Solve the following equations. Show all work to receive credit. No decimal answers. 8) 4x 2 = 100

Transcription

1 Algebra Worksheet Name Solve the following equations. Show all work to receive credit. No decimal answers. 1) 3x 5(2 4x) = 18 2) x = -19x 25 3) 2 6x+9 b 4 = 7 4) = 2x 3 4 5) 3 = 5 7 x x+1 6) 4(2x 1) 5x = 2 +4(3 x) 7) 2 = 13 4y+1 8) 4x 2 = 100 9) 3x 2 1 = 26 10) Solve for y: 3y 2x = 12

2 For #11 14: Solve and graph each inequality. Show all work for credit. No decimal answers. 11) 5x 3 > 2x ) 12 (2h + 5) > 6h 9 13) b < 6 14) 8 2(5x + 1) < -8x ) Factor the trinomial: x 2 7x ) Factor the trinomial: a 2 + 3a 10 17) 18) Find the area of a circle with a circumference of 10π. 19) A rectangle has a width of 6 cm and a length of 8 cm. Find the length of the diagonal of the rectangle. 20) Multiply: (2x + 5)(3x 1 ) 21) Simplify: ) Simplify: 16 9

3 Algebra Worksheet Name For #1 12: Graph each line on a coordinate system. Identify the domain and range. 1) y = -x 4 2) y = 3(x 1) + 2 3) y = 5 (x + 4) 3 4) y = -5 5) y = 1 x + 5 6) x = ) y = 2x 8) y 5 = -2(x + 1) 9) y = -3x 1 10) x = 1 11) y = 5x 4 12) x = 2

4 For #13 23, write the equation of each line (in slope-intercept form unless otherwise specified.) 13) A line has a slope of 1 and an y-intercept of 6. 19) A line is perpendicular to the line 3x + 6y = 7 10 and goes through the point (12, -10). 14) A line has a slope of -3 and passes through the point (1, -5). 20) A line contains the point (8, 12) and is parallel to the line passing through (7, -1) and (5, -2). 15) A vertical line passes through the point (2, -8). (special line) 16) A line is parallel to y = 5x 1 and goes through the point (-10, -3). 21) A line is parallel to the line -9x 3y = 1 and contains the point (-4, -1). 21) 17) A line is perpendicular to the line y = -4x + 6, passing through the point (8, -1). 23) Factor: x 2 + 5x ) A horizontal line passes contains the ordered pair (-5, -15). (special line) + *

5 Algebra 2 Worksheet 1.3 Name For #1 6: Match each graph to its equation. Not all equations will be used. 1) 2) 3) 4) 5) 6) Choices: a) f(x) = 2 x b) y = 3(x + 1) c) y = 3(x 1) d) y = (x 1) 2 3 e) b(x) = x 4 1 f) g(x) = (x + 4) 2 1 g) y = x h) h(x) = x 2 3 i) y = - x + 4 j) y = -3 x For #7 15, sketch the graph of each function, including its vertex. Also, what is the domain and range? 7) y = (x + 2) 2 8) y = x 1 2 9) g(x) = x 1 + 5

6 10) f(x) = 2(x 3) ) y = x ) y = 1 x ) y = x ) y = 3 x 4 15) h(x) = 3(x 2) ) Factor: x 2 8x ) Multiply: (x 2)(3x + 1) 18) Solve: 5 x + 3 = ) Write the equation of a line in slope-intercept form that is 21) perpendicular to y = -x + 4, passing through (-3, -2). 20) Write the equation of a line in slope-intercept form that is parallel to 3x 4y = 8, passing through (8, 5).

7 Algebra Worksheet Name For #1 9, sketch a graph of each function and identify its domain and range. 1) y = x 3 4 2) g(x) = ) y = x 2 2x ) f(x) = 2 x 4 5) y = (x + 4) 3 5 6) y = 1 x 2 7) f(x) = 1 x+1 8) y = 2 x 3 5 9) h(x) = 4(x + 2) ) The function y = x 3 is transformed with a horizontal shift to the right 3 units, a vertical reflection, and a vertical stretch by a factor of 2. Which of the following shows the new equation of the function? A) y = 2(x + 3) 3 1 B) y = -2x C) y = -(x 3) D) y = -2(x 3) 3 11) Write the equation of the function graphed.

8 Factor each trinomial: 12) x 2 3x ) x x ) x 2 8x 20 15) Solve: 3 6(a 2) = 5(a + 8) 4a 16) Solve and graph: 7x 3 > 8x + 9 2x 3y = 8 17) Solve the system: { 3x + 3y = 2 18) 19) Write the equation of a line parallel to y = 7x 5, passing through the point (-3, 4). 20) Write the equation of a line perpendicular to y = 3x + 5, passing through the point (6, -1). 21) Write the equation of a horizontal line passing through (-11, 14).

9 Algebra Worksheet Name For #1 4, graph each piecewise function. 1 x 2 if x 1 4 1) y = { 3 if 1 < x < 3 (x 4) 2 if x 3 x if x < 0 2) g(x) = { 1 if x 0 5 if 6 < x 2 3) y = { 1 if 2 < x 2 3 if 2 < x 6 (x 4) 2 3 if x < 2 4) h(x) = { 1 if 2 x 3 2x + 5 if x > 3 For #5 6: Write the equations for the piecewise functions shown below. 5) 6)

10 7) Factor: x 2 9 8) Factor: x 2 7x 30 9) Factor: x x ) Simplify: ) Write the equation of a horizontal line passing through (-18, -15). 12) Write the equation of a line perpendicular to the line y = 6x 1, passing through (12, -2). 13) Which of the following is the correct simplification of 50? 14) Multiply: (3x 1)(3x + 1) A) 5 10 B) 10 5 C) 2 5 D) 5 2 For #15 16: Your cell phone plan costs $75/month and gives you unlimited talk, and 500 text messages per month, and no data plan. After 500 text messages, it costs $.10 per text you send. 15) Write a piecewise function to represent this situation. 16) How much will it cost to send 750 text messages? For #17 18: You go to the grocery store to buy some Snickers. A bag of Snickers costs $3.45, but if you buy 4 or more bags, they only cost $3.00 per bag. 17) Write a piecewise function to represent this situation. 18) How much would it cost to purchase 7 bags of Snickers? 19) Find the missing length: 20) The area of a circle is 144π cm 2. Find the radius y

11 Algebra 2 Ch 1 Practice Test Name For #1 6, solve each equation and solve and graph each inequality. No decimal answers! 2) 5 2(4x + 1) 6x = 9x + 7 1) 3x 5 2 = 4 7x 11 3) 5 b 2 = 13 4) -11x + 2 > -5(2x 3) 4 5) 6 2x > -4x ) Solve for y: 2x 3y = -12 For #7 18, for each function, sketch a graph, describe the transformation(s) from the parent function, and identify the domain and range. 7) y = -x 3 8) y = (x 1) ) y = 1 x 4 3 Transformations: Transformations: Transformations: D: D: D: R: R: R:

12 10) y = 1 x ) y = 2x+3 12) f(x) = x Transformations: Transformations: Transformations: D: D: D: R: R: R: 13) y = -2x 14) y = -2(x + 1) ) y = -3x 2 1 Transformations: Transformations: Transformations: D: D: D: R: R: R: 16) f(x) = 2 x ) y = 3(x 1) ) g(x) = 1 x + 2 Transformations: Transformations: Transformations: D: D: D: R: R: R:

13 19) Write the equation of a line, in slope-intercept form, that passes through (-12, 7) and is perpendicular to y = -2x ) Write the equation of a line, in slope-intercept form, that passes through (-4, -8) and is parallel to 3x 4y = 1. 21) Write the equation of a horizontal line passing through (7, -1). 22) Write the equation of a line, in slope-intercept form, passing through (-12, 4) and (-8, -1). 23) Factor: x 2 15x ) Factor: x 2 + 9x ) Factor: x 2 x 12 26) What is the range of the function shown? a) (, 4] b) [4, ) c) (, 2] d) [ 2, ) e) (, ) 27) A circle has area of 25π ft 2. Find the circumference of the circle, in terms of π.

14 28) Write the equation of a vertical line passing through (9, -14.) 29) Write the equation of a line, in slope intercept form, that contains the point (12, -9) and is parallel to the line passing through (7, -1) and (10, -2). For #30 33, graph each piecewise function. 3x 6 if x 2 30) y = { 2 if 2 < x < 1 x if x 1 31) g(x) = { (x + 3)2 4 if x < 0 x if x 0 2 if 6 < x 2 32) y = { 1 if 2 < x 2 3 if 2 < x 6 x 2 1 if x < 1 33) h(x) = { 4 if 1 x 3 2x 3 if x > 3 34) Write the equations for the piecewise function shown. For #35 36: Your cell phone plan costs $68/month and gives you unlimited talk, and 1000 text messages per month, and no data plan. After 1000 text messages, it costs $.20 per text you send. 35) Write a piecewise function to represent this situation. 36) How much will it cost to send 1200 text messages?

15 Ch 1 Practice Test Answers 1) ) ) 12 4) x < -13 5) x > 2 6) y = 2 x ) vertical reflection, down 3 8) right 1, up two 9) vertical compression by a factor of 3, right 4 D: all real numbers D: all real numbers D: all real numbers R: all real numbers R: y > 2 R: y > 0 y = 2 x+3 10) left 2, down 3 11) vertical reflection, left 3 12) vertical reflection, up 1 D: all real numbers; x 2 D: all real numbers D: all real numbers R: all real numbers; y 3 R: y < 0 R: all real numbers 13) vertical reflection, vertical stretch 14) vertical reflection, vertical 15) vertical reflection, vertical stretch by a factor of 2 by a factor of 2, left 1, up 3 by a factor of 3, down 1 D: all real numbers D: all real numbers D: all real numbers R: all real numbers R: all real numbers R: y < -1 16) vertical reflection, up 5 17) vertical stretch by a factor of 3, up 2 18) vertical reflection, up two D: all real numbers D: all real numbers D: all real numbers; x 0 R: y < 5 R: all real numbers R: all real numbers; y 2 9) y = 1 x ) y = 3 x 5 21) y = -1 22) y = 5 x 11 23) (x 14)(x 1) ) (x + 5)(x + 4) 25) (x 4)(x + 3) 26) A 27) 10π ft 28) x = 9 29) y = 1 x ) 31) 32) 3 3 x if x < 2 33) 34) y = { 1 if 2 x 1 3 if x > 1 68 if t ) C(t) = { (t 1000) if t > ) $108