# The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION MATHEMATICS A. Wednesday, August 16, :30 to 11:30 a.m.

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2 Part I Answer all questions in this part. Each correct answer will receive 2 credits. No partial credit will be allowed. For each question, write on the separate answer sheet the numeral preceding the word or expression that best completes the statement or answers the question. [60] While solving the equation 4(x + 2) = 28, Becca wrote 4x + 8 = 28. Which property did she use? () distributive (3) commutative (2) associative (4) identity Use this space for computations. 2 What is the value of p in the equation 2(3p 4) = 0? () (3) 3 (2) 2 (4) Jordan and Missy are standing together in the schoolyard. Jordan, who is 6 feet tall, casts a shadow that is 4 inches long. At the same time, Missy casts a shadow that is 4 inches long. How tall is Missy? () 38 in (3) ft (2) 86.4 in (4) ft 6 in 4 The faces of a cube are numbered from to 6. What is the probability of not rolling a on a single toss of this cube? () (3) 6 6 (2) (4) 4 What is the product of 0x 4 y 2 and 3xy 3? () 30x 4 y (3) 30x y (2) 30x 4 y 6 (4) 30x y 6 Math. A Aug. 06 [2]

3 6 Sal keeps quarters, nickels, and dimes in his change jar. He has a total of 2 coins. He has three more quarters than dimes and five fewer nickels than dimes. How many dimes does Sal have? () 3 (3) 20 (2) 8 (4) 2 Use this space for computations. 7 A micron is a unit used to measure specimens viewed with a microscope. One micron is equivalent to inch. How is this number expressed in scientific notation? () (3) (2) (4) The accompanying graph shows the high temperatures in Elmira, New York, for a -day period in January. Temperature ( F) M T W T F Day Which statement describes the data? () median = mode (3) mean < mode (2) median = mean (4) mean = mode 9 What is the image of point ( 3,4) under the translation that shifts (x,y) to (x 3,y + 2)? () (0,6) (3) ( 6,8) (2) (6,6) (4) ( 6,6) Math. A Aug. 06 [3] [OVER]

4 3 0 For which value of x is the expression x 2 undefined? () 2 (3) 3 (2) 2 (4) 0 Use this space for computations. Which transformation does not always result in an image that is congruent to the original figure? () dilation (3) rotation (2) reflection (4) translation 2 What is the first step in simplifying the expression ( ) 2? () square (3) subtract 3 from 2 (2) add 4 and (4) multiply 3 by 4 3 In the accompanying diagram, line is parallel to line m, and line t is a transversal. t m Which must be a true statement? () m + m 4 = 80 (3) m 3 + m 6 = 80 (2) m + m 8 = 80 (4) m 2 + m = 80 4 What is the sum of 0 and 32? () 82 (3) 9 2 (2) (4) 2 Math. A Aug. 06 [4]

5 Which ordered pair is in the solution set of the system of inequalities shown in the accompanying graph? Use this space for computations. y x () (0,0) (3) (,) (2) (0,) (4) (3,2) 6 Julia has four different flags that she wants to hang on the wall of her room. How many different ways can the flags be arranged in a row? () (3) 6 (2) 0 (4) 24 7 If x = 4 and y = 2, the value of 2 xy 2 is () 32 (3) 4 (2) 8 (4) 8 8 The measures of two consecutive angles of a parallelogram are in the ratio :4. What is the measure of an obtuse angle of the parallelogram? () 20 (3) 00 (2) 80 (4) 60 Math. A Aug. 06 [] [OVER]

6 9 The graph of the equation x + 3y = 6 intersects the y-axis at the point whose coordinates are () (0,2) (3) (0,8) (2) (0,6) (4) (6,0) Use this space for computations. 20 What is the value of w in the equation 4 w + 8 = 3 w 7? () 2.4 (3) (2) 0.2 (4) Which list shows the numbers. 02, 82, 8, and in order from smallest to largest? (). 02,,, (3),. 02,, (2),,,. 02 (4),,. 02, One of the roots of the equation x 2 + 3x 8 = 0 is 3. What is the other root? () (3) 6 (2) 6 (4) 2 23 The expression 2x 2 x 2 is equivalent to () x 0 (3) x 2 (2) 2 (4) 2x 4 Math. A Aug. 06 [6]

7 24 The coordinates of A are ( 9,2) and the coordinates of G are (3,4). What are the coordinates of the midpoint of AG? () ( 3,8) (3) ( 6,6) (2) ( 6,6) (4) ( 2, 0) Use this space for computations. 2 What is the total number of points of intersection of the graphs of the equations x 2 + y 2 = 6 and y = x? () (3) 3 (2) 2 (4) 4 26 In the next Olympics, the United States can enter four athletes in the diving competition. How many different teams of four divers can be selected from a group of nine divers? () 36 (3) 3,024 (2) 26 (4) 6,6 27 When Albert flips open his mathematics textbook, he notices that the product of the page numbers of the two facing pages that he sees is 6. Which equation could be used to find the page numbers that Albert is looking at? () x + (x + ) = 6 (3) (x + )(x + 3) = 6 (2) (x + ) + (x + 2) = 6 (4) x(x + ) = 6 28 Point (k, 3) lies on the line whose equation is x 2y = 2. What is the value of k? () 8 (3) 6 (2) 6 (4) 8 Math. A Aug. 06 [7] [OVER]

8 29 Which statement is logically equivalent to the statement If Corey worked last summer, he buys a car? () If Corey does not buy a car, he did not work last summer. (2) If Corey buys a car, he worked last summer. (3) If Corey did not work last summer, he does not buy a car. (4) If Corey buys a car, he did not work last summer. Use this space for computations. 30 Which line is perpendicular to the line whose equation is y + 6 = 3x? () y = x + 7 (3) y = x + 7 (2) y = x + 7 (4) y = x + 7 Math. A Aug. 06 [8]

9 Part II Answer all questions in this part. Each correct answer will receive 2 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only credit. [0] 3 In Clark Middle School, there are 60 students in seventh grade. If 2 of these students take art only, 8 take music only, and 9 do not take either art or music, how many take both art and music? Math. A Aug. 06 [9] [OVER]

10 32 Running at a constant speed, Andrea covers miles in 2 2 hours. At this speed, how many minutes will it take her to run 2 miles? 33 In the accompanying diagram of right triangles ABD and DBC, AB =, AD = 4, and CD =. Find the length of BC, to the nearest tenth. B A 4 D C Math. A Aug. 06 [0]

11 34 Dan is sketching a map of the location of his house and his friend Matthew s house on a set of coordinate axes. Dan locates his house at point D(0,0) and locates Matthew s house, which is 6 miles east of Dan s house, at point M(6,0). On the accompanying set of coordinate axes, graph the locus of points equidistant from the two houses. Then write the equation of the locus. y x Math. A Aug. 06 [] [OVER]

12 3 A recent survey shows that the average man will spend 4,288 hours sleeping, 8,72 hours working, 8,68 hours watching television, 9,94 hours commuting,,662 hours kissing, and 363,447 hours on other tasks during his lifetime. What percent of his life, to the nearest tenth of a percent, does he spend sleeping? Math. A Aug. 06 [2]

13 Part III Answer all questions in this part. Each correct answer will receive 3 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only credit. [6] 36 Debbie goes to a diner famous for its express lunch menu. The menu has five appetizers, three soups, seven entrées, six vegetables, and four desserts. How many different meals consisting of either an appetizer or a soup, one entrée, one vegetable, and one dessert can Debbie order? Math. A Aug. 06 [3] [OVER]

14 37 Triangle ABC has coordinates A(2,0), B(,7), and C(,). On the accompanying set of axes, graph, label, and state the coordinates of ΔA' B' C', the reflection of ΔABC in the y-axis. y B (,7) A (2,0) C (,) x Math. A Aug. 06 [4]

15 Part IV Answer all questions in this part. Each correct answer will receive 4 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only credit. [8] 38 AB and CD intersect at E. If m AEC = x 20 and m BED = x + 0, find, in degrees, m CEB. Math. A Aug. 06 [] [OVER]

16 39 Manuel plans to install a fence around the perimeter of his yard. His yard is shaped like a square and has an area of 40,000 square feet. The company that he hires charges \$2.0 per foot for the fencing and \$0.00 for the installation fee. What will be the cost of the fence, in dollars? Math. A Aug. 06 [6]

17 Tear Here Tear Here Scrap Graph Paper This sheet will not be scored.

18 Scrap Graph Paper This sheet will not be scored. Tear Here Tear Here

20 MATHEMATICS A MATHEMATICS A Rater s/scorer s Name (minimum of three) Maximum Credits Rater s/scorer s Question Credit Earned Initials Part I Tear Here Part II Part III Part IV Maximum 84 Total Total Raw Checked by Scaled Score Score (from conversion chart) Tear Here Math. A Aug. 06 [20] MATHEMATICS A

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