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SPRING FINAL Review Algebra I 2016
SPRING FINAL Review Algebra I 2016 1. (2A) Henry has $85.50 to spend on candy at the store each month. What is a reasonable range for this data? 2. (2I) Meg is making three placemats for her table, all of them will be equal in size and shape. If she lines the edge of each of them with ribbon she will need 80 inches of ribbon for the perimeter of each placemat. She will use 240 inches of ribbon for this project. Write a system of equations to represent this situation. 3. (2I) Write the equation of the line in the graph below. 4. (3B) What is the rate of change? 5. (3C) The cost, 𝐶, of getting your car repaired is given by where ℎ is the number of hours in labor the mechanic works on your car, 55 is the cost per hour the mechanic charges, and 190 is the cost for the parts needed to repair your car. This situation is represented by 𝐶 = 55ℎ + 190. What would the 𝒙-intercept represent in this situation? 6. (5A) Solve the equation for 𝑥. 8. (3C) Write the equation of this line in standard form. 9. (6A) What is the range of 𝑓(𝑥) = 2𝑥 2 + 9? 𝒙 5 4.5 2 1.5 0.5 y 60 180 240 540 600 7.(5C) A system of equations is used to produce the set of points in the table below. What is the x value of the solution? 𝑥 −6 −3 𝑦 −18 −12 𝑦 18 12 3 0 0 6 -6 6 9 −12 12 8(𝑥 − 6) = −2𝑥 − 6.9 SPRING FINAL Review Algebra I 2016 10. (7A) The table below represents a quadratic equation. Complete a new table and fill in the gaps as 𝑔(𝑥) 𝑥 best you can. 𝑥 −1 2 5 6 9 10 12 14 11. (6C) Write the quadratic equation of the graph below in vertex form. 𝑓(𝑥) = 𝑎(𝑥 − ℎ)2 + 𝑘 𝑔(𝑥) −55 −16 5 8 5 0 −16 −40 12. (6A) The table below shows ordered pairs that satisfy the quadratic function 𝑓. Between 𝑥 𝑓(𝑥) what interval would I −2 31 find: −1 20 1. f(x) = 3 0 11 1 4 2. f(x) = 0 2 −1 3. f(x) = -2.5 3 −4 4 −5 -4 5 14. (7A) Between what two numbers would I find the positive zero of this parabola? Between what two numbers would I find the negative solution? 15. (8A) What are the zeroes of the function 𝑦 = 𝑥 2 − 16 13. (7B) A quadratic function 𝑓 has 𝑥-intercepts at −6 and 2. Write a quadratic function in standard form to represent this situation. 16.(3D) A teacher wants to spend less than $300 on supplies for paper and pencils. Supplies for 1 ream of paper cost $4 and supplies for 1 box of pencils cost $9. This relationship is shown in the graph below. 1. Could she buy 20 reams of paper and 25 boxes of pencils? 2. Could she buy 10 reams of paper and 25 boxes of pencils? SPRING FINAL Review Algebra I 2016 17. (9C) The half-life of an element is the length of time it takes for the number of atoms in a sample to be decreased by half. One element, which has a half-life of 35 years has a function in the form: 𝒕 𝒚 = 𝒂(𝟎. 𝟐𝟓)𝒙 18. (9C) The value of a boat is depreciating at a rate of 7% per year. In 2004, the boat was worth $192,000. Find the worth of the boat in 2013. This represents the amount 𝑦 of a substance remaining after 𝑡 years, where 𝑎 is the initial amount and 𝑥 is the length of the half-life in years. Write an equation that could be used to find the decay of a 6-gram sample of this element after 8 years? 19. (7C) Given the following quadratic equations: 𝑓(𝑥) = −𝑥 2 + 64 𝑔(𝑥) = −2𝑥 2 − 51 ℎ(𝑥) = 𝑥 2 + 14 20. (7C) Write an equation for the function g(x) in vertex form. It is 𝑓(𝑥) = (𝑥 − 8)2 + 10 translated 2 units up and 5 units left. 1. Do they have the same y-intercept? 2. Do they have the same axis of symmetry? 3. Do they have the same vertex? 4. Do the have a max or a min vertex? 21. (8B) An object is launched into the air. The table below shows the object’s height above the ground at various times. Use a quadratic regression on your calculator to find the height at 11 seconds. 23. (7C) Identify the transformations of the graph of the parent function 𝑓(𝑥) = 𝑥 2 needed to obtain the graph of 𝑔(𝑥) = −3(𝑥 + 2)2 + 4. 22. (8A) What is the solution to: 5𝑥 2 − 14𝑥 = 3 24. (8A) What are the solutions to the quadratic equation: 𝑦 = 3𝑥 2 − 7𝑥 + 6? SPRING FINAL Review Algebra I 2016 1 25. (9D) The function 𝑓(𝑡) = 300( )𝑡 4 represents the number of Moose in Yellowstone park after t years. If this function is graphed on a coordinate grid, what would be the meaning of the 𝑦-intercept? 28. (10E) The area of a rectangular piece of wood is represented by: 26. (10D) Simplify the following expression: (3𝑥 − 2)(5𝑥 + 7) 29. (10F) Factor completely: 4𝑥 2 − 81𝑦 2 Find the dimensions of the piece of wood. 6𝑥 7 𝑦 2 z−1 30𝑥 4 𝑦 2 𝑧 −4 inches. 30. (11B) Simplify the following expression: 1 (81𝑎7 )2 2𝑟 2 − 13𝑟 + 21. 31. (11B) Find the area of a square with a side length of 27. (10E) The base of a triangle is 4 inches less than twice its height. If the area of the triangle is 132 square inches, write an equation in standard form to find the height of the triangle in inches? Notes: