Honors Algebra 2 - Summer Review Assignment Name______This assignment should serve as a review of the algebra skills necessary for success in Algebra 2 with Analysis. Our hope is that this review will keep your mind mathematically active during the summer, identify weaknesses in algebra, if they exist, and prepare you for the fun and challenging year ahead. We expect that you come to class knowing this material and ready to continue learning algebra. Answer all questions on separate paper. SHOW ALL WORK. This assignment will be collected on the first day of school. Enjoy your summer. See you in September ready to learn !!!!
I. Evaluate/Simplify. 6 63 1. -3 – – 12 2. (-4)2 - 3. - 42 + 82 4. 2x3 – 3x2 + 5x when x = -3 2 18 1 3 5 2 1 3 5. 3ab2 + 5a2b -1 when a = 2 and b = -2 6. 7. 8. 2 2 2 3 2 5 1 2 1 2 3 1 2 3 5 3 2 1 3 2 1 3 9. x 10. 11. x 5 3 2 5 3 8 5
II. Simplify by adding, subtracting, multiplying or dividing. 3 2 1. (3x + 2) + (-4x + 3) 8. -4x(2x - 6x – 5x + 1) 16. (24t 6 32t 5 8t 2 ) (8t 2) 2 2. (-6x + 2) + (x + x – 3) 9. (x + 5)(x – 2) 5 3 2 3 2 24x 4x 10x 16 3. (6x + 1) – (-7x + 2) 10. (x + x + x + 1)(x – 1) 17. 4. (x2 – 5x + 4) – (8x – 9) 11. (3 – 2x)2 8 5. -3x(x – 1) 12. (x2 – 5)2 u 2u 2 u5 6. (1.2x3 + 4.5x2 – 3.8x) + 13. (x + 5)3 18. 3 2 2 u (-3.4 x - 4.7x + 23) 14. (3x + 2)(4x + 5) 5 4 2 4 2 50x 7x x 7. (0.5x - 0.6x + 0.7) – 15. (25t 3 15t 2 30t) (5t) 19. (2.3x4 + 1.8x – 3.9) x
III. Solve the systems of equations by the indicated method. 1. linear combination 2. substitution 3. graphing 4. any method 5x + 4y = 6 -2x + y = 8 3x - 2y = 5 -x + 2y = 11 -2x - 3y = -1 y = -3x – 2 -6x + 4y = 7 3x - 2y = -13
IV. Solve the linear equations 1 1 1. 4(3 x) 2(x 6) 2. 3x 2(x 1) 0 3. 8x 1.5 3x 4. (6x 24) 20 (12x 72) 3 4 x 1 5. 3 2 6. x 4 2 (3 x) 7. 2(3x 6) 8 6x 8. a + (a – 3) = (a + 2) – (a + 1) 5 2 V. Factor completely 1. x2 - x - 72 2. 2a2 -11a+ 15 3. 10x4 – 15x3 4. 9x2 - 64 5. x2 + 11x + 28 6. x2 – 72 + 6x
VI. Solve the quadratic equations 1. x2 + 10x - 9 = 0 2. x2 + 6x = 0 3. x2 - 3x = 10 4. 5x2 = 7x 5. (2x + 1)(x + 3) = 0 6. x2 = 4x + 32 7. 2x2 - 3x - 2 = 0 8. x2 = 16 9. x2 + 5x - 1 = 0
VII. Write equations for the lines satisfying the given conditions 4 1. through ( 0, -1 ) with slope = -1 2. through ( -2, 3 ) with slope = 3 3. through ( 3, -1 ) with zero slope 4. vertical, through ( 5, 4 ) 5. through ( 2, 3 ) and ( 7, -2 ) 6. through ( 3, 4 ) and ( -2, 4 ) VIII. Simplify completely. Do not leave negative exponents in answers. 1. ( -3x2 + 4x - 7 ) + ( 2x2 - 7x + 8 ) 3. ( 39a4 - 4a3 + 2a2 - a - 7 ) - ( 10a4 + 3a3 - 2a2 - a + 8 ) 4. 2x2z ( 3x - 2z) 5. -3xy3 (x - 2y) 6. (3x2 + x - 1) (2x - 3) 8. ( 8a3b2 ) ( 2a-4 b-5 ) 9. (-3x2y3z )3 10. ( 15a4b2c )0 12. (3x + 7)(2x – 5) 13. (x + 6)2
IX. Simplify completely. Assume all variables represent positive quantities. 3 1. 32 2. 3. 48 xy5 5
4. 8 + 18 - 32 5. 21 14 6. 16 a3 b2
X. Given matrices A, B and C as shown. Find the value of each expression below, where possible. If an operation cannot be performed, explain why. 5 3 2 5 1 1 3 0 A B 0 2 C 3 2 0 5 2 3 1 4 1. A + C 2. 2B 3. C – A 4. A + B 5. dimensions of A 6. dimensions of B
XI. Set up and simplify or solve each application problem below. 1. Find a simplified expression for the area of a rectangle with length = 2x + 3 and width = x - 2 2. Find a simplified expression for the area of a square with side = 2x + 5 3. The area of a square with side 2x - 1 is 49. Find the value of x. 4. A baseball diamond is a square 90 feet on each side. How far is it from 1st to 3rd base? 5. Find the length of a diagonal of a rectangle having length = 40 cm and width = 55 cm. 6. An isosceles right triangle has leg = 4 in. What is the length of the hypotenuse?
XII. Accurately graph ON GRAPH PAPER. (Check your answers on your graphing calculator) 3 1. y = - x + 4 2. y = 3x - 2 3. y = (x - 2)2 + 1 4 4. y = x2 + 6x + 1 5. 2x + 3y = 12 6. y = | x | 7. y = | x + 2| 8. y = | x | + 3 9. y > 2x + 1 10. y < -3x + 4 11. y 4 12. x = - 2 13. y < 5 14. x ≥ -2 15. line through ( -1, 3 ) with slope = 0
Online Resources if you don’t remember or know an objective. www.purplemath.com http://www.khanacademy.org/