(2) = 137 /13 (45 / dt)log(2) = log(137 /13) dt = 13.24

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Shauna Cooper
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1 Correct answer: A 4 WYSE Academic Challenge Sectional Mathematics 008 Solution Set ( sin α + sinα cosα + cos α ) ( + sin( )) ( + ) (sinα + cosα ) α Correct answer: D If Xthe number of girls, then we want P(0)+P()++P(4) OR -[P(5)+P(6)], that is 57/64 3 Correct answer: C 3 We can treat the right side of the equation as a + ar + ar + ar +, where a and a r Sums of this form converge to, which would simplify to x r x x x x 3 This makes the equation x x Solve to get x 3 x (x )(x 3) x, x 3, x 4 (incidentally, x can t be a solution because it would create division by 0 in the right side 4 Correct answer: D In a trapezoid circumscribed about a circle, the sum of the lengths of the legs equal the sum of lengths of the bases; therefore, a+ b 4 The height of the trapezoid equals the diameter of the circle Therefore, the area equals A (a+ b) h Correct answer: B The equation can be re-written as log 3(x + 4x), 4± 6 4()( 9) OR x + 4x 9 0 x Correct answer: C For vectors of the form ai + bj, length is a + b 3 + ( ) 36 7 Correct answer: A f(x) 0x 5x f (x) 60x 60x 60x (x ) The second derivative equals zero at x 0 and x It changes its sign at x, so the only inflection point is at x 8 Correct answer: D 45/ dt () 37 /3 (45 / dt)log() log(37 /3) dt Sectional Solution Set

2 9 Correct answer: A Although we could convert to Cartesian coordinates and find the distance, it is easier to use law of cosines on the triangle created by the two points and (0,0) The distance is a + b abcosθ where a /3, b /4, and θ π / 3 π /4 π / (/ 3) (/ 4) (/ 3)(/ 4)cos( π /) 0 Correct answer: E x y 6x 4y 3(x x) y + 4y+ y ± 3(x ) This is a pair of straight lines Correct answer: A The derivative of a constant is zero Correct answer: E 3(x ) (y + ) kx Let now be x 0 The equation is of the form y Pe We have the two points (-0, 4000) and (0, 48000) This means P and we can solve for k using k( 0) e x, so k and the equation is y 48000e Solve for when x 40 to get y Correct answer: B p p (p ) p + ( p ) p p, since p < 0 4 Correct answer: A 4 The expression may be re written as: (x + 3)(x 4) Vertical asymptotes are x -3 and x 4, so the sum Correct answer: C 4x 4x y + 4y 0 4(x x) (y 4y) 0 4(x x ) (y 4y + 4 4) 0 4(x x + 05) (y 4y + 4) (x 05) (y ) 7 4(x 05) (y ) (x 05) (y ) This means we end up with 7 7 7/4 7 ( ) ( ) 7 ( ) ( ) a 7/4, b, and c 7 / / Sectional Solution Set

3 6 Correct answer: B 3 + i x i 3 + i + i i + i 3 + 6i + i + i (i ) 3 + 7i i 5 7 Correct answer: E 8 < 6 x < 8 4< x < < x < 7 8 Correct answer: D A Amy s $, B Betsy s $, C Charlie s $, x $ left 08A x, 035B x, 053C x A + B + C 00000, so x/08 + x/035 + x/ Solve to get x A 0593 so A Correct answer: D The equation has a solution only if a 0 There are two cases x 0x a This equation can be rewritten as x 0x a 0 with the discriminant D ( 0) 4 a 00 4a x 0x a This equation can be represented as x 0x + a 0 with the discriminant D ( 00) 4 ( a) a The second discriminant is positive for a 0, so the second equation has two solutions for any non-negative value of a Therefore, the first equation must have exactly one solution, so the discriminant must be equal to 0: 00 4a 0 Therefore, a 5 0 Correct answer: A f( x+ 5) ( x+ 5 ) + (x+ 5 x ) x x Correct answer: B 85% of 38%, or 33%, of all trees die and are attacked 6% of 6%, or 6%, of all trees die and are not attacked This means , or 484% of all trees die The 33% represents 33 / 484, or 66708% of those that have died Correct answer: C A s( s a)( s b)( s c) wheres ( a+ b+ c)/ A 8(8 4)(8 5)(8 7) 98 3 Correct answer: B Ans B: x x + 3x + 5x 5 5 8x 0 5 and Correct answer: C SA 4π r, V 3 4/3π r Since 4 r 000, π r 8906, and V Sectional Solution Set

4 5 Correct answer: D Let a be the length of the legs of the triangle Then, the length of the hypotenuse is a p and the perimeter equals a+ a+ a a(+ ) p Therefore, a and + p p p 3 A a a p ( + ) Correct answer: E P(g from A and w from B) OR P(w from A and w from B)(3/7)(5/7)+(4/7)(6/7) (5+4)/49 39/49 7 Correct answer: B The height of the rectangle is 7 inches, and the width of the rectangle is 5 3 inches This means the perimeter is , or 33 inches 8 Correct answer: C Let us square the equation 7 a + a 3+ a a : 7 a + a 7 a + a 3+ a a + 3+ a a 4 Therefore, 7 a + a 3+ a a 6, so 9 Correct answer: A 7 a + a 3+ a a 3 5(r) 450e 34 5r ln(34 / 450) r r 0% - Go To Next Page Sectional Solution Set

5 30 Correct answer: A The perimeter of A is exactly 3 inches Since the area of triangle A is twice the area of B, each side of A is times as long as the matching side on triangle B Some students may have memorized this fact or will do proof through example The general proof of this argument is rather complex: We can express the area of a triangle in terms of any one side squared times a trigonometric expression of the three angles For example, in the following triangle, x is the length of one side, and a, b, and c are the angle measures: b a c By law of sines, the left side has length of xsinc sinb x The height of the triangle would then be xsinc sina sinb This means the area of the triangle can be expressed as xsinc 05 x sina sinb sinc sina x sinb Any similar triangle would have an area that sinc sina includes an identical value for sinb If a similar triangle has twice the area and has side y in the same spot as side x on our triangle, then: sincsina sincsina y x sinb sinb, y x, y x This ratio will hold for all three sides 3 Correct answer: D sin x sin(x) cos x cos(x) + sin x sin(x) cos(x x) + tan x tanx + sec(x) cos x cos(x) cos x cosx cos x cos(x) cosx 3 Correct answer: E 00 ( ) Correct answer: D Rectangular solid 4 * 3 * 4 cubic feet height of prism is 5 39 feet, so prism is 05 * 3 * 39 * cubic feet This makes the overall volume equal to 3937 cubic feet 008 Sectional Solution Set

6 34 Correct answer: E Let a and b be legs of the right triangle Then A ab 5 and a + b 4 Therefore ab 00 and a + b 576 If we add these two equations, we will get a + ab + b ( a + b) Therefore, a + b 6, so the perimeter equals p a + b Correct answer: E This is a binomial probability We could add up P () + P (3) + + P (0), but it s easier to calculate (P (0) + P ()) (095^0 + 0 * 095^9 * 005) Correct answer: B x 3 x 5 a 3a 5 (a 5)(a+ ) a 5 x 5 Let x a, then x + x a + a (a )(a+ ) a x 37 Correct answer: B 3 + (x 5) 80, so x 3 4x + 3 7, Correct answer: D x x (3y 5) 3 x+ 3 3y 5 y 39 Correct answer: A By matrix algebra, C AB U This means [ U] 40 Correct answer: C 3 9 4, so x - Let x sin a, then we need to find co s(x), knowing that a sinx Let us express cos(x) in terms of sin x : ( ) cos(x) cos x sin x sin x sin x sin x a 008 Sectional Solution Set

Math 005A Prerequisite Material Answer Key

Math 005A Prerequisite Material Answer Key 1. a) P = 4s (definition of perimeter and square) b) P = l + w (definition of perimeter and rectangle) c) P = a + b + c (definition of perimeter and triangle)