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Accelerated Alg 2 Midterm Review: Chapter 1 NAME: 1. What is the difference between integers and rational numbers? PERIOD: Can a number be in both groups? 2. What is the difference between rational and irrational numbers? 3. Simplify: a) ½ (2a+1) b) 3(2x-y) – 4(x-2y) 4. Solve: a) 2x – (1-x)=11-x b) 2(5x-3) – x = 3(3x-2) 5. Evaluate: x ³- 4x² + x + 6 a) x=2 b) x= -1 6. Solve for x: a) A= ½xy b) 4P = ½ (x-y) c) y= Chapter 2 1. Solve and graph the solutions: a) 7y-2 (y-4) > 6 - (2-y) b) -3 < 4c + 5 1 2. Solve and graph the solutions: a) l2x + 1l = 7 b) l2y+9l < 13 c) l4-xl > 5 3. Write an inequality statement to solve each situation: a) Find all sets of three consecutive odd integers whose sum is between 20 and 30. SET UP DO NOT SOLVE 1 (x+y) 5 b) Find all sets of three consecutive integers whose sum is at least 14. SET UP DO NOT SOLVE c) Find the set of two smallest integers if one number is four more than three times a number and their difference is greater than 18. SET UP DO NOT SOLVE d) Find the two greatest integers if one number is eight less than another and their sum is less than or equal to 14. SET UP DO NOT SOLVE 4) If it takes an airplane 3 h to fly 360 mi with the wind and 4 h to make the return trip against the wind. Find the speed of the wind and the air speed of the airplane. SET UP AND SOLVE Chapter 3 1. Find the x and y intercepts of each equation: a) x = 4 b) y = -2 c) 2x – 3y = -6 2. Find the slope of the line passing through (-8, 3) and (-1, 5). 3. Find the equation in standard form of a line with a slope of ½ and containing point (-4, 5) 4. Find the equation of a line containing points (-2, 8) and (2, 7). Write your equation in slope intercept form, then in standard form 5) Rewrite in standard form. If already in standard say so. c) a) y = -5 b) -2x + y = 9 2 4 x y 2 3 5 d) -3 = 2x + 5 y 6) Solve the system of equations: a) 3p + 2q = -2 9p – q = -6 b) 3x + 3y = 6 5x – 6 y = 15 7) When would a system of equations have no solution? 8) Evaluate b) Given f(y) =y2 + y - 2, find f(-4) a) Given f (x) = 3 – 2x, find f (-7) c) Given g(x) = 7 x -3, find g (-16) 8 9) Which do not represent linear equations? a) x=6 b)3x=y c) y = 9 Why? d) y = 3/x 10. Write the inequality statement for each graph shown. e) 1 4 x – y = -3 2 7 11. Give the domain and range (possible x values or possible y values) of the relation graphed below. Chapters 4 and 5 1. Simplify a. (x-4)(2x²-5x+3) b. (4x-5)² c. (x+1)2 2. Factor Completely a. 16x4-1 d. 3x³+12x-15x g. (x+5)2 – (x+5) + 6 b. 8n³-1 e. 14x²-31x-10 c. 125w³+27 f. 6(y-2)2 – 7(y-2) -10 h. (3x+5)2 – (3x+5)2 3. Simplify a. (xn+2) (x3n) c. b. y n 3 y 2n y 20n y 5n d. x³x xn+4 4. Write with positive exponents -3 -2 a. x y z x 3 y 2 b. 5x 4 x 3 c. 2 y 5. Simplify 17. -8( -4x3y4)( ½ x5y) 18. (10ab 5)(-2a3)4 4 Calculator Work 1. Find the inverse of each matrix. 2 a) 5 1 b) 0 1 1 3 0 1 0 2 2 1 2. Given the following matrices A= 4 6 5 1 2 5 B= a) Find CB 1 2 C= 3 0 b) Find 3C – A c) Can you add, subtract, and multiply between all the matrices above? Tell me which ones can be added together. Tell me which ones can be multiplied together and in what order. 3. Solve each system of equations a) 2p – 5q = 14 p + 3 q =5 2 4. Given the following data, find the linear regression equation. a) X: Y: -1 -7 X: Y: -5 2 0 -3 3 15 -2 -12 -1 -9 b) -2 5 0 8 -4 3 2 13