Pre-Calculus 11 Practice Exam

Transcription

1 Name: Date: [ID-1] Pre-alculus 11 Practice Exam Selected Response 1. What is the value of S 22 for the series ë? D Determine the sum of the series ë D No sum since r <1 3. lbert has set up a giant display of cans in his father s store. The bottom row has 97 cans, the next rows have 94 cans, 91 cans, 88 cans and so on. Which row has 19 cans? D The population of a community was at the beginning of ssuming a rate of growth of 2.5% per year since 2007, what will the population be at the beginning of 2028? Round your answer to the nearest unit D The population of a community was at the beginning of The population of this community decreases each year at a rate of 3%. What will the population be at the beginning of 2020? Round your answer to the nearest unit D What other angles have the same reference angle as 118? 62, 208, , 242, , 208, 332 D 28, 62, Determine the exact values of sinθ, cosθ, and tanθ if the terminal arm of angle θ passes through the point ( 3, 2). sinθ = 2 / 13 cosθ = 3 / 13 tanθ = 2 / 3 sinθ = 3 / 13 cosθ = 2 / 13 tanθ = 2 / 3 sinθ = 3 / 13 cosθ = 2 / 13 tanθ = 2 / 3 D sinθ = 2 / 13 cosθ = 3 / 13 tanθ = 2 / 3 8. n angle is in standard position such that cosθ= 4. What are the possible values of θ, to the nearest degree, 7 if 0 θ 360? 30 and and and 235 D 35 and 55 1

2 9. Factor. 4x 2 ( ) 2 +8x 2 ( )+3 ( 2x+1) ( 2x+3) ( 2x 1) ( 2x+1) ( 2x 3) ( 2x 1) D ( 2x+1) ( 2x+1) 10. What is the domain and range for the quadratic function below? Ìx x R Ó and Ìy y R,y 3 Ó Ìx x R,x 3 Ó and Ìy y R Ó Ìx x R,x 6 Ó and Ìy y R Ó D Ìx x R Ó and Ìy y R,y 3 Ó 11. What is the equation of the axis of symmetry for y=3(x 8) 2 6? x = 6 x = 8 x = 3 D x = What is the equation of the axis of symmetry for y= 5x 2 4x 5? x = 2 x = 2 5 x = 2 D x = Determine the equation of the quadratic function graphed below. y = 1 ( x+3 2 )2 +3 y = 1 ( x 3 2 )2 3 y = 1 ( x+3 2 )2 +3 D y = 1 ( x 3 2 ) How many zeros does a quadratic function have if its axis of symmetry is x= 1 and its maximum value is 30? 2 Not enough information 0 D Determine the roots of the function y=x 2 16x ± 53 8 ± 53 8 ± 5 3 D 8 ± 5 3 2

3 16. How many roots does a quadratic function have if its axis of symmetry is x=6 and its minimum value is 24? Not enough information 0 2 D Which equation below has no real solution(s)? 2x 2 4x+2=0 2x 2 4x 6=0 2x 2 4x 1=0 D 2x 2 4x+8=0 18. Last year an organization sold 800 tickets for its annual fundraiser. Tickets cost $16 each. This year the organization hopes to raise more money by raising the ticket price. The total revenue the organization will earn when the ticket price is increased by x dollars is modelled by the function: R( x) = ( x) ( 16+x) What is the maximum total revenue the organization can earn this year if they raise ticket prices? What is the new ticket price? $ ; $24.00 $ ; $24.67 $ ; $23.33 D $ ; $ State the domain of the function f( x) = 5 6x. Ì Ó Ì Ó x x R, x 5 6 x x R, x 6 5 Ì x x R, x Ó D Ì x x R, x Ó Simplify x 14 y 16 z 13 3x 4 y 5 z x 2 yz 5x 4 y 5 z x 2 yz 3xyz 3 25x 11 y 13 z 10 D x 14 y 16 z Simplify. 18x 6 y 11 3x 3 y 5 2y 9x 3 y5 4y 3x 3 y5 2y D 3x y 2x 4 y The legs of a right triangle measure and Find the exact area of this triangle D 168 3

4 23. simplified rational expression 2x+7 10x 8 has domain Ì x x R, x Ó 4, 2 5. The original expression is: ( x+2) ( 2x+7) ( 10x 8) ( x+2) ( x 2) ( 2x+7) ( 10x 8) ( x 2) D ( 2x+7) ( 10x 8) ( x 2) ( x 2) ( 2x+7) ( 10x 8) 24. State all non-permissible values for the expression below. 25. Simplify. x 2 4x 5 +17x+15 x 2 6x+5 2x2 x 2 +7x 8 x 8, 1, 15, 5, and 1 x 8, 1, and 5 2 x 15 D x 8 and x 2 1 x 1 7x 6 ( x 2) ( x 1) 7 ( x 2) ( x 1) 7x 10 ( x 2) ( x 1) D 7x Solve. 27. Evaluate. x x+1 = 4 x x 2 3x x 4 x = 7 x = 4 and 1 x = 7 and 1 D x = ( 6) D Given the graph of f( x) below, determine the solutions to the equation f( x) = 4. 2 and 6 2 and 6 2 D No solution 4

5 29. Given the graph of f(x) below, determine the solutions to the equation f( x) = 2. No solution 3 and 7 5 and 7 D Which graph represents the solution to 2x 2 3 =2? D 31. Solve. 4x y= 2 y=x 2 +2x+2 (0, 6) (0, 2) and ( 6, 26) (0, 2) and (6, 22) D (0, 6) 32. Which ordered pair is a solution to the inequality 4x y>3? (4, 17) (0, 2) ( 2, 14) D (3, 12) 5

6 33. The graph of f(x) is given below. What is the correct graph of y= 1 f( x)? D 34. Which inequality corresponds to the graph below? x 2 x 12<0 x 2 x 12 0 x 2 x 12>0 D x 2 x Graph the solution to the inequality x 2 +2x 8>0. D 6

7 onstructed Response 36. wrestler is cutting weight for an upcoming tournament. doctor has determined that it is safe for the athlete to lose 6 pounds in the first week and 85% of the previous weight cut in each subsequent week. How much weight can this wrestler safely lose in 10 weeks? Round to the nearest unit. 37. Riley wants to determine the height of the certain building. She measures the angle of elevation to the top of the building to be 60. Riley moves 3.0 m farther away from the building and measures the angle of elevation to be 56. Determine the height of this building to the nearest metre. 38. What is the length of x to the nearest metre? 39. In, c = cm, b = cm, and =29. Solve every possible triangle that contains these measurements. Round sides to the nearest tenth of a centimeter and angles to the nearest degree. 40. In, c = 21 cm, b = 6.75 cm, and =52. Solve every possible triangle that contains these measurements. Round sides to the nearest tenth of a centimeter and angles to the nearest degree. 41. flare is launched from a boat. The height, h, in metres of the flare above the water is modelled by the function h( t) = 4.9t t+3 where t is the number of seconds after the flare is launched. How long is this flare in the air before it hits the water? Round your answer to two decimal places. 42. What is the equation of the function y=4x 2 24x 7 in vertex form? 43. Determine the coordinates of the vertex for the function f( x) =3x 2 6x certain rectangle measures 35 m 25 m. This rectangle's area is doubled by extending each side by the same amount. Determine the dimensions of the enlarged rectangle to the nearest tenth of a metre. 45. Solve. Round to the nearest tenth. 4x =x 46. Jason can complete a certain job in 10 hours. onor and Jason can complete this same job in 2 hours. How long would it take onor to complete this job alone? Write your answer in hours and minutes. 47. car travels 575 km. bus traveling 3 the average speed of the car takes 2 hours longer to travel the same 4 route. What was the average speed of the bus? Round to the nearest unit. 7

8 48. What is the inequality that corresponds to the graph below? 49. Solve. 2x 8 =x 2 +6x Solve. y=5x 2 3x+3 y= 4x 2 +5x+5 8

9 ID: Pre-alculus 11 Practice Exam nswer Section MULTIPLE HOIE D D D D D D D D SHORT NSWER lbs m m 39. Solution #1: 1 74, 1 77, a ; Solution #2: 2 106, 2 45, a Since b < h no triangle can be constructed using this information s 42. y=4x 3 ( ) Ê Ë Á 1,0ˆ m 37.1 m 45. x = hours 30 minutes 1

10 ID: km/h 48. y> 5 4 (x 3) x = 12, ( 0.20, 3.82) and (1.09, 5.69) 2