Mathematics 0 Midterm Eam Review Chapter : Radicals Chapter 6: Quadratic Functions Chapter 7: Quadratic Equations. Evaluate: 6 8 (A) (B) (C) (D). Epress as an entire radical. (A) (B) (C) (D). What is the perimeter of the given diagram in simplest radical form? (A) 0 7 (B) 7 (C) 8 7 (D) 8 7 7 8 8 6. Simplif: (A) 6 (B) 6 (C) + 6 (D) + 6. Rationalize the denominator: (A) (B) 6 (C) (D) 6 6. Determine the width, w, of the given rectangle. w Area = 7 80 (A) 0 (B) 6 0 l = 9 (C) 0 (D) 8 0 7. Simplif: (A) 6 8 (B) 8 (C) 8 (D) 6 8 8. Simplif: 7 6 (A) 9 (B) 9 (C) (D) 9. Solve for : (A) = (B) = (C) = (D) =
0. Solve for : 6 (A) = (B) = (C) = (D) = 7. Solve for : 8 6 (A) = (B) = (C) = (D) =. Solve for : 0 0 (A) = 0 (B) = 0 (C) = (D) =. Perform the operations indicated and epress the answer in simplest radical form. (a) 6 8 8 7 (b) (c) 0. Solve for : 9. Which is the verte for the quadratic function = ( + ) 8? (A) (, 8) (B) (, 8) (C) (, 8) (D) (, 8) 6. Which is the verte for the quadratic function = +? (A) (, ) (B) (, ) (C) (, 6) (D) (, ) 7. Which is a quadratic function? (A) f ( ) (B) f ( ) ( ) (C) f ( ) 0 D) f ( ) 7 8. Which is the intercept for the quadratic function f() = ( + )( )? (A) 6 (B) (C) 0 (D) 6 9. Which is the intercept for the quadratic function = +? (A) (B) (C) 0 (D) 0. What is the range for the function ( 7)? (A) (B) (C) (D). Which represents the range for the graph? (A) 9 (B) 0 (C) (D) 6, R R - - - - - 6 7 -
. Which statement about the quadratic function = with verte (, ) is correct? (A) There is a minimum value of. (B) There is a minimum value of. (C) There is a maimum value of. (D) There is a maimum value of.. A parabola opens down and has intercepts at and 6. Which represents the function in factored form? (A) = ( )( + 6) (B) = ( + )( 6) (C) = ( )( + 6) (D) = ( + )( 6). Which is the function in Verte Form represented b the graph? (A) = ( ) + (B) = ( + ) + - 6 - - - - - - (C) = ( ) + - (D) = ( + - ) + - - - 6. Which is the equation of the ais of smmetr for the function = + 9? (A) = 6 (B) = (C) = (D) = 6 6. Which is the equation of the ais of smmetr for the function = 7? (A) = 7 (B) = 0 (C) = (D) = 7 7. Which is the equation of the ais of smmetr for the function = ( + )( 6)? (A) = (B) = (C) = (D) = 8. The height of an object in meters, thrown upward from a window, after t seconds is given b the equation h t t.9 9.6 When is the maimum height reached? (A) sec (B) sec (C) 9.6 sec (D).9 sec 9. The area of a rectangular enclosure is given b the function A() = + 0, where is the width, in meters. What is the width that will produce a maimum area? (A) m (B) m (C) 0 m (D) 0 m 0. Which represents the number of -intercepts for the function. = ( + ) + (A) (B) (C) (D) none. Which quadratic function doesn t have intercepts? (A) = + (B) = + (C) = ( )( + ) (D) = ( )
. Which represents the quadratic function = ( )( + ) in standard form? (A) = + (B) = + 9 (C) = 6 + 9 (D) = + 6 9. The Beatles Fan Club has 6000000 members and charges $.00 per month. If the Club raises membership fees b $.00 per month the epect 0000 fewer members per month. Which represents the revenue function? (A) R ( 6000000 )( 0000) (B) R ( 6000000 )( 0000) (C) R ( 6000000 0000 )( ) (D) R ( 6000000 0000 )( ). A farmer constructs a rectangular enclosed fence in an open field using 00m of fencing. Which quadratic function models the maimum area of the enclosed region? (A) (C) A ( ) (00 ) (B) A ( ) (00 ) A ( ) (0 ) (D) A ( ) (0 ). Determine the following information from the graph. Equation of Ais of Smmetr: - 6 - - - 6 Verte: Maimum or Minimum Value: Y intercept: X intercepts: - 8-0 Domain: Range: 6. Determine the quadratic function, of the parabola graphed below, in factored form. 6 - - 6 - - - 6
7. The flight of a golf ball is represented b the function h(t) = t + t, where height, h, is given in meters and time, t, is given in seconds. The path of the ball can be seen in the graph below. 8 6 0 8 6 h(t) t (a) What is the height of the ball at seconds? (b) What is the maimum height of the ball? (c) When does the ball reach its maimum height? (d) How long is the ball in the air? (e) What is the domain and the range? 8. Given the function = 8 + determine the following information and sketch the graph. Equation of Ais of Smmetr: Verte: Maimum or Minimum value is Number of intercepts: Y intercept: Domain: Range: 8 7 6-8 - 7-6 - - - - - - 6 7 8 - - - - - 6-0 - - - 9 8 7 - - -
9. Determine the following information and sketch the graph of the given function. = ( + ) Direction of Opening: Verte: Equation of the Ais of Smmetr: Maimum or Minimum Value: Number of intercepts: Y Intercept: Domain: Range: - - - - - - - - - - -6-7 -8-9 -0 0. Determine the quadratic function, in verte form, for the given graph. - - - - - - - - - - -6. The trajector of a rocket is represented b the function h(t) = t + 0t +, where h is height in meters and t is time in seconds. (a) What is the initial height of the rocket before it takes flight? (b) What is the height of the rocket at. seconds? (c) At what time does the rocket reach its maimum height? (d) What is the maimum height reached b the rocket?
. A storage space is to be constructed using 00 m of wire mesh fencing. If the warehouse is to be used as one side of the storage space, what dimensions will produce a maimum area? What is the maimum area of the storage space? WAREHOUSE. A dair farmer has a rectangular field for his cows to graze. The farmer decides to surround the field with 60 m of fencing. (a) Determine the quadratic function that models the area as a function of its width,. (b) Determine the maimum area of the rectangular field. (c) What is the length and the width of the rectangular field? (d) State the domain and the range of the variables in the function.. Global Gm charges it members $ 0 for a monthl membership. The club has 600 members. Global Gm estimates that for each $ increase in the monthl fee will cause them to lose 0 members. (a) Determine the revenue function. (b) Determine the maimum revenue that the gm can generate. (c) What will be the new gm membership fee that will create a maimum revenue?
. A travel agenc offers a group rate of $800 per person for a week in Ireland if people sign up for the tour. For each additional person who signs up, the price per person is reduced b $00. (a) Determine the revenue function. (b) Determine the maimum revenue that can be generated. (c) What will be the new price per person be to generate the maimum revenue? 6. Which represents the roots for: 7 = 0? (A) 6 (B) 0 and 6 (C) 6 and 6 (D) 7 7. Which are the zeros of the quadratic function: = ( )( + )? (A) = and = (B) = and = (C) = and = (D) = and = 8. A diver springs off a diving board into a quadratic trajector that is modeled b the function h(t) = t + t + 6 where h(t) represents height in meters and t is time in seconds. Determine the time it takes for the diver to hit the water. (A) 0. sec (B) sec (C) sec (D) 6 sec 9. Based on the roots of = 0, which graph represents the quadratic function =? (A) (B) - - - - - - - - - - - - - - - - (C) (D) - - - - - - - - - - - - - - - -
0. Which quadratic function has zeros of and? (A) f() = ( + )( + ) (B) f() = ( + )( ) (C) f() = ( )( + ) (D) f() = ( )( ). Which quadratic equation has roots of and? (A) + = 0 (B) + + = 0 (C) = 0 (D) + = 0. What are the zeros of the quadratic equation 9 = 0? (A) = (B) = (C) = (D) = 9 9. An eagle swoops down to catch a rodent on the ground. If the path traveled b the eagle is represented b h(t) = t t 8, where h(t) represents height in meters and t is time in seconds, at what time does the eagle catch the rodent? (A) sec (B) sec (C) sec (D) 8 sec. Which graph represents a quadratic function with two equal, real zeros? (A) (B) (C) (D). When will the graph of a quadratic function have two real roots? (A) When b ac > 0 (B) When b ac = 0 (C) When b ac < 0 (D) Never 6. Mike used the quadratic formula, as shown below, to solve the quadratic equation 8 + 9 = 0 He made an error in his calculations. In which step did Mike first make his mistake? (A) Step (B) Step (C) Step (D) Step Step : Step : 8 6 8 8 () ()(9) Step : 8 7 Step : 7
7. A rectangular rug 8 feet b 6 feet is placed in a room such that a strip of bare floor of uniform width surrounds the rug. If the total area of the bare floor and rug combined is 0 ft, which quadratic equation represents this situation? (A) ( 8 )( 6 ) = 0 (B) ( 8 + )( 6 + ) = 0 (C) ( 8 )( 6 ) = 0 Rug (D) ( 8 + )( 6 + ) = 0 8. The sum of the squares of two consecutive even integers is 00. Which equation models this situation? (A) + ( + ) = 00 (B) + ( + ) = 00 (C) + ( + ) = 00 (D) + ( + ) = 00 9. Solve the following quadratic equations using factoring: a) = 8 b) = 0 c) = + 0 d) + = 6 e) + 0 = + 7 f). = 80 0 g) + = 0 60. Solve the following using the quadratic formula: a) + = 0 b) + 0 + 7 = 0 6. Determine the EXACT roots of the following: a) = 0 b) = c) + = 0 d) + = b) e). = 8.9 6. Determine the quadratic equation, a + b + c = 0, that has the following roots. a) = 9 = b) = = c) = = d) = ± 6. A javelin is thrown into the air and its height is modeled b the function h(t) = t + t + where h(t) represents height, in meters, t seconds after being released. (a) (b) (c) What is the initial height of the javelin just prior to being released? What is the height of the javelin at seconds? At what times does the javelin attain a height of meters? 6. A rocket is fired into the air according to the equation h t = t + t + 8 where t is the time in minutes and h is the height in meters. (a) Determine the time(s) the rocket is at a height of meters. (b) Determine when the rocket hits the ground.
6. A missile s path when fired from a ship is given b h(t) = t + t + 8, where h(t) is the height of the missile in meters and t is the time in seconds. (a) When does the missile hit the water? (b) Approimatel when does the missile reach a height of m? 66. The revenue made b a drama theater is represented b R = 0 + 80 + 00, where is the number of shows the drama group performs. How man shows should the drama group have to make a profit of $ 000? 67. A rectangular swimming pool has length 0 m and width 0 m. There is a deck of uniform width surrounding the pool. The area of the pool is the same as the area of the deck. Write a quadratic equation that models this situation and use it to determine the width of the deck. 0 m 0 m 68. Susan decides to build a uniform deck around her pool which has dimensions of 0 m b 0 m. If the total area of the pool and deck measures 00m then write a quadratic equation that models this situation and use it to determine the width of the uniform strip denoted b? 0 m Pool 0 m 69. A rectangular garden, measuring 0 m b m, has a uniform strip removed from the edge of one length and the edge of one width to make a concrete walkwa. If the area of the remaining garden is 0 m, what will be the width of the concrete walkwa? m 0 m 70. (a) The product of two odd consecutive integers is 6. Determine the integers. (b) The sum of the squares of two even consecutive integers is. Determine the integers.
ANSWERS. C. C. D. A. C 6. B 7. C 8. C 9. A 0. D. B. D.(a) 7 (b) 9 6 (c) 8 0.. C 6. D 7. B 8. D 9. C 0. C. B. D. B. B. C 6. B 7. C 8. B 9. A 0. B. A. C. D. C. Ais of smmetr: = Verte: (, 9 ) Minimum value of 9 intercept = 0 intercepts = 0 and 6 Domain: R Range: 9 6. = ( + )( ) 7(a) m (b) 6 m (c) sec (d) sec (e) domain: 0 t range: 0 h 6 8. Ais of Smmetr: = Verte: (, ) Minimum value of Number of intercepts: intercept = Domain: R Range: - - - - - - - 9. Direction: downwards Verte: (, ) Ais of smmetr: = Maimum value of Number of intercepts: 0 intercept = 9 Domain: R Range: -6 - - - - - - - - - - -6-7 -8 0. = ( + ) (a) m (b) 0.7 m (c) sec (d) m. Dimensions: 00 m 00 m Maimum Area = 0 000 m (a) A() = + 80 (b) 600 m (c) l = 0 m, w = 0 m (d) Domain: 0 80 Range: 0 A 600
(a) R = 80 + 600 + 000 (b) $ 000 (c) $ 80 (a) R = 00 + 600 + 600 (b) $ 00 (c) $00 6. C 7. C 8. C 9. A 0. C. D. B. C. C. A 6. C 7. D 8. A 9(a) = 0, (b) = (c) =, (d) =, (e) = 9, (f) =, 8 (g) = 0, 60(a) = (b) = 6(a) = (b) =, (c) = (d) =, (e) =, 6(a) + 8 = 0 (b) = 0 (c) 0 7 = 0 (d) = 0 6(a) m (b) 9 m (c). sec, sec 6(a) seconds (b) 6 seconds 6(a) seconds (b). seconds 66. 0 shows 67. + 00 600 = 0, width = m 68. + 60 00 = 0, width =. m 69. width = m 70(a) { 9, 7 }, { 7, 9 } (b) { 6, }, {, 6 }