Welcome to Honors Algebra II with Trigonometry at Metamora High School! Summer Review Information

Transcription

1 Welcome to Honors Algebra II with Trigonometry at Metamora High School! Summer Review Information Dear Parents and Students, Mathematics is a discipline that constantly builds on previous knowledge. Students entering Honors Algebra II / Trig will be expected to recall and apply the material that they learned in previous honors courses. The Honors Algebra II / Trig course will begin in Chapter 4 of the textbook. It will be assumed that you have completely mastered all topics in the first three chapters. I am including problems from these three chapters. Please take some time this summer to go over these problems. We have even included the solutions for you! When you return to school in the fall, be prepared to ask questions on any problems that have you stumped. There will be a test over this prerequisite material in the first few days of class to help determine your placement and readiness for Honors Algebra II / Trig. Students will not turn in this packet. They are not required to do all the problems. Some class time will be used prior to the test for questions. If you lose this packet, the high school guidance department will have extra copies available. Please refer to the school website to find a listing of all of our math classes. Feel free to contact our department chair, Mrs. Stone, at cstone@mths.us if you have any questions. Have a wonderful summer! The Mathematics Department Metamora High School

2 Honors Algebra II / Trig Chapter 1 1. Name a rational number that is not an integer. Name an integer that is not a whole number. Name any irrational number. Name all the number sets 0 belongs to. 2. Solve for h: A = 2πr 2 + 2πrh Solve each equation. Show work! 3. 2x + 3 = 7 4. y = 15 Solve each inequality. Show a graph of your solution. 5. 3t 5 > 31 t x > a (a 4) 25 Define a variable then solve using an algebraic inequality: 8. Sarah pays $10 admission to an amusement park then wants to ride the roller coaster as many times as she can. If she had $32 to start with and the roller coaster tickets are $3 each, how many times can she ride?

3 Solve each inequality. Show a graph of your solution set. 9. 5x or 2x + 1 > < 4y + 10 < x x 2 > x > x 5 < -8

4 Honors Algebra II / Trig Chapter 2 1. Graph the relation and name its domain and range. Then determine whether it is a function. {(-3,4), (-2,4), (-1,-1), (0,2), (3,-1)} 2. Determine whether each is a function. Answer yes or no. a. b. d. c. e. D R

5 3. Let f(x) = x 3 x. Find each of the following: a. f(-2) b. f(5) c. f(a) 4. Identify each as linear or not linear. a. y + 3 x = 4 b. 4x 2y = 1 c. f(x) = 0.5x + 3 d. h(x) = -2x 2 e. y = 3 x 5. Name the x- and y-intercepts for 3x 2y = 18. Express your answers as ordered pairs. 6. Rewrite each in standard form: a. y = - ½ x + 7 b y + 9x = 0 7. Find the slope of the line that passes through each pair of points: a. (3,-2) and (7,9) b. (-4,3) and (5,-3)

6 8. The median weekly earnings for American workers in 1990 was $414 and in 1999 was $549. Find the average rate of change between 1990 and Find the equation of the line that has a slope of -⅓ and passes through (-6,1). 10. Write an equation of the line that passes through (2,-5) and (4,3). 11. Write an equation of the line through (-1,0) that is parallel to the line whose equation is 6x 2y = The table below shows the relationship between the number of field goals attempted and the number of points scored by one basketball player over a 6-game period. Enter the data into your graphing calculator. Field Goals Attempted (a) Points Scored (p) a. Find the equation of the best-fit line using your calculator. Round to the nearest hundredth. b. Use your equation to predict how many points will be scored when 20 field goals are attempted. Comment briefly on any danger associated with this prediction.

7 13. Determine whether each graph represents a constant function, an absolute value function, a step function, or a piecewise function. Then identify the domain and range. a. b. Graph each of the following: 14. A line through (-3,1) with an undefined slope. 15. f(x) = 1 x if x < 2 3 if x 2

8 16. y = x y ½ x y < 3x 19. A school is buying new computers. They will buy desktop computers costing $1,000 per unit, and laptop computers costing $1,200 per unit. The total cost of the computers cannot exceed $80,000. Write an inequality that describes this situation then graph it. Computers Purchased

9 20. Determine the value of t so that the line through (1.6, t) and (2,5) has slope Graph: y < 3 x

10 Honors Algebra II / Trig Chapter 3 Calculator Portion Solve using your graphing calculator. Express your answer as an ordered pair or an ordered triple. 1. 3x + 2y = x 4y + z = -10-5x + y = -9 5x + 2y z = 11-3x + 2y 3z = 3 3. Find the coordinates of the vertices of the figure formed by the solution of the system below. x 2-4 y 3 x + y Solve. Beth and Doug opened a sports memorabilia shop. They decided to sell pennants and hats. On the first day of operations, Beth sold 22 pennants and 70 hats and collected a total of $1,292. Doug sold 37 pennants and 42 hats, collecting $1,037. Set up a system of equations (show the system) and solve for the price of a single pennant and a single hat.

11 Honors Algebra II / Trig Chapter 3 Non-Calculator Portion Solve each system using the indicated method. Express your answer as an ordered pair. 1. 2x y = x + 5y = 26 y = -5x +14 7x 3y = 9 SUBSTITUTION ELIMINATION Set up a system of equations (BUT DO NOT SOLVE). 3. The swim team paid $446 for team suits. The suits for men cost $18 each and the suits for women cost $32 each. Seventeen suits were purchased. Set up a system of equations that could be used to find the price of each gender s suits. 4. Bill, Gertrude, and Harriet each went shopping for hot dogs, buns, and ketchup. Bill purchased 50 dogs, 25 buns, and 5 bottles of ketchup and spent $ Gertrude bought 40 dogs, 60 buns, and 3 bottles of ketchup and spent $73. Harriet bought 125 dogs, 70 buns, and 20 bottles of ketchup and spent $180. Set up a system of equations that could be used to find the individual prices of dogs, buns, and bottles of ketchup.

12 Honors Algebra II / Trigonometry Summer Review Answer Sheet Chapter ; 5 ; π ; whole, rational, real, integer. A h = r 2π r x = 2, 5 3. { } 4. y = { 17, 1} 5. t > 9 6. x < a 2 8. x = # tickets 22 x ; she can ride a 3 maximum of 7 times. 9. x 4 or x > < y < x x > 6 or x < all real numbers x < or x > 3 3 Chapter 2 1. Domain: { 3, 2, 1, 0,3} Range: { 1, 2, 4} It is a function. 2. (a) yes (b) yes (c) yes (d) no (e) no 3. (a) 6 (b) (c) a a 4. (a) not linear (b) linear (c) linear (d) not linear (e) not linear 5. (6,0) & (0, 9) 6. (a) x + 2y = 14 (b) 3x 4y = 5 7. (a) (b) 3 8. $15 / year 1 9. y = x y = 4x y = 3x (a) pˆ = 1.35a

13 (b) points. We are extrapolating from our data. 13. (a) absolute value or piecewise function. Domain: R Range: x 2 (b) step function Domain: 4 x 2 Range: { 1,0,1,2,3, 4} y = # desktops x = # laptops 1, 000y + 1, 200x 80,

14 Chapter 3 (calculator portion) 1. (2,1) 2. (1,3,0) 3. (-6,3), (2,3), (2,-4), (1,-4) 4. $11 pennant; $15 hat (Non-calculator portion) 1. (3,-1) 2. (3,4) 3. x=number of male suits y=number of female suits 18x+32y=446 x+y=17 4. d=price of hot dog b=price of hot dog bun k=price of ketchup 50d+25b+5k= d+60b+3k=73 125d+70b+20k=180