Math 1 chapter si practice eam MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Which equation matches the given calculator-generated graph and description? Decide without using our calculator. 1) 1) Parabola; opens upward A) -3 = 2 B) -3 = 2 C) 3 = 2 D) 3 = 2 2) 2) Circle; center (0, 0); radius 3 A) 2 + 2 = 3 B) 2 + 2 = 9 C) 2 + 2 = 1 D) 2 + 2 = -9 3) 3) Parabola; opens left A) = 2 B) = - 2 C) = - 2 D) = 2 1
) ) Circle; center (-3, 2); radius A) ( + 3) 2 + ( - 2) 2 = B) ( + 2) 2 + ( - 3) 2 = C) ( - 3) 2 + ( + 2) 2 = D) ( - 2) 2 + ( + 3) 2 = SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find the center-radius form of the equation of the circle satisfing the given conditions. ) Center (2, 0), radius 1 ) 6) Center - 3, - 9, radius 6 6) 7) Center (2, 2), tangent to the -ais 7) Graph the circle if possible. 8) 2 + ( - ) 2 = 2 8) - - - - 2
9) ( + 2) 2 + 2 = 9) - - - - Find the center and radius of the circle. ) 2 + 2 = -8 + 8 ) 11) 9 2-9 + 9 2 + 9-2 = 0 11) Find the coordinates of the verte and the direction of opening of each parabola. 12) = -( + 2) 2 + 9 12) 13) = ( + 3) 2 + 13) Give the focus, directri, and ais for the parabola. 1) - 1 36 2 = 1) 1) = 6 2 1) Write an equation for the parabola with verte at the origin. ) Focus (0, ) ) Find an equation for the parabola with verte at the origin. 17) Through (-, ), opening to the left 17) 18) Through (3, -6), opening downward 18) Find an equation of a parabola that satisfies the given conditions. 19) Verte (8, -6), focus (11, -6) 19) 20) Verte (3, -3), focus (3, 2) 20) For the given parabola, give the coordinates of the verte, the ais, the domain, and the range. 21) = ( - 3) 2 + 21) 3
22) = ( + 3) 2 + 2 22) Graph the parabola. 23) = -( - 8) 2 + 23) - - - - 2) = 2 + 2-3 2) - - - - 2) = -2 2 + 2-2 2) - - - -
26) = 2 - - 2 26) - - - - 27) = -2 2 + + 27) - - - - MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Which equation matches the given calculator-generated graph and description? Decide without using our calculator. 28) 28) Ellipse; foci (0, ±) A) 2 2 + 2 9 = 1 B) 2 2-2 9 = 1 C) 2 + 2 6 = 1 D) 2 2 + 2 9 = 1
29) 29) Center (0, 0); vertical transverse ais A) 2 9 + 2 2 = 1 B) 2 2-2 9 = 1 C) 2 9-2 2 = 1 D) 2 9 + 2 2 = 1 30) 30) Horizontal major ais; center (-1, 3) A) ( + 1)2 + ( - 3)2 = 1 B) ( - 1)2 + ( + 3)2 = 1 C) ( - 1)2 + ( + 3)2 = 1 D) ( + 1)2 + ( - 3)2 = 1 31) 31) Hperbola; center (-1, 3) A) ( - 3)2 - ( + 1)2 = 1 B) ( - 1)2 - ( - 3)2 = 1 C) ( - 3)2 - ( + 1)2 = 1 D) ( - 3)2 - ( + 1)2 = 1 6
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Graph the ellipse. 32) ( + 3) 2 + 2( - 2) 2 = 0 32) - - - - 33) (- 3)2 2 + ( + 2)2 9 = 1 33) 20 12 8-20--12-8 - 8 12 20 - -8-12 - -20 Find an equation of the ellipse. 3) An ellipse with center at origin, length of major ais 1 and -intercepts ± 3) 3) An ellipse with endpoints of major ais at (0, 9), (0, -9); c = 3) 36) An ellipse with foci at (-2, -) and (, -); major ais length of 36) 37) An ellipse with center at (, 2), a = 7, b =, and major ais vertical 37) 7
Graph the hperbola. 38) 2-2 6 = 1 38) - - - - 39) 36 2-2 = 76 39) - - - - 0) 9( - 2) 2 - ( + ) 2 = 1 0) - - - - Find an equation of the hperbola. 1) Vertices at (0, 7), (0, -7); foci at (0, 8), (0, -8) 1) 2) Foci at (, 0), (-, 0); transverse ais with length 6 2) 8
Write the equation in standard form for an ellipse or a hperbola centered at (h, k). 3) 6 2-2 - 12 + 30-69 = 0 3) ) 12 2-8 + 2 + 32 + 11 = 0 ) Solve. ) The roof of a building is in the shape of the hperbola 2-7 2 = 3, where and are in meters. Refer to the figure and determine the height, h, of the outside walls. ) A = 9 m Provide the proper response. 6) If an ellipse has vertices at (-, 0), (, 0), (0, 2), and (0, -2), what is its domain? What is its range? 6) 7) In the ellipse ( + 7)2 36 + ( - )2 smmetr? The vertical ais of smmetr? = 1, what is the equation of the horizontal ais of 7) Identif the equation as a parabola, circle, ellipse, or hperbola. 8) 2 + 2 = 8) 9) 2-2 = 2 9) 0) = 2 2-31 0) 1) ( - ) 2 = 9-2 1) Identif the tpe of graph. 2) 2 = 1-2 1 2) 3) 2 6 + 2 6 = 1 3) 9
) 2 2 + 28 + 2 2-36 = -29 ) ) 2-11 + = 0 ) 6) -2 2 + + 2-6 - 32 = -26 6) Find the eccentricit of the ellipse or hperbola. 7) 8 2-9 2 = 72 7) 8) 2 + 2 = 36 8) 9) 2-2 = 1 9) Find an equation for the conic. If the conic is a parabola, assume that the verte is at the origin. If the conic is an ellipse or hperbola, assume that it is centered at the origin. 60) Focus at (2, 0) and e = 1 2 60) 61) Focus at (6, 0) and e = 3 2 61) Find the eccentricit of the conic section shown in the graph. 62) = -21 20 62) (3, 1.7) -20 (, 0) 20-20 Solve the problem. 63) Suppose that the orbit of a particular planet around the sun is an ellipse with equation 2 672 + 2 = 1, where and are measured in millions of miles. Find the eccentricit 661 of this ellipse. (Round to the nearest thousandth.) 63) Provide an appropriate response. 6) Suppose that AC < 0 in the equation A 2 + B + C 2 + D + E = 0. What kind of graph does this equation have? 6)
6) True or False? A parabola has eccentricit 1. 6) 66) True or False? An ellipse has eccentricit between 0 and 1. 66) 67) True or False? A hperbola has eccentricit greater than 1. 67) Graph the pair of parametric equations b hand, using values of t in [-2,2]. Make a table of t-, -, and -values, using t = -2, -1, 0, 1, and 2. Then plot the points and join them with a line or smooth curve for all values of t in [-2,2]. Do not use a calculator. 68) = -t - 2, = 2t - 1 68) t -2-1 0 1 2 - - - - 69) = t 2-1, = -t + 2 69) t -2-1 0 1 2 - - - - 11
70) = -t 2-3, = t + 2 70) t -2-1 0 1 2 - - - - Find a rectangular equation for the plane curve defined b the parametric equations. 71) = t, = 2t +, for t in (0, ) 71) 72) = t - 3, = t 2 +, for t in (-, ) 72) 73) = t 3, = 7t 2, for t in (-, ) 73) Give two parametric representations for the plane curve. 7) = 3 + 7, in - 7 3, 7) Solve. 7) The motion of a projectile that is fired at a angle with the horizontal is given b = v0 2 2 t, = v 0 2 2 t - t2, for t in [0, k]. Suppose a projectile is fired with an initial velocit of 0 feet per second at an angle of with the horizontal. Find (a) the time when it reaches maimum altitude (b) the maimum altitude. 7) 76) The motion of a projectile that is fired at a 30 angle with the horizontal is given b = v0 3 2 t, = v 0 2 t - t2, for t in [0, ). Suppose a projectile is fired with an initial velocit of 300 feet per second at an angle of 30 with the horizontal. Find (a) the time when it strikes the ground and (b) the range (horizontal distance covered). 76) 77) The motion of a projectile that is fired at a 60 angle with the horizontal is given b = v0 2 t, = v 0 3 2 t - t2, for t in [0, ). Suppose a projectile is fired with an initial velocit of 0 feet per second at an angle of 60 with the horizontal. Find (a) the time when it reaches maimum altitude (b) the maimum altitude. 77) 12
78) A projectile moves so that its position at an time t is given b the equations = 2t and = 176t - t 2 for t in [0, 11]. Graph the path of the projectile and find the equivalent rectangular equation. Use the window [0, 700] b [0, 800]. 78) 700 600 00 00 300 200 0 0 200 300 00 00 600 Provide an appropriate response. 79) True or false? The parametric equations = t 2, = 3t - 2 will graph a parabola. 79) 80) True or false? The parametric equations = t 2, = 3t - 2 will graph a line. 80) 13