation has two real roots, and Find all the rational zeros of the function a. c., b., 0,, d., 0,,, 0.(calculator) 22. Find for the following functions. 23. Find b. d. for the following functions. 24. Find b. d. for the following functions. b. d. 25. Find for the following functions.

7 a., c., b., d., 26. Find for the following functions. a., c., b., d., Find the inverse of the given relation. 27. a. b. c. d. 28. b. d. 29. etermine whether each pair of functions are inverse functions. 1) 2) a. Only 2 is an inverse function. b. Only 1 is an inverse function. c. Neither 1 nor 2 is an inverse function. d. oth 1 and 2 are inverse functions. 30. Simplify. b. d. 31. Simplify.

8 b. d. Simplify. 32. b. d. 33. b. d. 34. b. d. 35. b. d. Write the given radical using rational exponents. 36. b. d. Simplify each expression. 37. b. d.

9 38. b. d. Solve the given equation. 39. a. 104 c. 9 b. 34 d a c b d a c. 0.1 b d a. b. n = n = c. 8 n = 9 d. n = 7 Solve the given inequality a. 312 c. 96 b. 4 d. 6 a. n < 3 c. n < 9 b. 9 d. 27 n < n < 5 5 Simplify the given expression b. d.

10 b. d. 47. b. d. etermine the equations of any vertical asymptotes and the values of x for any holes in the graph of the rational function. 48. a. asymptotes: ; hole: b. asymptotes: ; hole: c. asymptotes: ; hole: d. asymptotes: ; hole: Graph the rational function. 49. f(x) = a. y c y x x

11 b. y d y x x If y varies directly as x and when, find y when. a. 168 c. 168 b. 16,800 d. 16, If y varies directly as x and when, find y when. a. 1,400 c b. 2,240 d Suppose y varies jointly as x and z. Find y when x = 2 and z = 11, if y = 160 when x = 3 and z = 8. Round your answer to the nearest hundredth, if necessary. a. 1, c b d Suppose y varies jointly as x and z. Find y when and, if when and. Round your answer to the nearest hundredth, if necessary. a. 3, c b d If y varies inversely as x and when, find y when. Round your answer to the nearest hundredth, if necessary. a c b d In order to sustain itself in its cold habitat, a Siberian tiger requires 25 pounds of meat per day. 55. Write an equation to represent the amount of meat needed m to sustain x Siberian tigers for d days. b. d. 56. How much meat would seven Siberian tigers need for the month of pril? a. 750 pounds c pounds b. 175 pounds d pounds It has been found that the average number of daily phone calls between two cities is directly proportional to the product of the populations and of the two cities and inversely proportional to the square of the distance d between the cities. That is,.

12 57. The distance between lbany, New York, and leveland, Ohio, is about 480 miles. If the average number of daily phone calls between the cities is 250,000, find the value of k and write the equation of variation. Round to the nearest thousandth. The population of lbany and leveland is 95,000 and 2,900,000 respectively. a c b d The average merican drinks about eight servings of hydrated beverages everyday. 58. Each member of a household of four members drinks the same amount of hydrated beverages each day as the average merican. How many servings of hydrated beverages (w) would the members of the household consume in a week? a. 28 c. 224 b. 32 d Monica runs on a treadmill at an average speed of 7.5 miles per hour for 15 minutes. If, the next day, she runs the same distance at a speed of 8 miles per hour, what is the average time taken? a minutes c. 16 minutes b minutes d minutes 60. Many areas of Northern alifornia depend on the snowpack of the Sierra Nevada Mountains for their water supply. If 300 cubic centimeters of snow will melt to 33 cubic centimeters of water, how much water does 600 cubic centimeters of snow produce? a cubic centimeters c cubic centimeters b. 66 cubic centimeters d cubic centimeters Identify the type of function represented by the graph y x a. absolute value function c. square root function b. constant function d. direct variation function

13 y x a. square root function c. constant function b. quadratic function d. identity function 8 7 y x 1 a. absolute value function c. rational function b. quadratic function d. inverse variation function 64. Identify the type of function represented by the equation y = x. a. inverse variation function c. identity function b. constant function d. absolute value function Identify the type of function represented by the equation a. absolute value function c. inverse variation function b. direct variation function d. identity function 66. y = 8x a. absolute value function c. constant function

14 b. identity function d. direct variation function a. absolute value function c. constant function b. inverse variation function d. direct variation function a. quadratic function c. rational function b. identity function d. absolute value function a. absolute value function c. identity function b. direct variation function d. constant function a. absolute value function c. direct variation function b. inverse variation function d. identity function Solve the inequality. heck your solution. 71. b. d. 72. b. or d. or Sketch the graph of the given function. Then state the function s domain and range. 73. y = 1.2(3) x a. 5 y c. 5 y x x The domain is all real numbers and the range is all negative numbers. The domain is all real numbers and the range is all positive numbers.

15 b. 5 y d. 5 y x x The domain is all real numbers and the range is all negative numbers. 74. y = 2(4) x a. y c. The domain is all real numbers and the range is all positive numbers y x x b. The domain is all real numbers and the range is all real numbers. y 60 d. The domain is all real numbers and the range is all positive numbers. y x x The domain is all real numbers and the range is all positive numbers. The domain is all real numbers and the range is all positive numbers. 75. Use and to approximate the value of the expression.

16 a c. 8 b. 2,304 d Solve the given equation. If necessary, round to four decimal places a. 26 c b d. 4 a c b d Solve the given inequality. If necessary, round to four decimal places b. d. a. a < c. a < b. a < d. a < Express the given logarithm in terms of common logarithms. Then approximate its value to four decimal places. 80. a. ; c. ; b. ; d. ; a. ; c. ; b. ; d. ; Evaluate the expression. a. e c. b. d. 2 Solve the given equation. Round to the nearest ten-thousandth, if necessary a c. 1.5 b d. 0 a. 1.4 c b d

17 Solve the given inequality. Round to the nearest ten-thousandth, if necessary. 85. b. d. 86. Eros Industries bought a laser printer for $3400. It is expected to depreciate at a rate of 12% per year. What will the value of the printer be in 3 years? Round to the nearest dollar. a. $2317 c. $4777 b. $2992 d. $ Kronos Industries bought a desktop for $3000. It is expected to depreciate at a rate of 10% per year. What will the value of the desktop be in 4 years? Round to the nearest dollar. a. $1968 c. $2700 b. $2057 d. $ Ray Industries bought a touch screen monitor for $1200. It is expected to depreciate at a rate of 25% per year. What will the value of the monitor be in 3 years? Round to the nearest dollar. a. $142 c. $900 b. $506 d. $ Merlin Industries bought a laptop for $2100. It is expected to depreciate at a rate of 14% per year. What will the value of the laptop be in 5 years? Round to the nearest dollar. a. $912 c. $1806 b. $988 d. $ n anthropologist finds there is so little arbon-14 remaining in a prehistoric bone that instruments cannot measure it. This means there is less than 0.2% of the amount of arbon-14 the bones would have contained when the person was alive. How long ago did the person die? (The constant for arbon-14 is ) a. 13,411 years c. 45,020 years b. 22,491 years d. 51,788 years 91. paleontologist finds a bone that might be a sauropod s bone. In the laboratory, she finds that the arbon-14 found in the bone is of that found in a living bone tissue. ould this bone have belonged to a sauropod? Explain your reasoning. (Hint: The sauropods lived from 200 million years ago to 145 million years ago. The constant for arbon-14 is ) a. No, because the amount of arbon-14 found indicates a period before the sauropods even came into existence. b. No, because the amount of arbon-14 found indicates a period after the sauropods became extinct. c. Yes, because the number of years calculated is in the range of 200 million years and 145 million years ago. d. Yes, because the amount of arbon-14 found in the bone is one-tenth of that found in a living bone tissue. 92. Radioactive iodine is used to determine the health of thyroid gland. It decays according to the equation, where t is in days. Find the one-fourth life of this substance. Round to the nearest integer. a. 2 c. 16 b. 7 d The Freeman family bought a new apartment five years ago for $80,000. The apartment is now worth $199,200. ssuming a steady rate of growth, what was the yearly rate of appreciation? a. 19.1% c. 23% b. 20% d. 24.9%

18 The Gross National Product (GNP) is the value of all the goods and services produced in an economy, plus the value of the goods and services imported, less the goods and services exported. uring the period , the GNP of anada grew about 4.8% per year, measured in 2003 dollars. In 1994, the GNP was $5.9 billion. 94. ssuming this rate of growth continues, in what year will the GNP reach $10 trillion? a c b d National Income (NI) is the sum of the incomes that all individuals in an economy earn in the forms of wages, interest, rents, and profits. It excludes government transfer payments and is calculated before any deductions are taken for income taxes. uring the period , the NI of ustralia grew about 5.2% per year, measured in 2003 U.S. dollars. In 1994, the NI was $4 billion. 95. ssuming this rate of growth continues, what will the NI of ustralia be (in billions) in the year 2015? a. $52.48 c. $11.60 b. $33.88 d. $ ssuming this rate of growth continues, in what year will the NI reach $15 trillion? a c b d acteria usually reproduce by a process called binary fission. In this type of reproduction, one bacterium divides to form two bacteria. Under ideal conditions, some bacteria reproduce every 15 minutes. 97. Find the constant k for this type of bacteria under ideal conditions. a c b d Solve by using the measurements,, and. Round measures of sides to the nearest tenth and measures of angles to the nearest degree. P r q Q p R a.,, c.,, b.,, d.,, 99. The upper part of a tree, broken by wind, makes an angle of 38º with the ground. The horizontal distance from the root of the tree to the point where the top of the tree meets the ground is 20 meters. Find the height of the tree before it was broken.

19 a m c m b m d m 100. Two boys are on opposite sides of a tower. They sight the top of the tower at 33º and 24º angles of elevation respectively. If the height of the tower is 100 m, find the distance between the two boys. a m c m b m d m 101. In a tourist bus near the base of Eiffel Tower at Paris, a passenger estimates the angle of elevation to the top of the tower to be 60. If the height of Eiffel Tower is about 984 feet, what is the distance from the bus to the base of the tower? a. 492 feet c feet b feet d feet 102. kite at a height of 75 meters from the ground is attached to a string inclined at to the horizontal. Find the length of the string to the nearest meter. a. 43 m c. 130 m b. 87 m d. 150 m 103. preprogrammed workout on a treadmill consists of intervals walking at various rates and angles of incline. 1% incline means 10 units of vertical rise for every 100 units of horizontal run. If the treadmill bed is 32 inches long, what is the vertical rise when set at a 4% incline? a in. c in. b. 5 in. d. 80 in preprogrammed workout on a treadmill consists of intervals walking at various rates and angles of incline. 2% incline means 2 units of vertical rise for every 100 units of horizontal run. t what angle, with respect to the horizontal, is the treadmill bed when set to a 20% incline? Round to the nearest degree. a. 4 c. 11 b. 6 d. 20 Find the value of the given trigonometric function b. d b. d. 2 Find the exact values of the remaining five trigonometric functions of θ Suppose θ is an angle in the standard position whose terminal side is in Quadrant III and. a.,,,, and b.,,,, and

20 c. d.,,,, and,,,, and 108. Suppose θ is an angle in the standard position whose terminal side is in Quadrant III and csc. a.,,,, and b. c. d.,,,, and,,,, and,,,, and 109. Suppose θ is an angle in the standard position whose terminal side is in Quadrant IV and. a.,,,, b. c. d.,,,,,,,,,,,, 110. Suppose θ is an angle in the standard position whose terminal side is in Quadrant IV and. a.,,,, b. c. d.,,,,,,,,,,,, 111. Suppose θ is an angle in the standard position whose terminal side is in Quadrant II and. a. b.,,,,,,,,

21 c. d.,,,,,,,, Solve the given triangle. Round the measures of sides to the nearest tenth and measures of angles to the nearest degree R p q Q r P,, a.,, c.,, b.,, d.,, The given point P is located on the unit circle. Find and a. ; c. ; b. ; d. ;

22 114. a. ; c. ; b. ; d. ; 115. Find the exact value of the function. a. 1 c. b. d Solve x = rctan 3 by finding the value of x to the nearest degree. a. 72 c b d Solve x = Sin 1 2 by finding the value of x to the nearest degree. a. 60 c b. 30 d Find the value of cot (os 2 ). Round to the nearest hundredth. 3 a c b d Find the value of cos (Sin 7 ). Round to the nearest hundredth. 20 a c b d. 1.21

23 REVIEW FOR FINL 2 SEMESTER nswer Section MULTIPLE HOIE 1. NS: Multiply the constants and then multiply the powers using the Power of a Product Property. Multiply the powers of the same variable using the Power of a Product Property. Multiply the constants. simplified expression cannot contain negative exponents. PTS: 1 IF: asic REF: Lesson 6-1 OJ: Use properties of exponents to multiply monomials. NT: N 1 N 7 N 8 N 10 N 2 ST: IL J 6.2 IL J 6 TOP: Use properties of exponents to multiply monomials. KEY: Monomials Multiply Monomials 2. NS: Use the istributive Property and then multiply the monomials using the Product of Powers Property. id you use the istributive Property? id you multiply the monomials correctly? id you calculate the product of powers correctly? PTS: 1 IF: verage REF: Lesson 6-2 OJ: Multiply polynomials. NT: N 1 N 6 N 8 N 10 N 2 ST: IL J 6.2 IL J 6 TOP: Multiply polynomials. KEY: Polynomials Multiply Polynomials 3. NS: Use the istributive Property and then multiply the monomials using the Product of Powers Property. id you multiply the monomials correctly? id you distribute the terms correctly? id you use the Product of Powers Property? PTS: 1 IF: verage REF: Lesson 6-2 OJ: Multiply polynomials. NT: N 1 N 6 N 8 N 10 N 2 ST: IL J 6.2 IL J 6 TOP: Multiply polynomials. KEY: Polynomials Multiply Polynomials 4. NS: First, multiply the values and then divide the numerator and the denominator by the common factors. ivide the denominator by x, not x 2. ivide the numerator also with y.

24 id you multiply accurately? PTS: 1 IF: verage REF: Lesson 8-1 OJ: Simplify rational expressions with multiplication. NT: N 2 N 8 N 9 N 10 N 6 ST: IL J 8.7 TOP: Simplify rational expressions with multiplication. KEY: Rational Expressions Multiply Rational Expressions 5. NS: To divide two rational expressions, multiply by the reciprocal of the divisor. id you perform all the mathematical actions? id you divide correctly? To simplify the values, divide the denominator by b 3, not by b 4. PTS: 1 IF: verage REF: Lesson 8-1 OJ: Simplify rational expressions with division. NT: N 2 N 8 N 9 N 10 N 6 ST: IL J 8.7 TOP: Simplify rational expressions with division. KEY: Rational Expressions ivide Rational Expressions 6. NS: Express the question as a division expression, and then multiply by the reciprocal of the divisor. The numerator and the denominator are interchanged. id you eliminate all the common factors? id you simplify correctly? PTS: 1 IF: verage REF: Lesson 8-1 OJ: Simplify complex fractions. NT: N 2 N 8 N 9 N 10 N 6 ST: IL J 8.7 TOP: Simplify complex fractions. KEY: omplex Fractions 7. NS: Use the division algorithm. When dividing, you can add or subtract only similar terms. id you consider both the terms of the divisor? hange the signs of the product terms only. id you use the correct signs of the terms? PTS: 1 IF: dvanced REF: Lesson 6-3 OJ: ivide polynomials using long division. NT: N 1 N 6 N 7 N 9 N 2 ST: IL J 6.2 IL J 8.7 IL J 6 TOP: ivide polynomials using long division. KEY: Polynomials ivide Polynomials Long ivision 8. NS: Use the division algorithm. When dividing, you can add or subtract only similar terms.

25 id you consider both the terms of the divisor? hange the signs of the product terms only. id you multiply the divisor with the correct term? PTS: 1 IF: dvanced REF: Lesson 6-3 OJ: ivide polynomials using long division. NT: N 1 N 6 N 7 N 9 N 2 ST: IL J 6.2 IL J 8.7 IL J 6 TOP: ivide polynomials using long division. KEY: Polynomials ivide Polynomials Long ivision 9. NS: Replace the values of p(x) and simplify. id you substitute the correct values in the function? dd the value of the constant. The exponent value of the first term is 5, not 4. PTS: 1 IF: verage REF: Lesson 6-4 OJ: Evaluate polynomial functions. NT: N 1 N 7 N 8 N 10 N 2 ST: IL J 8 TOP: Evaluate polynomial functions. KEY: Polynomial Functions 10. NS: The end behavior is the behavior of the graph as x approaches positive infinity or negative infinity. The x-coordinate of the point at which the graph intersects the x-axis is called the zero of the function. What is the end behavior of the graph? id you verify the number of real zeros? heck the degree of the polynomial function. PTS: 1 IF: asic REF: Lesson 6-4 OJ: Identify general shapes of graphs of polynomial functions. NT: N 1 N 7 N 8 N 10 N 2 ST: IL J 8.2 IL J 8 TOP: Identify general shapes of graphs of polynomial functions. KEY: Polynomial Functions Graph Polynomial Functions 11. NS: The end behavior is the behavior of the graph as x approaches positive infinity or negative infinity. The x-coordinate of the point at which the graph intersects the x-axis is called the zero of the function. What is the end behavior of the graph? heck the degree of the polynomial function. id you verify the number of real zeros? PTS: 1 IF: asic REF: Lesson 6-4 OJ: Identify general shapes of graphs of polynomial functions. NT: N 1 N 7 N 8 N 10 N 2 ST: IL J 8.2 IL J 8 TOP: Identify general shapes of graphs of polynomial functions.

26 KEY: Polynomial Functions Graph Polynomial Functions 12. NS: The end behavior is the behavior of the graph as x approaches positive infinity or negative infinity. The x-coordinate of the point at which the graph intersects the x-axis is called the zero of the function. id you verify the number of real zeros? heck the degree of the polynomial function. What is the end behavior of the graph? PTS: 1 IF: asic REF: Lesson 6-4 OJ: Identify general shapes of graphs of polynomial functions. NT: N 1 N 7 N 8 N 10 N 2 ST: IL J 8.2 IL J 8 TOP: Identify general shapes of graphs of polynomial functions. KEY: Polynomial Functions Graph Polynomial Functions 13. NS: Make a table of values and plot the graph. id you use the correct equation to plot the graph? id you plot the correct graph? The degree of the polynomial is 5, not 4. PTS: 1 IF: verage REF: Lesson 6-5 OJ: Graph polynomial functions. NT: N 1 N 6 N 9 N 10 N 2 ST: IL J 8.2 IL J 8 TOP: Graph polynomial functions. KEY: Polynomial Functions Graph Polynomial Functions 14. NS: Make a table of values and plot the graph. id you plot the graph correctly? The degree of the polynomial is 4, not 3. id you use the correct equation to plot the graph? PTS: 1 IF: verage REF: Lesson 6-5 OJ: Graph polynomial functions. NT: N 1 N 6 N 9 N 10 N 2 ST: IL J 8.2 IL J 8 TOP: Graph polynomial functions. KEY: Polynomial Functions Graph Polynomial Functions 15. NS: Make a table of values to obtain the required answer. id you locate all the real zeros? You have obtained only some of the real zeros. oes the sign of the polynomial change between these consecutive values?

27 PTS: 1 IF: dvanced REF: Lesson 6-5 OJ: Locate real zeros of polynomial functions. NT: N 1 N 6 N 9 N 10 N 2 ST: IL J 8.4 IL J 8 TOP: Locate real zeros of polynomial functions. KEY: Polynomial Functions Zeroes of Polynomial Functions 16. NS: Make a table of values and graph the equation. relative minimum is a point that has no nearby points with a lesser y-coordinate. id you obtain the correct value of the relative maximum? id you find the correct coordinates of the function? PTS: 1 IF: verage REF: Lesson 6-5 OJ: Find the maxima and minima of polynomial functions. NT: N 1 N 6 N 9 N 10 N 2 ST: IL J 8.4 IL J 8 TOP: Find the maxima and minima of polynomial functions. KEY: Maxima of Polynomial Functions Minima of Polynomial Functions 17. NS: Group the monomials to find the GF (greatest common factor), factor the GF of each binomial, and then use the istributive Property to obtain the factors. Group the polynomial into binomials to find the GF. Factor the GF of each binomial. Use the istributive Property. PTS: 1 IF: verage REF: Lesson 6-6 OJ: Factor polynomials by grouping. NT: N 1 N 3 N 9 N 10 N 2 ST: IL J 6.2 IL J 8.7 IL J 6 TOP: Factor polynomials by grouping. KEY: Polynomials Factor Polynomials 18. NS: To find the coefficient of the x terms, find two numbers whose product is or 36 and whose sum is 13. Factor the GF of each group. The product of the coefficient of the x terms should be equal to the product of the coefficient of the x 2 term and the constant term. Use the istributive Property to obtain two binomial factors. PTS: 1 IF: dvanced REF: Lesson 6-6 OJ: Factor polynomials with addition recognizing the FOIL method. NT: N 1 N 3 N 9 N 10 N 2 ST: IL J 6.2 IL J 8.7 IL J 6 TOP: Factor polynomials with addition by recognizing the FOIL method. KEY: Polynomials Factor Polynomials FOIL Method 19. NS: Factor the equation and find the roots.

28 id you factor correctly? You have calculated the incorrect roots. id you calculate correctly? PTS: 1 IF: verage REF: Lesson 6-8 OJ: etermine the number and types of roots for a polynomial equation. NT: N 1 N 3 N 4 N 7 N 2 ST: IL J 8 TOP: etermine the number and types of roots for a polynomial equation. KEY: Polynomial Equations Roots Real Roots 20. NS: Factor the equation and find the roots. You have obtained the incorrect roots. id you calculate correctly? id you factor correctly? PTS: 1 IF: verage REF: Lesson 6-8 OJ: etermine the number and types of roots for a polynomial equation. NT: N 1 N 3 N 4 N 7 N 2 ST: IL J 8 TOP: etermine the number and types of roots for a polynomial equation. KEY: Polynomial Equations Roots Real Roots 21. NS: Use the Rational Zero Theorem. You must also include the positive rational zeros in the answer. id you apply the Rational Zero Theorem correctly? You must also include the negative rational zeros in the answer. PTS: 1 IF: verage REF: Lesson 6-9 OJ: Find all the rational zeros of a polynomial function. NT: N 1 N 3 N 4 N 7 N 2 ST: IL J 8.4 IL J 8 IL J 8 TOP: Find all the rational zeros of a polynomial function. KEY: Polynomial Functions Zeroes of Polynomial Functions 22. NS: Subtract g(x) from f(x) to obtain the required answer. id you find the value of the correct function? heck the calculation. id you subtract the functions correctly? PTS: 1 IF: verage REF: Lesson 7-1

29 OJ: Find the difference of functions. NT: N 1 N 6 N 7 N 10 N 2 ST: IL J 8.6 TOP: Find the difference of functions. KEY: Functions ifference of Functions 23. NS: Multiply f(x) and g(x) to obtain the required answer. The answer has an incorrect operator. You have multiplied the two functions incorrectly. id you check the calculations? PTS: 1 IF: verage REF: Lesson 7-1 OJ: Find the product of functions. NT: N 1 N 6 N 7 N 10 N 2 ST: IL J 8.6 TOP: Find the product of functions. KEY: Functions Product of Functions 24. NS: Multiply f(x) and g(x) to obtain the required answer. id you check the calculations? You have multiplied the two functions incorrectly. The answer has an incorrect operator. PTS: 1 IF: verage REF: Lesson 7-1 OJ: Find the product of functions. NT: N 1 N 6 N 7 N 10 N 2 ST: IL J 8.6 TOP: Find the product of functions. KEY: Functions Product of Functions 25. NS: ivide f(x) by g(x) to obtain the required answer. What is the solution of the function? id you include the correct sign in the answer? id you calculate correctly? PTS: 1 IF: verage REF: Lesson 7-1 OJ: Find the quotient of functions. NT: N 1 N 6 N 7 N 10 N 2 ST: IL J 8.6 TOP: Find the quotient of functions. KEY: Functions Quotient of Functions 26. NS: ivide f(x) by g(x) to obtain the required answer. What is the solution of the function? id you include the correct sign in the answer? id you calculate correctly? PTS: 1 IF: verage REF: Lesson 7-1 OJ: Find the quotient of functions. NT: N 1 N 6 N 7 N 10 N 2 ST: IL J 8.6

30 TOP: Find the quotient of functions. KEY: Functions Quotient of Functions 27. NS: The inverse relation is the set of ordered pairs obtained by reversing the coordinates of each original ordered pair. Write the inverse of all the ordered pairs in the relation. id you write all the values with the correct sign? id you check the sign of all the values? PTS: 1 IF: asic REF: Lesson 7-2 OJ: Find the inverse of a relation. NT: N 1 N 3 N 4 N 7 N 2 ST: IL J 8.6 IL J 8 TOP: Find the inverse of a relation. KEY: Relations Inverses of Relations 28. NS: The inverse relation is the set of ordered pairs obtained by reversing the coordinates of each original ordered pair. Write the inverse of all the ordered pairs in the relation. id you write all the values with the correct sign? id you check the sign of all the values? PTS: 1 IF: asic REF: Lesson 7-2 OJ: Find the inverse of a relation. NT: N 1 N 3 N 4 N 7 N 2 ST: IL J 8.6 IL J 8 TOP: Find the inverse of a relation. KEY: Relations Inverses of Relations 29. NS: Two functions f and g are inverse functions if and only if both of their compositions are the identity function. id you find both compositions in each pair? How will you determine whether a pair of functions are inverse functions? The composition of the second pair of functions is not an identity function. PTS: 1 IF: verage REF: Lesson 7-2 OJ: etermine whether two functions or relations are inverses. NT: N 1 N 3 N 4 N 7 N 2 ST: IL J 8.6 IL J 8 TOP: etermine whether two functions or relations are inverses. KEY: Functions Inverses of Functions 30. NS: Factor into squares where possible. Use the Product Property of Radicals to simplify. id you use the Product Property of Radicals? Factor terms in the radicand into squares if possible and then use the Product Property of Radicals. Write all the terms left in the radicand also.

31 PTS: 1 IF: verage REF: Lesson 7-5 OJ: Simplify radical expressions with multiplication. NT: N 1 N 7 N 9 N 10 N 2 ST: IL J 6.2 IL J 6 TOP: Simplify radical expressions with multiplication. KEY: Radical Expressions Simplify Radical Expressions 31. NS: Factor into squares where possible. Use the Product Property of Radicals to simplify. id you use the Product Property of Radicals? Write all the terms left in the radicand also. Factor terms in the radicand into squares if possible and then use the Product Property of Radicals. PTS: 1 IF: verage REF: Lesson 7-5 OJ: Simplify radical expressions with multiplication. NT: N 1 N 7 N 9 N 10 N 2 ST: IL J 6.2 IL J 6 TOP: Simplify radical expressions with multiplication. KEY: Radical Expressions Simplify Radical Expressions 32. NS: Find the principal square root of each term of the radicand and simplify the expression. heck the sign between the two radicals. heck for the interchanged digits before the radicals. ompute again and check the sign. PTS: 1 IF: verage REF: Lesson 7-5 OJ: dd and subtract radical expressions. NT: N 1 N 7 N 9 N 10 N 2 ST: IL J 6.2 IL J 6 TOP: dd and subtract radical expressions. KEY: Radical Expressions 33. NS: Find the square of the expression and simplify for the same radicands and numbers. heck the sign between the first number and the radical. You have to add the square of the radicals. You have not computed the square correctly. PTS: 1 IF: verage REF: Lesson 7-5 OJ: Multiply radical expressions. NT: N 1 N 7 N 9 N 10 N 2 ST: IL J 6.2 IL J 6 TOP: Multiply radical expressions. KEY: Radical Expressions 34. NS: Multiply the numerator and denominator by the conjugate of the denominator and simplify.

32 The radical multiplication is not correct. You have not multiplied the numerator by the conjugate of the denominator. heck your work and try again. PTS: 1 IF: verage REF: Lesson 7-5 OJ: ivide radical expressions. NT: N 1 N 7 N 9 N 10 N 2 ST: IL J 6.2 IL J 6 TOP: ivide radical expressions. KEY: Radical Expressions 35. NS: Multiply the numerator and denominator by the conjugate of the denominator and simplify. You have not multiplied the denominator by its conjugate. You have not multiplied the numerator by the conjugate of the denominator. heck your work and try again. PTS: 1 REF: Lesson 7-5 OJ: ivide radical expressions. NT: N 1 N 7 N 9 N 10 N 2 ST: IL J 6.2 IL J 6 TOP: ivide radical expressions. KEY: Radical Expressions 36. NS: For any real number b and any positive integer n,. id you use the Property of Powers correctly? Use the definition of on each term of the radicand. id you apply the Property of Powers to each term of the radicand? PTS: 1 IF: verage REF: Lesson 7-6 OJ: Write radical expressions as expressions with rational exponents. NT: N 1 N 6 N 8 N 9 N 2 ST: IL J 6 TOP: Write radical expressions as expressions with rational exponents. KEY: Rational Exponents Radical Expressions 37. NS: Use and simplify the results. id you subtract the powers correctly? Find a common denominator and subtract the powers. You have to subtract the powers.

33 PTS: 1 IF: verage REF: Lesson 7-6 OJ: Simplify expressions in exponential form. NT: N 1 N 6 N 8 N 9 N 2 ST: IL J 6 TOP: Simplify expressions in exponential form. KEY: Exponential Form 38. NS: For any real number b and any positive integer n,. You have not calculated the nth root correctly. Look at the nth root. Remember. PTS: 1 IF: verage REF: Lesson 7-6 OJ: Simplify expressions in radical form. NT: N 1 N 6 N 8 N 9 N 2 ST: IL J 6 TOP: Simplify expressions in radical form. KEY: Radical Form 39. NS: Isolate the radical in the original equation, and raise each side of the equation to the power equal to the index of the radical to eliminate the radical. heck the solution obtained by substituting the value of x in the original equation. id you isolate the radical? Isolate the radical by adding or subtracting the term without the radical from both the sides. Raise each side of the equation to the power equal to the index of the radical. PTS: 1 IF: verage REF: Lesson 7-7 OJ: Solve equations containing radicals. NT: N 1 N 6 N 9 N 10 N 2 ST: IL J 8 TOP: Solve equations containing radicals. KEY: Radical Equations Solve Radical Equations 40. NS: Find the least common denominator and multiply both sides by it. id you substitute the values correctly? id you solve the equation correctly? id you perform the correct arithmetic operation? PTS: 1 IF: dvanced REF: Lesson 8-6 OJ: Solve rational equations. NT: N 2 N 8 N 9 N 10 N 6 ST: IL J 8.5 IL J 8 TOP: Solve rational equations. KEY: Rational Equations Solve Rational Equations 41. NS: Find the least common denominator and multiply both the sides by it.

34 id you multiply correctly? id you calculate correctly? id you include the correct values in the formula? PTS: 1 IF: dvanced REF: Lesson 8-6 OJ: Solve rational equations. NT: N 2 N 8 N 9 N 10 N 6 ST: IL J 8.5 IL J 8 TOP: Solve rational equations. KEY: Rational Equations Solve Rational Equations 42. NS: Eliminate the bases and use the Property of Equality for Exponential Functions to solve the equation. id you check the exponent of the base on the right side of the equation? id you write the right side of the equation in the correct exponential form? id you check the exponent of the base on the left side of the equation? PTS: 1 IF: verage REF: Lesson 9-1 OJ: Solve exponential equations. NT: N 1 N 3 N 4 N 10 N 2 ST: IL J 8 IL J 6.6 TOP: Solve exponential equations. KEY: Solve Equations Exponential Equations 43. NS: Isolate the radical in the original inequality, and raise each side of the inequality to the power equal to the index of the radical to eliminate the radical. heck the solution obtained by substituting the value of x in the original equation. id you isolate the radical? id you check the values in the interval that satisfies the inequality? Raise each side of the inequality to the power equal to the index of the radical. PTS: 1 IF: dvanced REF: Lesson 7-7 OJ: Solve inequalities containing radicals. NT: N 1 N 6 N 9 N 10 N 2 ST: IL J 8 TOP: Solve inequalities containing radicals. KEY: Radical Inequalities Solve Radical Inequalities 44. NS: Eliminate the bases. Then, use the Property of Inequality for Exponential Functions and the istributive Property. id you check the exponential form of the right side of the inequality? Use the istributive Property while simplifying exponents. Rewrite each side of the inequality with the same base. PTS: 1 IF: verage REF: Lesson 9-1 OJ: Solve exponential inequalities. NT: N 1 N 3 N 4 N 10 N 2

35 ST: IL J 8 IL J 6.6 TOP: Solve exponential inequalities. KEY: Solve Inequalities Exponential Inequalities 45. NS: Find equivalent fractions that have a common denominator. Then, simplify each numerator and denominator and add the numerators. id you calculate the numerator correctly? dd the numerators and simplify. Find the common denominator and then add the numerators. PTS: 1 IF: verage REF: Lesson 8-2 OJ: dd rational expressions. NT: N 2 N 8 N 9 N 10 N 6 ST: IL J 8.7 TOP: dd rational expressions. KEY: Rational Expressions dd Rational Expressions 46. NS: Find equivalent fractions that have a common denominator. Then, simplify each numerator and denominator and add the numerators. efore adding numerators, find equivalent fractions that have common denominators. id you multiply correctly? Multiply the first fraction with the common denominator. PTS: 1 IF: verage REF: Lesson 8-2 OJ: dd rational expressions. NT: N 2 N 8 N 9 N 10 N 6 ST: IL J 8.7 TOP: dd rational expressions. KEY: Rational Expressions dd Rational Expressions 47. NS: Find equivalent fractions that have a common denominator. Then, simplify each numerator and denominator and subtract the numerators. Find the common denominator and then subtract the numerators. efore subtracting the numerators, find equivalent fractions that have common denominators. id you use the correct arithmetic action? PTS: 1 IF: verage REF: Lesson 8-2 OJ: Subtract rational expressions. NT: N 2 N 8 N 9 N 10 N 6 ST: IL J 8.7 TOP: Subtract rational expressions. KEY: Rational Expressions Subtract Rational Expressions 48. NS: If the rational expression of a function is written in the simplest form and the function is undefined for x = a, then x = a is a vertical asymptote. If the function is defined for x = a, then there is a hole in the graph at x = a. id you factor correctly?

36 id you calculate properly? id you find the correct asymptotes? PTS: 1 IF: dvanced REF: Lesson 8-3 OJ: etermine the limitations of domains and ranges of the graphs of rational functions. NT: N 2 N 8 N 9 N 10 N 6 ST: IL J 8.4 IL J 8 TOP: etermine the limitations of domains and ranges of the graphs of rational functions. KEY: Graph Rational Functions Vertical symptotes Point iscontinuity 49. NS: raw the vertical asymptote, make a table of values, plot the points, and draw the graph. You have taken the negative value for plotting the graph. Where is teh vertical asymptote? Graph the equation, not the inverse of the equation. PTS: 1 IF: dvanced REF: Lesson 8-3 OJ: Graph rational functions. NT: N 2 N 8 N 9 N 10 N 6 ST: IL J 8 TOP: Graph rational functions. KEY: Graph Rational Functions 50. NS: Use direct proportion to relate the values. id you use the negative sign? id you substitute the values correctly? id you use the correct equation for direct variation? PTS: 1 IF: asic REF: Lesson 8-4 OJ: Recognize and solve direct variation problems. NT: N 1 N 6 N 8 N 9 N 2 ST: IL J 6.2 IL J 8 IL J 8.3 IL J 6 TOP: Recognize and solve direct variation problems. KEY: irect Variation 51. NS: Use direct proportion to relate the values. id you multiply correctly? id you use the correct equation for direct variation? Have you used the correct equation to relate the values? PTS: 1 IF: asic REF: Lesson 8-4 OJ: Recognize and solve direct variation problems. NT: N 1 N 6 N 8 N 9 N 2

37 ST: IL J 6.2 IL J 8 IL J 8.3 IL J 6 TOP: Recognize and solve direct variation problems. 52. NS: KEY: irect Variation Use one set of proportions to find the other set of corresponding values in the equation. id you substitute the values of all the variables? Have you used all the values of the variables? id you use the correct equation for joint variation? PTS: 1 IF: dvanced REF: Lesson 8-4 OJ: Recognize and solve joint variation problems. NT: N 1 N 6 N 8 N 9 N 2 ST: IL J 6.2 IL J 8 IL J 8.3 IL J 6 TOP: Recognize and solve joint variation problems. KEY: Joint Variation 53. NS: Use one set of proportions to find the other set of corresponding values in the equation. id you substitute the values of all the variables? id you include the correct sign in the answer? id you use the correct equation for joint variation? PTS: 1 IF: dvanced REF: Lesson 8-4 OJ: Recognize and solve joint variation problems. NT: N 1 N 6 N 8 N 9 N 2 ST: IL J 6.2 IL J 8 IL J 8.3 IL J 6 TOP: Recognize and solve joint variation problems. KEY: Joint Variation 54. NS: Use inverse proportion to relate values in the following equation. id you substitute the values correctly? id you use the correct equation for inverse variation? id you forget to include the negative sign in the answer? PTS: 1 IF: verage REF: Lesson 8-4 OJ: Recognize and solve inverse variation problems. NT: N 1 N 6 N 8 N 9 N 2 ST: IL J 6.2 IL J 8 IL J 8.3 IL J 6 TOP: Recognize and solve inverse variation problems. KEY: Inverse Variation 55. NS: The total amount of meat needed can be represented by the product of meat required per day, the number of tigers, and the number of days.

38 This is the meat required for x Siberian tigers for one day. id you use all the values? This is the meat required for one Siberian tiger for d days. PTS: 1 IF: verage REF: Lesson 8-4 OJ: Solve real-world problems with direct, joint, and inverse variation. NT: N 1 N 6 N 8 N 9 N 2 ST: IL J 6.2 IL J 8 IL J 8.3 IL J 6 TOP: Solve real-world problems with direct, joint, and inverse variation. KEY: irect Variation Joint Variation Inverse Variation Real-World Problems 56. NS: The correct equation to represent the amount of meat needed is m = 25xd. id you multiply the number of tigers? id you multiply the number of days? What is the number of days in the month of pril? PTS: 1 IF: verage REF: Lesson 8-4 OJ: Solve real-world problems with direct, joint, and inverse variation. NT: N 1 N 6 N 8 N 9 N 2 ST: IL J 6.2 IL J 8 IL J 8.3 IL J 6 TOP: Solve real-world problems with direct, joint, and inverse variation. KEY: irect Variation Joint Variation Inverse Variation Real-World Problems 57. NS: Use the equation and substitute the values. id you use the correct values for calculation? The number of daily phone calls is inversely proportional to the square of the distance d between the cities. id you use the correct equation? PTS: 1 IF: dvanced REF: Lesson 8-4 OJ: Solve real-world problems with direct, joint, and inverse variation. NT: N 1 N 6 N 8 N 9 N 2 ST: IL J 6.2 IL J 8 IL J 8.3 IL J 6 TOP: Solve real-world problems with direct, joint, and inverse variation. KEY: irect Variation Joint Variation Inverse Variation Real-World Problems 58. NS: The correct equation to represent the total servings of hydrated beverages drunk by the household members is, where d is the total number of days and m is the total household members. id you include the daily servings drunk by an average merican? id you multiply the number of days in the week?

39 id you include the correct number of days? PTS: 1 IF: verage REF: Lesson 8-4 OJ: Solve real-world problems with direct, joint, and inverse variation. NT: N 1 N 6 N 8 N 9 N 2 ST: IL J 6.2 IL J 8 IL J 8.3 IL J 6 TOP: Solve real-world problems with direct, joint, and inverse variation. KEY: irect Variation Joint Variation Inverse Variation Real-World Problems 59. NS: Use the formula,. id you use the correct values while multiplying? Have you used the correct formula for calculating distance? id you place the decimal point correctly? PTS: 1 IF: dvanced REF: Lesson 8-4 OJ: Solve real-world problems with direct, joint, and inverse variation. NT: N 1 N 6 N 8 N 9 N 2 ST: IL J 6.2 IL J 8 IL J 8.3 IL J 6 TOP: Solve real-world problems with direct, joint, and inverse variation. KEY: irect Variation Joint Variation Inverse Variation Real-World Problems 60. NS: Use the equation of direct variation to find the other set of corresponding values. id you use the correct values? id you check the calculation. id you use the correct equation? PTS: 1 IF: dvanced REF: Lesson 8-4 OJ: Solve real-world problems with direct, joint, and inverse variation. NT: N 1 N 6 N 8 N 9 N 2 ST: IL J 6.2 IL J 8 IL J 8.3 IL J 6 TOP: Solve real-world problems with direct, joint, and inverse variation. KEY: irect Variation Joint Variation Inverse Variation Real-World Problems 61. NS: Identify the general function represented by the graph. The graph of an absolute value function is in the shape of a V. The graph of a constant function is a horizontal line that crosses the y-axis at a. The graph of a square root function is a curve that starts at a point and continues in only one direction. PTS: 1 IF: verage REF: Lesson 8-5

40 OJ: Identify graphs as different types of functions. NT: N 2 N 8 N 9 N 10 N 6 ST: IL J 8.1 IL J 8 TOP: Identify graphs as different types of functions. KEY: Graphs Types of Functions Functions 62. NS: Identify the general function represented by the graph. The graph of a quadratic function is a parabola. The graph of a constant function is a horizontal line that crosses the y-axis at a. The graph of an identity function passes through all points with coordinates (a, a). PTS: 1 IF: asic REF: Lesson 8-5 OJ: Identify graphs as different types of functions. NT: N 2 N 8 N 9 N 10 N 6 ST: IL J 8.1 IL J 8 TOP: Identify graphs as different types of functions. KEY: Graphs Types of Functions Functions 63. NS: Identify the general function represented by the graph. The graph of an absolute value function is in the shape of a V. Is the equation of a rational function applicable to this graph? oes the equation of an inverse variation function apply to this graph? PTS: 1 IF: asic REF: Lesson 8-5 OJ: Identify graphs as different types of functions. NT: N 2 N 8 N 9 N 10 N 6 ST: IL J 8.1 IL J 8 TOP: Identify graphs as different types of functions. KEY: Graphs Types of Functions Functions 64. NS: The identity function y = x is a special case of a direct variation function in which the constant is 1. The equation of an inverse variation function is. The equation of a constant function is y = a. The equation of an absolute value function is y = x. PTS: 1 IF: asic REF: Lesson 8-5 OJ: Identify equations as different types of functions. NT: N 2 N 8 N 9 N 10 N 6 ST: IL J 8.1 IL J 8 TOP: Identify equations as different types of functions. KEY: Equations Types of Functions Functions 65. NS: The general equation of an inverse variation function is. The equation of an absolute value function is y = x.

41 The equation of a rational function is. The equation of an identity function is y = x. PTS: 1 IF: asic REF: Lesson 8-5 OJ: Identify equations as different types of functions. NT: N 2 N 8 N 9 N 10 N 6 ST: IL J 8.1 IL J 8 TOP: Identify equations as different types of functions. KEY: Equations Types of Functions Functions 66. NS: The general equation of an absolute value function is y = x. The equation of an identity function is y = x. The equation of a constant function is y = a. The equation of a direct variation function is y = ax. PTS: 1 IF: asic REF: Lesson 8-5 OJ: Identify equations as different types of functions. NT: N 2 N 8 N 9 N 10 N 6 ST: IL J 8.1 IL J 8 TOP: Identify equations as different types of functions. KEY: Equations Types of Functions Functions 67. NS: The general equation of a constant function is. The equation of an absolute value function is y = x. The equation of an inverse variation function is. The equation of a direct variation function is y = ax. PTS: 1 IF: asic REF: Lesson 8-5 OJ: Identify equations as different types of functions. NT: N 2 N 8 N 9 N 10 N 6 ST: IL J 8.1 IL J 8 TOP: Identify equations as different types of functions. KEY: Equations Types of Functions Functions 68. NS: The general equation of a quadratic function is. The equation of an identity function is y = x. The equation of a rational function is. The equation of an absolute value function is y = x. PTS: 1 IF: asic REF: Lesson 8-5 OJ: Identify equations as different types of functions. NT: N 2 N 8 N 9 N 10 N 6 ST: IL J 8.1 IL J 8 TOP: Identify equations as different types of functions.