. What are the most important contributions by Galileo in the history of physics? Why do you think so? How do these contributions affect your life? Your journal entry must….

## Solve the system of equations using matrices. Use Gaussian elimination with backsubstitution. x + y + z = -5 x – y + 3z = -1 4x + y + z = -2

Pre-Calculus Quarter 4 Exam

1

Name: _________________________

Score: ______ / ______

1. Find the indicated sum. Show your work.

2. Locate the foci of the ellipse. Show your work.

𝑥

2

36 +

𝑦

2

11 = 1

Pre-Calculus Quarter 4 Exam

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3. Solve the system by the substitution method. Show your work.

2y – x = 5

x2 + y2 – 25 = 0

4. Graph the function. Then use your graph to find the indicated limit. You do not have to

provide the graph

f(x) = 5x – 3, f(x)

5. Use Gaussian elimination to find the complete solution to the system of equations, or state

that none exists. Show your work.

4x – y + 3z = 12

x + 4y + 6z = -32

5x + 3y + 9z = 20

Pre-Calculus Quarter 4 Exam

3

6. Solve the system of equations using matrices. Use Gaussian elimination with backsubstitution.

x + y + z = -5

x – y + 3z = -1

4x + y + z = -2

7. A woman works out by running and swimming. When she runs, she burns 7 calories per

minute. When she swims, she burns 8 calories per minute. She wants to burn at least 336

calories in her workout. Write an inequality that describes the situation. Let x represent the

number of minutes running and y the number of minutes swimming. Because x and y must be

positive, limit the boarders to quadrant I only.

Short Answer Questions: Type your answer below each question. Show your work.

8. A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that

each of these statements is true. Show your work.

Sn: 1

2

+ 42

+ 72

# + . . . + (3n – 2)2

𝑛(6𝑛

2−3𝑛−1)

2