PreCalculus
Chapter 10 Test
Name
Directions: Show all work and reasoning to receive full credit.
1
The Lincoln Center charges $21 for adults, $15 for senior citizens and $10 for children under 12 for
their holiday spectacular concert. The paid revenue for the show was $13,167 for 874 tickets sold.
There were 48 more children than adults. How many children attended the show?
2
Write the following system of equations in an augmented matrix and solve the system by using GaussJordan elimination to get the augmented matrix in reduced row echelon form.
2 x 9 y z 78
x 8 y 8 z 93
8 x y z 36
3
Solve the system of equations using the inverse method.
2 x 4 y 5 z 8
x 5 y 2 z 1
3x 3 y 3z 15
4
Use Cramer’s Rule to solve the system of equations.
6 x 7 y 4 z 50
6 x 4 y 8 z 62
5 x 4 y 7 z 66
5.
Write the partial fraction decomposition of the rational expression.
4x
2
2 x 3x 2
6.
Write the partial fraction decomposition of the rational expression.
x2 9
x4 2 x2 8
7.
Graph the region and find the maximum value of the objective function z 9 x 6 y subject to the
constraints:
4
x0
y0
3
x y 3
2 x 5 y 10
2
x y 1
1
-1
1
2
3
-1
8.
A sports drink company has two popular flavors, citrus and orange. Besides water, each contains two
important ingredients, potassium and sodium. Orange contains 5 grams of potassium per gallon and 2
grams of sodium per gallon. Citrus contains 3 grams of potassium per gallon and 6 grams of sodium per
gallon. The company has 360 grams of potassium and 480 grams of sodium available for production per
hour. Each gallon of orange produces a profit of $2 and each gallon of citrus produces a profit of $2.50.
Write an objective function and constraints. Find the number of each to produce maximum profit.
4
0
