Calculus pre-test DO NOT WRITE ON THIS TEST! Find the distance between the points (3, 17) and (-2, 5). 13 V145 C) 485 d) 3151 e) none of these Find the midpoint of the line segment joint the points (-3, 1) and (5, -7). a ) (-4, 4 ) (1 , -3) C ) ( - 4 , -3 ) d) (1. 4 ) e none of these x2 - 2x - 15 can be factored as: a) (x+ 2) (x - 15) b) (x+ 3) (x- 5) C) x (x - 2x - 15) d ) (x - 3) (x+ 2) e) does not factor Find the center of the circle: 4x2 + 4y2 - 2x + 8y - 1 = 0. (1 , -4) 19 (- 1, 4 ) C ) ( 1/2 , - 2 ) (1/4, -1) e) none of these D) If y = 1 2 then the point (x, y) could be in what quadrant (s)? (x # 0) X b) 11 or Ill c ) ll or IV 11 e) none of these 6) What values satisfy x2 - 7x + 9 = 0? 7+ 13 5 and 2 b) -1.7 and -5.3 2 C d) -9 and 1 d) none of these 7) x2 - y2 = (x+ y)(x-y) True False Only if x and y are positive Only if x and y are negative Only if x and y are perfect squares8) Factor x2 + y2 (x + y) (x + y) (x - y) ( x + y) x(x + y?) Only factors if x is positive and y is negative Does not factor 9) What does (9x) 1/2 equal? 9x gx ( $ ) 2 get b) 3 VX C ) ( 9 * ) 2 d) 9 VX e) Need more information 10) Simplify completely: x 2 . x- 3 X 5 a) x 5 b ) X " * 4 x 5 d) AL e) None of these 11) Find all points of intersection of the graphs of: x+y =2 and x2 + 3x - y = 3 (5, - 3 ), (1, 1) b) (0, -3), 10, 2) c ) (- 5 , - 3 ) , (1 , 1 ) (- 5, 7), (1, 1) el None of these Match: LETTERS CAN BE USED MORE THAN ONCE! 12) sin2TT + COS2TT a ) 0 e) Undefined 13) tan 2TT b ) -1 f ) 2 14) Cot IT C) 3 g) 1 15) 45 d) TT h) None of these 3 TC 16) 3 nt cos 417) If the point (-1, 1) lies on the graph of the equation Kx2 - xy + y2 = 5, find the value of K. a) 7 d) - 3 b ) 3 C) 5 e ) None of these 18) Find the slope of the line passing through the points (-1, 16) and (4, 2). 5 a) 14 b ) 14 5 C ) 5 14 14 d) 5 e) None of these 19) Find the domain of f(x) = V3 + 2 x a ) ( - 0o , - 3 C ) (-2 0) d) ( -0o . =2 3 ) ( - 3, 00 ) e) None of these 20) Given f(x) = x2 - 3x + 4, find f(x+ 2) -f(2) x2 - 3x + 4 b) x2 + X N C ) X2 + X - 8 d ) X2 - 3x - 4 e) None of these 21) Is the following function even or odd? f(x) = 3x4 - x2 + 2 a ) Odd b) Even C) Both d) Neither 22) If f ( x ) 1 Vx and g(x) = 1- x2, find f(g(x) ) 1 - X 2 a) b) c) 1 - X / - VX V1 - X 2 1 d) + 1 - x 2 e) None of these13) An open box is to be made from a rectangular piece of material 9 inches by 12 inches by cutting equal squares from each corner and turning up the sides. Let x be the length of each side of the square cut out of each corner. Write the volume V of the box as a function of x. V = x3 b) V = 108x V = x(9 - x) (12-x) d) V = x(9- 2x)(12-2x) None of these 24) Given f(x) = V2x - 1, find f-1(x). a) V 24 - 1 , y 2 1/2 6) x2 + 1 , x 20 C ) 1/2 (X 2 + 1 ) , x 2 1/2 d) e) None of these 2 x - 1 x > 1/ 2 25) The y-coordinate of the solution of the system of equations is: 3 x + y = 3 x - 3y = 2 a ) 11 3 00 / V 10 b ) 2 c )- d) 10 e) None of these 26) What is the slope of the line 2x - 3y = 12? a) WIN b ) N/W C) -4 d) 6 e) None of these 27) a - is the same as: atb a ) c ) b d ) 1 + e) None of these o1 - b) 1 + b b 28) The graph of 4x - y - 12 = 0 crosses the x-axis at x = . C a) 3 b ) - 3 c) 0 d) -12 e) None of these