1 Algebra II Hustle

#1 Calculus – Hustle #1 Calculus – Hustle  National Convention 2007  National Convention 2007A particle moves according to A particle moves according to the equations: the equations: x( t) =4 t3 + 6 t 2 - 24 t - 24 x( t) =4 t3 + 6 t 2 - 24 t - 24 y( t) =2 t3 + 3 t 2 - 12 t + 12 y( t) =2 t3 + 3 t 2 - 12 t + 12 z( t) = t3 +6 t 2 + 12 t + 20 z( t) = t3 +6 t 2 + 12 t + 20 At what instant(s) of time [value(s) of t] At what instant(s) of time [value(s) of t] is the particle not moving? is the particle not moving? NOTE: Time can be negative. NOTE: Time can be negative. If no such instant of time, write none. If no such instant of time, write none.Answer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5#1 Calculus – Hustle #1 Calculus – Hustle  National Convention 2007  National Convention 2007A particle moves according to A particle moves according to the equations: the equations: x( t) =4 t3 + 6 t 2 - 24 t - 24 x( t) =4 t3 + 6 t 2 - 24 t - 24 y( t) =2 t3 + 3 t 2 - 12 t + 12 y( t) =2 t3 + 3 t 2 - 12 t + 12 z( t) = t3 +6 t 2 + 12 t + 20 z( t) = t3 +6 t 2 + 12 t + 20 At what instant(s) of time [value(s) of t] At what instant(s) of time [value(s) of t] is the particle not moving? is the particle not moving? NOTE: Time can be negative. NOTE: Time can be negative. If no such instant of time, write none. If no such instant of time, write none.Answer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5 #2 Calculus – Hustle #2 Calculus – Hustle  National Convention 2007  National Convention 2007(ip )n (ip )n Evaluate: Evaluate: n=1 n! n=1 n!Answer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5#2 Calculus – Hustle #2 Calculus – Hustle  National Convention 2007 National Convention 2007(ip )n (ip )n Evaluate: Evaluate: n=1 n! n=1 n!Answer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5 #3 Calculus – Hustle #3 Calculus – Hustle  National Convention 2007  National Convention 2007For the equation For the equation x3+ y 3 +3 x 2 y - 3 x 2 + 3 xy 2 = - 11, x3+ y 3 +3 x 2 y - 3 x 2 + 3 xy 2 = - 11, using implicit differentiation find using implicit differentiation find dy dx at the point (2,- 1) . dy dx at the point (2,- 1) .Answer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5#3 Calculus – Hustle #3 Calculus – Hustle  National Convention 2007  National Convention 2007For the equation For the equation x3+ y 3 +3 x 2 y - 3 x 2 + 3 xy 2 = - 11, x3+ y 3 +3 x 2 y - 3 x 2 + 3 xy 2 = - 11, using implicit differentiation find using implicit differentiation find dy dx at the point (2,- 1) . dy dx at the point (2,- 1) .Answer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5 #4 Calculus – Hustle #4 Calculus – Hustle  National Convention 2007  National Convention 2007Let A be the number of infinite Let A be the number of infinite discontinuities and B be the number discontinuities and B be the number of removable discontinuities in the of removable discontinuities in the x4-2 x 2 + 1 x4-2 x 2 + 1 function f( x) = . function f( x) = . x3 - x x3 - x What is A- B ? What is A- B ?Answer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5#4 Calculus – Hustle #4 Calculus – Hustle  National Convention 2007  National Convention 2007Let A be the number of infinite Let A be the number of infinite discontinuities and B be the number discontinuities and B be the number of removable discontinuities in the of removable discontinuities in the x4-2 x 2 + 1 x4-2 x 2 + 1 function f( x) = . function f( x) = . x3 - x x3 - x What is A- B ? What is A- B ?Answer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5 #5 Calculus – Hustle #5 Calculus – Hustle  National Convention 2007  National Convention 2007 Given 24 m2 of cardboard, you are to Given 24 m2 of cardboard, you are to construct an open box (that is, a box construct an open box (that is, a box with no top). In cubic meters, what is with no top). In cubic meters, what is the largest volume this box can occupy? the largest volume this box can occupy?Answer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5#5 Calculus – Hustle #5 Calculus – Hustle  National Convention 2007  National Convention 2007 Given 24 m2 of cardboard, you are to Given 24 m2 of cardboard, you are to construct an open box (that is, a box construct an open box (that is, a box with no top). In cubic meters, what is with no top). In cubic meters, what is the largest volume this box can occupy? the largest volume this box can occupy?Answer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5 #6 Calculus – Hustle #6 Calculus – Hustle  National Convention 2007  National Convention 2007 What is the tangent line approximation What is the tangent line approximation of 14 , using 16= 4? of 14 , using 16= 4 ?Answer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5#6 Calculus – Hustle #6 Calculus – Hustle  National Convention 2007  National Convention 2007 What is the tangent line approximation What is the tangent line approximation of 14 , using 16= 4? of 14 , using 16= 4 ?Answer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5 #7 Calculus – Hustle #7 Calculus – Hustle  National Convention 2007  National Convention 2007 A circle’s radius is growing at a rate A circle’s radius is growing at a rate of 3 m s . At time t= 0 s the radius of 3 m s . At time t= 0 s the radius of the circle is 1 m . How fast is the of the circle is 1 m . How fast is the area of the circle growing (in m2 s ) area of the circle growing (in m2 s ) at time t= 3 s ? at time t= 3 s ?Answer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5#7 Calculus – Hustle #7 Calculus – Hustle National Convention 2007  National Convention 2007 A circle’s radius is growing at a rate A circle’s radius is growing at a rate of 3 m s . At time t= 0 s the radius of 3 m s . At time t= 0 s the radius of the circle is 1 m . How fast is the of the circle is 1 m . How fast is the area of the circle growing (in m2 s ) 2 area of the circle growing (in m s ) at time t= 3 s ? at time t= 3 s ?Answer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5 #8 Calculus – Hustle  National Convention 2007  National Convention 2007 1 骣 e2 ln x 2 x- 3 x - 1 1 琪骣 e2 ln x 2 x- 3 x - 1 2 琪琪 2 2 Let A= 琪 0 3 x . 琪 2 Let A= 0 3 x . 琪 3 琪 -2 ln( 4x) ( 2 x - 3) 琪 3 琪琪 -2 ln( 4x) ( 2 x - 3) 桫桫 Now replace every entry in A with its Now replace every entry in A with its derivative with respect to x, call this derivative with respect to x, call this new matrix B. What is the determinant new matrix B. What is the determinant of B? of B?Answer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5#8 Calculus – Hustle #8 Calculus – Hustle  National Convention 2007  National Convention 2007 1 骣 e2 ln x 2 x- 3 x - 1 1 琪骣 e2 ln x 2 x- 3 x - 1 2 琪琪 2 2 Let A= 琪 0 3 x . 琪 2 Let A= 0 3 x . 琪 3 琪 -2 ln( 4x) ( 2 x - 3) 琪 3 琪琪 -2 ln( 4x) ( 2 x - 3) 桫桫 Now replace every entry in A with its Now replace every entry in A with its derivative with respect to x, call this derivative with respect to x, call this new matrix B. What is the determinant new matrix B. What is the determinant of B? of B?Answer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5 #9 Calculus – Hustle #8 Calculus – Hustle  National Convention 2007 Let f( x) = sin ( ix) , what is f(19) ( x) ? (19) Let f( x) = sin ( ix) , what is f( x) ? (NOTE: i is the imaginary unit) (NOTE: i is the imaginary unit)Answer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5#9 Calculus – Hustle #9 Calculus – Hustle  National Convention 2007  National Convention 2007 Let f( x) = sin ( ix) , what is f(19) ( x) ? (19) Let f( x) = sin ( ix) , what is f( x) ? (NOTE: i is the imaginary unit) (NOTE: i is the imaginary unit)Answer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5#10 Calculus – Hustle #9 Calculus – Hustle National Convention 2007  National Convention 2007 A particle moves with acceleration A particle moves with acceleration 骣t 骣t a( t) = cos 琪 . The velocity of this a( t) = cos琪 . The velocity of this 桫2 桫2 particle is zero at time t = 0 . What is particle is zero at time t = 0 . What is the particle’s speed at time t = 3p ? the particle’s speed at time t = 3p ?Answer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5#10 Calculus – Hustle #10 Calculus – Hustle  National Convention 2007  National Convention 2007A particle moves with acceleration A particle moves with acceleration 骣t 骣t a( t) = cos 琪 . The velocity of this a( t) = cos琪 . The velocity of this 桫2 桫2 particle is zero at time t = 0 . What is particle is zero at time t = 0 . What is the particle’s speed at time t = 3p ? the particle’s speed at time t = 3p ?Answer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5#10 Calculus – Hustle #11 Calculus – Hustle  National Convention 2007  National Convention 2007 h h 骣 3 骣 3 Evaluate: lim琪 1 + Evaluate: lim琪 1 + h 桫 h h 桫 hAnswer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5#11 Calculus – Hustle #11 Calculus – Hustle  National Convention 2007  National Convention 2007 h h 骣 3 骣 3 Evaluate: lim琪 1 + Evaluate: lim琪 1 + h 桫 h h 桫 hAnswer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5#11 Calculus – Hustle #12 Calculus – Hustle  National Convention 2007  National Convention 2007 6 2 6 2 Evaluate: 2 dx Evaluate: 2 dx 3 x -1 3 x -1Answer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5#12 Calculus – Hustle #12 Calculus – Hustle  National Convention 2007  National Convention 20076 2 6 2 Evaluate: 2 dx Evaluate: 2 dx 3 x -1 3 x -1Answer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5#12 Calculus – Hustle  National Convention 2007 #13 Calculus – Hustle #13 Calculus – Hustle  National Convention 2007 National Convention 2007Let f( x) = x2 + 1, Let f( x) = x2 + 1, g( x) = fⅱ( f( x)) f( x) dx g( x) = fⅱ( f( x)) f( x) dx and g (0) = 2 , what is g( x) ? and g (0) = 2 , what is g( x) ?Answer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5#13 Calculus – Hustle #13 Calculus – Hustle  National Convention 2007 National Convention 2007Let f( x) = x2 + 1, Let f( x) = x2 + 1, g( x) = fⅱ( f( x)) f( x) dx g( x) = fⅱ( f( x)) f( x) dx and g (0) = 2 , what is g( x) ? and g (0) = 2 , what is g( x) ?Answer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5 #14 Calculus – Hustle #14 Calculus – Hustle  National Convention 2007  National Convention 2007For f( x) = e2x -10 e x + 12 x , what is For f( x) = e2x -10 e x + 12 x , what is the greatest value of x for which the the greatest value of x for which the tangent line is horizontal? tangent line is horizontal?Answer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5#14 Calculus – Hustle #14 Calculus – Hustle  National Convention 2007  National Convention 2007For f( x) = e2x -10 e x + 12 x , what is For f( x) = e2x -10 e x + 12 x , what is the greatest value of x for which the the greatest value of x for which the tangent line is horizontal? tangent line is horizontal?Answer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5 #15 Calculus – Hustle #15 Calculus – Hustle  National Convention 2007  National Convention 2007On what interval(s) is On what interval(s) is x3 x3 f( x) = + x2 -3 x + 1 both concave f( x) = + x2 -3 x + 1 both concave 3 3 up and decreasing? Please, express up and decreasing? Please, express your answer in interval notation i.e. your answer in interval notation i.e. x稳( a, b) ( c , d ) x稳( a, b) ( c , d )Answer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5#15 Calculus – Hustle #15 Calculus – Hustle  National Convention 2007 National Convention 2007On what interval(s) is On what interval(s) is x3 x3 f( x) = + x2 -3 x + 1 both concave f( x) = + x2 -3 x + 1 both concave 3 3 up and decreasing? Please, express up and decreasing? Please, express your answer in interval notation i.e. your answer in interval notation i.e. x稳( a, b) ( c , d ) x稳( a, b) ( c , d )Answer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5 #16 Calculus – Hustle #16 Calculus – Hustle  National Convention 2007  National Convention 2007 What is the area between the curve What is the area between the curve y= sin ( x) and the x-axis, from y= sin ( x) and the x-axis, from x = -p to x = p ? x = -p to x = p ?Answer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5#16 Calculus – Hustle #16 Calculus – Hustle  National Convention 2007  National Convention 2007 What is the area between the curve What is the area between the curve y= sin ( x) and the x-axis, from y= sin ( x) and the x-axis, from x = -p to x = p ? x = -p to x = p ?Answer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5 #17 Calculus – Hustle #17 Calculus – Hustle  National Convention 2007  National Convention 2007 sec2 x sec2 x Evaluate: dx Evaluate: dx 1+ tan2 x 1+ tan2 xAnswer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5#17 Calculus – Hustle #17 Calculus – Hustle  National Convention 2007  National Convention 2007 sec2 x sec2 x Evaluate: dx Evaluate: dx 1+ tan2 x 1+ tan2 xAnswer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5 #18 Calculus – Hustle #18 Calculus – Hustle  National Convention 2007  National Convention 2007 What is the arc length of the curve What is the arc length of the curve defined by x( t) = 3 t2 , y( t) = 4 t2 defined by x( t) = 3 t2 , y( t) = 4 t 2 from t = 0 to t = 2 ? from t = 0 to t = 2 ?Answer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5#18 Calculus – Hustle #18 Calculus – Hustle  National Convention 2007  National Convention 2007 What is the arc length of the curve What is the arc length of the curve defined by x( t) = 3 t2 , y( t) = 4 t2 defined by x( t) = 3 t2 , y( t) = 4 t 2 from t = 0 to t = 2 ? from t = 0 to t = 2 ?Answer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5 #19 Calculus – Hustle #19 Calculus – Hustle  National Convention 2007 National Convention 20072 2 Evaluate: xe- x dx Evaluate: xe- x dx 0 0Answer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5#19 Calculus – Hustle #19 Calculus – Hustle  National Convention 2007 National Convention 20072 2 Evaluate: xe- x dx Evaluate: xe- x dx 0 0Answer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5 #20 Calculus – Hustle #20 Calculus – Hustle  National Convention 2007  National Convention 2007What is the maximum value of the What is the maximum value of the function f( x) = - x3 +3 x + 1 for function f( x) = - x3 +3 x + 1 for x �[ 3,3] ? x �[ 3,3] ?Answer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5#20 Calculus – Hustle #20 Calculus – Hustle  National Convention 2007  National Convention 2007What is the maximum value of the What is the maximum value of the function f( x) = - x3 +3 x + 1 for function f( x) = - x3 +3 x + 1 for x �[ 3,3] ? x �[ 3,3] ?Answer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5 #21 Calculus – Hustle #21 Calculus – Hustle  National Convention 2007  National Convention 2007What is the first derivative of sin2(x 2 ) What is the first derivative of sin2(x 2 ) with respect to x? with respect to x?Answer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5#21 Calculus – Hustle #21 Calculus – Hustle MAQ National Convention 2007 MAQ National Convention 2007What is the first derivative of sin2(x 2 ) What is the first derivative of sin2(x 2 ) with respect to x? with respect to x?Answer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5 #22 Calculus – Hustle #22 Calculus – Hustle  National Convention 2007  National Convention 2007Let f( x) be a differentiable, invertible Let f( x) be a differentiable, invertible function, such that f (2) = 3. Let function, such that f (2) = 3. Let g( x) = f-1 ( x) . What is f (2) given g( x) = f-1 ( x) . What is f (2) given that g (2) = 7 and g (3) = 11? that g (2) = 7 and g (3) = 11?Answer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5#22 Calculus – Hustle #22 Calculus – Hustle  National Convention 2007  National Convention 2007Let f( x) be a differentiable, invertible Let f( x) be a differentiable, invertible function, such that f (2) = 3. Let function, such that f (2) = 3. Let g( x) = f-1 ( x) . What is f (2) given g( x) = f-1 ( x) . What is f (2) given that g (2) = 7 and g (3) = 11? that g (2) = 7 and g (3) = 11?Answer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5 #23 Calculus – Hustle #23 Calculus – Hustle  National Convention 2007  National Convention 2007(4+h)2 -( 4 - h) 2 (4+h)2 -( 4 - h) 2 Evaluate: lim Evaluate: lim h 0 2h h 0 2hAnswer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5#23 Calculus – Hustle #23 Calculus – Hustle  National Convention 2007  National Convention 2007(4+h)2 -( 4 - h) 2 (4+h)2 -( 4 - h) 2 Evaluate: lim Evaluate: lim h 0 2h h 0 2hAnswer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5 #24 Calculus – Hustle #24 Calculus – Hustle  National Convention 2007  National Convention 2007 sin( x) - cos( x) + 1 sin( x) - cos( x) + 1 Evaluate: lim Evaluate: lim x 0 x3-3 x 2 + 3 x x 0 x3-3 x 2 + 3 xAnswer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5#24 Calculus – Hustle #24 Calculus – Hustle  National Convention 2007  National Convention 2007 sin( x) - cos( x) + 1 sin( x) - cos( x) + 1 Evaluate: lim Evaluate: lim x 0 x3-3 x 2 + 3 x x 0 x3-3 x 2 + 3 xAnswer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5 #25 Calculus – Hustle  National Convention 2007  National Convention 2007 What is f (1) if What is f (1) if 3 2 f( x) =( - x -1) ( x + 1) ( 2 x - 3) ? 3 2 f( x) =( - x -1) ( x + 1) ( 2 x - 3) ?Answer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5#25 Calculus – Hustle #25 Calculus – Hustle National Convention 2007  National Convention 2007 What is f (1) if What is f (1) if 3 2 f( x) =( - x -1) ( x + 1) ( 2 x - 3) ? 3 2 f( x) =( - x -1) ( x + 1) ( 2 x - 3) ?Answer : ______Answer : ______Round 1 2 3 4 5 Round 1 2 3 4 5#25 Calculus – Hustle

1 Algebra II Hustle

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