Precalculus Exam 1 Name: ____________________________

Problem 1: Linear Regression (be sure to answer all questions completely, 14 points).

Year AFVs

Precalculus Exam 1 Name: ____________________________

a)

Precalculus Exam 1 Name: ____________________________

(correlation coefficient is the “r” value)

e) Graph the data on the grid below and graph the linear regression equation you generated in part b).

Problem 2: Triangles and linear equations (8 points)

Precalculus Exam 1 Name: ____________________________

a. Sketch , given that

b. What are the slopes for line segments

= ______________ , ,

c. What are the equation for the line segments (in slope-intercept form)

= ______________ , ,

Problem 3: Geometry of Lines

Precalculus Exam 1 Name: ____________________________

(The graph below is not required for you to use, only if you desire to use it)

Problem 4: Exploring Slope-Intercept Form

Precalculus Exam 1 Name: ____________________________

Problem 5: Solving Three Variable Systems

Precalculus Exam 1 Name: ____________________________

Problem 6: Interpreting Solutions to Three Variable Systems

Precalculus Exam 1 Name: ____________________________

Problem 7: Organizing and Interpreting Information using Matrices

Precalculus Exam 1 Name: ____________________________

Library A has 10,000 novels, 5000 biographies, and 5000 children’s books. Library B has 15,000 novels, 10,000 biographies, and 2500 children’s books. Library C has 4000 novels, 700 biographies, and 800 Children’s books.

a. Express each library’s number of books as a matrix. Label the matrices A, B, and C.

b. Find the total number of each type of book in all 3 libraries. Express the steps using matrices and the solution as a matrix.

c. How many more books of each type does Library A have than Library C? Express the steps using matrices and the solution as a matrix.

d. Find A + B. Does the matrix have meaning in this situation? Explain.

Problem 8: Scalar Multiplication of Matrices

Precalculus Exam 1 Name: ____________________________

The drink menu from a fast-food restaurant is shown at the right. The store owner has decided that all of the prices must be increased by 10%.

a. Write matrix C to represent the current prices.

b. What scalar can be used to determine a matrix N to represent the new prices?

c. Find N.

d. What is N – C? What does this represent in this situation?

Problem 9: Matrix Operations

Precalculus Exam 1 Name: ____________________________

The Wolf family owns three bed and breakfasts in a vacation spot on the North Shore. A room with a single is $220 a night, a room with two beds is $250 a night, and a suite is $360.

a. Write a matrix for the number of each type of room at each bed and breakfast. Then write a room-cost matrix.

b. Write a matrix for total daily income for each B&B, assuming that all the rooms are rented.

c. What is the total daily income from all three bed and breakfasts, assuming that all the rooms are rented?