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☰ Search Explore Log in Create new account Upload × Math 125 Practice Test #3 (Chapter 8 and Chapter 9) 1. 2. Evaluate the following radicals with real numbers, if possible. a) 3 64 b) 16 c) 5 32 d) b) 54a8b5 3 Evaluate the given expressions. 5 a) 16 4 4. 81 Simplify the following radicals, if possible. Assume all variables represent positive real numbers. a) 75k 7 q10 3. 4 b) 216 2 3 Use properties of exponents and simplify the expression. Express your answers with positive exponents. 1 1 4 a) 3 x x 2 3 (2 x 5 ) 4 b) x 3 10 4 m 2 / 3 c) 3 / 4 m 3 / 8 a 1 / 4 a 2 5. Find the distance and midpoint between the two points 4 3 , 2 5 and 2 3 ,10 5 6. Add or subtract. a) 4 3 54 x 5 5 x 3 16 x 2 7. Multiply. a) 8. a 2 2 b) 45x3 18x 2 50 x 2 20 x3 2 3 6 34 6 Rationalize the denominators. a) 9. 3 b) 3 5 18 3 12 b) 3 3x 4y 4 Solve each equation. 2x 3 3 x a) c) 3 11 5 b) x d) x 4 x 2 x5 5 10. Perform each operation and express the result in the standard form of a complex number. 5i a) 8 4i 7 2i b) 2 4i 11. Multiply. 12. Solve using the square root property. a) a 2 40 2 6 b) ( x 3)2 49 13. 14. 15. 16. Solve by completing the square. a) x 2 6 x 11 0 b) 2 x 2 5 x 1 0 Solve by using the quadratic formula. a) 2 x 2 6 x 1 b) 9a 2 4 2a Solve by factoring. 2 x 3 x a) x 2 3 x 18 b) Solve the given equations. a) 4 x 2 25 0 b) x 4 6 x 2 8 0 c) 2 x 5 x 2 0 2 3 2 1 3 d) x 6 x 5 17. Find the discriminant and determine the number and type of solution of the quadratic equation. a) 9 x 2 42 x 49 0 b) 8 x 2 18 x 5 18. Solve the inequality, graph and write your answer in interval notation. a) x 2 3x 10 0 b) x7 x 40 < 12 c) 3x 1 0 x2 d) x2 2 x 19. At a point 16 feet from the base of a tree, the distance to the top of the tree is 4 feet more than the height h of the tree. Find the height of the tree. 20. Graph the given quadratic functions. Find the vertex, the x and y-intercepts, and the axis of symmetry and label them. Which way does the parabola open? a) f ( x) 2( x 1)2 b) g ( x) x 2 5 c) h( x ) 2 x 2 8 x 9 21. Graph the given quadratic functions by completing the square first and then finding other key points. a) f ( x) x 2 2 x 8 b) h( x) x 2 6 x 9 22. If an object is thrown upward with an initial velocity of 384 ft/second, then its height y after t seconds is given by the equation y 384t 32t 2 . a) Find the maximum height attained by the object. b) Find the number of seconds it takes the object to hit the ground. _____________________________________________________________________________ _____ Answer key is on the next page. Answer Key: 1. a) 4 2. a) 5k 3 q 5 3. a) 32 4. a) 3x12 5. Distance = 2 107 ; Midpoint = 3, 6 5 6. a) 22 x 7. a) 9a 12 a 4 8. 5 6 a) 6 9. a) x 2 10. a) 48 44i 11. 2 3 12. a) a 2i 10 b) x 4, 10 13. a) x 3 i 2 b) x 5 33 4 14. a) x 3 7 2 b) a 1 i 35 9 15. a) x 6,3 3k b) 1 36 1 b) 16x 2 c) 3 2x 2 5 a) x i 2 1 c) x , 4 4 d) 3 b) 3a 2b 3 2a 2b2 11 16. c) 2 b) Not a real number a5/ 2 m 23 / 12 b) x 5 x 2 x 2 b) 30 27 2 3 b) 6 xy 2 2 y2 c) 11 5 2 b) x 4 1 b) 1 i 2 b) x 1, 9 4 b) x 2, x 2 d) x 1, x 125 d) x 2 17. a) D 0 so 1 real solution 18. a) (, 5] [2, ) c) 19. , 2 1 , 3 b) D 484 0 so 2 real solutions 2 b) 6, 7 2 d) , 0 3 By the Pythagorean theorem: h2 162 (h 4)2 The height of the tree is 30 feet. 20 a). Vertex: (1, 0) ; x-intercept: (1, 0) ; y-intercept: (0, 2); Axis of symmetry: x 1 ; opens up 20 b). Vertex: (0,5) x-intercept: ( 5, 0) y-intercept: (0, 5) Axis of symmetry: x 0 opens down 20 c). Vertex: (2,1) x-intercept: None y-intercept: (0, 9) Axis of symmetry: x 2 opens up 21 a). f ( x) ( x 1)2 9 ; Vertex: (1, 9) f (0) 8 i.e. (0, 8) is the y-intercept f (4) 0 and f (2) 0 i.e. (4, 0) and ( 2, 0) are the x-intercepts f (2) 8 ; Axis x 1 21 b). f ( x) ( x 3)2 18 ; Vertex: (3,18) f (0) 9 i.e. (0,9) is the y-intercept (3 3 2, 0) are the x-intercepts, but they are not useful for graphing f (6) 9 ; Axis x 3 22 a). The maximum height attained by the object is 1152 feet. 22 b). It takes the object 12 seconds to hit the ground. Download 1. Math M125Ch8_to_Ch9PracticeEx3.doc The Mathematics 11 Competency Test Practice Test Group 5C with solution Chapter 3 Formulas for Exponent and Radicals Algebraic Rules for Prime Numbers Factors Greatest Common Factor or “GCF” Chapter 1C – Polynomials Midterm Review 1. Solving Nonlinear Equations Answers to Midterm 1 ; Lesson 38 PRACTICAL CLASSES 8 studylib © 2017 DMCA Report