# Math 116 - Chapter 5 & 6 Study Guide

1. Write the solution to the system of linear equations that corresponds to the augmented matrix shown. Three parts.
2. Multiply two matrices together.
3. Evaluate a 3×3 determinant.
4. Solve the system of linear equations by the method of substitution.
5. Solve the system of linear equations by the method of elimination.
6. Solve the system of llinear equations using Gauss-Jordan elimination.
7. Solve the system of linear equations using Cramer's Rule.
8. Identify the equation of the graphed relation.
9. Solve a 3×3 system linear equations using the RREF function on the calculator.
10. Solve the system of linear equations by graphing.
11. Solve the system of linear equations using matrix algebra and inverses. Since this will be done on the calculator, your work can consist of the matrices you enter into the calculator and the expression used to find the solution.
12. Find the system of linear equations that has the given solution. Remember that you need as many equations as variables to get an unique solution.
13. Solve the matrix equations for X. Three parts. Remember the placeholder for matrices is the multiplicative identity I. For example AX-5X = (A-5I)X, not (A-5)X. Also, AX + X = (A+I)X. There is no matrix division, you have to multiply by the inverse instead.
14. Write the first five terms of the sequence.
15. Find the most apparent pattern for the general term of the sequence.
16. Simplify the expression involving the ratio of the factorials:
17. Find the sum, given in summation notation.
18. Expand the binomial using the binomial expansion theorem.
19. Given the first term and common difference, find a specific term in an arithmetic sequence.
20. Given the first term and last term of an arithmetic sequence, find the sum of the terms of the sequence.
21. Given the first term and common ratio, find a specific term of a geometric sequence.
22. Given the first term and common ratio, find the sum of the first n terms of a geometric series.
23. Given an infinite geometric series in summation form, find the sum.
24. Write the equation of the conic section that is described.
25. Write the equation of the conic section that is described.
26. Given the domain and range of a function and a series of new functions, identify the translation and the new domain and range.
27. Describe the polynomial function. Make a sign chart.
28. Describe the rational function. Make a sign chart.
29. Solve the equation for x. Four parts. This will include factoring, exponential equations, and logarithmic equations. In particular, pay attention to those problems where you need to make a u-substitution to make something look like a quadratic equation. As a hint, 3x+1 could be written as 3(3x).
30. Combine the expression into a single logarithm. Two parts.
31. Simplify the expressions involving combinations of logarithms and exponential functions.

## Notes

• The first eight problems on the exam must be worked without a calculator. Once you have completed that part of the exam, turn it in and pick up the second part. You may use a calculator on the second part.
• There are two take home portions of this exam, each worth 25 points. It is due the day of the exam.
• Show work on the exam even if the calculator will do the problem for you. For questions that indicate you should use a particular method to solve a system of equations, be sure to show enough work so that I can see that you know that method.
• You may put notes onto one 8.5"×11" sheet of paper to use during part 2 of the exam. You may use both sides of the paper. The notesheet must be handwritten and an original copy (don't just copy someone else's sheet). It will be collected with the exam.

## Point values per problem

### Part 1 - No Calculator or notes

 # Pts 1 2 3 4 5 6 7 8 Total 6 6 5 6 6 6 6 18 59

### Part 2 - Calculator and notes

 # Pts 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Total 6 6 6 3 9 4 4 4 4 5 4 4 4 4 4 6 6 12 9 6 16 6 9 141

### Part 3 - Take Home - Matrices

 # Pts 1 2 3 4 5 6 7 8 9 Total 2 2 2 2 3 2 2 2 8 25

### Part 4 - Take Home - Sequences & Series

 # Pts 1 2 3 4 5 Total 5 5 5 5 5 25