ALGEBRA 2 HONORS - CHAPTER 2 TEST

Transcription

1 Name: lass: Date: ID: LGER 2 HONORS - HPTER 2 TEST Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Find the value of f( 9) and g(4) if f( x) = -4x + 8 and g ( x) = 6x + 25x -2. (4pts) a. f( 9) = 44 g(4) = b. f( 9) = 16 g(4) = c. f( 9) = 4 g(4) = d. f( 9) = 28 g(4) = State whether the given equation or function is linear. Write yes or no. Explain your reasoning. (5pts) f(x) = 3x + 2 a. No, the equation is not linear. It is not of the form f(x) = mx + b. b. No, the equation is not linear. It is in the form x + y = c. c. Yes, the equation is linear. It is of the form f(x) = m + b d. Yes, the equation is linear. It is of the form f(x)= mx + b 4. Find the slope of the line that passes through the pair of points ( 1, 3) and ( 8, 10). (5pts) 5 a. 11 b. 8 c d Find the slope of the line that passes through the pair of points ( 6.1, 1.25) and (0.35, 8.9). (5pts) a b c d Write the equation 10y = 12x in standard form. Identify,, and. (5pts) a. 100x - 120y = 7 where = 100, = -120, and = -7. b. 100x - 7y = 7 where = 100, = -120, and = 7. c. 120x + 100y = -7 where = 120, = 100, and = 7. d. 120x - 100y = -7 where = 120, = -100, and = -7. 1

2 Name: ID: 6. Graph the line that passes through (2, 5), parallel to the graph of 1.4x + 8.5y = 3. (5pts) a. a. x-inter b. cept at (0.38, 0) b. x-inter c. cept at (0.75, 1) c. x-inter 7. Graph the line that is perpendicular to the graph of 8x + 4y = 3 and intersects that graph at its x-intercept. (5pts) cept at (0.75, 3) 2

3 Name: ID: 8. Write an equation in slope-intercept form for the line that satisfies the following condition. Passes through (6, 11), parallel to the line that passes through (2, 4) and (23, 23) (5pts) a. y = x b. y = 39 7 x c. y = x + 6 d. y = 19x Write an equation in slope-intercept form for the line that satisfies the following condition. Passes through (29, 8), perpendicular to the graph of y = 1 x + 17 (5pts) 13 a. y = 385x b. y = -13x c. y = 1 13 x d. y = -13x + (-13) Identify the type of function represented by the graph. 10. (5pts) a. absolute value function c. quadratic function b. inverse variation function d. rational function Identify the type of function represented by the equation. 11. y = -7.5x (5pts) a. absolute value function b. direct variation function c. identity function d. constant function 3

4 Name: ID: Short nswer Identify the type of function represented by the equation 12. y = 5x + 2 (5pts) 13. Graph the line that passes through ( 1, 5), perpendicular to a line whose slope is (5pts) 15. Write an equation in slope-intercept form for the line that satisfies the following condition. slope 1 and passes through (4, 17) 2 (5 Pts) Graph each function. Identify the domain and range. 16. g(x) = x (5pts) 14. Write an equation in slope-intercept form for the line that satisfies the following condition. (5PTS) slope 5 and passes through (2, 28) 4

5 Name: ID: Ï -6 if x < r(x) = Ì Ô 2 x if - 1 x < 3 (6POINTS) ÓÔ 2x + 1 if x! (4PTS) monthly phone bill, b, in dollars, consists of a $28 service fee plus $0.14 per minute, m, for long distance calls. Write the amount of the bill as a function of the minutes used. How much will the monthly bill be when 70 minutes of long distance calls were made in a month? 19. I QUESTIONS: (MXIMUM OF 5 POINTS - 3 EXTR REDIT) When an object is thrown up in the air with a given initial height and velocity, its position is given as a function of time by starting with the initial height, adding the product of the initial velocity and the time, and adding the product of half the gravitational acceleration and the square of the time to that. On the surface of the earth, the acceleration due to gravity is 9.8 m/s 2. If an object is thrown from a height of meters at an initial velocity of 7.87 meters per second, write the position function of the object. Use the position function to find the position of an object after 3 seconds. (cceleration is negative if an object is thrown up.) 5

6 Name: ID: Find ND STTE the x-intercept and the y-intercept of the graph of each equation. Then graph the equation. 20. GRPH LL PROLEMS IN ONE GRPH and LEL each line (6PTS) ). x = 2 ). 9x + 6y = 27 )g(x) = 5x ) X-intercept: ) X-intercept: Y-intercept: Y-intercept: ) X-intercept: Y-intercept: Other 21. Graph the Fumction f(x) = [[ x ]] + 3 (4Pts) 6

7 LGER 2 HONORS - HPTER 2 TEST nswer Section MULTIPLE HOIE 1. NS: Substitute x = 9 in the equation f(x) and x = 4 in the equation g(x). D orrect! You have to substitute the values of f(x) and g(x) in the subsequent equations. Did you substitute the value in f(x) as well? You have subtracted instead of adding. PTS: 1 DIF: verage REF: Lesson 2-1 OJ: Find functional values. TOP: Find functional values. KEY: Functional Values Functions 2. NS: D ny linear function can be written in the form f(x) = mx + b, where m and b are real numbers. D Is the given equation in a linear form? Did you perform the mathematical actions correctly? What is the form of this equation? orrect! PTS: 1 DIF: verage REF: Lesson 2-2 OJ: Identify linear equations and functions. ST: M M TOP: Identify linear equations and functions. KEY: Linear Equations Functions 3. NS: D The standard form of the equation is x + y =, where! 0 and and are non-zero numbers. What is the standard form of linear equations? What is the coefficient of y? Did you apply the mathematical operators correctly? D orrect! PTS: 1 DIF: asic REF: Lesson 2-2 OJ: Write linear equations in standard form. TOP: Write linear equations in standard form. ST: M M KEY: Linear Equations Standard Form 1

8 4. NS: D The slope of a line is the ratio of the change in the y-coordinates to the corresponding change in the x-coordinates. That is, the slope of a line = y 2 - y 1 x 2 - x 1. Substitute the values of x 1, y 1, x 2, and y 2 to find the slope of the line. D Did you calculate the ratio of change in the y-coordinates to the change in the x-coordinates? Is this the correct ratio of change in the y-coordinates to the change in the x-coordinates? The values of x- and y-coordinates are to be subtracted and not added. orrect! PTS: 1 DIF: verage REF: Lesson 2-3 OJ: Find and use the slope of a line with integer points. TOP: Find and use the slope of a line with integer points. KEY: Slope Integers Graphs 5. NS: The slope of a line is y 2 - y 1 x 2 - x 1. Substitute the values of x 1, y 1, x 2, and y 2 to find the slope of the line. D Did you calculate the ratio of change in the y-coordinates to the change in x-coordinates? orrect! Is this the correct ratio of change in y-coordinates to the change in x-coordinates? You have to calculate the ratio of change in the y-coordinates to ratio of change in the x-coordinates. PTS: 1 DIF: dvanced REF: Lesson 2-3 OJ: Find and use the slope of a line with decimal points. TOP: Find and use the slope of a line with decimal points. KEY: Slope Decimals Graphs 2

9 6. NS: Use the equation y - y 1 = m Ê x - x ˆ 1 to find the equation of the line passing through the point. You have to perform calculations on both x- and y-coordinates to obtain a parallel line. orrect! Is this the correct slope of line? PTS: 1 DIF: verage REF: Lesson 2-3 OJ: Graph parallel lines. TOP: Graph parallel lines. KEY: Graphs Parallel Lines 7. NS: Substitute the values of x 1 and y 1 in the equation y - y 1 = m Ê x - x ˆ 1 to get the equation of the line passing through the x-intercept. orrect! Do the lines appear to be perpendicular?. What should be the slope of the intersecting line? PTS: 1 DIF: verage REF: Lesson 2-3 OJ: Graph perpendicular lines. TOP: Graph perpendicular lines. KEY: Graphs Perpendicular Lines 8. NS: The point-slope form of the equation of a line is y - y 1 = m Ê x - x ˆ 1, where Ê x,y ˆ 1 1 are the coordinates of a point on the line and m is the slope of the line. D orrect! Substitute the values of the x- and y-coordinates in slope formula to calculate the slope. You have calculated the value of y-intercept incorrectly. You have to calculate the ratio of change in x- and y-coordinates. PTS: 1 DIF: dvanced REF: Lesson 2-4 OJ: Write an equation of a line parallel to a given line. ST: M TOP: Write an equation of a line parallel to a given line. KEY: Parallel Lines Equations of Parallel Lines 3

10 9. NS: The point-slope form of the equation of a line is y - y 1 = m Ê x - x ˆ 1, where Ê x,y ˆ 1 1 are the coordinates of a point on the line and m is the slope of the line. The slopes of perpendicular lines are opposite reciprocals. D What must the slope be if the line is perpendicular to the given line? orrect! The slope value is incorrect. Did you calculate the y-intercept correctly? PTS: 1 DIF: dvanced REF: Lesson 2-4 OJ: Write an equation of a line perpendicular to a given line. ST: M TOP: Write an equation of a line perpendicular to a given line. KEY: Perpendicular Lines Equations of Perpendicular Lines 10. NS: Identify the general function represented by the graph. The graph of an absolute value function is in the shape of a V. Does the equation of an inverse variation function apply to this graph? orrect! D Does the equation of a rational function apply to this graph? PTS: 1 DIF: asic REF: Lesson 2-7 OJ: Identify graphs as different types of functions. ST: M M M TOP: Identify graphs as different types of functions. 11. NS: The general equation of a direct variation function is y = ax. KEY: Graphs Types of Functions Functions The equation of an absolute value function is y = x. orrect! The equation of an identity function is y = x. D The equation of a constant function is y = a. PTS: 1 DIF: asic REF: Lesson 2-7 OJ: Identify equations as different types of functions. ST: M M M TOP: Identify equations as different types of functions. KEY: Equations Types of Functions Functions 4

11 SHORT NSWER 12. NS: Square root function If an equation includes an expression inside the radical sign, the function is a square root function. Its graph is a curve that starts at a point and continues in only one direction. Make a table of values, plot the points, and then draw the graph. PTS: 1 DIF: dvanced REF: Lesson 2-7 OJ: Identify graphs and equations as different types of functions. ST: M M M TOP: Solve multi-step problems. KEY: Multistep Problems 5

12 13. NS: Substitute the values of x 1 and y 1 in the equation y - y 1 = m Ê x - x ˆ 1 to get the equation of the line passing through the point ( 3, 5). PTS: 1 DIF: verage REF: Lesson 2-3 OJ: Graph perpendicular lines. TOP: Graph perpendicular lines. KEY: Graphs Perpendicular Lines 14. NS: y = 5x + 18 Substitute the values of the x- and y-coordinates in the equation y - y 1 = m Ê x - x ˆ 1. Manipulate the equation to get it in the slope-intercept form. PTS: 1 DIF: dvanced REF: Lesson 2-4 OJ: Write an equation of a line given the slope and a point on the line. ST: M TOP: Write an equation of a line given the slope and a point on the line. KEY: Equations of Lines Slope Graphs 15. NS: y = 1 2 x - 19 Substitute values of the x- and y-coordinates in the equation y - y 1 = m Ê x - x ˆ 1. Manipulate the equation to get it in the slope-intercept form. PTS: 1 DIF: dvanced REF: Lesson 2-4 OJ: Write an equation of a line given the slope and a point on the line. ST: M TOP: Write an equation of a line given the slope and a point on the line. KEY: Equations of Lines Slope Graphs 6

13 16. NS: Ï Domain = all reals; Range = Ì Ô y y! 2 ÓÔ Ô Ô PTS: 1 DIF: verage REF: Lesson 2-6 OJ: Identify and graph step functions, constant function, identity functions, absolute value functions and piecewise functions. ST: M M M TOP: Solve multi-step problems. KEY: Multistep Problems 17. NS: Ï Domain = all reals; Range = Ì Ôy y < 15 ÓÔ 2 or y! 17 2 Ô Ô PTS: 1 DIF: dvanced REF: Lesson 2-6 OJ: Identify and graph step functions, constant function, identity functions, absolute value functions and piecewise functions. ST: M M M TOP: Solve multi-step problems. KEY: Multistep Problems 7

14 18. NS: b = m; $37.80 First write the linear function for the situation and then solve it to find the required answer. PTS: 1 DIF: verage REF: Lesson 2-1 OJ: nalyze and graph relations and find functions values. TOP: Solve multi-step problems. KEY: Multistep Problems 19. NS: x(t) = -4.9t t , where t denotes the time and x denotes the position after t seconds; 8.32 meters First write the linear function for the situation and then solve it to find the required answer. PTS: 1 DIF: dvanced REF: Lesson 2-1 OJ: nalyze and graph relations and find functions values. TOP: Solve multi-step problems. KEY: Multistep Problems 20. NS: 2 3 ; none The y-coordinate of the point at which a graph crosses the y-axis is called the y-intercept. Likewise, the x-coordinate of the point at which it crosses the x-axis is the x-intercept. PTS: 1 DIF: asic REF: Lesson 2-2 OJ: Identify linear equations and functions, write linear equations in standard form and graph them. ST: M M TOP: Solve multi-step problems. KEY: Multistep Problems 8

15 OTHER 21. NS: PTS: 1 9