Final Exam Practice Problems Simplify completely.

Transcription

1 1) Final Exam Practice Problems Simplify completely. d) e) (Decimal answer ok here) f) g) 2) 3) d) 4) Do NOT leave an exponent in your answer for a)-c). Write final answer with positive exponents. d) e) f) g) h) i) j) k) l) m) n) o) p) q) 5) Assume that all variables represent nonnegative real numbers. d) e) f) g) h) i) j) k) l) m) n) Perform the indicated operation(s). 6) d) e) 7) Find the degree of each polynomial. d) e) f) g) 8) d) e) f) g) h) Page 1 of 6

2 i) Write answer in scientific notation. Factor completely. If the polynomial is not factorable, state that it is prime. 9) d) e) f) g) h) i) j) k) 10) Solve for the variable. You must check your answers for extraneous solutions! d) e) Write answer as a fraction. f) b) c) d) e) f) g) h) i) j) k) l) Miscellaneous 11) Evaluate the expression for the given value of the variable. a) for b) for and c) for and 12) Solve for. Solve for. 13) Solve each inequality and graph the result using the provided number line. 14) Find the exact area of a circle whose diameter is 12 meters. Be sure to include units. 15) Write in decimal notation. Write in scientific notation. 16) Fill in the blank so that the polynomial is a perfect-square trinomial. 17) True or false. Circle one. a) T F b) The zero polynomial is the only polynomial that has no degree. T F c) T F d) T F e) T F f) T F g) The degree of is 10 T F Page 2 of 6

3 h) T F 18) Find the LCD of and. Note: Do NOT multiply/foil. Leave answers with exponents. 19) Provide the formulas below. Slope: Slope-Intercept: Point-Slope: 20) Find the slope and -intercept of the line. 21) Write an equation of a line that meets the specified conditions. Write answers in slope-intercept form. a) has slope and passes through b) has slope and passes through c) has 0 slope and passes through d) has undefined slope and passes through e) is perpendicular to the -axis and passes through f) passes through and Note: Not just finding slope here. 22) a) Find the slope of. b) Find an equation of the line parallel c) Find an equation of the line perpendicular to passing through. to passing through. Write answer in slope-intercept form. Write answer in slope-intercept form. 23) Find an equation of each graph. Write answers in slope-intercept form. 24) Graph each line. Plot at least 3 clear points. One of these points must be either an x- OR y-intercept. d) 25) Find the slope of the line passing through and. 26) Graph the region described by the inequality. Plot at least 3 clear points. One of these points must be either an x- OR y-intercept. Incorrect graphs will earn NO points. Show work using a test point. 27) MULTIPLE CHOICE Choose the correct answer. I. All vertical lines have the form d) None of the these II. All horizontal lines have the form d) None of the these III. The slope of a line perpendicular to the line is equal to d) e) f) g) h) i) j) None of these Page 3 of 6

4 IV. Refer to the given graph. Circle either True or False. is a solution to the inequality. True False is a solution to the inequality. True False is a solution to the inequality. True False V. Fill in the blank: Parallel lines have the. 28) Draw a line with: a) positive slope b) negative slope c) zero slope d) no slope (undefined slope) 29) A system of equations, when graphed, is 30) Solve the system of equations by graphing. shown. Find the solution. For each graph, plot the y-intercept and at least one more point. 1) 31) For credit, solve the system 32) For credit, solve the system using the using the substitution method. addition method. 33) Solve using the method of your choice (substitution or addition). Write solutions as ordered pairs whenever possible. If there is not a unique solution, state the reason. For answers with infinite solutions, be sure to use set-builder notation:. a) b) c) d) e) f) Answer has fractions. 34) Draw graphs to represent a system of 2 equations in 2 variables that describes the following: a) one unique solution b) no solution c) an infinite number of solutions 35) Fill in the blank. a) If a system of linear equations in 2 variables has NO solution, this means the lines when graphed are. Page 4 of 6

5 b) If a system of linear equations in 2 variables has an infinite number of solutions, this means the lines when graphed are. c) Suppose lines and are perpendicular. The system of equations formed by these two lines has solution(s). a) no b) one c) two d) three e) infinitely many 36) Fill in the blank. Match each slope with the correct letter. Write your choice in the provided space. (A) Negative Slop (B) Positive Slope (C) Undefined Slope (D) Zero Slope 37) Evaluate each, if possible. If the expression is not a real number, write NR. d) e) f) g) h) i) j) 38) Rationalize the denominator. (This means your final answer should not have any radicals in the denominator.) d) e) Hint 38d: After rationalizing, you will need to simplify. Hint 38e: Final answer has a 1 in the denominator. Word Problems ALL word problems: For FULL CREDIT, you must (I) DEFINE (Example: number of pennies.) (II) SET UP and (III) SOLVE 39) A flagpole is 8 meters tall. A man stands 10 meters from the base of the pole. How far is it from the feet of the man to the top of the pole? Simplify your answer. 40) Double the sum of a number and 19 is the same as 22 less than triple the same number. Find the original number. (Variable has already been defined.) I) Define variable: II) Equation: III) Solve: 41) Two cars leave Folsom at the same time. One car travels east at 44 mph and the other west at 52 mph. In how many hours will the two cars be 384 miles apart? Use. I) Define variable: II) Equation: III) Solve: Answer: hours 42) Bonnie and Clyde invested $9000 for one year. Part of it was invested at 12% and the remainder was invested at 8%. At the end of one year the couple had earned exactly $1000 in simple interest. How much did they invest at each rate? Note: DO NOT SOLVE. I) Define variable: II) Page 5 of 6

6 43) Dora s buddy Boots has $4.65 in change. He has twice as many nickels as quarters. He has three less dimes than he has quarters. How many of each coin does he have? (Hint: It is incorrect to add the number of coins and setting it equal to $4.65.) I) Define variable: II) Equation: _ III) Solve: Answers: # of nickels = # of dimes = # of quarters = 44) Dora has a math final exam that counts twice as much as a test. She had 4 tests with grades of 88, 77, 99, and 62. What score does she need to obtain on the final exam to earn an average of more than 95 for the course? 45) It takes Pete 4 hours to complete one homework assignment. It takes Bob 11 hours to complete the same homework assignment. How long would it take Pete and Bob to complete the homework assignment working together? Express answer as a fraction or mixed number. 46) Melissa drove to Dallas while Kerri drove to Houston in the same amount of time. Melissa drove 360 miles, while Kerri drove 240 miles. Melissa traveled 30 mph (miles per hour) faster than Kerri on her trip. What was the average speed in mph for each woman? 47) Twice one number plus five times a second is one. Twice the second plus three times the first is twelve. Find the numbers. 48) A jet plane flew 2400 kilometers against the wind in a time of 6 hours. It refueled and flew back the same distance with the wind in 4 hours. Find the wind speed and the speed of the jet in still air in kilometers per hour. 49) A chemist has a 25% acid solution and an 40% acid solution. She wishes to mix together some of each to obtain 20 deciliters of a 37% solution. How much of each should she use? 50) Bob held a fundraiser and had 86 customers on Saturday. He charged $4 to wash regular-sized cars and $3.50 to wash compact cars. The gross receipts for the day were $323. How many cars of each type were washed? 51) The hypotenuse of a right triangle is 20 meters in length. One leg is 4 meters shorter than the other leg. Find the length of each leg. Page 6 of 6