Welcome to Honors Algebra II Trigonometry at Morton High School! 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 Algebra I and Geometry. To help ensure your success in Honors Algebra II Trig, the high school mathematics department has compiled a list of problems that represent some of the most frequently used Algebra concepts. 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 Trigonometry. Algebra II- Trig Honors Review Test is scheduled for Friday, August, 009. This test will be worth 00 points. Class time will be provided on Thursday, August nd for questions. If you should happen to lose this packet, you can find it posted on the Morton High School website at http://mhs.morton709.org/my_class/math.php You will find a listing of all of our classes. Please select Algebra II Trig Honors Summer Review. If you have any questions, contact Mrs. Durand at rosie.durand@morton709.org. Have a wonderful summer! The Mathematics Department Morton High School
Algebra /Trigonometry Honors Summer Review Packet. Graph the following numbers on a number line: 4,, 0,,.. Use symbols to write the following statement: Negative two is less than negative one half. Tell whether the statement is true or false.. < 4. >. 4 = 4 6. 7 = 7 Simplify. 7. [(6 ) 4 ] 8. 9+ 8 6+ 9. 6+ + ( ) 0. + ( 8) + 9. 7+ ( 4) ( ).. (4.6 ). ( 7) + 4( 6) 4. ( 6c )(4d)( ) 8. 4 ( 6) ( ) 4( 8) ( 4) 6x + 0x 6. 7. ( )( ) Evaluate each expression if r =, s =, and t =, x =, y = 8. r + s rst 9. y+ 9. ( y )( y) s + ( r t) 0. x x 8 r+ s+ t. k = k + k. ( x ) = x+ 4..( u + ) = 7.. 0.( x ) = x+ 6. ( x ) x= (x+ ) 7. z ( z ) = z 8. (t ) t = (t ) 6x ( x 4) 9. = 8 Solve the equation for the given variable. 0. x y = 0forx. S = gt + vtforv Express each answer in simplest form in terms of the given variable.. A rectangular garden that is w ft wide is enclosed by 0 ft of fencing. How long is the garden?. The perimeter of an isosceles triangle is 00 cm, and its base is b cm long. How long is each leg? 4. In a basketball game, one team s score is two points less than half the other team s score, which is x. What is the difference in the scores?. The length and the width of a rectangle are consecutive even integers, and the length is x cm. Find (a) the area and (b) the perimeter of the rectangle.
6. Two jets leave an airport at noon, one flying north at r mi/h, and the other flying south at twice that speed. After h, how far apart are the planes? 7. Jessica s bank contains 8 quarters and dimes, of which q are quarters. Find the total value of the coins in dollars. 8. Amy has $8 less than Maria. Together they have $0. How much money does each girl have? 9. A music dealer ran a sale of records and tapes. Records were reduced to $7 each and tapes to $7.0 each. The dealer sold 60 more records than tapes for a total sale of $60. How many records did the dealer sell? 40. The perimeter of a certain basketball court is 66 ft, and its length is ft more than its width. Find the dimensions of the court. 4. The measure of a supplement of an angle is degrees greater than three times the measure of a complement. Find the measure of the angle. 4. At 0:0 A.M. two planes leave Houston, one flying east at 60 km/h and the other flying west at 640 km/h. At what time will they be 00 km apart? 4. A jar contains 40 coins consisting of dimes and quarters and having a total value of $4.90. How many of each kind of coin are there? 44. At noon a train leaves Bridgton heading east at 90 mi/h to Cogsville, 40 mi away. At : P.M. a train leaves Cogsville heading west to Bridgton at 00 km/h. At what time will they pass each other? 4. x 8 = 7 46. 4( x) = (x 4) 47. Solve the formula m = ( a+ b) forb 48. Using n for the variable, translate this word phrase into an algebraic expression: Twice the sum of a number and its square. 49. Express your answer in terms of x: What is the perimeter of a rectangle that is x cm wide and cm longer than it is wide? 0. Two cars, heading toward each other on a divided highway, are 0 mi apart. If one car travels 4 mi/h and the other 0 mi/h faster, in how many hours will the cars pass each other?. On a number line, the coordinate of point A is, and the coordinate of point B is 7. Find the coordinate of the point halfway between A and B. Simplify... + 4. (a + )
. ( 4+ 8) (4 ) 6. 8m 6n m +n 7. (x y) 4(x y) 4 0x 8. ( a ) + a 9. 6( 7) ( ) ( ) 60. 4 6. Evaluate ( y ) x if x = 4 and y =. 6. ( x)= x + 6. Solve A = π ( r+ h) forh 64. The hourly wages of three workers are consecutive even integers. If the highest-paid worker s hourly wage is x, what is the sum of all three workers hourly wages? 6. The perimeter of a rectangle is 4 cm. If the length is y cm, what is the width? 66. The school book store sold 8 more pencils than pens one day. The cost of a pencil is $.0, and the cost of a pen is $.0. If the day s sales of pens and pencils totaled $8.90, how many pencils were sold? 67. A woman drove part of a 8 mile trip at 0 mi/h and the rest at mi/h. Find the distance she traveled at 0 mi/h if her total driving time was h and 0 min. 68. On a number line, point A has coordinate 4, and point B has coordinate the coordinate of the point two thirds of the way from A to B. 69. List 0.6, 0.8,.4,, and 0. in order from least to greatest. Simplify 70. (4+ 6) 7. 8 7 ( ) + 7. 8m 4 9m + 7 7. 76. ( ) ( ) 74. (x y) 4(6y x) 7. 9 x Evaluate if x =, y = 4, and p = 77. ( x+ y) x + y 78. p(4 p)(p + ) 79. 80. x 7= x+ 8. 6(x 4) = 7(4x + ) 9 7 p p ( 6) ( 4) 8+ 8. Express your answer in terms of the given variable. A car s gas tank held x gallons of gas before a trip. The trip consumed three quarters of the gas in the tank, but 0 gallons of gas were added after the trip. How much gas is now in the tank? 4
8. A man invested $6000, part of it at % simple interest and the rest at 7% simple interest. If his annual interest income is $7, how much did he invest at each rate? Solutions.. <. False 4. True. True 6. True 7. 8. 4 9. 0. -0. 8. -.8. -9 4. cd. 6. - 7. x x+ 8. 6 9. 0.. -.. φ 4.. -7. 6. -4 7. 8. R 9. 4 0. x = y+ s. v= + gt. 60 w. 0 b 4. x + t. (a) x(x ) cm or x(x+) cm (b) (4x + 4 ) cm 6. 9r miles apart 7. (0.q +.80) dollars 8. Maria - $9, Amy - $ 9. 80 records 40.49 ft x 84 ft 4. 0 4. : pm 4. 4 dimes and 6 quarters 44. :0 pm 4. 46. 47. b = m a 48. ( n+ n ) 49. 4x + 0 0. ½ hours.. 0. 4. a + ½. 6. 7m 4n 7. x + y 8. a 9. 60. 6 + x 6. 6 6. A 6. h= r π 64. x 6 6. y 66. 4 pencils 67. 7 miles 68. 69., 0.8, 0., 0.6,. 4 70. 7. 7. m 7. 4 74. 9x 4y 7. 8 76. 4x 9 77. 78. 4 79. 4 80. 0 8. 0 8. ( x + 0) gallons 8. $400 at % and $600 at 7% 4