MATHB. June 2007 Part I

Transcription

1 MATHB 17 June 007 Part I Answer all questions in this part. Each correct answer will receive credits. No partial credit will be allowed. For each question, write in the space provided the numeral preceding the word or expression that best completes the statement or answers the question. [40] rn 1. The accompaning graph represents the equation = f(x}which graph represents g(x), if g(x) = -f(x)? BTl BEl E]j,BEl (1) () (3) (4) x. During a single da at radio station WMZH, the probabilit that a particular song is plaed is.38. Which expression represents the probabilit that this song will be plaed on exactl 5 das out of? das? (1) 7Cs(.3W(.6)S (3) I'l38)\6) () 7Cl38)\6i (4) scl3w(.6)1 _ 3. Which equation is best represented _~ b the accompaning graph? (1)=e (3)=6x+1 ()=6x 1 (4)=-x + I x 3 _ 4. Jack is planting a triangular rose garden. The lengths of two sides of the plot are 8 feet and 1 feet, and the angle between them is 87. Which expression could be used to find the area ofthis garden? (1) 8 l sin 87 (3) cos 87 ()8 1 cos87 (4)1 8 1 sin What could be the approximate value of the correlation coefficient ". " 0 o for the accompaning scatter plot? (I) (3) 0.1 "0 " ()-0.16 (4) _

2 18 MATH B June 007 MATH B June What is one solution of the accompaning sstem of equations? (1) (3, 5) (3) (-,1) () (0, 5) (4) (0, 3) 7. Which inequalit is represented b the accompaning graph?.. I l'lli'l II I II Ii == -x + 5 == -0.5x + 3 (I)lx+1>5 ()lx+31: (3)lx-Ils5 (4)lx-5t:::: 8. The volume of a soap bubble is represented b the equation V == 0.094JA3, where A represents the surface area of the bubble. Which expression is also equivalent to V? l ~ (1) 0.094A () 0.094A 3 (3) 0.094A 6 9. The fraction _3_ is equivalent to 16-1 (1) () (3) (4) (0.094A 3 ):Z (4) A function,f, is defined b the set {(, 3), (4, 7), (-1, 5)}. If f is reflected in the line == x, which point will be in the reflection? (I) (5, -1) () (-5,1) (3) (1, -5) (4)(-1,5) 11. Which equation is represented b the accompaning graph? (I)==cosx (3)==cosx ()==cos Ix (4)==1 cosx 1. Which expression is in simplest form? (1)... () _9_ (3) x -4 x x +9 x The expression 3- xis equivalent to } -1 x (1) 1 3 () _1 3 (3) 3 ~-n n x - -1 ~ 1t (4) x - 6x + 9 x - x-6 (4) -3 6 _ 7 _ 8 _ 9 _ )1 '/' I, ;f;.' 14. The expression 1+ J + 'if3 is equivalent to (I) "L.j;; () "L nn (3) "L n,n n~l n~o n=l 3 1 (4) "Ln;; 15. Which set of ordered pairs does not represent a function? (I) {(3, -), (-, 3), (4, -1), (-1, 4)} () {(3, -), (3, -4), (4, -I), (4, -3)} (3) {(3, -), (4, -3), (5, -4), (6, -5)} (4) {(3, -), (5, -), (4, -), (-1, -)} 16. Cerise waters her lawn with a sprinkler that spras water in a circular pattern at a distance of 15 feet from the sprinkler. The sprinkler head rotates through an Sprinkler h angle of 300 0, as shown b the shaded area in the accompaning diagram. What is the area of the lawn, to the nearest squarefoot, that receives water from this sprinkler? (I) 79 () 94 (3) 589 (4) Which number is the discriminant of a quadratic equation whose roots are real, unequal, and irrational? (I) 0 () -5 (3)7 (4) The formula S == 0.)t + 73 is used to determine the speed ofsound, S, in meters per second, near Earth's surface, where t is the surface temperature, in degrees Celsius. Which graph best represents this function? -f-' f'f'-+c (I) () (3) (4) If + i and - i are the roots of the equation x 4x + c == 0, what is the value of c? (I) -5 () 5 (3) -4 (4) 4 0. The expression sin A + cos A is equivalent to sin A (I) 1 () sin A (3) sec A (4) csc A n=l

3 0 MATH B - June 007 MATH B - June Part II Answer all questions in this part. Each correct answer will receive credits. Clearl indicate the necessar steps, including appropriate formula correct numerical answer with no work shown will receive onl 1 credit. [1] 4. Denise is designing a storage box in the shape of a cube. Each side of the box has a length of 10 inches. She needs more room and decides to construct a larger box in the shape of a cube with a volume of,000 cubic inches. B how man inches, to the nearest tenth, should she increase the length of each side of the original box? 1. A population of wolves in a count is represented b the equation pet) = 80(0.98)', where t is the number of ears since Predict the number of wolves in the population in the ear lff(x) = log x and g(x) = Y + 14, determine the value of (f a g)(5).. The accompaning table shows the enrollment of a preschool from 1980 through 000. Write a linear regression equation to model the data in the table. Year (x) Enrollment () On a stamp honoring the German mathematician Carl Gauss, several complex numbers appear. The graph below shows two of these numbers. Express the sum I; of these numbers in a + bi form. I1 P 3. In the accompaning diagram of circle 0, chords AB and CD intersect at E. If AE = 3, EB = 4, CE = x, and ED = x - 4, what is the value of x? B j I( j Real

4 MATH B - June 007 Part III Answer all questions in this part. Each correct answer will receive 4 credits. Clearl indicate the necessar steps, including appropriate formula correct numerical answer with no work shown will receive onl 1 credit. [4] MATH B - June A landscape architect is working on the plans for a new horse farm. He is laing out the exercise ring and racetrack on the accompaning graph. The location of the circular exercise ring, with point R as its center, has alread been plotted Iff(x) = 3x - 7 and g(x) = x -7x + 1, find f(x) 7 g(x) for all values of 18x+30 3x -7x-0 x for which the expression is defined and express our answer in simplest fonn. 8. In the accompaning diagram of a streetlight, the light is attached to a pole at R and supported b a brace, PQ, RQ = 10 feet, RP = 6 feet, LPRQ is an obtuse angle, and mlpqr = 30. Find the length of the brace, PQ ' to the nearest foot. "a Q 30' I.i ~!.. Write an equation that represents the outside edge of the exercise ring. The equation of the outside edge of the racetrack is ~ + L = I. Sketch the outside edge of the racetrack on the graph Conant High School has 17 students on its championship bowling team. Each student bowled one game. The scores are listed in the accompaning table. Find, to the nearest tenth, the population standard deviation of these scores. Score (x,) Frequenc (I,) , "$1 '/~~ j. 31. The average annual snowfall in a certain region is modeled b the function Set) = 0 + locos (!t1, where S represents the annual snowfall, in inches, and t represents the numbgr 6f ears since What is the minimum annual snowfall, in inches, for this region? In which ears between 1970 and 000 did the minimum amount of snow fall? [The use of graph paper is optional.] How man of the scores fall within one standard deviation of the mean?

5 4 MATH B - June The path of a rocket fired during a fireworks displa is given b the equation set) = 64t - 16t?, where t is the time, in seconds, and s is the height, in feet. What is the maximum height, in feet, the rocket will reach? In how man seconds will the rocket hit the ground? [The use of graph paper is optional.] Part IV Answer all questions in this part. Each correct answer will receive 6 credits. Clearl indicate the necessar steps, including appropriate formula correct numerical answer with no work shown will receive onl 1 credit. [1] 33. Given: quadrilateral ABCD with vertices A(-, ), B(S, -4), C(6, -10), and D(-4, -4). State the coordinates of A'B'C'D', the image of quadrilateral ABCD under a dilation of factor 1. Prove that A 'B'C'D' is a parallelogram. [The use of graph paper is optional.] 34. A jet is fling at a speed of S6 miles per (! :!::" hour. The pilot encounters turbulence due to a ';:)~ SO-mile-per-hour wind blowing at an angle of47, V) 470 _ as shown in the accompaning diagram. 56 mph Find the resultant speed of the jet, to the nearest tenth ofa mile per hqur. Use this answer to find the measure of the angle between the resultant force and the wind vector, to the nearest tenth ofa degree.