The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION INTEGRATED ALGEBRA. Tuesday, January 24, :15 a.m. to 12:15 p.m.

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2 Part I Answer all 30 questions in this part. Each correct answer will receive credits. No partial credit will be allowed. For each question, write on the separate answer sheet the numeral preceding the word or epression that best completes the statement or answers the question. [60] 1 Which epression is equivalent to 64? (1) (8 )(8 ) (3) ( 8)( 8) () (8 )(8 ) (4) ( 8)( 8) Use this space for computations. Mr. Smith invested \$,500 in a savings account that earns 3% interest compounded annuall. He made no additional deposits or withdrawals. Which epression can be used to determine the number of dollars in this account at the end of 4 ears? (1) 500(1 0.03) 4 (3) 500(1 0.04) 3 () 500(1 0.3) 4 (4) 500(1 0.4) 3 3 What is 45 epressed in simplest radical form? (1) 3 5 (3) 6 5 () 5 5 (4) 18 5 Integrated Algebra Januar 1 []

3 4 Which graph does not represent a function? Use this space for computations. (1) (3) () (4) 5 Timm bought a skateboard and two helmets for a total of d dollars. If each helmet cost h dollars, the cost of the skateboard could be represented b (1) dh (3) d h () dh (4) d h Integrated Algebra Januar 1 [3] [OVER]

4 6 The graph of is shown below. Use this space for computations. Which graph represents? (1) (3) () (4) Integrated Algebra Januar 1 [4]

5 7 Two equations were graphed on the set of aes below. Use this space for computations. Which point is a solution of the sstem of equations shown on the graph? (1) (8,9) (3) (0,3) () (5,0) (4) (, 3) 8 Bron is 3 ears older than Doug. The product of their ages is 40. How old is Doug? (1) 10 (3) 5 () 8 (4) 4 Integrated Algebra Januar 1 [5] [OVER]

6 9 The actual dimensions of a rectangle are.6 cm b 6.9 cm. And measures the sides as.5 cm b 6.8 cm. In calculating the area, what is the relative error, to the nearest thousandth? (1) (3) 0.0 () 0.05 (4) 0.01 Use this space for computations. 10 Which graph represents the inequalit 3? (1) (3) () (4) Integrated Algebra Januar 1 [6]

7 11 Which set of data can be classified as quantitative? (1) first names of students in a chess club () ages of students in a government class (3) hair colors of students in a debate club (4) favorite sports of students in a gm class Use this space for computations. 1 Three fair coins are tossed. What is the probabilit that two heads and one tail appear? (1) 1 8 (3) 3 6 () 3 8 (4) 3 13 What is the sum of and 5 6 4? (1) 8 5 (3) () (4) For which values of is the fraction undefined? 5 6 (1) 1 and 6 (3) 3 and () and 3 (4) 6 and 1 Integrated Algebra Januar 1 [7] [OVER]

8 15 What is the slope of the line that passes through the points (, 3) and (5,1)? Use this space for computations. (1) 3 (3) 4 3 () 3 (4) 4 3 ( 3 4 ) 16 The epression is equivalent to (1) 4 4 (3) 8 4 () 4 5 (4) In the diagram below, circle O is inscribed in square ABCD. The square has an area of 36. A B O D C What is the area of the circle? (1) 9π (3) 3π () 6π (4) 36π 18 Which point lies on the graph represented b the equation 3 8? (1) (,7) (3) (,4) () (0,4) (4) (7, ) Integrated Algebra Januar 1 [8]

9 19 The equation of the ais of smmetr of the graph of 3 7 is Use this space for computations. (1) 3 4 (3) 3 () 3 4 (4) 3 0 The bo-and-whisker plot below represents the ages of 1 people What percent of these people are age 15 or older? (1) 5 (3) 75 () 35 (4) 85 1 Campsite A and campsite B are located directl opposite each other on the shores of Lake Omega, as shown in the diagram below. The two campsites form a right triangle with Sam s position, S. The distance from campsite B to Sam s position is 1,300 ards, and campsite A is 1,700 ards from his position. Lake Omega A 1,700 ards B 1,300 ards S What is the distance from campsite A to campsite B, to the nearest ard? (1) 1,095 (3),140 () 1,096 (4),141 Integrated Algebra Januar 1 [9] [OVER]

10 Which set builder notation represents {, 1, 0, 1,, 3}? (1) { 3 3, where is an integer} () { 3 4, where is an integer} (3) { 3, where is an integer} (4) { 4, where is an integer} Use this space for computations. 3 The roots of the equation are (1) 0 and 9 (3) 0 and 3 () 0 and 9 (4) 0 and 3 4 Which equation is an eample of the use of the associative propert of addition? (1) 7 7 () 3( ) 3 3 (3) ( ) 3 ( 3) (4) 3 ( ) ( ) 3 5 Given: A {, 4, 5, 7, 8} B {3, 5, 8, 9} What is A B? (1) {5} (3) {, 3, 4, 7, 9} () {5, 8} (4) {, 3, 4, 5, 7, 8, 9} Integrated Algebra Januar 1 [10]

11 6 The diagram below shows right triangle LMP. Use this space for computations. L 3 5 M 4 P Which ratio represents the tangent of PLM? (1) 3 4 (3) 4 3 () 3 5 (4) Mr. Stanton asked his students to write an algebraic epression on a piece of paper. He chose four students to go to the board and write their epression. Robert wrote: 4( 5) 17 Meredith wrote: z Steven wrote: 9w 0 Cnthia wrote: Which student wrote an algebraic epression? (1) Robert (3) Steven () Meredith (4) Cnthia 8 If s t, then equals r rs t (1) (3) rs t rs 1 () (4) rs t Integrated Algebra Januar 1 [11] [OVER]

12 9 A scatter plot was constructed on the graph below and a line of best fit was drawn. Use this space for computations What is the equation of this line of best fit? (1) 5 (3) 5 5 () 5 (4) What is the sum of 5 and 5 epressed in simplest form? (1) 1 (3) () (4) Integrated Algebra Januar 1 [1]

13 Part II Answer all 3 questions in this part. Each correct answer will receive credits. Clearl indicate the necessar 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 onl 1 credit. All answers should be written in pen, ecept for graphs and drawings, which should be done in pencil. [6] 31 The length and width of the base of a rectangular prism are 5.5 cm and 3 cm. The height of the prism is 6.75 cm. Find the eact value of the surface area of the prism, in square centimeters. Integrated Algebra Januar 1 [13] [OVER]

14 3 Case purchased a pack of assorted flower seeds and planted them in her garden. When the first 5 flowers bloomed, 11 were white, 5 were red, 3 were blue, and the rest were ellow. Find the empirical probabilit that a flower that blooms will be ellow. 33 Epress in simplest form: 1 3 Integrated Algebra Januar 1 [14]

15 Part III Answer all 3 questions in this part. Each correct answer will receive 3 credits. Clearl indicate the necessar 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 onl 1 credit. All answers should be written in pen, ecept for graphs and drawings, which should be done in pencil. [9] 34 Solve algebraicall for : ( 4) 1 _ (5 3) Integrated Algebra Januar 1 [15] [OVER]

16 35 On the set of aes below, solve the following sstem of equations graphicall. State the coordinates of the solution Integrated Algebra Januar 1 [16]

17 36 A turtle and a rabbit are in a race to see who is first to reach a point 100 feet awa. The turtle travels at a constant speed of 0 feet per minute for the entire 100 feet. The rabbit travels at a constant speed of 40 feet per minute for the first 50 feet, stops for 3 minutes, and then continues at a constant speed of 40 feet per minute for the last 50 feet. Determine which animal won the race and b how much time. Integrated Algebra Januar 1 [17] [OVER]

18 Part IV Answer all 3 questions in this part. Each correct answer will receive 4 credits. Clearl indicate the necessar 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 onl 1 credit. All answers should be written in pen, ecept for graphs and drawings, which should be done in pencil. [1] 37 The sum of three consecutive odd integers is 18 less than five times the middle number. Find the three integers. [Onl an algebraic solution can receive full credit.] Integrated Algebra Januar 1 [18]

19 38 A sandwich consists of one tpe of bread, one tpe of meat, and one tpe of cheese. The possible choices are listed below. Bread: white, re Meat: ham, turke, beef Cheese: American, Swiss Draw a tree diagram or list a sample space of all the possible different sandwiches consisting of one tpe of bread, one tpe of meat, and one tpe of cheese. Determine the number of sandwiches that will not include turke. Determine the number of sandwiches that will include re bread and Swiss cheese. Integrated Algebra Januar 1 [19] [OVER]

20 39 Shana wants to bu a new biccle that has a retail price of \$ She knows that it will be on sale net week for 30% off the retail price. If the ta rate is 7%, find the total amount, to the nearest cent, that she will save b waiting until net week. Integrated Algebra Januar 1 [0]

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 hpotenuse adjacent hpotenuse opposite adjacent 1 Area trapezoid A = h(b 1 + b ) Volume clinder V = πr h Surface Area Coordinate Geometr rectangular prism clinder Δ m = = Δ SA = πr + πrh 1 1 SA = lw + hw + lh Integrated Algebra Januar 1 [3]

24 INTEGRATED ALGEBRA Tear Here Tear Here Integrated Algebra Januar 1 [4] Printed on Reccled Paper INTEGRATED ALGEBRA

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