Seminar Alg Basics. Name: Class: Date: ID: A. Multiple Choice Identify the choice that best completes the statement or answers the question.

Transcription

1 Class: Date: Seminar Alg Basics Multiple Choice Identify the choice that best completes the statement or answers the question. Use a pattern to answer each question. 1. How many line segments are in figure 14? a. 17 c. 14 b. 56 d. 42 Evaluate the expression for the given value of the variable(s). 2. x 2 4x 4; x = 3 a. 3 b. 1 c. 11 d. 17 1

2 3. Use the vertical-line test to determine which graph represents a function. a. c. b. d. Write an equation of the line, in point-slope form, that passes through the two given points. 4. points: ( 3,3), (9, 3) a. (y 3) 1 (x 3) c. (y 3) 2(x 3) 2 b. (y 3) 2(x 3) d. (y 3) 1 (x 3) 2 What is the equation of the given line in standard form? Use integer coefficients. 5. y 6.9x 5.1 a. 69x 10y 51 c. 69x 10y 51 b. 69x 10y 51 d. 69x 10y 51 2

3 Make a scatter plot and describe the correlation. 6. The table lists the results from a survey (of questionable accuracy) of adults and how much they spend on a night out. The table displays the values rounded to the nearest whole number. Make a scatter plot. How would you describe the correlation between a person's age and how much he or she spends on a night out? Age (years) Average cost of a night out ($)

4 a. c. b. As age increases, the average cost increases; there is a positive correlation. d. As age increases, the average cost decreases; there is a negative correlation. As age increases, the average cost decreases; there is a positive correlation. As age increases, the average cost increases; there is a negative correlation. 4

5 The function f(x) is represented by the given table. What are the corresponding values of the given g(x)? 7. The function f(x) is represented by the table below. What are the corresponding values of g(x) for the transformation g(x) 6f(x)? x f(x) a. x g(x) b. x g(x) c. x g(x) d. x g(x)

6 Write an inequality for the graph. 8. a. 3x 4y 12 c. 3x 4y 12 b. 4x 3y 12 d. 4x 3y 12 What are the vertex and the axis of symmetry of the equation? 9. y 2x 2 24x 16 a. vertex: ( 6, 88) axis of symmetry: x 6 b. vertex: ( 6, 88) axis of symmetry: y 6 c. vertex: ( 6, 88) axis of symmetry: x 88 d. vertex: ( 6, 88) axis of symmetry: x 88 What is the equation, in standard form, of a parabola that contains the following points? 10. ( 2, 11.5), (0, 2.5), (4, 20.5) a. y 1.5x 2 1.5x 2.5 c. y 1.5x 2 1.5x 2.5 b. y 2.5x 2 1.5x 1.5 d. y 1.5x 2 1.5x 2.5 What is the expression in factored form? 11. 5x 2 22x 15 a. (5x 3)(x 5) c. (5x 3)(x 5) b. (x 3)(5x 5) d. (5x 5)(x 3) x 2 25 a. (4x 5) 2 c. (4x 5)(4x 5) b. (4x 5)( 4x 5) d. ( 4x 5)(4x 5) 6

7 13. A landscaper is designing a flower garden in the shape of a trapezoid. She wants the length of the shorter base to be 3 yards greater than the height, and the length of the longer base to be 5 yards greater than the height. For what height will the garden have an area of 360 square yards? Round to the nearest tenth of a yard. a yards c yards b yards d yards Use the Quadratic Formula to solve the equation. 14. x 2 6x 5 0 a. 5, 1 c. 5, 11 b. 1, 5 d. 2, What is the solution of the quadratic system of equations? Ï Ô y x 2 16x 32 Ì ÓÔ y x 2 2 a. ( 7, 3) ( 23, 5) b. ( 3, 89) ( 5, 137) c. ( 3, 7) ( 5, 23) d. (3, 7) (5, 23) Short Answer 16. Write an expression for the volume of a cylinder with a height 7 in. greater than its radius. Other 17. A park planner has sketched a rectangular park in the first quadrant of a coordinate grid. Two sides of the park lie on the x- and y-axes. A trapezoidal flower bed will be bounded by the line y x 7, the x-axis, and the vertical lines x 1 and x a, where a 1. The area A of the trapezoid is modeled by A 1 2 a2 7a Assume that lengths along the axes are measured in meters. For what value of a will the trapezoid have an area of 23 square meters? Use the Quadratic Formula to find the answer. 7

8 Seminar Alg Basics Answer Section MULTIPLE CHOICE 1. ANS: D PTS: 1 DIF: L3 REF: 1-1 Patterns and Expressions OBJ: To identify and describe patterns NAT: CC A.SSE.3 A.1.a STA: L1.2.1 A1.1.1 TOP: 1-1 Problem 2 Expressing a Pattern With Algebra KEY: algebraic expression 2. ANS: B PTS: 1 DIF: L3 REF: 1-3 Algebraic Expressions OBJ: To evaluate algebraic expressions NAT: CC A.SSE.1.a N.1.d N.3.a N.3.b A.3.b A.3.d STA: L1.2.1 A1.1.1 TOP: 1-3 Problem 3 Evaluating Algebraic Expressions KEY: evaluate 3. ANS: B PTS: 1 DIF: L2 REF: 2-1 Relations and Functions OBJ: To identify functions NAT: CC F.IF.1 CC F.IF.2 A.1.g A.1.i A.2.b A.3.f STA: L1.2.1 A2.1.1 A2.1.2 A2.1.3 TOP: 2-1 Problem 4 Using the Vertical-Line Test KEY: vertical-line test function 4. ANS: A PTS: 1 DIF: L3 REF: 2-4 More About Linear Equations OBJ: To write an equation of a line given its slope and a point on the line NAT: CC A.CED.2 CC F.IF.7 CC F.IF.8 CC F.IF.9 G.4.d A.2.a A.2.b STA: L1.2.1 TOP: 2-4 Problem 2 Writing an Equation Given Two Points KEY: point-slope form 5. ANS: B PTS: 1 DIF: L3 REF: 2-4 More About Linear Equations OBJ: To write an equation of a line given its slope and a point on the line NAT: CC A.CED.2 CC F.IF.7 CC F.IF.8 CC F.IF.9 G.4.d A.2.a A.2.b STA: L1.2.1 TOP: 2-4 Problem 3 Writing an Equation in Standard Form KEY: standard form of a linear equation 6. ANS: C PTS: 1 DIF: L3 REF: 2-5 Using Linear Models OBJ: To write linear equations that model real-world data NAT: CC A.CED.2 CC F.IF.4 CC F.IF.6 CC F.BF.1 A.2.e D.1.c D.2.e D.2.f D.5.d STA: A2.4.3 TOP: 2-5 Problem 1 Using a Scatter Plot KEY: scatter plot correlation 7. ANS: D PTS: 1 DIF: L2 REF: 2-6 Families of Functions OBJ: To analyze transformations of functions NAT: CC F.IF.7 CC F.BF.3 G.2.c G.4.d A.1.e A.1.h A.2.b STA: A2.4.1 A2.1.7 A2.4.2 A2.3.1 A2.3.3 TOP: 2-6 Problem 4 Stretching and Compressing a Function KEY: parent function transformation 8. ANS: B PTS: 1 DIF: L4 REF: 2-8 Two-Variable Inequalities OBJ: To graph two-variable inequalities NAT: CC A.CED.2 CC F.IF.7.b TOP: 2-8 Problem 4 Writing an Inequality Based on a Graph KEY: linear inequality 9. ANS: A PTS: 1 DIF: L2 REF: 4-2 Standard Form of a Quadratic Function OBJ: To graph quadratic functions written in standard form NAT: CC A.CED.2 CC F.IF.4 CC F.IF.6 CC F.IF.7 CC F.IF.8 CC F.IF.9 CC F.BF.1 STA: A2.1.3 TOP: 4-2 Problem 1 Finding the Features of a Quadratic Function KEY: Graph functions expressed symbolically standard form vertex of a parabola axis of symmetry 10. ANS: C PTS: 1 DIF: L4 REF: 4-3 Modeling With Quadratic Functions OBJ: To model data with quadratic functions NAT: CC F.IF.4 CC F.IF.5 A.2.f STA: A2.1.3 TOP: 4-3 Problem 1 Writing an Equation of a Parabola KEY: quadratic function quadratic model 1

9 11. ANS: C PTS: 1 DIF: L3 REF: 4-4 Factoring Quadratic Expressions OBJ: To find common and binomial factors of quadratic expressions NAT: CC A.SSE.2 N.5.c A.2.a TOP: 4-4 Problem 3 Factoring ax^2+bx+c when abs(a) not = 1 KEY: factoring 12. ANS: C PTS: 1 DIF: L2 REF: 4-4 Factoring Quadratic Expressions OBJ: To factor special quadratic expressions NAT: CC A.SSE.2 N.5.c A.2.a TOP: 4-4 Problem 5 Factoring a Difference of Two Squares KEY: difference of two squares factoring 13. ANS: A PTS: 1 DIF: L3 REF: 4-6 Completing the Square OBJ: To solve equations by completing the square NAT: CC A.REI.4.b A.2.a A.4.c A.4.g TOP: 4-6 Problem 2 Determining Dimensions 14. ANS: B PTS: 1 DIF: L2 REF: 4-7 The Quadratic Formula OBJ: To solve quadratic equations using the Quadratic Formula NAT: CC A.REI.4.b A.2.a A.4.c A.4.e A.4.f TOP: 4-7 Problem 1 Using the Quadratic Formula KEY: Quadratic Formula 15. ANS: C PTS: 1 DIF: L3 REF: 4-9 Quadratic Systems OBJ: To solve and graph systems of linear and quadratic equations NAT: CC A.CED.3 CC A.REI.7 A.4.a A.4.d TOP: 4-9 Problem 3 Solving a Quadratic System of Equations SHORT ANSWER 16. ANS: (r 3 7r 2 ) PTS: 1 DIF: L2 REF: 4-4 Factoring Quadratic Expressions OBJ: To find common and binomial factors of quadratic expressions NAT: CC A.SSE.2 N.5.c A.2.a TOP: 4-4 Problem 1 Factoring ax^2+bx+c when a=+/-1 KEY: factoring quadratic expression OTHER 17. ANS: meters, or about 3.49 PTS: 1 DIF: L4 REF: 4-7 The Quadratic Formula OBJ: To solve quadratic equations using the Quadratic Formula NAT: CC A.REI.4.b A.2.a A.4.c A.4.e A.4.f TOP: 4-7 Problem 2 Applying the Quadratic Formula KEY: Quadratic Formula 2