Algebra 2/Trigonometry Summer Review Packet
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1 Algebra 2/Trigonometry Summer Review Packet This packet is designed to help you review the mathematical topics that you will need to be successful at AOSR. To receive full points for this required packet, you are required to submit this during first week of school. You must show your work and answer each problem for full credit. Name:
2 Explain in your own words what each word means to you in terms of mathematics: a) Evaluate b) Simplify c) Solve Order of Operations Evaluate each expression. Write your answer in simplest form Fractions Evaluate each expression. Write your answer in simplest form. Where applicable, leave answers as improper fractions. (Reduce, reduce, reduce) 4. + " " 7. " Simplifying Expressions Simplify each expression. Write your answer in simplest form. 8. 7x + 12x x 40x 9. 5 y + y 3 y 2n Evaluating Expressions Evaluate each expression for the given values. Write your answer in simplest form. 10. when x = 3 and y = () when x = 3 and y = 3
3 Exponents Simplify each expression. Write your answer in simplest form. Where applicable, leave answers as improper fractions. The simplified expression should have no negative exponents x 13. x y What is anything raised to the zero power? 16. Complete the table by raising each value of x to the given power. (Note: you will be responsible for knowing the following values without a calculator) x x x x x Radicals Simplify each radical (look for the largest perfect square). Do NOT write in decimal form
4 Solving Linear Equations Solve each equation. Do NOT write your answers as decimals. If you get a fraction, write it in a reduced improper fraction x + 11 = 15 6x x + 5 = 4 x x 2 = Rewriting Formulas Solve for the indicated variable. 24. Solve for r. A = πr 25. Solve for h. V = πr h Solving Linear Inequalities Solve the inequality. Then graph your solution on a number line. 26. x 7 < x 1 14 x x x + 2 < 10 or 2x 4 > 4
5 Solving Absolute Value Equations and Inequalities Solve each absolute value equation and inequalities. Remember that there should be two answers. 30. x = x + 3 = x < 3 Application problems Solve each application problem. Write your final answer in a complete sentence that is in context to the problem. 33. You have borrowed $529 from your parents to buy a mountain bike. Your parents are not charging you interest, but they want to be repaid as soon as possible. You can afford to repay them $20 per week. How long will it take you to repay your parents? 34. You are working on a project in woodshop. You have a wooden rod that is 72 inches long. You need to cut the rod so that one piece is 6 inches longer than the other piece. How long should each piece be? Slope Use the slope formula to calculate the slope of each line given the points. Slope = m = rise run = y x = y 2 y 1 x 2 x , 4 ; 6, , 4 ; 8, 1
6 Graphing Linear Equations Graph each linear equation on the axis provided. Find both the x and y- intercepts. Make sure to label your axis and scale. 37. y = 2x y = x y = x 40. 8x 2y = 14 Writing Linear Equations Write the equation of each line in slope- intercept form. y = mx + b ; where m = slope and b = y intercept 41. 0, 4 ; m = , 5 ; m = , 9 ; ( 4, 7)
7 Linear Inequalities in Two Variables Graph each linear inequality on the given xy- coordinate plane. Don t forget to shade all solutions. 44. y < 3x y x + 1 Solving Systems of Linear Equations Solve each linear system by the given method. Write your answer as a coordinate point. 46. Solve by graphing. y = x 5 x + 3y = Solve by substitution. 3x y = 4 5x + 3y = Solve by elimination (linear combination). 5x + 2y = 10 3x 6y = 18
8 49. Explain in your own words when a linear system has one solution, no solution, or infinitely many solutions. Graphing Systems of Linear Inequalities Graph each linear system on the given xy- coordinate plane. Shade all solutions that satisfy both inequalities. 50. y x y > 2x 7 y > 1 4x + 4y < 12 Linear Systems Problem Solving Solve each application problem with a system of linear equations. Write your answer as a complete sentence in context to the problem. 52. Tickets to a production of Romeo and Juliet at Green River Community College cost $5 for general admission or $4 with a student ID. If 184 people paid to see a performance and $812 was collected, how many of each type of ticket were sold? 53. Carmelo and LeBron found that the width of their basketball court was 44 feet less than the length. If the perimeter was 288 feet, what were the length and the width of their court?
9 Polynomial Operations Perform the indicated operation. Write your answer in simplest terms (combine like terms) y y 55. 3x + 7x 6 (3x + 7x) 56. 2x + 3 3x x + 6 (x 6x 2) Factoring Factor each polynomial. Use the following steps to help you factor. 1. Factor out the greatest common factor. If is one, then don t factor out the GCF. 2. If the polynomial is a binomial (two terms), check to see if it is a difference of two squares. If the polynomial is a trinomial (three terms), check to see if it is a perfect square trinomial. If not, then factor the trinomial as you learned in your last algebra class. 3. Check the factored form by multiplying x 20x 59. x + 2x x 8x x x + 3x x + 2x 8x
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