AFM Review Test Review
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1 Name: Class: Date: AFM Review Test Review Multiple Choice Identify the choice that best completes the statement or answers the question. What are the solutions of the inequality?. q + (q ) > 0 q < 3 q > 3 q > 6 q < 6 What are the solutions of the inequality?. + 0w 8(w + ) w 4 w 48 w 4 w n 4 3n + 6 n 0 n 3 n 4 n 8 What are the solutions of the inequality? 4. 3( x + ) 3x 6 x all real numbers x no solution. 0x 0 7x 3x x 8 all real numbers x 8 no solution Is the number written in scientific notation? If not, explain Yes; the number is written in scientific notation. No; the first factor is not a number between and 0. No; it is not written as a number times a power of 0. What is each number written in scientific notation? 7.,0,000, What is each number written in standard notation?
2 Name: What is the simplified form of each expression? 9. ( a 3 b 6 ) 3 (a 4 b ) 7 a 37 b 3 a 37 b 3 a 37 b 3 a 7 b 8 What is the simplified form of each expression? 0. c 8 d c 4 d 8 c d 4 c 4 d 4 d 4 d c d 4 What is the simplified form of the expression?. Ê Ë Á t 4 0y 4 ˆ 4 0t 6 y y 6 t 6 40t 6 4y t 6 0y What is the factored form of the following expressions?. d + d + 3 (d + 8)(d + 4) (d 8)(d + 4) (d 8)(d 4) (d + 8)(d 4) What is the factored form of the expression? 3. 0x + 4x + 40 (x + )(x 8) (x )(x + 8) (x + )(x + 8) (x )(x 8) 4. 6x + 7x + (3x 4)(x + 3) (3x + 4)(x + 3) (3x 4)(x 3) (3x + 4)(x 3) What is the factored form of the expression?. 4x 8y (x + 9)(x 9) (x + 9y) (x + 9y)(x 9y) (x 9y) 6. k 8h (k 9h )(k + 9) h (k + 9)(k 9) (k + 9h)(k + 9h) (k + 9h)(k 9h)
3 Name: What is the factored form of the expression? 7. g 3 + 0g 8g 4 (g + 4)(3g 6) (g + 6)(3g 4) (g 6)(3g + 4) (g 4)(3g + 6) What is the factored form of the expression? Factor completely k 3 6k + 64k 0 (3k + 44)(6k ) (3k + 4)(6k ) (3k 4)(6k + ) (33k 4)(66k + ) Simplify the radical expression. 9. 7c d 4 cd 36 c d 4 6 c d 4 6c d c 0. 4q 4q 3 6q 4q 4 6q 4 4q Simplify the expression Ê ˆ Ë Á Solve the equation. 4. x = 4x
4 Name: Solve the equation. Identify any extraneous solutions.. x = 4x + is a solution to the original equation. The value 6 is an extraneous solution. 6 and are solutions. 6 and are both extraneous solutions. 6 is a solution to the original equation. The value is an extraneous solution. Simplify the rational expression. State any excluded values. 6. x 8 x 4 ; where x 4 3 x 8; where x 7. x + 7 x + 4x x 3 ; where x 3, 7 x 7 ; where x 7 x 3; where x 3 x 7 Multiply. 8. y 9 y y y 3 (y + 3) y + 3 (y 3) (y 3) 9. x + 9x + 0 6x 6(x + 4) (x + ) 6 x x + 6(x + ) (x + 4) 6 Divide. 30. x 4 (x ) x 8 x 3 (x )(x 3) x 8 (x )(x + 3) x 8 x (x 8)(x 3) (x + )(x 3) x 8 4
5 Name: 3. x + 9x + 0 x x 4 x x + 4 x 4 x + x x + x 4 9x s s s + 3s 0 s s + s s s s s s s s s What is the simplest form of the expression? a 3 b 6 4a 4 b 3 a a 4 b 3 4a 4a 4 3 b a none of these What is the simplest form of the product? 34. 0x 7 y 7 6xy 4 x 4 y 6 7y x 4 y 6 0x 4 y 3y 30x 4 y y 3. 90x 8 x 3x 8 x x 3x 8 8x 7 none of these What is the product of the radical expression? Ê ˆ Ë Á Ê Ë Á 8 + ˆ What is the solution of the equation? 37. (x + 6) = ( x + 6) = ( 8 + 0x)
6 Name: 39. Solve the equation. x = 7 -, no solution Solve the absolute value equation x + = x = 3 or x = 3 no solutions x = 3 or x = 3 x = or x = x + + = 3 x = 7 6 or x = x = 7 6 or x = x = or x = x = 7 6 or x = 3 6 Solve the equation. Check for extraneous solutions x = 3x + x = or x = 8 x = x = or x = x = x = 4x + 4; x = 4 8 x = 7 x = 4 8 or x = 7 x = 7 or x = Problem 44. Factor. 343m n 3 4. Factor: x 3 6y 3 6
7 AFM Review Test Review Answer Section MULTIPLE CHOICE. ANS: D PTS: DIF: L3 REF: 3-4 Solving Multi-Step Inequalities OBJ: 3-4. To solve multi-step inequalities TOP: 3-4 Problem 3 Using the Distributive Property. ANS: C PTS: DIF: L3 REF: 3-4 Solving Multi-Step Inequalities OBJ: 3-4. To solve multi-step inequalities TOP: 3-4 Problem 4 Solving an Inequality With Variables on Both Sides 3. ANS: C PTS: DIF: L REF: 3-4 Solving Multi-Step Inequalities OBJ: 3-4. To solve multi-step inequalities TOP: 3-4 Problem 4 Solving an Inequality With Variables on Both Sides 4. ANS: C PTS: DIF: L3 REF: 3-4 Solving Multi-Step Inequalities OBJ: 3-4. To solve multi-step inequalities TOP: 3-4 Problem Inequalities With Special Solutions. ANS: D PTS: DIF: L3 REF: 3-4 Solving Multi-Step Inequalities OBJ: 3-4. To solve multi-step inequalities TOP: 3-4 Problem Inequalities With Special Solutions 6. ANS: A PTS: DIF: L3 REF: 7- Scientific Notation OBJ: 7-. To write numbers in scientific and standard notation TOP: 7- Problem Recognizing Scientific Notation KEY: scientific notation DOK: DOK 7. ANS: D PTS: DIF: L3 REF: 7- Scientific Notation OBJ: 7-. To write numbers in scientific and standard notation TOP: 7- Problem Writing a Number in Scientific Notation KEY: scientific notation 8. ANS: D PTS: DIF: L3 REF: 7- Scientific Notation OBJ: 7-. To write numbers in scientific and standard notation TOP: 7- Problem 3 Writing a Number in Standard Notation KEY: scientific notation 9. ANS: B PTS: DIF: L4 REF: 7-4 More Multiplication Properties of Exponents OBJ: 7-4. To raise a product to a power TOP: 7-4 Problem 4 Simplifying an Expression With Products 0. ANS: D PTS: DIF: L3 REF: 7- Division Properties of Exponents OBJ: 7-. To divide powers with the same base TOP: 7- Problem Dividing Algebraic Expressions. ANS: B PTS: DIF: L3 REF: 7- Division Properties of Exponents OBJ: 7-. To raise a quotient to a power TOP: 7- Problem 4 Simplifying an Exponential Expression. ANS: A PTS: DIF: L3 REF: 8- Factoring x^ + bx + c OBJ: 8-. To factor trinomials of the form x^ + bx + c TOP: 8- Problem Factoring x^ + bx + c Where b > 0, c > 0
8 3. ANS: B PTS: DIF: L4 REF: 8-6 Factoring ax^ + bx + c OBJ: 8-6. To factor trinomials of the form ax^ + bx + c TOP: 8-6 Problem Factoring When ac Is Positive 4. ANS: C PTS: DIF: L3 REF: 8-6 Factoring ax^ + bx + c OBJ: 8-6. To factor trinomials of the form ax^ + bx + c TOP: 8-6 Problem Factoring When ac Is Positive. ANS: B PTS: DIF: L4 REF: 8-7 Factoring Special Cases OBJ: 8-7. To factor perfect-square trinomials and the differences of two squares TOP: 8-7 Problem 4 Factoring a Difference of Two Squares KEY: difference of two squares 6. ANS: D PTS: DIF: L3 REF: 8-7 Factoring Special Cases OBJ: 8-7. To factor perfect-square trinomials and the differences of two squares TOP: 8-7 Problem 4 Factoring a Difference of Two Squares KEY: difference of two squares 7. ANS: B PTS: DIF: L3 REF: 8-8 Factoring by Grouping OBJ: 8-8. To factor higher-degree polynomials by grouping TOP: 8-8 Problem Factoring a Cubic Polynomial KEY: factoring by grouping 8. ANS: C PTS: DIF: L3 REF: 8-8 Factoring by Grouping OBJ: 8-8. To factor higher-degree polynomials by grouping TOP: 8-8 Problem Factoring a Polynomial Completely KEY: factoring by grouping 9. ANS: D PTS: DIF: L4 REF: 0- Simplifying Radicals OBJ: 0-. To simplify radicals involving products and quotients TOP: 0- Problem Removing Variable Factors KEY: radical expression 0. ANS: B PTS: DIF: L3 REF: 0- Simplifying Radicals OBJ: 0-. To simplify radicals involving products and quotients TOP: 0- Problem 3 Multiplying Two Radical Expressions KEY: radical expression. ANS: A PTS: DIF: L3 REF: 0-3 Operations With Radical Expressions OBJ: 0-3. To simplify sums and differences of radical expressions TOP: 0-3 Problem Simplifying to Combine Like Radicals KEY: like radicals. ANS: D PTS: DIF: L3 REF: 0-3 Operations With Radical Expressions OBJ: 0-3. To simplify sums and differences of radical expressions TOP: 0-3 Problem Simplifying to Combine Like Radicals KEY: like radicals 3. ANS: D PTS: DIF: L3 REF: 0-3 Operations With Radical Expressions OBJ: 0-3. To simplify products and quotients of radical expressions TOP: 0-3 Problem 3 Multiplying Radical Expressions KEY: radical expression
9 4. ANS: C PTS: DIF: L3 REF: 0-4 Solving Radical Equations OBJ: 0-4. To solve equations containing radicals TOP: 0-4 Problem 3 Solving With Radical Expressions on Both Sides KEY: radical equation. ANS: D PTS: DIF: L3 REF: 0-4 Solving Radical Equations OBJ: 0-4. To identify extraneous solutions TOP: 0-4 Problem 4 Identifying Extraneous Solutions KEY: radical equation extraneous solution 6. ANS: A PTS: DIF: L REF: - Simplifying Rational Expressions OBJ: -. To simplify rational expressions TOP: - Problem Simplifying a Rational Expression KEY: rational expression excluded value 7. ANS: A PTS: DIF: L3 REF: - Simplifying Rational Expressions OBJ: -. To simplify rational expressions TOP: - Problem Simplifying a Rational Expression Containing a Trinomial KEY: rational expression excluded value 8. ANS: A PTS: DIF: L3 REF: - Multiplying and Dividing Rational Expressions OBJ: -. To multiply and divide rational expressions TOP: - Problem Using Factoring 9. ANS: D PTS: DIF: L3 REF: - Multiplying and Dividing Rational Expressions OBJ: -. To multiply and divide rational expressions TOP: - Problem Using Factoring 30. ANS: D PTS: DIF: L REF: - Multiplying and Dividing Rational Expressions OBJ: -. To multiply and divide rational expressions TOP: - Problem 4 Dividing Rational Expressions 3. ANS: A PTS: DIF: L3 REF: - Multiplying and Dividing Rational Expressions OBJ: -. To multiply and divide rational expressions TOP: - Problem 4 Dividing Rational Expressions 3. ANS: C PTS: DIF: L3 REF: - Multiplying and Dividing Rational Expressions OBJ: -. To multiply and divide rational expressions TOP: - Problem 4 Dividing Rational Expressions 33. ANS: A PTS: DIF: L3 REF: 6- Multiplying and Dividing Radical Expressions OBJ: 6-. To multiply and divide radical expressions TOP: 6- Problem Simplifying a Radical Expression KEY: simplest form of a radical 34. ANS: B PTS: DIF: L3 REF: 6- Multiplying and Dividing Radical Expressions OBJ: 6-. To multiply and divide radical expressions TOP: 6- Problem 3 Simplifying a Product KEY: simplest form of a radical DOK: DOK 3
10 3. ANS: A PTS: DIF: L3 REF: 6- Multiplying and Dividing Radical Expressions OBJ: 6-. To multiply and divide radical expressions TOP: 6- Problem 4 Dividing Radical Expressions KEY: simplest form of a radical 36. ANS: B PTS: DIF: L REF: 6-3 Binomial Radical Expressions OBJ: 6-3. To add and subtract radical expressions TOP: 6-3 Problem 4 Multiplying Binomial Radical Expressions 37. ANS: A PTS: DIF: L3 REF: 6- Solving Square Root and Other Radical Equations OBJ: 6-. To solve square root and other radical equations TOP: 6- Problem Solving Other Radical Equations KEY: radical equation DOK: DOK 38. ANS: A PTS: DIF: L4 REF: 6- Solving Square Root and Other Radical Equations OBJ: 6-. To solve square root and other radical equations TOP: 6- Problem 4 Checking for Extraneous Solutions KEY: radical equation DOK: DOK 39. ANS: A PTS: 40. ANS: C PTS: DIF: L3 REF: -6 Absolute Value Equations and Inequalities OBJ: -6. To write and solve equations and inequalities involving absolute value NAT: N..g N.3.c A..a A.4.c STA: A.B..b TOP: -6 Problem Solving an Absolute Value Equation KEY: absolute value 4. ANS: B PTS: DIF: L3 REF: -6 Absolute Value Equations and Inequalities OBJ: -6. To write and solve equations and inequalities involving absolute value TOP: -6 Problem Solving a Multi-Step Absolute Value Equation KEY: absolute value 4. ANS: A PTS: DIF: L3 REF: -6 Absolute Value Equations and Inequalities OBJ: -6. To write and solve equations and inequalities involving absolute value TOP: -6 Problem 3 Checking for Extraneous Solutions KEY: absolute value extraneous solution DOK: DOK 43. ANS: C PTS: DIF: L3 REF: -6 Absolute Value Equations and Inequalities OBJ: -6. To write and solve equations and inequalities involving absolute value TOP: -6 Problem 3 Checking for Extraneous Solutions KEY: absolute value extraneous solution DOK: DOK PROBLEM 44. ANS: (7m + 4n)(49m 8mn + 6n ) PTS: 4
11 4. ANS: (x 6y)(x + 6xy + 36y ) PTS:
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