Calculus Preparation & Placement Evaluation, 2009 Department of Mathematics Wilfrid Laurier University Sample Evaluation Simplifying Expressions 1. 50 1 +9 5 25 2 ( 1) = A. 36 B. 46 3 4 2 + 4 5 2. 127 40 B. p D. 54 3 = 8 A. 12 3. C. 14 C. 117 40 D. 25 8 3 is an example of a number from which set? A. the natural numbers B. the integers C. the rational numbers D. the irrational numbers 4 2 1 = 3+3 1 4. A. undefined 5. 2 64x1=2 y 9 A. 6. 2=3 A. 7. x 6 (x 3) If x 6= A. B. 32x1=3 y 6 C. 1 8x1=3 y 6 D. 128x C. 2 2x x 1 D. 4 (x 1 1) 2 (x 1=2 3) B. 3 1; 2, then 2 (x + 1) (x2 + 4) 9 32 D. 51 64 x (x x 3 2 x B. 3) 10 x 2x 1 = 2 x C. p x 3 x 6 D. p x 3 x+1 = 2x 4 1 (x3 y 1=2 x 3 x+2 x4 16 1=6 25=3 = B. 2x + 2 If x > 3, then 8. C. 2 (x + 3) x 2 A. q 15 16 = 256 3x1=2 y 6 If x 6= 1, then B. C. 2) 1 2 (x + 4) (x + 1) D. 2 (x + 2) (x + 1) (x2 + 4) 9. If x 6= 3, then A. 12 x2 x+4 x 1 10. x x2 = 4x + 3 B. 4+x 1 x C. The remainder, when 9 + 3x + 4x3 A. 1 If h 6= 0, then x + h + 1 h 11. A. h (x + 1) (x + h + 1) 12. If x > A. 3 C. 13. 9 , then 2 3 D. (x + 3) (x + 4) (x 3) (x 1) 2, is: C. 61 D. 15 B. 1 (x + 1) (x + h + 1) 1 x+1 = 1 (x + 1) (x + h + 1) C. x 1 2x4 is divided by x B. 9 2 4 x 1 D. 2 (x + 1) 2x p = 2x + 9 p B. 2x 9 p 3 + 2x + 9 18 D. p 3+ 2x + 9 p x 3 + 2x + 9 9 x Which of the following statements are true? I. a b b = 1+ a b A. All of them 14. The expression x2 A. (x 2 3) + 2 II. m =0 0 III. p x2 B. I, III and IV 9=x 2 IV. (q + 2) = q 2 + 4 3 C. III and IV D. I only 6x + 2, upon completing the square, is the same as: 2 B. (x 3) 2 C. (x + 3) 7 7 D. (x 5 15. In the expansion of (2x + 1) , the coefficient of the x3 term is: A. 80 B. 20 C. 40 2 D. 8 2 3) 1 Solving Equations and Inequalities 16. The solution to 9 (x + 8) = 2x A. x = 17. 38 3 x) is: (4 38 3 B. x = C. x = The possible values of x for which (2x + 1) (x A. x = 18. 1 ;3 2 4) = 1 ;4 2 B. x = B. m C. m A. x = 20. B. x = 2 p x2 + 9 = 1 x + 5y 3, y = D. x = 1; 3 2 D. m > 9 9 x are: D. no solution 4; 4 =4 5x + 20y A. x = 4; 3 C. x = 4 Solve the system of equations: 19 2 6x + m = 0 have no real solutions? 9 The possible values of x for which 19. D. x = 7 are: C. x = For which value(s) of m would the equation x2 A. m = 9 19 2 = 13 7 5 B. x = 17, y = C. inconsistent (no solution) 13 5 D. dependent (infinite solutions) 21. A rectangle has a perimeter of 40 cm. If the length is 2 cm longer than twice the width, nd the area of the rectangle? A. 84 cm2 22. B. 6 cm2 The set fx 2 R j x A. ( 6; 2) [ (0; 1) 23. The solution of x2 A. 24. 2 x 4 0 or C. 14 cm2 6<x< 2g can be expressed in interval notation as: B. [ 6; 2] [ [0; 1) 2x B. 8 4 C. [ 6; 2] [ (0; 1) 2 ,2 9 B. x = D. ( 6; 2) [ [0; 1) 0 is the set of all x such that: x C. x 2 Find all possible solutions of the equation j5x A. x = D. 40 cm2 3 4 D. x 4 or x D. x = 2 9 2j = 4x. C. x = 2 2, 2 2 or x 2 25. If jaj < jbj, then which of the following is true? A. a < b C. B. a < b or b < a < b or b < a < D. b a< b a < b < a or a < b < a Functions and Graphing 26. 27. If f (x) = x2 + 3x then f (h + 6) = A. h2 + 3h + 42 B. h2 + 15h + 54 C. h2 + 3h + 6 D. h2 + 3h + 54 Which of the following represents a function? A. f( 9; 4) ; ( 9; 8) ; ( 3; 3) ; (0; 5)g B. f( 9; 5) ; ( 3; 5) ; (0; 5) ; (3; 5)g C. f( 3; 9) ; ( 3; 3) ; ( 3; 0) ; ( 3; 6)g 28. The domain of p A. x 6= 29. 31. is the set of all x such that: x2 B. C. 2 > x 2<x<2 D. x < 2 or x > 2 The function f (x) = x2 1 can be defined by: ( ( x2 1 if x 0 x2 1 if x 1 A. f (x) = B. f (x) = 2 1 x if x < 0 1 x2 if x < 1 ( x2 1 if 1 x 1 1 x2 if x < 1 or x > 1 The function h (x) = x2 + 2x A. f (x) = x2=3 g (x) = x2 + 2x C. f (x) = x4=3 g (x) = (2x) 2=3 D. f (x) = ( x2 1 if x 1 or x 1 x2 if 1<x<1 can be thought of as the composition f 2=3 1 g, where: B. f (x) = x2 + 2x g (x) = x2=3 D. f (x) = x2 + 2x g (x) = 2 3 3 The inverse function of y = (x + 4) + 8 is: A. y = (x 32. 4 2; 2 C. f (x) = 30. 1 D. f( 9; 4) ; (0; 5) ; (0; 5) ; (9; 4)g 1=3 4) B. y = (x 1=3 4) 8 C. y = x1=3 12 D. y = (x 1=3 8) Which of the following is not a polynomial? A. f (x) = x2 4 + 6x B. f (x) = x 2 C. f (x) = +4 4 p 3 D. f (x) = x3 4 4 33. If the graph of y = f (x) is obtained from the graph of y = x4 by shifting it one unit down and two units to the right, then the formula for the function y = f (x) is: A. f (x) = (x 34. 4 2) 1 4 B. f (x) = (x + 2) 1 C. f (x) = (x The relationship between the graphs of y = f (x) and y = 4 1) + 2 4 D. f (x) = (x + 2) + 1 f (x) is: A. a reflection in the x-axis B. a reflection in the y-axis C. a reflection in the line y = x D. a reflection through the origin 35. Graph the region represented by the solution of 6x 7y A. B. C. D. 42. Geometry 36. A. 37. p The distance between the points P (3; 7) and Q (6; 9) is: p 5 B. 13 C. 13 p 175 An equation of the line with a slope of 3 and passing through the point (2; 1) is: A. 3x 38. D. y 7=0 B. 3x y C. 3x 5=0 The vertex of the parabola given by y = 4x2 A. (1; 10) 8x B. (1; 6) y+5=0 y+3=0 2 is: C. ( 1; 2) 5 D. 2x D. ( 1; 10) 39. Which of the following represent lines: I. y = 3 II. xy = 3 A. IV only 40. III. x2 + y 2 = 3 B. I and IV IV. x + y = 3 C. I, II and IV D. All of them A circle centered at (0; 0) with radius 1 has equation: A. x2 + y 2 = 0 B. x2 C. x2 D. x2 + y 2 = 1 y2 = 0 y2 = 1 Exponential and Logarithmic Functions The expression log3 41. A. 1 3 42. 1 27 evaluates to: B. 3 C. 9 D. Considering the domain x 2 ( 3; 0) [ (3; 1), the expression log A. log jx 3j log (x + 3) 3 log jxj C. log (x + 3) + log jx 43. B. 3j The equation log5 (2x A. x = 2 44. 45. is equivalent to: log 9 log jxj 2 log jxj log 9 3 log jxj 3) = 0 has solution: B. x = 4 The equation 4x = 8x A. x = 15 D. 3 log jxj x2 9 x3 1 9 5 C. x = 3 2 D. no solution has solution: B. x = 10 The function f (x) = 2x+3 C. x = D. x = 5 5 1 has an inverse function given by: A. f 1 (x) = log2 (x + 3) + 1 B. f 1 (x) = log2 (x + 1) C. f 1 (x) = log2 (x D. f 1 (x) = 2x 3) + 1 6 3 +1 3 Trigonometry 46. Convert 135 to radian measure: A. 135 radians 47. Evaluate cos 1 A. 2 48. B. 135 radians 5 6 C. 3 radians 4 D. 3 radians 4 . The angle is in radians. B. 1 2 C. p 3 2 p 3 2 D. Find the value of c in the given right triangle if B = radians and a = 6 cm. 3 A. 12 cm 49. B. 2 cm p C. 4 3 cm p D. 3 3 cm C. D. Find the value of Angle C in the given triangle p if B = radians, b = 3 cm and c = 3 2 cm. 6 A. 4 50. radians B. p 2 radians 2 3 radians p The function given by f ( ) = 3 sin (2 ) + 4 has period: A. 2 B. C. 4 7 D. 3 2 radians
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