FINAL EXAM REVIEW ITEMS Math 0312: Intermediate Algebra Name 1) Find the SUM of the solutions of the equation. 82 + 0 = 16 Use the quadratic formula to solve the equation. (All solutions are real numbers.) 2) 2 = 3 - Choose the equation that matches the graph. 3) 8) ( + 7)2 9) (- 2)(2 + 2 + ) ) (3a + c)(3a - c) Factor b grouping. 11) 3 + 2 + 6 + 30 12) 32r2 + 12r - 8r - 3 Perform the indicated operation. 13) - 2-3 - - - - - A) f() = 2-2 - B) f() = -2 + 2 - C)f() = 2 + 2 + D) f() = 2 + 2-1) Perform the long division to find the remainder. + 3 2 +1 + 9 Simplif the comple fraction. 1) 9 + 3 + 1 12 Use the square root propert to solve the equation. ) 2 = 12 ) ( - 17)2 = 81 6) Find the SUM of the solutions of the following quadratic equation. 2 + 9-36 Find the product. 7) (a - 8b)(-7a - 6b) Find the domain of the function. 16) f() = -7-17) f() = 20 - Factor the trinomial. Factor. 18) 2 - - 90 19) 6z2 + z - 6 1
Factor completel. 20) One of the factors of u2-3u - 0 is Solve the equation. 30) 82-3 = -9 Factor completel. 21) 302 + 2 + 12 + Factor completel. 22) 33 + 92-30 31) 8k2 - k - 7 = 0 Epress the rational epression in lowest terms. 32) 2 + 3-2 + - 12 Factor completel. 23) 3-33 Solve the problem. 2) The product of two consecutive negative integers is 89 more than their sum. Find the larger integer. 2) The length of a rectangular storage room is 3 feet longer than its width. If the area of the room is 0 square feet, find its dimensions. Give the quadrant in which the point is located. 26) (, -11) 27) Find the slope of the line through (-, ) and (2, 6). Find the slope and the -intercept of the line. 28) - + 8 = 8 Graph the following line. 29) Through (0, 6), m = 1 Solve the equation. 33) (2z - ) = 7(z + 3) Solve the equation for the specified variable. 3) 9k + ar = r - 6 for r Solve the formula for the specified variable. ne 3) I = nr + R for n 36) Simplif b reducing to lowest terms: 2 + + 3 + 8 Perform the indicated operation and simplif. 37) 6p - 6 6p2 p 8p - 8 Simplif the comple fraction. 38) Simplif. 39) 9 + 3 s s + 1 12 r - 1 - r - 1 + - - - - Solve b sstem to find the value of the solution. 0) 2 + 3 = - - 6 = 8 2
Solve the absolute value equation or indicate that the equation has no solution. 3) -6c + 7-7c + 13 1) 6 + + 8 = 13 Evaluate the function. 2) f() = - 8 Find f(-1) 3) f() = 2 + + 8 Find f() Solve the equation. Be sure to check our proposed solution b substituting it for the variable in the given equation. ) 8-3 = -2 + Solve the equation. ) 2-1 3 = 6) - 3 2 = 7 Simplif. Assume that all variables represent positive real numbers. ) 162-72 - 128 ) 6 + 6 96 + 216 6) 2-98 + 200 Find the - and -intercepts for the equation. Then graph the equation. 7) 2 - = Epress using positive eponents. Then simplif. 1-3 7) 3 - - - Simplif the epression. Write our answer with onl positive eponents. 8) -3 9-2 9) Simplif: 81 6-3/2 Perform the indicated operation. Give the result in standard form. 0) 6 + i - 6i - Perform the indicated operation and simplif. 8) 2-16 - 7 2 + + 9) Perform the indicated operation. 3 2 2-7 8 2 1) 2 + 3i + 6i Solve and graph. 2) 7z + 1 > 6z + 7 3
Graph the linear inequalit. 60) 3 + 2 Find the slope of the line. 6) - - - - - - - - 61) + 3-2 - - - - 62) Find the quotient when 6m2 + 17m - 28 is divided b m +. 63) For f() = 2 + 3 + 2, the parabola opens. A) To the left B) Upward C) To the right D) Downward
Answer Ke 1) -3 2) {-2 + 7, -2-7} (9.2) Use Quadratic Formula to Solve Equation (Real Soln) 3) D (9.6) Match Equation with Graph ) 2 3, -2 3 (9.1) Use Square Root Propert to Solve Equation ) {8, 26} (9.1) Use Square Root Propert to Solve Equation 6) -9 7) -3a2 + 26ab + 8b2 (.) Multipl Two Binomials 8) 162 + 6 + 92 (.) Square Binomial 9) 3-8 (0.) Multipl Polnomials ) 9a2-2c2 (.) Multipl Conjugate Binomials 11) ( + )(2 + 6) (6.1) Factor b Grouping 12) (8r + 3)(r - ) (6.1) Factor b Grouping 13) + 2 (6.) Divide b Binomial 1) 6 1) 36 (6.3) Simplif Comple Fraction 16) (-, ) or (, ) (2.3) Find the Domain of a Function 17) (-, 20] (2.3) Find the Domain of a Function 18) ( + 9)( - ) (.6) Factor Trinomial with Lead Coefficient +/- 1 19) (2z + 3)(3z - 2) (.6) Factor Trinomial with Lead Coefficient > 1 20) (u - 8) (.6) Factor Trinomial with Lead Coefficient +/- 1 21) ( + 2)(6 + ) (.) Factor b Grouping 22) 3( - 2)( + ) (.6) Factor Trinomial with Common Factor
Answer Ke 23) ( - 7)(2 + 7 + 9) (.7) Factor Sum or Difference of Cubes 2) -9 (.8) a: Solve Apps: Numbers 2) feet b 8 feet (1.) Solve Problems Modeled b Quadratic Equations 26) Quadrant IV (3.1) Name the Quadrant in Which Point is Located 27) 1 3 (3.2) Calculate Slope 28) Slope 1 ; -intercept (0, 1) 2 29) (3.3) Find Slope and -Intercept from Standard Form - - - - (3.2) Graph Line Given Point and Slope 30) = 3 ± i 279 16 (8.2) Solve B Quadratic Formula (Comple) 31) - 1 8, 7 (.9) Solve;Zero Factor Propert 32) + + 6 (6.1) Reduce Rational Epression 33) 37 (.3) c: Remove Parentheses, Collect Terms, and Solve 3) r = 3) n = -9k - 6 a - 1 or r = 9k + 6 1 - a (2.2) Solve Equation for Specified Variable -IR Ir - E (2.2) Solve Formula for Specified Variable 6
Answer Ke 36) 37) + 2 2 + 2 + 9p 2 (6.1) Multiplication and Division of Rational Epressions 38) 36 s (6.3) Simplif Comple Fraction 39) 2 - r r (6.3) Simplif Comple Fraction (Complicated) 0) No solution (.1) Solve Linear Sstem b Elimination Method 1) {- 3 2, 1 6 } (1.6) Solve Equations Involving Absolute Value 2) -9 (7.1) Use f() Notation 3) (7.1) Use f() Notation ) 1 Solve Linear Equations ) {60} (2.1) Solve Linear Equation Having Fractions 6) {-2} (6.6) Solve Rational Equation 7) 27 (12.1) f: Change Negative Eponent to Positive 8) 613 (.1) Simplif Using Product Rule 9) 12 729 (0.3) Understand and Use Rational Eponents 0) 6 61 + 6 61 i (7.6) Divide Comple Numbers 1) 28 61 + 3 61 i (7.6) Divide Comple Numbers 2) (6, ) -1 0 1 2 3 6 7 8 9 11 12 13 (2.) Solve Inequal: Graph & Give Interval Notation 7
Answer Ke 3) (-, 6] -1 0 1 2 3 6 7 8 9 11 12 13 (2.) Solve Inequal: Graph & Give Interval Notation ) -61 2 (7.3) Simplif Sum/Diff of Radicals (Inde = 2) ) 9 6 (7.3) Simplif Sum/Diff of Radicals (Inde = 2) 6) 6 2 (7.3) Simplif Sum/Diff of Radicals (Inde = 2) 7) (2, 0), (0, -1) - - - 8) 9) 60) - (3.1) Find Intercepts and Graph 2-6 + 28 ( - )( + )( + 1) (6.2) Add or Subtract Rational Epressions 8 2 - - - - (3.) Graph Linear Inequalit 8
Answer Ke 61) - - - - (3.) Graph Linear Inequalit 62) 6m - 7 (6.) Divide b Binomial 63) B (8.) Determine How Parabola Opens 6) 2 (3.2) Find Slope Given Graph of Line 9