MATH TEST 4 REVIEW TO THE STUDENT: To best prepare for Test 4, do all the problems on separate paper. The answers are given at the end of the review sheet. PART NON-CALCULATOR DIRECTIONS: The problems on this part of the Review Sheet are similar to those ou can epect on the non-calculator part of the test. For that reason, ou should do these problems without our graphing calculator. Show all our steps. Support all answers with appropriate reasoning. If a graph is requested, label it completel. If a table is requested, include and circle the relevant rows. Answer application problems using complete sentences. Chapters 8 Review. Find the domain of 0 f( ). Write the answer in interval notation.. Write the slope-intercept form of the line satisfing the given conditions. Perpendicular to 8, passing through (,) 7 Parallel to, passing through (0,). Use the table to solve < 4, where represents a linear function. Write the solution set as an inequalit 0 4 4 4 Solution # 4. Solve the inequalit 0 4, giving the answer in interval notation. Solution #4. Solve the equation.
. Solve the sstem, writing the answer as an ordered pair: 9 7. Solve the sstem, writing the answer as an ordered triple: z z 8 z Solution #7 8. Factor completel: 8t 7 4a b Solution #8 9. Solve: 7 0 0 9 4 0. Simplif: 9 Solution #0b 8 ( 4). Solve the rational equations. Check our result.. Simplif the comple fraction: 4 Solution #b Solution #. Simplif the epression. Assume that all variables are positive. 9 c. ab 0ab Solution # 4. Rationalize the denominator:
. Find the domain of f. Write our answer in interval notation. f( ) 4 Solution #. Solve: ( ) 0. Check our answer. Solution # 7. Write in standard form: ( i) ( i) Solution #7b i i 8. Find the verte on the graph of the equation f ( ). Solution #8 9. Find the maimum -value on the parabola determined b. 0. Write the equation in verte form and identif the verte. Solution #0. Solve using the method of our choice: 40 0 z 4z. A graph of a b c is shown. Solve a b c 0 State whether a > 0 or a < 0. c. Determine whether the discriminant is positive, negative or zero. Solution #
. Without using a calculator, give the eact value of: cos sin 4 c. tan Solution # 7 4. Sketch a right triangle that has as one of its acute angles. Let sec. Find the eact values of the other five trigonometric ratios of without using our calculator. Solution #4 B. Without using our calculator, find if tan A 0 in the right triangle to the right. Solution # A C Chapter 9 Review. Evaluate the eponential function for the given values of. f( ) = and = c. f( ) ( ) = 0 and = d. Solution #b, c f( ) = and = 4 f( ) = 0 and = 4
. A table for a function f is given. i. Determine whether f represents linear or eponential growth. ii. Find a formula for f. 0 4 f() 0 0 40 80 Solution #a 0 4 f() 0 0. Use the graph of Ca to find C and Solution # 4. Evaluate without a calculator: log 8 ln e c. log0.00. Simplif, using inverse properties: d. log 0,000 e. ln e 4 f. log 4 Solution #4b,c,d c. d. log7 0 log 9 e ln ln e Solution #b,d
. Write the epression b using sums and differences of logarithms of and. ln( ) log Solution #b c. log 7. Write as the logarithm of one epression. log 4 log 4 ln ln 4 c. log log log Solution #7c PART - GRAPHING CALCULATOR DIRECTIONS: You ma use our graphing calculator on this part of the review sheet. Support all answers with appropriate reasoning. Follow the same directions for suppling graphs and tables as in the non-calculator part. Alwas answer application problems using complete sentences. I. Chapters 9 Review. If $800 are deposited in an account that pas 7.% annual interest at the end of each ear, approimate the amount in the account after ears. Solution #. Solve, approimating answers to the nearest hundredth. log 9 7. The wing span L of a bird with weight W can sometimes be modeled b L 7.4 W, where L is in inches and W is in pounds. Estimate the weight of a bird with a wing span of inches. 4. From 90 to 970, per capita consumption of energ in millions of Btu can be modeled b f ( ) 0. 97 90,84 where is the ear. During what ear was per capital energ consumption at its lowest? Find this minimum value.. Wind speeds are usuall measured at heights from to 0 meters above the ground. For a particular da, f ( ).4ln( ) 7 computes the wind speed in meters per second meters above the ground, where. Solution # Find the wind speed at a height of 8 meters. Estimate the height at which the wind speed is 0 meters per second.
. Graph f using our graphing calculator. State whether the graph illustrates eponential growth, eponential deca, or logarithmic growth. f ( ) ln( ) f( ) Solution # 7. Evaluate f() for the given value of, approimating answers to the nearest hundredth. f( ) 0.8, =. f ( ) ln( ), = 8. Solve, approimating answers to the nearest hundredth when appropriate. 0 00 g. log 80 h. log 4 c. e 8 i. Solution #8i, j d. 0.8 0. e. ln 4 j. ln() ln( ) ln f. ln 9. Use the change of base formula to approimate each epression to the nearest hundredth. log 78 log Solution 9a 0. An investor deposits $00 in a mutual fund that returns % annuall. Determine the time required for the investment to double in value.. In 000 the population of Nevada was million and growing continuousl at an annual rate of.%. The population of Nevada in millions ears after 000 can be modeled b 0.0 f ( ) e. Graph f in [0, 0, ] b [0, 4, ]. Does this function represent eponential growth or deca? Predict the population of Nevada in 00. Solution # c. Estimate the ear when the population might reach million. 0.004 t. A colon of bacteria can be modeled b N( t) 000e, where N is measured in bacteria per milliliter and t is in minutes. Evaluate N(0) and interpret the result. Solution # Estimate how long it takes for N to double.. Sketch the angles in standard position. 0 4. Find a positive and negative angle that are coterminal with the given angle. 70 Solution #4 7
. Perform the following conversions. Give eact answers. radians to degrees 4 70 to radians. Find the length of an arc intercepted b a central angle 0 r inches. Give the eact answer. Solution # in a circle of radius 8
TEST 4 REVIEW ANSWER KEY Non-Calculator Part Chapters 8 Review., (, ). 7. 0 4. (,0]. 4,. No solutions 7. ( 4, 0, ) 8. (t )(4t t 9) (a b)(a b) 9.,, 0... 4. 0ab c. 0 4.. (4, )., 4 7. + i i 8. (,) 9. 7 0. ( ) ; (, )., 8., a < 0 c. Positive. c. 7 4. sin ;cos ; tan ;csc ;cot 7 7., = Chapter 9 Review. ; ; 8 c. ; 8 d. ;. i. Eponential growth ii. () i. Linear growth ii.. C = ½; a = 4. 4 9
c. d. e. 4 f.. 7 /9 c. d.. ln ln log log c. log log 7. log 4(0 ) ln( ) c. log Graphing Calculator Part Chapters 9 Review. $7.0. 0 8. log7. log..7 lbs 4. 90 0 million Btu. 9.9 m/sec 8. m. Logarithmic growth Eponential deca 7. 0.7.89 8. 4 c. ln 9.0 log 0. d. 9.90 log 0.8 e. f. 0.8 e e. 74. 40 g. 0 h. 00 4log i. log log.84 j. 9..07.4 0. 7 rs. Growth About. million c. 008. 000; there were 000 bacteria/ml present initiall About 49. min. 4. 40, 90,.. 4π inches 0