Name Advanced Math Functions & Statistics. Non- Graphing Calculator Section A. B. C.

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1 1. Compare and contrast the following graphs. Non- Graphing Calculator Section A. B. C. 2. For R, S, and T as defined below, which of the following products is undefined? A. RT B. TR C. TS D. ST E. RS R = [ 0 5 ] S =[ 1 4] T = [ ] 3. What is the product of A anda 1? a. If A is a 2x2 matrix b. If A is a 3x3 matrix c. If A is a 4x4 matrix 4. Determine the solution set of the equation: x(x 2 + 3)(x 2 49) = What are the zeros of the function: f(x) = x 3 + 2x 2 19x 20? 6. Given the function: y = a(x 3)(x 1 )(x + 6) where a > 0, 2 a. Describe the end behavior of the function. b. Determine the zeros of the function. c. Sketch a graph of the function. 7. What are the vertical asymptotes of g(x) = (x+1)(x 3) (x 2)(x+5)? 8. Sketch the graph of f(x) = 2 x

9. Find the horizontal asymptote of f(x) = 2x2 4x+3 3x 2 +x+2. 10. Find the x-intercept(s) of f(x) = x2 81 x 2 +2x 3. 11. Write an equation that could be the equation of the graph below. 12.

2 9. Find the horizontal asymptote of f(x) = 2x2 4x+3 3x 2 +x Find the x-intercept(s) of f(x) = x2 81 x 2 +2x Write an equation that could be the equation of the graph below. 12. Let f(x) = x and g(x) = 5 x Describe g(x) in terms of the parent function. 13. Evaluate log Classify each of the following functions as even, odd or neither. Explain. A. f(x) = 15x 4 2x 3 + 3x 2 2x + 18 B. f(x) = 9x 4 + x 2 8 C. f(x) = 2x 3 8x + 7 D. f(x) = 14x x E. f(x) = 14x x 2

3 Graphing Calculator Section 15. Find the sum of the first 7 terms in the geometric series k Given the sum: 25 k 1 2 a. Does the sum represent an arithmetic series, or a geometric series? b. Identify the first term of the series. c. Identify the common difference or common ration of the series. 17. Find the 10 th term in the geometric sequence 12, 72,432,. 18. An auditorium has 50 rows of seats. The first row has 110 seats. The second row has 115 seats. The third row has 120 seats. Each successive row has two more seats than the row before it. How many seats are there in the 50 th row? 19. Find the sum of the first 20 terms in the arithmetic series For two 3 3 matrices, A and B, the element in the second row and third column of the product matrix AB is the sum of the products of the corresponding elements in the _ row/column of matrix _ and the _ row/column of matrix 21. If p(x) = 12x 3 and q(x) = 5x 2 + 2, then which of the following is the value of q(p( 2))? 22. If f(x) = 1 2x and g(x) =, what is the domain of f(g(x))? x+5 x According to the rational root theorem, a list of all the possible rational roots of the equation 3x 4 + 3x 2 6x + 26 = 0 is: 24. Find the quotient and remainder of (5x 4 3x 2 + 2x 5) (x 4). 5wx 25. Use the properties of logarithms to expand the expression log yz. 26. Determine the amount of money in a money market account providing an annual rate of 3.5% compounded monthly if the invested amount of $18,500 is left in the account for 10 years. 3

4 27. Which of the following sets of data exhibits exponential behavior? Explain. Identify the other 3 graphs. 28. Find the balance in an account at the end of 15 years if $10,000 is invested at an interest rate of 8% compounded continuously. 29. Suzi s report has 25 less than 3 times the number of words in Elaine s report. Together the two reports have 725 words. Write a system of equations can be solved to find the number of words in each report. You do not have to solve the system. 30. What is the solution to the system of equations shown below? 6x y 2z = 26 { 2x 2y + 6z = 28 x + y 4z = 19 4

5 Task 1 Constructed Response Non-Graphing Calculator Section Write the letter of the function name in the blank beside the graph. A. Constant B. Linear C. Quadratic D. Cubic E. Square Root F. Cube Root G. Exponential H. Logarithmic I. Absolute Value J. Greatest Integer K. Rational 5

Task 3 g(x) = x 4 + 4x 3 13x 2 28x + 60 A. Find the end behavior of the function above. B. Determine the maximum number of possible zeros and maximum turning points for the function above. C.

6 Task 3 g(x) = x 4 + 4x 3 13x 2 28x + 60 A. Find the end behavior of the function above. B. Determine the maximum number of possible zeros and maximum turning points for the function above. C. Determine the possible number of positive and negative real roots. D. List all possible rational roots for the function above. Find the rational roots of the function. E. Sketch a graph of the function. Graphing Calculator Section 6

7 Task 5 (10 points) The first four figures of a pattern are shown here: A. Complete the following table to show the number of squares on the bottom row of each figure and the total number of squares that make up each figure. Figure 1 Figure 2 Figure 3 Figure 4 Number of squares on the bottom row 2 Number of squares in whole figure 3 B. If the pattern were continued to the 28 th figure, how many squares would be on its top row? What would be the total number of squares in the 28 th figure? C. Write a rule that describes how to find the number of squares on the top row of the nth figure. D. What rule could you use to find the total number of squares in the nth figure? E. Discuss the difference between an arithmetic sequence and a geometric sequence, and give an example of each. Task 6 (10 points) 7

8 Find the balance for each account after 10 years if an initial deposit of $22,500 is made in an account that earns 7% interest A. compounded annually B. compounded quarterly C. compounded monthly D. compounded continuously E. What is the amount of time required for the investment to double at a rate of 7% if the interest is compounded continuously? 3 F. Expand: log 3 x 2 y 3 G. Expand: ln ( x5 y 4 z 3 ) H. Condense: log log 6 x 2 log 6 y log 6 z I. Condense: 3ln(x 2 6) 4 ln y J. Solve:2 log 4 2x = 3 8

The final is cumulative, but with more emphasis on chapters 3 and 4. There will be two parts.

Math 141 Review for Final The final is cumulative, but with more emphasis on chapters 3 and 4. There will be two parts. Part 1 (no calculator) graphing (polynomial, rational, linear, exponential, and logarithmic