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Algebra 1 FINAL EXAM Preview Semester 2: Short Answer Name ______________________ Make sure you SHOW YOUR WORK!!! 1. Graph the following lines on the grid provided and determine the solution. y 2x 1 y x 4 Solution: (___, ___) 3. Solve the following system of equations by the elimination method. x y 6 x y 4 Solution: (___, ___) 2. Solve the following system of equations using the substitution method. y x 3 6x 3y 0 Solution: (___, ___) 4. Solve the following system of equations by the elimination method. (multiply first) 2x 3y 13 x y 1 Solution: (___, ___) 5. You have started your own lawn mowing business. Your cost to buy equipment and advertise was $320. If every lawn costs $8 for gas and oil, and you charge $12 for mowing each lawn, how many lawns must you mow before you break even? Write the equations and solve. Remember to label your answer. 6. Solve the equation by showing all work: 2x 4 6 (get rid of first) Solution: _____________ Simplify completely. 7. 10x 8 y 2 5x 2 y 5 8. Solution: _____________ 3 a 2 b 7 Solution: _____________ 9. Find the degree of the polynomial: 3x3 + 4x5 + y Degree: _________ 10. A researcher studied the number of overnight stays in U.S. National Park Service campgrounds and in the backcountry of the national park system over a 5 year period. The researcher modeled the results, in thousands, with the following polynomials. Campgrounds: Backcountry: – 7.1x2 – 180x + 5800 21x2 – 140x + 1900 What polynomial models the total number of overnight stays in both campgrounds and backcountry? Total = _____________________________ 11. On Monday Jill had $80 in her account. On Tuesday she had $40 in her account and on Wednesday she had $20. If this pattern continues, write a rule for the nth term of the geometric sequence. an = a1 • r(n − 1) 12. You bought a new computer for $3500 in 2005. The computer depreciates at a rate of 18% per year. What is the value of the computer 3 years after you bought it? Round to the nearest cent. Use the formula: y = a(1 – r)t Solution: _____________ 13. Find the product: (x + 5)(x2 – 7x + 12) (FOIL or box) Solution: _____________________ 14. The arc of a ball that is thrown underhand can be modeled by the equation y = x2 + 4x + 7. Complete the T-chart below for the equation. y = x2 + 4x + 7 X –1 –2 –3 Y 15. Use the T-chart from problem #16 to graph the equation. The given graph shows the downward movement of a person jumping on a trampoline. Use it to answer the following questions. 15. Circle One: Maximum or Minimum 16. Vertex: ________ 17. y-intercept: ___________ 18. In your own words, describe how the graph of y = 6x2 and y = 1 2 x are different in two separate 2 ways? (up vs. down and narrow vs. wide) ________________________________________________________________________________ ________________________________________________________________________________ ________________________________________________________________________________ 19. Find the coordinates for the vertex of y = 2(x – 4)2 + 1. a) Vertex: _______ 20. Factor by special case. 16x2 - 49 ( _______)( _______) 21. Solve the equation. (2x – 3)(x + 2) = 0 x = _____ and x = _____ 22. Factor and solve: x2 – 2x – 35 (______)(______) = 0 x = _____ and x = _____ 23. Use the quadratic formula to find the solutions to : 4x2 – 4x - 15 b (b) 2 4ac x 2a 24. Find the discriminant of 2x2 – 8x + 10 = 4 25. The data below shows the number of hours per week a group of students spent watching television. Make a histogram to represent the data. 7 10 1 5 14 22 6 8 0 11 13 3 4 14 5