Overlake School Summer Math Packet Algebra 2 Honors

Transcription

1 Overlake School Summer Math Packet Algebra 2 Honors Name: Instructions 1. This is the packet you should be doing if you re entering Algebra 2 Honors in the Fall. 2. You may (and should) use your notes, textbook, the internet, friends, family, and other resources to help you complete this packet. The packet is meant as a review, not as a test. 3. You should work on this packet in a place where you can concentrate without distractions, and work at least an hour at a time as opposed to in small intervals. 4. Once you are finished, go back and highlight any problems you had a lot of difficulty completing or have questions about. Then answer the Post-Packet Questions below. Expectations 1. This packet will be collected on the first day of class. It will count similar to a homework assignment towards your first semester grade. 2. Expect a quiz on the material covered by this packet during the first week of the semester. If there are any topics that you feel rusty on, make sure to review them before the semester starts or with your teacher during the first week of class. 3. This packet should take you no more than 5 hours. 4. If, due to extenuating circumstances, you are unable to do this packet, please contact Wing L. Mui, math department chair, at wmui@overlake.org before the beginning of the school year. Post-Packet Questions Answer these questions after you re done with the packet so your teacher can get a better sense of your progress. 1. What resources did you use to do this packet? Check all that apply. notes from last year textbook from last year the internet friends and family a tutor other: 2. How long did it take you to finish the packet? (t = the time it took for you to finish the packet in hours) t < 1 1 < t < 3 3 < t < 5 t > 5

2 Directions: Show all work! Mysterious and unsupported answers will receive no credit. Do not use a calculator unless the instructions for the question explicitly state that you should use one. 1. Solve each system of equations using the method specified. Write your solution as an ordered point. a. Solve using substitution. b. Solve using elimination. x + 2y = 2 { 5x 3y = 29 5x + 2y = 24 { 4x + 3y = 29 c. Solve by graphing. x y = 3 { x + 4y = 8 d. Solve using any method. 7x 3y = 23 { x + 5y = Find the x-intercept and y-intercept for each equation. Use the two points to graph the line. a. 4x 3y = 24 b. x + 5y = 10

3 3. Rewrite each equation in slope-intercept form (y = mx + b), then state the slope and write the y-intercept as an ordered pair. slope-intercept form slope y-intercept a. 8x 2y = 12 b. 3x = 16 4y c. 2y + 5 = 3(x + 5) 4. Graph each of the lines from #3. 3a. 3b. 3c. 5. Write the equation of the line graphed in slope-intercept form and in standard form. Standard Form: Ax + By = C Slope-intercept Form: Standard Form:

4 6. Given: A = ( 2, 1) and B = (5, 6) a. Find the slope of the line that passes through A and B. b. Find the equation of the line, in point-slope form, that passes through A and B. Point-slope Form: y y 1 = m(x x 1 ) 7. Use order of operations to simplify the following expressions. a ( 2) 3 b. 25 [(3 7) + (12 5)] 2 c. 3( 5+4) + 4(5 7) 2 3 ( 3) d. (4 7) 2 + ( 2 ( 2)) 2 e f

5 8. Use the properties of exponents to simplify each expression completely. Your answer should not contain any negative exponents. a. 3 2 b. ( 3) 2 c. ( 3) 3 d. 6x 3 2x 5 e. (3x 4 y 3 ) 2 f g. (2wv)3 12w 3 v h. (3a) 2 i. (3x 2 ) 3 ( 2x 3 ) 4 j. (5xy 3 ) 3 ( 2x 2 y 7 ) 2 k. 2xy(3x 3 ) 4 (x 5 y 4 ) 2 l. (3a 2 ) 2 3(a 1 ) 3 m. 4x 25y3 15y 2 36x 2 n. ( 15x3 y 4 3x 2 y ) (2x2 3y 3) 2 o. a2x a 4x a x

6 9. Use the properties of radicals to simplify each expression. Remember to rationalize the denominator and leave your final answer in simplest radical form. NO decimal approximations! 3 a. 75 b. 27 c. x 2 d e. (2 5) 2 f g. 16x 2 h. 24x 6 y 5 z 3 3 i j. 1 2 k l. 12m5 n 10 27mn 4 m. 3 3 n o. abc ab c

7 10. Expand each expression by distribution, multiplying and/or using FOIL. a. (3x 1)(2x + 5) b. (x 2)(x 2 2x + 4) c. (x 3)(x 4) d. (3x 2) 2 e. (ab + xy)(ab xy) f. (a 2b) Factor each expression completely. Remember to take out the GCF first. a. x 2 4x + 3 b. 6x 2 x 2 c. x x x 3 d. x 2 y 2 e. x 4 + y 4 f. 4b 2 25a 2 g. r 3 s rs 3 h. 3x x + 30

8 11. continued i. 15x 2 y xy 2 50x 3 y 3 j. m 2 (r 7) 16(r 7) k. 7x 2 15xy + 2y 2 l. x 2 + 6x + 9 y Simplify each expression. a. 5 + x b c. (x+3) x(x+3) (x 2)(x+1) (x 2) d. x2 6x 7 x 1 x 2 1 x 2 +4x+3 e. 3 x2 +4x+3 1+x x+2 x x 13. How do you know if an equation is a quadratic equation?

9 14. What is the general solution to ax 2 + bx + c = 0? *Hint: quadratic formula* 15. When is it necessary to use the quadratic formula when solving a quadratic equation? 16. Solve each equation for x. a. 3x 6 = 2x + 3 b. 3 4 (x 16) = (1 3x) c. x 2x+1 = 3 5 d. x 2 = x e x 1 = 2 3 x 3 f. 4 + = x+1 5

10 16. continued g. 15x 5 3x 1 = 5 h. x 2 2x 15 = 0 i. 3x 2 + 4x + 7 = 6 j. 2x 2 = 9x 7 k. 3x 2 = 6x l. x 2 2x + 2 = 2x m. 5 x 2 = x 3 n. x 2 + (x + 1) 2 = (x + 2) 2

11 17. Solve for x and graph the solution set on the number line. a x 21 b (x 1) 7x > Graph the solution set. a. y < 1 3 x + 5 y > 2x 4 b. { y 2 x Is the point (0, 5) a solution? Is the point (0, 5) a solution? Is the point (5, 0) a solution? Is the point (0, 4) a solution? Is the point (6, 6) a solution? Is the point ( 3, 0) a solution?

12 19. For the following problems, clearly define your variable(s), write an equation (or system of equations) to represent the situation, then solve. Write your answer in the form of a complete sentence. You may use a calculator to assist in calculations for these problems. a. When mailing a package, the first ounce costs $0.32. Each additional ounce adds $0.24 to the cost. Let x be the number of ounces over one-ounce. If a package costs $1.52 to mail, how much does it weigh? b. A store charges 8% tax on all items. If the final price of an item with tax included was $16.74, what was the tag price on the item? c. The sides of a triangle are three consecutive odd integers. The perimeter of the triangle is 57 inches. Find the lengths of all three sides.

13 19. continued d. Elizabeth has been pricing Amtrak train fares for a family trip to Portland. Three adults and four children must pay $159. Two adults and three must pay $112. Find the price of an adult s ticket and the price of a child s ticket. e. A beginner s artist kit costs $6.35 and contains 2 brushes and 5 jars of paint. The standard kit has 4 brushes and 12 jars of paint and costs $ Assuming that all brushes cost the same and all jars cost the same, what are the prices of a single brush and a single jar? f. Kay Oss can solve equations at the rate of 26 per hour. Her friend, Dan D. Lyons, can solve equations at a rate of 20 per hour. When they start their homework, Kay has already solved 3 equations in study hall and Dan has already solved 8. How long will it take until they have solved the same number of equations? How many equations will they each have solved?