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PRECALCULUS SUPPLEMENTARY III

# PRECALCULUS SUPPLEMENTARY III - AP CALCULUS PRECALCULUS...

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AP CALCULUS PRECALCULUS SUPPLEMENTARY III Problems : 1) Simplify: x x xx 2 2 2 2 1 1 21 + ÷ −+ ++ A) 1 B) x x + 1 1 C) () x + +− 1 11 3 2 D) x 1 3 2 E) x x + 1 1 2) Let line l 1 pass through the points , and ( ) 20 , and let line l 2 be perpendicular to line l 1 and pass through the point 1 2 0 , . What is the area of the triangle formed by the lines l 1 , l 2 and the y -axis? A) 25 8 B) 25 16 C) 25 4 D) 25 32 E) 25 2 3) Let fx x m x x n =+−+ 3 32 . If x = 2 and x = 3 are two of the roots of ( ) , then what is the value of the other root? 4) Consider Δ ABC that is constructed such that cos cos cos A a B b C c == . What type of triangle is Δ ABC ? A) isosceles B) right-angled C) equilateral D) scalene E) right-angled isosceles 5) The equations of three sides of a square are yx = + 4 , = − + 6 and = − + 10 . Find all possible equations for the fourth side of the square. 6) a) If log 3 40 y = , then what is the value of log 81 y b) Solve for x : ln ln ln 2 93 2 1 −− ++ = c) Solve for x : ln ln = d) Solve for x : logloglog x = 0

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7) Consider the function () fx x x = + 2 1 . a) Identify all vertical and horizontal asymptotes. b) Find the domain of . c) The inverse of exists. Find the equation of the inverse function, ( ) 1 . d) Find the value of a such that fa = 1 4 . 8) Determine whether the functions ye x = 1 and ( ) yx =− ln 1 are inverses of each other. 9) The graph of yg x = is shown below. a) Sketch the graph of x + 22 on the same axes. b) If gx is a polynomial, what is the smallest possible degree of ( ) ? c) If is a polynomial, what are the factors of ( ) ? d) If is a polynomial, what might be its equation?
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PRECALCULUS SUPPLEMENTARY III - AP CALCULUS PRECALCULUS...

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