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Download Advanced Algebra II Semester #1 Review Questions Handout
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Transcript
Advanced Algebra II Semester #1 Review Questions Handout If you want to be as successful as possible on the exam, there is no substitute for hard work and preparation. The questions in this handout are designed to help you identify topics that you feel very confident about and topics that you may need to spend more time on and get help with if necessary to master. If you struggled with a section of questions, look the topics up in your notes/text, spend additional time reviewing the concepts, work additional problems, and get help if needed. The best way to prepare for any exam is to form study groups and attack the concepts/material together. Work cooperatively on the problems and help each other out when someone doesn’t understand a problem/concept. Explaining the material to someone else is a great way to master concepts. Finally, I have all of the lectures on my hard drive if you need to listen to my explanations of certain topics one more time. Bring me a flash drive and we can look up and transfer the lectures you need from my computer to your flash drive. Directions: Complete each of the following. Use your notes, work together, and ask for help as needed. 1) Check all of the different number sets that the number “23” a part of? _____ Complex Numbers _____ Real Numbers _____ Imaginary Numbers _____ Rational Numbers _____ Irrational Numbers _____ Integers _____ Whole Numbers _____ Natural/Counting Numbers 2) Check all of the different number sets that the number “-7” a part of? _____ Complex Numbers _____ Real Numbers _____ Imaginary Numbers _____ Rational Numbers _____ Irrational Numbers _____ Integers _____ Whole Numbers _____ Natural/Counting Numbers 3 3) Check all of the different number sets that the number “ ” a part of? 5 _____ Complex Numbers _____ Real Numbers _____ Imaginary Numbers _____ Rational Numbers _____ Irrational Numbers _____ Integers _____ Whole Numbers _____ Natural/Counting Numbers 4) Check all of the different number sets that the number “ 23 ” a part of? _____ Complex Numbers _____ Real Numbers _____ Imaginary Numbers _____ Rational Numbers _____ Irrational Numbers _____ Integers _____ Whole Numbers _____ Natural/Counting Numbers 5) Check all of the different number sets that the number “ 53i ” a part of? _____ Complex Numbers _____ Real Numbers _____ Imaginary Numbers _____ Rational Numbers _____ Irrational Numbers _____ Integers _____ Whole Numbers _____ Natural/Counting Numbers 6) Check all of the different number sets that the number “0” a part of? _____ Complex Numbers _____ Real Numbers _____ Imaginary Numbers _____ Rational Numbers _____ Irrational Numbers _____ Integers _____ Whole Numbers _____ Natural/Counting Numbers 7) Check all of the different number sets that the number “ 144 ” a part of? _____ Complex Numbers _____ Real Numbers _____ Imaginary Numbers _____ Rational Numbers _____ Irrational Numbers _____ Integers _____ Whole Numbers _____ Natural/Counting Numbers 8) Check all of the different number sets that the number “ 34 5i ” a part of? _____ Complex Numbers _____ Real Numbers _____ Imaginary Numbers _____ Rational Numbers _____ Irrational Numbers _____ Integers _____ Whole Numbers _____ Natural/Counting Numbers 9) Check all of the different number sets that the number “ .2396654... ” a part of? _____ Complex Numbers _____ Real Numbers _____ Imaginary Numbers _____ Rational Numbers _____ Irrational Numbers _____ Integers _____ Whole Numbers _____ Natural/Counting Numbers 10) What is the sum of 56 and 93? 11) What is the quotient of 244 and 4? 12) What is the quotient of 13) What is the sum of 3 6 and ? 5 7 3 6 and ? 5 7 14) What is the difference of 15) What is the product of 3 6 and ? 5 7 3 6 and ? 5 7 16) Simplify the following expressions: a) 3 2 x 5 y 3 4 3x 5 y 8 c) 5 3 6i e) 2 5 3i 4 6 7i b) 2 x 43x 5 d) 5 6i 4 7i f) x 3 5 3x 4 2 2x 6 17) Solve each of the following. Graph the solutions for the inequalities. Set up 2 cases when absolute value is involved. a) 3x 5 5 x 4 9 b) x 2 5 x 6 c) 2 x 7 x 4 7 x 4 d) 3 x 5 2 x 6 e) x 2 8 x 9 0 f) 3x 2 11 or 2x+5 21 g) 3x 2 x 7 6x 9 h) 3x 2 5 x 2 0 i) 2x 5 15 and 3x-4 23 j) 3 2 x 3 27 k) 3x 2 5 x 1 4 l) 2 x 5 4 12 m) 2 x 3 6 18 n) 2 x 5 5 14 18) Determine the equation of the line that passes through the point (4,3) and has slope 3 . 2 Write the equation in slope-intercept form. 19) Find the equation of the line that passes through the point (6,5) and runs parallel to the line 5 x 2 y 4 . Write the equation in slope-intercept form. 20) Write the equation of the line that passes through the point (4,7) and runs parallel to the x-axis. 21) Write the equation of the line that runs through the point (-5,6) and runs perpendicular to the line 5 x 3 y 12 . Write the equation in slope-intercept form. 22) Given the function f x 2 x 4 , find f (6) . 3 3x 4 if x -3 23) Given the function f ( x) 2x+5 if -3<x 4 find each of the following: -3x+1 if x>4 a) f ( 1) b) f (6) c) f (8) 24) Graph each of the following: a) 2 x 5 y 15 b) 3 x 4 y 8 25) Graph the following piecewise function: 26) Graph the following system of inequalities: 4 3 x 7 if x -3 f ( x) 1 x 2 if x>-3 3 x 2 y 10 3x 2 y 2 x5 27) Graph the following step function: 3 -1 g ( x) 2 4 5 if x<-4 if -4 x<-1 if -1 x<2 if 2 x<5 if x 5 28) Find the common solution for the following system of equations: 29) Find the common solution for the following system: 5 x 2 y 10 3 x 6 y 18 3x y 4 5x 3 y 9 30) Find the common solution for the following system: x 6 y 2 z 8 x 5 y 3z 2 3 x 2 y 4 z 18 31) Factor each of the following polynomials: a) 2 x 3 20 x 2 50 x b) x 2 9 x 22 c) 15 x 2 7 x 2 d) x3 8 e) x 3 16 x f) x 4 27 x 32) Solve each of the following quadratic equations: a) 4 x 5 32 b) x 2 6 x 18 0 c) x 2 13 x 36 0 d) 6 x 2 48 0 e) 6 x 2 31x 35 f) x 2 4 x 12 2 33) Determine how many solutions each of the following equations will have: a) 3x 5 8 will have _____ solutions. b) x5 9 x3 0 will have _____ solutions. c) 3x3 2 x 2 5 x 6 0 will have _____ solutions. d) x 2 4 0 will have _____ solutions. 34) Graph the following parabola: y x2 4x 1 . 35) Graph the following parabola by completing the square: y 2 x 2 12 x 14 36) Graph the following parabola by completing the square: y 1 2 x 2x 1 3 37) Graph the following absolute value equation: y 2 x 3 4 38) Graph the following absolute value equation: y 2 x4 5 3 39) Simplify each of the following: 2 1 3 2 a) 3 2 4 5 5 4 3 2 5 1 3 4 b) 5 4 1 2 5 0 6 3 0 2 4 2 0 2 5 5 1 c) 4 3 6 3 2 d) 2 3 6 5 .5 40) Solve and graph each of the following inequalities: a) x 2 6 x 27 0 b) x 3 x 2 25 0 c) x 2 6 x 15 0 d) 2 x 2 6 x 3 0 41) Simplify each of the following radical expressions: a) 3 27 c) 3 2 2 e) 3i 8 g) 2 5 3 6 b) 2 8 3 18 48 d) 2 5 4 3 f) 2 27 4i 12 h) 5 4 3i 42) Given the parabolic equation y 3 2 x 4 3 , what are the coordinates of the vertex? 5 43) What would the equation for the parabola, in vertex form, be if the vertex is 4,5 and the vertical stretch value is -3? 44) Which way will the curve you found in question #41 open? Good “Skill” On The Exam There is no substitute for hard work, discipline, dedication, and preparation. Luck is not involved with you being successful on the Semester Exam.