Algebra 1 Sem 2 Part A REVIEW ink2.notebook Algebra 1 Sem 2 Part A Review May 19, 2017 2. Solve the following system of equations using the substitution method. Make sure you SHOW YOUR WORK!!! 1. Graph the following lines on the grid provided and determine the solution. Solution: _____________ Solution: _____________ 4. Solve the following system of equations by the elimination method. 3. Solve the following system of equations by the elimination method. Solution: _____________ Solution: _____________ 1 Algebra 1 Sem 2 Part A REVIEW ink2.notebook 5. Use elimination to solve the system of equations. May 19, 2017 6. You have started your own gardening business. Your cost to buy equipment and advertise was $250. If every garden costs $12 for fertilizer and plants, and you charge $17 for each garden, how many gardens must you put in before you break even? Write the equations and solve. Remember to label your answer. COST = REVENUE 8. Given the following systems, identify which one has 1 solution, which one has no solution and which one has many solutions. Then EXPLAIN why they have that type of solution. 7. Determine how many solutions exist in the graph shown. a. no solution b. one solution c. infinitely many solutions d. cannot be determined 2 Algebra 1 Sem 2 Part A REVIEW ink2.notebook Find the simplest form of each. No decimal answers. Find the simplest form of each. No decimal answers. May 19, 2017 Find the simplest form of each. No decimal answers. 14. Express the perimeter of the figure as a polynomial in simplest form. 3 Algebra 1 Sem 2 Part A REVIEW ink2.notebook Simplify completely. (No negatives in your final answer.) May 19, 2017 Simplify completely. (No negatives in your final answer.) 17. 6y8 ¥ 4y3 20. Abe, Connor, and Evan all simplified the same exponential expression. Circle the one(s) that is correct and explain why. Simplify completely. (No negatives in your final answer.) Why: _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ 4 Algebra 1 Sem 2 Part A REVIEW ink2.notebook The given graph shows the downward movement of a person jumping on a trampoline. Use it to answer the following questions. May 19, 2017 26. Find the coordinates for the vertex and the equation for the axis of symmetry of y = 3(x + 2)2 – 5. 21. Circle One: Maximum or Minimum 22. Vertex: ________ a) Vertex: _______ 23. yintercept: ___________ 24. Domain: ___________ b) Axis of symmetry: ________ 25. Range: __________ 27. In your own words, describe how the graph of y = –2x2 and are different in two separate ways? Factor each trinomial completely. 28. 6x2y – 18x3y2 + 9x 29. m2 + 17m + 72 5 Algebra 1 Sem 2 Part A REVIEW ink2.notebook May 19, 2017 Factor each trinomial completely. Factor each trinomial completely. 30. 3n2 – 6n – 144 31. Factor by grouping: 6x2 – 9x + 8x – 12 Factor each trinomial completely. 33. Factors and solve: x2 – x – 42 32. Factor: 4x2 – 11x – 3 (______)(______) = 0 x = _____ and x = _____ 6 Algebra 1 Sem 2 Part A REVIEW ink2.notebook May 19, 2017 Solve each equation completely by showing all work. 34. a) Factor the following 2 trinomials: 2x2 – 4x – 30 2x2 – 7x – 15 35. (3x + 7)(x – 5) = 0 36. 81x2 – 25 = 0 b) Look at how you factored each trinomial and compare the two methods. Solve each equation completely by showing all work. 37. 5(x – 4)2 = 45 38. Solve the equation 2x2 – 28x + 48 = 0 using the quadratic formula. 7 Algebra 1 Sem 2 Part A REVIEW ink2.notebook 39. Find the discriminant for the equation 2x2 + 4x – 9 = 0 41. A rock is dropped from a bridge 128 ft above the water. The equation h = –16t2 + 128 models this situation. When does the rock hit the water? Round answers to the nearest hundredth. May 19, 2017 40. How many real solutions does the equation 3x2 – 4x + 1 = 0 have? 42. A football is thrown out of bounds to stop the clock at a velocity of 40 ft/sec from the quarterback’s arm, which is a height of 5 ft. If the clock stops when the football touches the ground out of bounds, use the equation H = –16t2 + 40t + 5 to find how long it takes to stop the clock. Round answer to the nearest hundredth. 8 Algebra 1 Sem 2 Part A REVIEW ink2.notebook May 19, 2017 44. Given x2 – 8x = 12, x2 + 7x + 12 = 0, y = x2 – 2x – 15, 5x2 + 4x – 64 = 0 43. Solve x2 – 6x = 40 by completing the square. a) Which equation would you solve by graphing? EXPLAIN WHY. b) Which equation would you solve by factoring? EXPLAIN WHY. c) Which equation would you solve by completing the square? EXPLAIN WHY. d) Which equation would you solve by the quadratic formula? EXPLAIN WHY. 9
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