MATHEMATICS 17 Third Long Exam

Set II

I. TRUE OR FALSE. Write TRUE if the statement is always true. Otherwise, write FALSE. 1 1. The graphs of f (x) = 2x−2 and g(x) = x+2 are symmetric with respect to the y-axis. 2 2. If a horizontal line passes through the graph of h(x) at two points, then it is not a one-to-one function. 3. The graphs of two inverse functions are symmetric with respect to the origin. x

4. 22 = 22x II.

Solve for x.

1. 81x

2 −1

− 27x−1 = 0

2. log(x − 5) + log(x + 10) = 2 3. 3x − 2 · 3−x = 1 III.

Problem Solving. Perform as indicated.

1. Find the value of k such that when (kx + 2)(x − 1)(x − 4) + 2 is divided by x − 5, the remainder is 50. 2. Find all rational zeros of p(x) = 6x4 − 25x3 + 25x2 + 3x − 5. 3. Find the inverse of f (x) = x2 − 4x + 1 by restricting its domain. 4. Find the sum of all multiples of 7 between 100 and 200. 5. A square has side 10 cm long.The midpoints of the sides are joined to form another square. The process is repeated on the second square to form a third square and so on. Find the sum of the areas of the squares. Find the total perimeter of the squares. 6. If a1 , a2 , a3 , a4 , a5 form an arithmetic sequence and the sum of the first two and the last two terms are 5 and 23, respectively, what is the value of a3 ?

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