ACP ALGEBRA II MIDTERM REVIEW PACKET
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1 ACP ALGEBRA II MIDTERM REVIEW PACKET 0-8 Name Per Date This review packet includes new problems and a list of problems from the textbook. The answers to the problems from the textbook can be found in the back of the textbook and a detailed solution on Section -4 Solving Absolute Value Equations Vocabulary: Absolute value, empty set, equation, solution, variable p.0- #5-odd,-4odd,4,49,5. Solve each equation. Remember to check your solutions! p 4 b. 4w 5w Section - Relations and Functions Vocabulary: Dependent and independent variable, domain/range, relation/function, function notation, vertical line test p.60-6 #-odd,5,6,,4-5odd. Find the value of each of the following for the functions: f x 4x 8 and g x 6x 5x f 9 b. g( a ) c. g(x + ).. Determine whether each relation is a function. Also, identify the domain and range.,,,,,4, 8,0 b. 6yx c. d. x y
2 Section -6 Special Functions (graphing absolute value functions and piecewise functions) Vocabulary: Absolute value function, constant function, identity function, parent graph, piecewise function p.9-94 #8-all,5,6,9,0,-4all,44 4. Graph each function. Identify the x-intercepts, y-intercepts, vertex, domain, and range g( x) x 9 b. g( x) x 6 5. Graph each function. Identify the domain and range. Be sure to use proper notation. x, x 0 g x x 6, 0 x x4, x0 f x, x x 5, x 0 b.
3 6. Write the definition (the equations) of the function shown in the graph below. Identify the range of the graph also. Section.Graphing inequalities Page 98 #5-odds. Graph each inequality a) 5xy 5 b) xy 0 c) xy Section -Solving Systems of Inequalities by Graphing Pages 5-6 #5-9odd, -9odd 8. Solve each system of linear inequalities by graphing x y xy a) b) c) xy4 y x x y d) x x 4 e) y 4 x x y 6
4 Section -4 Linear Programming Vocabulary: constraints, feasible region, bounded, unbounded, vertices, maximize, minimize Pages - #-odd 9. Graph the following constraints. Determine the vertices of the critical region, then test these vertices to determine the point that maximizes AND minimizes the system. x 0 y 0 y 8 x y4 5x y50 f ( x, y) 5x 4y 0. In the x-y plane, if a point with coordinates (a,b) lies in the solution set of the system of inequalities above, what is the maximum possible value of b? (SAT) y 5x y 5x Section 5- Monomials Vocabulary: Coefficient, constant, degree, monomial, power, scientific notation, simplify, standard notation, p.6- #-4odd,45-5odd. Simplify the expression. Assume that no variable equals zero. Remember: leave no negative exponents. 4 x y x y b. x y 6xy
5 Section 5- Polynomials Vocabulary: Binomial, FOIL method, like terms, polynomial, terms, trinomial p.- #5-odd,-5odd,5. Find 5 p for the polynomial: 5 4 p x 5x 5x 0x 6x. Simplify. x 4 4x 9 6x 4 5x b. x 6xy y 9x 4xy d. x4x 8 c. a ab 9a b a b e. x5x f. 4x54x 5 x h. x 4 x x g. 5 6 Section 5- Dividing Polynomials Vocabulary: Long division, synthetic division p.6- #,5,,-4odd,49 4. Simplify. 8a 0a a b. 4mn 6 40m n 4m n 5. Simplify by synthetic or long division. w w 4w w b. 4 6y 5y 8y 6 y Section 5-4 Factoring Polynomials Vocabulary: Difference of cubes, difference of squares, greatest common factor, grouping, perfect square trinomial, sum of cubes p.4- #5-odd,4,49 6. Factor completely. x 5x 8 b. 0x x c. 8x 5 d. 5 p 0 p4 e. x 8x 40 f. 49 8n 4 g. c 6
6 Section 5-5 Roots of Real Numbers Vocabulary: cube root, nth root, principal root, square root p.48 #5-55odd. Simplify. 8 44x b. 6 9m 6 n 4 c x y d. e. 65x 49 8 f. x 8 Section 5-6 Radical Expressions Vocabulary: Conjugates, like radical expressions, rationalizing the denominator p.54-5 #5-45odd,49 8. Simplify 88x y b c x y d. 64y y 0 0 e. 5x 5 8 x f. g h i j. k. l. 5 6 m.
7 Section 5- Rational Exponents Vocabulary: Rational exponents p.6 #5-5odd,-4odd 9. Write 0 in radical form. 0. Write each expression using rational exponents. 6 4d b. a 5 b. Evaluate each expression. b Simplify each expression. x x b. 4 y c. y y 4 6 d. a a a 6 Section 5-8 Radical Equations. Solve each equation. x 6 b. y 0 c. ( x ) 8 d. x 5 0 e. x 5 4 f. y 5 y g. y y 4 5 h. x 5 x i. x x 4 Section - Operations on Functions Let f ( x) x 6 and g x x x. Find: ( ) f g f gx b. f gx c. f gx d. x e. f ( g( x )) f. g f x g. f( g (0)) h. f g
8 . For the set of ordered pairs, find f gx and g f x f,,,4,, 5 g 5,, 6,,, Section -8 Inverse Functions and Relations 4. Find the inverse:,, 5,, 8,9, 0, b. f ( x) x 6 c. x gx ( ) 8 5. Use function composition to determine if the functions are inverse functions. x 4 4 9x 6 f f x and gx x x 8 b. g x x 8 and
9
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