MATHEMATICS 17Third Long Exam Set II

I. TRUE OR FALSE. Write TRUE if the statement is always true. Otherwise, writeFALSE.

1. The graphs of f(x) = 2x−2 and g(x) =1

2x+2are symmetric with respect to the y-axis.

2. If a horizontal line passes through the graph of h(x) at two points, then it is not aone-to-one function.

3. The graphs of two inverse functions are symmetric with respect to the origin.

4. 22x= 22x

II. Solve for x.

1. 81x2−1 − 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, theremainder 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 anothersquare. 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 thelast two terms are 5 and 23, respectively, what is the value of a3?

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