Precalculus Supplementary

Precalculus Supplementary - AP CALCULUS PRECALCULUS...

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AP CALCULUS PRECALCULUS SUPPLEMENTARY Problems : 1) Find all positive values of k for which the equations 32 xk kx += have a common solution for x . 2) A parabola has its vertex at the point with coordinates ( ) 13 , and also passes through the point () 16 , . Find the equation of the parabola. 3) Solve for the system: yx x yx =++ =+ 2 67 1 . Give a geometric description of the system and its solution. 4) Find all real values of x which satisfy the equation: x x −= 2 1. A) x = 1 B) x = 1 and x = 4 C) x = D) x = 2 and x =− E) x = 2 5) For what real values of k will the equation xy k 22 24 0 ++−+= describe a circle of radius 3? A) k = B) k = 8 C) k D) k 9 E) k = 6) Find all real values of x that satisfy the following equations: a) log log 55 1 xx ++ b) 10 32 5log x = c) 34 21 = d) x 2 3 −+= e) 2 3 2 3 = f) 2 92 0 1 2 −+ = Hint : If a b = 1, then there are three cases. The cases are a = 1and b is any number, a is any nonzero number and b = 0 and lastly a 1 and b is an even number. 7) The diameter of a circle has endpoints A , and ( ) B 710 , . Show that the equation of this circle is: ( ) ( )( ) yy −− + = 37 41 0 0 Hint : Let Pxy , be any point on the circle. Note that = APB 90 o and therefore mm 12 1 where m 1 is the slope of PA and m 2 is the slope of PB .
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8) Find the possible values of k for which the graph of yk x xk =+ + 2 86 a) crosses the x -axis. b) lies on the x -axis. 9) Solve the non-linear system: () 51 5 yx xy += Hint : Let x y u and x y v −= . 10) ( Brazilian Junior Math Contest ) Consider right Δ ABC with area 50 2 cm . Let point D be the midpoint of BC and AB cm = 25 2 . The arcs BC and CD are semi-circles. What is the area of the shaded zone? 11) ( Chinese Junior Math Contest ) Given that for positive integers n , ( )( ) 12 12 1 6 22 2 +++= ++ L n nn n . Find the value of 1 3 2 4 3 5 200 202 ×+×+×++ × L .
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Precalculus Supplementary - AP CALCULUS PRECALCULUS...

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