Immaculate Heart Academy Summer Math Assignment for Algebra II Honors and Algebra II/Pre- Calculus- STEM COURSE CODES (50 and 551- STEM) LEARN PRACTICE EXCEL You are taking Algebra II Honors or Algebra II/Pre- Calculus Honors- STEM in the fall. A mastery of and proficiency in performing the following Algebra and Geometry skills will be necessary for success in this Algebra II Honors or Algebra II/Pre- Calculus honors level course. Referencing class notes from Algebra I Honors or Algebra I/Algebra II Honors and Geometry Honors will be very helpful in doing the problems presented in this review. Work on each problem in order. Copy the problem onto loose- leaf paper except where you are directed to show all work in the space provided or to present graphs. Show all work in a neat and organized manner. Box in your final answer. Complete this entire assignment and bring it to class on the first day. This assignment is mandatory. We recommend that you periodically go to this packet during the summer rather than attempting to do all of it in your last week. That will allow you to really process these important skills. You will be given a proficiency test within the first week of school on the topics in this assignment. If you demonstrate mastery of these topics (grade of 90 or better) you will be awarded a bonus point at the end of the first quarter. The most significant reward to you will be your smooth transition into Algebra II Honors or Algebra II/Pre- calculus Honors STEM this September!! At the end of this assignment are several links to websites that you might find helpful should you have any problems with your assignments. Name: Date: Math Class last year: Teacher: 1
I. Perform the indicated operation(s). You must find the LCD and simplify your answer. Do not use a calculator. 1. 8 + 5 1. 7 4 1 1. 5 1 1 6 4. 8 9 + + 1 5. 1 + 1 + 1 4 6. 9 11 5 5 6 7. 1 + 4 10 1 5 8. 8 4 + 1 9. 7 15 4 5 + 10. 1 8 10 + 5 4 11. 5 1 8 4 1. 4 8 5 6 1. 9 5 + 1 14. 1 0 + 8 II. Perform the indicated operation(s). Simplify the result. Do not use a calculator. 1. x 8 1. 8x 1 4. 4x 4. 1 5. 1 4 6. 5 7. 18x 9 8. x +10 9. 56 + x 8 10. 45 5x 5 11. 4x 4 1. 15x 7 5
III. SLOPE 1. Identify the Slope Formula:. Use the slope formula to find the slope through the following pairs of points: a. (,) (1, 5) b. ( 4,1) (6,1) c. 0, 9, 17 d. 6, 1 6,. Determine the value of y so the line passing through this pair of points has the given slope: (, ),(7, y);m = 1 4. Determine the slope of the graph of the linear function f, given: ( ) = 1, f ( 5) = 1. f IV Writing Equations of lines. Use the point slope formula y y 1 = m(x x 1 ) to write the equation of the line: 1. That passes through the points 0, 9, 17.. That is parallel to y = x 4 and passes through the point ( 1,5).. That is perpendicular to y = x + 1 and passes through the point ( 5,).
V. Use the points A (4, 1) and B (8, ). Show all work in the space provided. a) Present the graph of AB. b) Find the midpoint of AB Midpoint: c) Find the slope of AB using the Slope Formula. Confirm by box- counting. Slope: d) Determine the slope of the line perpendicu- lar to AB Ans.: e) Write an equation of the line that is the perpendicular bisector of AB in point- slope form, slope- intercept form and standard form. f) Write the function whose graph is the line AB. (Use correct mathematical notation) Point- Slope Form: Slope- Intercept Form: VI. Rewrite Formulas Function: 1. Solve the formula I = prt for r.. Solve the formula A = 1 bh for b.. Solve the formula F = 9 c + for c 4. Solve the formula P = l + w for w. 5 5. Solve the formula A = 1 (b 1 + b )h for b 1 6. Solve the formula C = πr for r. 7. Solve the formula A = πr for r. 4
VII. GRAPHING. Show all work in the space provided. 1. Using the slope- intercept method, GRAPH: 4x 5 y = 15 m = b = y- intercept: Any line parallel to this line would have a slope of. Any line perpendicular to this line would have a slope of. Domain = Range = Define points that lie on the graph of this function:,, and.. Given: 8x y = 8, graph using intercept points. Be sure to demonstrate your procedure algebraically in the space below. x- intercept point: y- intercept point: 5
SOLVE this system graphically.. 15x 10 y = 80 6x + 8 y = 80 Solution: Confirm your solution by algebraic substitution. 4. SOLVE this system of linear inequalities graphically. x 5y < 5 x y < x < 4 6
VIII. SOLVE each of the following absolute value equations. Be sure to check solutions. 4x + 7 = 11 x 8 + = 1... 4x + 10 = 6x IX. Solve each of the following absolute value inequalities. Show all work below. Present final results in set- builder notation and interval notation. 1. x + 8 1 < 5 Set- builder Notation:. 5 x 8 + 4 1 Set- builder Notation: 7
X. SIMPLIFY each expression - no negative exponents. Review the following Properties of Exponents: m n m n Rule #1: Product of Powers a a = a + Rule #: Power of a Power m ( ) n m n a = a Rule #: Power of a Product ( ) m m m a b = a b Rule #4: Zero Exponent 0 a,a = 1 0 Rule #5: Negative Exponent Rule n 1 a =,a 0 n a m a n a m m a a = m,b b b Rule #6: Quotient of Powers m n = a,a 0 Rule #7: Power of a Quotient 0 1. 4. ( 7) ( 7). (1x) 4. ( 4x) ( 5x) 5. ( 7x y) ( x 4 ) 6. ( 4r s) ( s ) 7. m 4 8. y x 9. 10. t x 4 y ( )0 s 11. 4b 1 a 4 1. 11 8 1. x z 4 xa 14. 18b c 4bc ab 5a c 15. 4x y 5 x y 9x y 4 1xy 8
XI. FACTOR completely remember to first present polynomial expression in standard form and when leading coefficient is negative to factor out a negative. Write prime if the expression is not factorable. 1. y + y 4. n + 16n 57. x + 17x + 66 4. z + 14z 45 5. 1b 17b 99 6. t + 17t + 66 7. 18d 54d + 8 8. 4n + 4n 88 9. a b 10. 4x 9 11. 169 x 1. 5x 49 y 1. x + 5x + 6 14. x + 5 15. x 7x 6 XII. SOLVE. Remember, if a quadratic equation cannot be solved by factoring, you may solve it by using the Quadratic Formula or by completing the square. 1. (x )(x + 7) = 0. 5(x + )(x 5) = 0. x x = 0 4. x + 7x +10 = 0 5. x 9x = 14 6. x 9x 5 = 0 7. 7x 10x + = 0 8. x +19x = 4 9. 10x + x 10 = x + 8 x 10. x 5 = 11. 8 y = 6 1. 4 (x 4) = 48 9 1. (8h ) = +10(1 h) 14. x + 5x = x 10x 15. 9x + 5x 0 = 1 x 16. 6x 8x + = 0 17. 8x + 4x + 5 = 0 18. (x 1) = 4x + 9
XIII. Real World Applications. All work should be done in the space provided below each problem. A. Modeling with mathematical functions: For each write a verbal model that describes the given scenario, label each unknown and then write an algebraic function that will model the information in each problem. Use the function and/or write an equation that you will use to answer each question. Answer each question using a complete sentence in correct units. 1. In outer space, the distance an object travels varies directly with the amount of time that it travels. An asteroid travels 000 miles in 6 hours. Verbal Model: Let Statement(s): Algebraic Model: Demonstrate the use of this model to determine the distance traveled by an asteroid after 10 hours.. A climber is on a hike. After hours, he is at an altitude of 400 feet. After 6 hours, he is at an altitude of 700 feet. What is his average rate of change in feet per hour? Verbal Model: Let Statement(s): Algebraic Model: At this rate determine the climber s altitude at the end of additional hours.. A room s length is feet less than twice its width. The area of the room is 15 square feet. What are the room s dimensions? Be sure to include labeled sketch, let statements, equation, and neatly executed solution. 10
XIV. Write in simplest form. No decimal answers are allowed. 1.. 56. 15 4. 7 5. 15 6. 16 5 XV. Review of Right Triangle Trigonometry: Based on the ratios of 0 60 90 and 45 45 90 triangles and definitions of sinθ, cos θ, tanθ, csc θ, sec θ and cotθ, solve each of the following triangles. Simplify your answers. Rationalize the denominator. No decimal answers. Solve for x and y: 1... 11
4. 5. a) Solve for x b) Find the trigonometric ratios: sinθ,cosθ,tanθ 6. a) Solve for x b) Find the trigonometric ratios: sinθ,cosθ,tanθ Helpful websites: 1. http://www.purplemath.com. http://www.khanacademy.org/. http://www.algebra-class.com/ 4. http://www.themathpage.com/alg/algebra.htm 1