Pre Calculus 11 Practice Midyear Exam 2014

Transcription

1 Class: Date: Pre Calculus 11 Practice Midyear Exam 201 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which of the following numbers occurs in the sequence 12, 8,, 0,,...? A 6 C 2 B 3 D The common difference in the arithmetic sequence 2, 6, 1, 22,... is A 8 C 16 B 3 D 8 3. Which of the given formulas for the general term of the sequence 9, 1, 7, 15, 23,... is correct? A t n = 8n 17 C t n = 8n 1 B t n = 8n 17 D t n = 8n 1. The sum of the series ( 5) + ( 7) + ( 9) + ë + ( 19) is A 96 C 192 B 30 D The sum of an arithmetic series where t 1 = 2, t 3 = 7, and n = 15 is A C B 2.5 D The common ratio for the geometric sequence 8, 1, 0.125, ,... is A 1 8 C 8 B 8 D The eighth term in the sequence , , , , is A 9 C 5 B 1 9 D 5 8. The first three terms of the sequence given by t n = 11 1 n 1 Ê ˆ Á A 11, 121, 1331 C 11, 11 16, 11 6 B 11, 11, are D 11, 11 3, The sum of the geometric series ë is A 559 C B D

2 10. Determine the sum of the infinite geometric series A 33 C 33 2 B What is the sum of the infinite geometric series D ( 8 / 9) + 15( 8 / 9) ( 8 / 9) 3 + ë? A 120 C B 135 D Determine the sum of the infinite geometric series with t 1 = 2 and r = 1 5. A 1 3 C 1 2 B 5 3 D The sum of an infinite geometric series is 20 3 and its common ratio is 1. What is the first term of the series? A 1 C 80 3 B 5 D The first three terms of the sequence defined by t n = 0.3n are A 0.5, 0.8, 1.1 C 0.2, 0.1, 0. B 0.3, 0.2, 0.7 D 0.3, 0.8, What are the x-intercepts of y = (x 6)(y 9)? A 6 and 9 C 6 and 9 B 6 and 9 D 6 and 9 2

3 16. What is the quadratic function in vertex form for the parabola shown below? A B f( x) = 8(x 2) C f( x) = 8(x + 1) f( x) = 8(x 1) D f( x) = 8(x 1) What is the vertex of y = 7(x + 5) 2 +? A (5, ) C ( 5, ) B (, 5) D (7, ) 18. If the points ( 1, ) and (2, 13) are on the graph of the quadratic function f( x) = 7x 2 + bx + c, what are the values of b and c? A b = 3 and c = 9 C b = 9 and c = 3 B b = 7 and c = D b = and c = What is the equation of the quadratic function y = x 2 26x + 1 in vertex form? A y = (x + 13) C y = (x + 13) B y = (x 13) D y = (x 13)

4 20. The vertex of the quadratic function y = ( 7 / 9)x 2 ( 1 / 6)x 1 / 81 is A Ê Á 3 / 28, 31 / 9072 ˆ C Ê Á 31 / 9072, 3 / 28 ˆ B Ê Á 31 / 9072, 3 / 28 ˆ D Ê Á 3 / 28, 31 / 9072 ˆ 21. Convert y = 2.5x x 5.9 to vertex form. Round coefficients to two decimal places, if necessary. A y = 2.5( x + 7.3) C y = 2.5( x 7.3) B y = 2.5( x 7.3) D y = 2.5( x + 7.3) What is the axis of symmetry for the quadratic function y = ( 1 / 3)x 2 ( 1 / 2)x 1? A x = 1 8 B x = 117 C x = D x = How many x-intercepts does the graph of the quadratic function f( x) = 2.3x 2 6.9x.6 have? A unknown C 1 B 2 D 0 2. What are the roots of the quadratic function y = 0.5x x + 6? A C and 3 B and 3 D 6

5 25. Factor x 2 20x + 75 completely. A ( x 5) ( x + 15) C ( x + 5) ( x 15) B ( x + 5) ( x + 15) D ( x 5) ( x 15) 26. Factor x x 120 completely. A ( x 2) ( x 15) C ( x + 2) ( x 15) B ( x + 2) ( x + 15) D ( x 2) ( x + 15) 27. A rectangle has dimensions x + 10 and 5x, where x is in centimetres. If the area of the rectangle is 72 cm 2, what is the value of x, to the nearest tenth of a centimetre? A x = 2.0 C x = 11.2 B x =.6 D x = The value of k that makes the expression x x + k a perfect square trinomial is A 1296 C 0 B 1 D 72 5

6 29. The vertex form of x x + 11 = 0 is A ( x + 5) 2 2 = 0 C ( x + 2) 2 5 = 0 B ( x 2) = 0 D ( x 2) 2 5 = A rectangle with an area of 250 cm 2 is x centimetres wide and (x + 8) centimetres long. To the nearest tenth of a centimetre, the width and length are A 50.0 cm and 50.0 cm C 6.2 cm and 5.2 cm B 6.2 cm and 5.2 cm D 1.0 cm and 11.0 cm 31. The number of real roots for the equation y = 30.6x x 39.8 is A 2 C 1 B 0 D impossible to tell 32. Determine the value of the expression x 2 + y 3 when x = 7 and y =. A 56 C 26 B 11 D Simplify A C B 33 7 D Simplify the expression 5 6 ( ) A 3 8 ( 3 5 ) C B 23 2 ( 3 6 ) D 5 8 ( 3 5 ) The volume, V, in cubic units, of a cylinder is given by V = πr 2 h, where r is the radius and h is the height, both in the same units. Find the exact radius of a cylinder with a height of 6 cm and a volume of 576π cm 3. Express your answer in simplest form. A 1 cm 6 C 9 cm B 8 cm D 3 cm 6

7 36. Find a simplified expression for the area of this shape A C 95 B D Express ( 19 7)( ) in simplest form. A C 12 B 2 3 D Express in simplest form. A C 3 7 B D An equilateral triangle has an area of 6.93 cm 2. What is the side length of the triangle, to the nearest tenth of a centimetre? A 2.3 cm C 1.9 cm B 3.5 cm D.0 cm 7

8 0. An equilateral triangle has an area of 3.3 cm 2. What is the height of the triangle, to the nearest tenth of a centimetre? A 3.8 cm C 10.0 cm B 3.5 cm D 8.7 cm 1. Determine the range of the function y = x 2. A {y R} C {x R} B {y R, y 0} D {x R, x 2} 2. Solve 7x = 5. A x = 25 9 B x = Solve x 15 x + 56 = 0. A x = B x = C x = 5 7 D x = 5 9 C x = 9 or x = 6 D x = 6 or x = 9. When fully simplified, ignoring non-permissible values, 6x 9 3x x 8 is equal to 3 9x 6 A 2 9 x 8 C 2 9 x B 9 2 x D 9 2 x 8 8

9 5. Simplify the rational expression x 8 y 5 Ê Á 2xy ˆ 3 Ê Á x 8 y 5 ˆ 3 A 8x 33 y 3 C B 8 y 19 x Simplify the rational expression 5x + 3 x 2 8x x 3. Ê 2xy. Express your answer with positive exponents only. Á 8 ˆ D 1 y x 33 1 x y 3 A 8x 2 + 5x 6 C 3x 2 + 3x 9 x 3 x 3 B 8x 2 + 5x 6 D 3x 2 + 3x 9 x 2 x 2 x When fully simplified, ignoring restrictions on the variable, x 2 + 9x x + 5 x 2 + 7x x x A C 2 21x 9 2x x + 32 ( x + 5) ( x + ) ( x + 3) ( x + 8) ( x + 5) 2x B D x + 9 ( x 2 + 9x + 20) ( x 2 + 7x + 12) ( x + 5) ( x + ) ( x + 3) is equal to 8. Courtney and Kurtis are planning to travel 60 km in a car by travelling at x kilometres per hour for the first half of the distance, and then increasing their speed by 5 km/h to finish the distance. Which is the correct simplified expression for the total time of the trip? 30x x A C x( x + 5) 2x + 5 B 60x x + 5 D 60x x x + 5 ( ) 9. Solve the rational equation x 6 5 x = 0. Identify all non-permissible values. A x = ±6 5, x 6 C x = ± 30, x 0 B x = 30, x 6 D x = 5 6, x Solve x x = x 2 2x x x 2 A x = 3 and x = 2 and x = 8 C x = and x = 8 and x = 8 B x = and x = 8 D x = 2 9