Honors and Regular Algebra II & Trigonometry Summer Packet

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1 Honors and Regular Algebra II & Trigonometry Summer Packet Hello Students, Parents, and Guardians! I hope everyone is enjoying the summer months and the time to rela and recoup. To add to your summer fun, those students entering Algebra II & Trigonometry (honors and non-honors) in the fall need to complete a summer packet! Students should realize that the packet will be graded for completion and will count as the first quiz grade of the year. You MUST show your work to receive full credit on each problem. It is recommended that students complete the packet slowly over the entire summer, instead of leaving it for the last minute. The packet covers a great deal of topics and will take some thought and effort on the student s part to complete. It will be due on the first day of class. The summer packet should get students thinking about the topics they will be studying in Algebra II & Trigonometry. It is a brief review of the concepts they studied in Geometry and Algebra I (with more focus on Algebra I). If needed, students can refer to notes and tetbooks of previous courses. They may also use a calculator for any of the questions. In addition, students are encouraged to work on the packet on their own, but are allowed to discuss problems with fellow students. Students are epected to know: the Pythagorean Theorem, the Quadratic Formula, the formulas for the area and perimeter of triangles, rectangles, and squares, as well as the number of angles in a triangle and the relationship between the diameter and radius of a circle. They should have a strong understanding of linear equations and graphs, factoring, and some eperience with quadratic equations. If students find they have forgotten some of this information, they should review before the start of the school year. If, throughout the summer, students or parents have any questions, please feel free to contact Britta Milks, Head of the Math Department (bmilks@solebury.org). Good luck with the packet and enjoy the rest of your summer! 1

2 Algebra II Summer Packet DO NOT do problems on this sheet, please use other paper. DO NOT do problems on this sheet, please use other paper. DO NOT do problems on this sheet, please use other paper. 1. Translate into an algebraic epression: seven less than half a number.. Translate into an algebraic equation: five more than one third of a number is si less than twice the number.. Use the commutative law of multiplication to write an epression equivalent to: wd +sn 4. Use the associative law of addition to write an epression equivalent to: 4 + (wd + ) 5. Use the distributive law to write an epression equivalent to: (wd + s) 6. Simplify. 7. Evaluate: a. 1 (10 4( - 8)) b (-7) c. ( 1 8) d. 4(18 8) e. 6[11m (4m 1)] (7 m) y, for = 6 and y = - y 8. Simplify and write the final answers with positive eponents only: 0 5 a. 5 f. ( n v ) 0 b. ( 5 ) 5 5 g. (6ab c )( a c ) c d. ( ) 6 y h. e y 9. Identify each polynomial as a monomial, binomial, or trinomial. Indicate its degree: 4 15 a) 10 z 9z b) 19 c) 100 5y 10. Add. Then simplify by collecting like terms: (11 4 5) ( 4 6) 11. Subtract. Then simplify by collecting like terms: ( y y 7y ) (4y y y )

3 1. Multiply. Then simplify by collecting like terms: a) (5 7) b) ( 8y 1)(y 7) c) ( 6 7) d) (4a 5)( a 5a 1) 6 5 1y 4 y 1. Divide. Then simplify by collecting like terms. 4y Simplify y 15. Simplify. 16. Simplify Convert to decimal notation: Convert to scientific notation: Convert to scientific notation: 10,000,000, Simplify and write your answer in scientific notation: ( )( ) 1. Factor completely: a. 4 4a 64a b. 1 c d e. y 4y 48 f g. 64 h. 8y 8. Solve for the variable indicated: 1 a. A bh, for b b. p q Q, for p c. A By C, for y

4 . Solve the following equations for and simplify, if possible: 1 9 t 4 a. 4 8 e. t t b. ( 1) 8 f. ( 4) 10 0 c d Solve and graph on the real number line. a. 5( ) 1 b. 6 ( 1) 5 5. Solve and graph on the -y ais. y > g. 6 h. 7 0 hint for h: use quadratic formula 6. Find the slope and y-intercept of the following linear equation: 5 y 6 7. Find an equation of a vertical line containing the point (-4, 5), and find its slope. 8. Find the slope of the following linear equation, and graph the line: y = 9. Find the and y- intercepts of the following linear equation, and graph the line: y 1 0. Find an equation for the line containing the point (-1, -) and having slope m = Find an equation for the line containing the points (4, ) and (-, -7). Find an equation of a line perpendicular to, y = 5 1, that passes through the point (-1, ).. Solve the following system by (a) graphing, (b) elimination and (c) substitution: y 5 y 6 4. Simplify each of the following square roots. a. 00 b c Find the area of a square if the length of one side is 6cm. 6. Find. 7cm 15cm 4

5 7. Find the measure of each angle in the following: Line are parallel, find and y 4-y 6 +y 9. Find the area of the triangle below. ft 0ft 40. Find the area of a circle with a diameter of 1cm. 41. If RS 9and RT 15, find ST R S T Word Problem Section: 1. Economy Rent-A-Car rents compact cars at a rate of $5 plus 15 cents per mile. Draw a graph that can be used to predict the cost of renting a car. Let the horizontal ais represent the number of miles driven and the vertical ais the total cost. Write an equation of the line that represents this situation and use the equation to predict the number of miles that can be driven for a total cost of $100.. At a restaurant, Jessica wants to leave at least a 15% tip for the waitress that served her. If the bill was $1, what is the minimum amount Jessica should leave for the tip?. On a test of 64 items, a student got 56 correct. What percent were correct? 5

6 4. A ta-eempt charity received a bill of $197.9 for a printer. The bill incorrectly included a sales ta of 5%. How much should the charity pay? 5. The price of a computer was reduced to a sale price of $1, This was a 15% reduction. What was the original price? 6. The sum of three consecutive integers is -87. What are the integers? 7. While traveling, you notice that you traveled 65 miles in 55 minutes. If your speed does not change, how long will it take you to travel 50 miles? 8. There were 00 tickets sold for a volleyball game. Tickets for students were $ each and for adults were $ each. The total amount collected was $50. How many of each type of ticket was sold? 9. Two cars leave Houston at the same time. One car is traveling north and the other car is traveling south. If the one traveling North is traveling 15 miles per hour faster than the one traveling South and they are 45 miles apart after hours, how fast is each car traveling? 10. A telephone pole is 10 m high. The telephone company needs to attach a wire to the top of the pole that runs down to the ground, in order to keep the pole in place. If the wire must end at a point that is 7 m from the base of the pole, how long must the wire be? 11. Find the total area of the shaded rectangles: 9 6

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