ALGEBRA 1 Semester Final Exam Review #1 Name Date: Semester Exam will cover the following: Unit 4 Linear Functions Slope, slope intercept form, standard form Write equations of linear functions given different pieces of information: table, graph, two points, a word problem. Compare linear functions (application problems) Unit 5 Systems of Equations & Inequalities Solve by graphing, substitution, & elimination. Writing systems from word problems. Unit 6 Polynomials & Factoring Add, sub, & multiply polynomials Factor out GCF, trinomials, difference of two squares, & grouping. Solve quadratic equations Unit 7 Quadratic Functions Solve quadratic equations by the quadratic formula Use the discriminant to describe the number and nature of solutions Graph quadratics and name vertex, zeros, axis of symmetry, and max/min Solve systems of quadratics & linear functions by graphing and with graphing calculator. Analyze graphs of quadratics Modeling with quadratic functions: motion of an object under the force of gravity Unit 4: 1. The slope of a vertical line =. The slope of a horizontal line = 3. Find the slope: (4, -) (-1, 7) 4. The slope-intercept form of a line with a slope of -/3 and y-int -4: 5. Find the x and y intercepts of 3x + 7y = 1 x-int: y-int: 6. Use the points (, 6), (3, 10) to write an equation of the line that: a.) is in standard form: b.) is parallel to the given line (same slopes): c.) is perpendicular to the given line (slopes are opposite reciprocals)
7. The cost of having a car towed is given by the linear function C ( x) = 3 x + 85, where ( x) C is in dollars and x is the number of miles the car is towed. Find the cost of having the car towed 13 miles. A) $39 B) $114 C) $14 D) $88 8. An example of a linear equation is f ( x) 8 4x A) at -4 B) at 0 C) at 8 D) at 4 9. Use the table to find the x-intercept. A) 3 B) 4 C) 5 D) no y-intercept =. Where does the graph start at on the y-axis? 10. The cost of having a garage door replaced requires two fees: a $55 service call to the home and then a $30 per hour labor charge. Which of the following represents the correct function notation? 11. Determine the slope and y-intercept of the function f ( x) 9 9 = x 1. Complete the table. Identify the slope, y-intercept, and write an equation. 13. Hans needs to rent a moving truck. The information is provided in the following table. Complete the table. Write an algebraic equation for the total cost, C, based on the number of days, d. Truck Rental Company: total cost, C $60 0 $100 1 $140 3 4 days, d
Unit 5: 14. Solve the system by substitution 15. Solve the system by elimination x= 5y 3x + 5y = 16 x + 5y =15 8x 5y = 8 16. A tour group split into two groups when waiting in line for food at a fast food counter. The first group bought 6 slices of pizza and 5 soft drinks for $8.93. The second group bought 5 slices of pizza and 5 soft drinks for $5.50. How much does one slice of pizza cost? Directions: Solve the systems of equations by elimination: 17. 18. 19. Graph the equation 5x + 3y = 15. 0. Solve the system of inequalities:
Unit 6: Multiply: 1. (3p + 9)(p 7). (3x + 4y)(3x 4y) 3. (3x + 8) 4. Find the GCF of 18ab c 3 and 54ab Factor: Remember to look for a GCF first!!! 5. 3x 75y 6. x y + x 9xy 9 7. 6a + 0a 16 8. x 4 9. x 8x + 16 30. Factor then solve the equation x 4x = 0. 31. A rectangle with positive area has length represented by the expression 3x + 5x 8 and width by x + 6x. Write expressions in terms of x for the perimeter and area of the rectangle. Give your answers in standard polynomial form and show your work. a. Perimeter: b. Area:
Unit 7: 3. An arrow is shot into the air. A function representing the relationship between the number of seconds it is in the air, t, and the height of the arrow in meters, h, is given by: h ( t) = 4.9t + 9.4t +. 5 a. What is the maximum height of the arrow? b. How long does it take for the arrow to reach it s maximum height? 33. Solve the following equations for r. Show your method and work. If no solution is possible, explain how you know. a. r + 1r + 18 = 7 b. r + r 3 = 4 c. r + 18r + 73 = 9 d. r 7 = r + r 1 34. Ryker is given the graph of the function y = x 4. He wants to find the zeros of the function, but is unable to read them exactly from the graph. Find the zeros using the quadratic formula.
35. If the quadratic formula is used to find the roots of the equation x 6x 19 = 0, the correct roots are: a) 19 ± 11 6 b) 8.3 & -.3 c) 11 36. The equation y = x + 3x 18 is graphed on the set of axes below. a.) Based on this graph, what are the roots of the equation x + 3x 18 = 0? A) -3 and 6 B) 0 and -18 C) 3 and -6 D) 3 and -18 37. Determine the domain and range of the graph below. 38. Using the equation 3x + 5x 1 = 0, find the value of the discriminant, use the value to determine the number of solutions, and find the solutions. Discriminant: # of Solutions: Solutions: