Math Diploma Exam 1. The graph of y = f( x) is shown below. The partial graph of y = f( x) is shown below.

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1 Diploma Exam Math 0- Name: The graph of y = f( x) is shown below. The partial graph of y = f( x) is shown below. Mylana transforms y = f( x) such that the equation of the new graph is g( x) + = f( x + 4). Below are the partial graphs of four transformations of y = f( x).. The graph of y = g( x) lies in Quadrant A. I B. II C. III D. IV The range of the graph of y = f( x) is y 4. The graph of the function y = f( x) is stretched vertically about the x-axis by a factor of and then translated 9 units down to become the graph of y = g( x).. The range of the graph of y = g( x) is A. ÎÍ 7, ) B. ÎÍ 5, ) C. ÎÍ, ) D. ÎÍ 0, ). The partial graph that represents y = f( x) is i and the partial graph that represents y = f ( x) is ii. A. i. Graph ii. Graph B. i. Graph 4 ii. Graph C. i. Graph ii. Graph D. i. Graph 4 ii. Graph

2 4. The equation a = b y can be expressed in the logarithmic form A. y = log a b a B. y = log b C. y = log b ( a) D. y = log ( a) b 5. Given that log b a = c, where a, b > 0, and b, a b simplified expression for log b a is A. b c B. b c C. c D. c A student constructed the following table of values for a third-degree polynomial. x y The equation of the polynomial described by the table of values is A. y = 4 x( x 5) ( x + 4) B. y = 4 x( x + 5) ( x 4) C. y = x( x 5) ( x + 4) D. y = x( x + 5) ( x 4) The graph of the function y = f( x) is shown below. A student is solving the equation log a ( a ) + log a ( a + ) =, where a >, by using an algebraic process. 6. By correctly simplifying the equation above, the student could obtain the equation A. a 5a = 0 B. a a = 0 C. a a 4 = 0 D. a a + = 0 8. When the graph of y = f( x) is transformed to the graph of y = points is A. B. C. D. 4 f( x), the number of invariant

3 A student made the following statements about the graph of the exponential function f( x) = ab x 4, where a >, b >. The y-intercept is at 4 The y-intercept is at ( a 4). The domain is the set of all real numbers. 4 The range is {y y > 4, y ò } 5 The graph has one x-intercept. 6 There is no x-intercept. 9. The three statements above that are true for the graph of y = f( x) are numbered,, and. (Record all three digits of your answer in any order below.) One factor of the polynomial x + 7x x 5 is x +. The remaining factor can be expressed in the form ax + bx c.. The values if a, b, and c are, respectively,,, and. (Record all three digits of your answer below.) The following statements are made with reference to the unit circle. Statement I The point A, lies on the unit circle. Statement II The point B, lies on the unit circle. Statement III For any point on the unit circle, x + y =. Statement IV Any point that lies on the unit circle can be described as sinθ, cos θ. 0. In 40 minutes, the number of radians the minute hand of a clock will travel through is A. π 0 B. 4π C. π D. π 0.. The statements that are true are numbered A. I and IV B. III and IV C. II and III D. I and III If cot θ = and csc θ < 0, where 0 θ < π, then the value of θ can be expressed as aπ b. Possible values of a and b are, respectively, A. 5 and 6 B. 5 and C. and D. and 6

4 Carol is asked to solve the equation sinx + 8 = sinx algebraically, where 0 x < 60. Carol simplifed the equation to the form sinx = a. 4. The value of a is A. B. C. D. In 008, the province of Alberta had three area codes: 780, 40, 587. Telephone numbers in Alberta consist of the area code followed by a 7-digit number that cannot begin with the digits 0 or, and the digits can be repeated. 5. How many different phone numbers were available in the province of Alberta in 008? A B C D In a particular family of 8 children, there are 5 boys and girls. A photographer is hired to take a series of family pictures of the children. For one of the pictures, the photographer selects boys and girl and arranges them in a row. 6. The number of different ways of arranging the three children for this picture is A. 0 B. 60 C. 60 D. 80 Two rational functions are given below. x 7 x f( x) = g( x) = x 5x x 6x + 8 The equations of the vertical asymptotes for the function y = f( x) are x = a and x = b. The equations of the vertical asymptotes for the function y = g( x) are x = c and x = d. 7. In the functions above, the value of a is (Record in the first box) b is (Record in the second box) c is (Record in the third box) d is (Record in the fourth box) Below are five statements about the graph of f( x) = 6sin x + π + 0. The period of the graph is f( x) is 4π. The y-intercept of the graph is f( x) is 4. The amplitude of the graph is f( x) is 6. 4 The graph of g( x) = 4cos( x π) + has the same maximum as f( x). 5 The graph of f( x) is the same as the graph of h( x) = 6sin x + 0 if h x ( ) is translated horizontally π units left. 8. The three statements above that are correct are numbered,, and. (Record all three digits of your answer in any order.) 4

5 Bob simplifies the left-hand side of the identity tanx sinx = cos x as shown below. tanx sinx sinx tanx sinx Step sinx cos x sinx Step Step Step 4 Step 5 Step 6 sinx cos x sinx sin x cos x sinx sinx cos x cos x sinx sinx cos x sin x sinx cos x sinx cos x cos x sin x 9. The first recorded error in Bob s simplification is in Step. A student is asked to identify which of the n following problems can be solved using r. The number of different arrangements using all the letters of the word POSITIVE. The number of different 5-player teams that can be selected from 7 boys and 6 girls. The number of line segments that can be drawn using the vertices of an 8-sided polygon that are marked on a circle. 4 The number of different ways to choose cupcakes from a display of 8 different cupcakes at a coffee shop. 5 The number of different ways to assign the job of stage manager and costume director in a school play, if 5 students apply. 0. The three problems above that can be solved using n r are numbered,, and. (Record all three digits of your answer in any order.) 5

6 Diploma Exam Answer Section. C. C. B 4. A 5. C 6. B 7. A 8. D 9. 5 or 5 or 5 or 5 or 5 or 5 0. B. 5. D. B 4. B 5. D 6. D or 054 or 504 or or 54 or 45 or 45 or 54 or or 4 or 4 or 4 or 4 or 4