The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA. Tuesday, January 27, :15 to 4:15 p.m.

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2 Part I Answer all 30 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] 1 If A {1, 2, 3, 4, 5, 6, 7, 8} and B {2, 4, 6, 8, 10, 12}, the intersection of sets A and B is (1) {10, 12} (3) {1, 3, 5, 7} (2) {2, 4, 6, 8} (4) {1, 2, 3, 4, 5, 6, 7, 8, 10, 12} Use this space for computations. 2 What is the value of n in the equation 0.2(n 6) 2.8? (1) 8 (3) 20 (2) 2 (4) xy 3 The expression 3 is equivalent to 6xy (1) 4x 2 y 3 (3) 4x 9 y 4 (2) 4x 3 y 3 (4) 4x 3 y 2 4 Which situation is represented by bivariate data? (1) A student lists her algebra quiz grades for one month. (2) A wrestler records his weight before each match. (3) A musician writes down how many minutes she practices her instrument each day. (4) An ice cream vendor tracks the daily high temperature and how many ice cream bars he sells each day. Integrated Algebra Jan. 15 [2]

3 5 A cylinder has a circular base with a radius of 3 units and a height of 7 units. What is the volume of the cylinder in cubic units? (1) 2 (3) 63 (2) 42 (4) 147 Use this space for computations. 6 The graph of f(x) is shown below. y x Based on this graph, what are the roots of the equation f(x) 0? (1) 1 and 5 (3) 2 and 9 (2) 1 and 5 (4) 1 and 5 and 5 7 Jose wants to ride his bike a total of 50 miles this weekend. If he rides m miles on Saturday, which expression represents the number of miles he must ride on Sunday? (1) m 50 (3) 50 m (2) m 50 (4) 50m Integrated Algebra Jan. 15 [3] [OVER]

4 8 Four students are playing a math game at home. One of the math game questions asked them to write an algebraic equation. Use this space for computations. Brandon wrote: 3(5x 0) William wrote: 7 2(6 x) Alice wrote: 15x Kayla wrote: 11 2x 3 Which student wrote an algebraic equation? (1) Brandon (3) Alice (2) William (4) Kayla 9 A student spent 15 minutes painting a 2-foot by 3-foot bulletin board. To the nearest tenth of a minute, how long did it take the student to paint 1 square foot? (1) 0.4 (3) 2.5 (2) 1.5 (4) What is an equation of the line that passes through the points (2,1) and (6,5)? (1) y 3 2 x 2 (3) y 2 3 x 1 (2) y 3 2 x 4 (4) y 2 3 x What is 10 7x 3 5x 7 (1) 2x (3) (2) 29 2x expressed in simplest form? (4) 29 35x 55 35x Integrated Algebra Jan. 15 [4]

5 12 In the box-and-whisker plot below, what is the 2nd quartile? Use this space for computations (1) 25 (3) 45 (2) 30 (4) The length of a rectangle is three feet less than twice its width. If x represents the width of the rectangle, in feet, which inequality represents the area of the rectangle that is at most 30 square feet? (1) x(2x 3) 30 (3) x(3 2x) 30 (2) x(2x 3) 30 (4) x(3 2x) Which set is a function? (1) {(3,4), (3,5), (3,6), (3,7)} (3) {(6,7), (7,8), (8,9), (6,5)} (2) {(1,2), (3,4), (4,3), (2,1)} (4) {(0,2), (3,4), (0,8), (5,6)} 15 The weights of 40 students were recorded. If the 75th percentile of their weights was 140 pounds, what is the total number of students who weighed more than 140 pounds? (1) 10 (3) 30 (2) 20 (4) 4 16 What is the slope of the line represented by the equation 4x 3y 7? (1) 7 4 (3) 3 4 (2) 7 3 (4) 4 3 Integrated Algebra Jan. 15 [5] [OVER]

6 17 What is expressed in simplest radical form? Use this space for computations. (1) 7 6 (3) 87 (2) 7 12 (4) In ABC below, the measure of A 90, AB 6, AC 8, and BC 10. Which ratio represents the sine of B? (1) 10 8 (2) 8 6 (3) (4) The equations 6x 5y 300 and 3x 7y 285 represent the money collected from selling gift baskets in a school fundraising event. If x represents the cost for each snack gift basket and y represents the cost for each chocolate gift basket, what is the cost for each chocolate gift basket? (1) \$20 (3) \$30 (2) \$25 (4) \$54 20 Which equation represents the axis of symmetry of the graph of the equation y x 2 4x 5? (1) x 2 (3) y 2 (2) x 4 (4) y 4 Integrated Algebra Jan. 15 [6]

7 x 2 21 For which value of x is the expression undefined? 2x 1 Use this space for computations. (1) 0 (3) 1 2 (2) 2 (4) Last year, Nick rode his bicycle a total of 8000 miles. To the nearest yard, Nick rode an average of how many yards per day? 1 mile = 1760 yards 1 year = 365 days (1) 22 (3) 1659 (2) 236 (4) 38, The set of integers is not closed for (1) division (3) addition (2) multiplication (4) subtraction 24 A model rocket is launched into the air from ground level. The height, in feet, is modeled by p(x) 16x 2 32x, where x is the number of elapsed seconds. What is the total number of seconds the model rocket will be in the air? (1) 1 (3) 0 (2) 2 (4) 16 Integrated Algebra Jan. 15 [7] [OVER]

8 25 The diagram below shows the path a bird flies from the top of a 9.5-foot-tall sunflower to a point on the ground 5 feet from the base of the sunflower. Use this space for computations. x To the nearest tenth of a degree, what is the measure of angle x? (1) 27.8 (3) 58.2 (2) 31.8 (4) Which set of numbers represents the lengths of the sides of a right triangle? (1) {7, 24, 25} (3) {10, 12, 14} (2) {9, 16, 23} (4) {14, 16, 18} 27 How many different seven-letter arrangements of the letters in the word HEXAGON can be made if each letter is used only once? (1) 28 (3) 720 (2) 49 (4) 5040 Integrated Algebra Jan. 15 [8]

9 28 Three students each rolled a wooden cube with faces painted red, white, and blue. The color of the top face is recorded each time the cube is rolled. The table below shows the results. Use this space for computations. Student Number of Rolls Red White Blue If a fourth student rolled the cube 75 times, based on these experimental data, approximately how many times can the cube be expected to land with blue on top? (1) 25 (3) 35 (2) 30 (4) Dominick graphs the equation y a x where a is a positive integer. If Gina multiplies a by 3, the new graph will become (1) narrower and open downward (2) narrower and open upward (3) wider and open downward (4) wider and open upward Integrated Algebra Jan. 15 [9] [OVER]

10 30 Mr. Suppe recorded the height, in inches, of each student in his class. The results are recorded in the table below. Use this space for computations Which cumulative frequency histogram represents the data? (1) (3) (2) (4) Integrated Algebra Jan. 15 [10]

11 Part II Answer all 3 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 1 credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil. [6] 31 As shown in the diagram below, a ladder 12 feet long leans against a wall and makes an angle of 72º with the ground. 12 ft Find, to the nearest tenth of a foot, the distance from the wall to the base of the ladder. Integrated Algebra Jan. 15 [11] [OVER]

12 32 Carla bought a dress at a sale for 20% off the original price. The sale price of the dress was \$ Find the original price of the dress, in dollars. Integrated Algebra Jan. 15 [12]

13 33 The probability that a student owns a dog is 1. The probability that the same student owns 3 a dog and a cat is 2. Determine the probability that the student owns a cat. 15 Integrated Algebra Jan. 15 [13] [OVER]

14 Part III Answer all 3 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 1 credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil. [9] 34 A DVD costs twice as much as a music CD. Jack buys 2 DVDs and 2 CDs and spends \$45. Determine how much one CD costs, in dollars. [Only an algebraic solution can receive full credit.] Integrated Algebra Jan. 15 [14]

15 35 Noj has the following test scores: 76, 84, 69, 74, 91 His teacher will allow him to retake the test on which he scored lowest. Noj wants an average of at least 82. Determine the least number of additional points Noj must score on the retest. Integrated Algebra Jan. 15 [15] [OVER]

16 36 Graph y x and x 5 on the axes below. y x State the coordinates of a point in the solution set. Integrated Algebra Jan. 15 [16]

17 Part IV Answer all 3 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 1 credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil. [12] 37 The Rock Solid Concrete Company has been asked to pave a rectangular area surrounding a circular fountain with a diameter of 8 feet, as shown in the diagram. 15 ft Fountain 36 ft Find the area, to the nearest square foot, that must be paved. Find the cost, in dollars, of paving the area if the Rock Solid Concrete Company charges \$8.95 per square foot. Integrated Algebra Jan. 15 [17] [OVER]

18 38 Solve the following system of equations algebraically: y x 2 5x 17 y x 5 Integrated Algebra Jan. 15 [18]

19 Integrated Algebra Jan. 15 [19] 39 Perform the indicated operations and express the result in simplest form: xy x xy x y x x y y ( )

20

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

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

23 Reference Sheet Tear Here Tear Here Trigonometric Ratios sin A = cos A = tan A = opposite hypotenuse adjacent hypotenuse opposite adjacent 1 Area trapezoid A = h(b b 2 ) Volume cylinder V = πr 2 h Surface Area Coordinate Geometry rectangular prism cylinder Δy m = = Δx SA = 2πr 2 + 2πrh y 2 y 1 x 2 x 1 SA = 2lw + 2hw + 2lh Integrated Algebra Jan. 15 [23]

24 INTEGRATED ALGEBRA Tear Here Tear Here Printed on Recycled Paper INTEGRATED ALGEBRA

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