Name:___________________________Class:_____________________Date:_______
All Systems Go (1-6) Unit 4
Indicate the answer choice that best completes the statement or answers the question.
1. The admission fee of a theater is $2.50 for adults and $1.25 for children. On a certain day, 700 people went to the
theater for a concert and $1375 was collected. How many children and how many adults attended the concert?
a. 300 adults, 400 children
b. 400 adults, 1100 children
c. 400 adults, 300 children
d. 600 adults, 100 children
2. A hotel has 150 rooms. The charges for a double room and a single room are $270 per night and $150 per night
respectively. On a night when the hotel was completely occupied, revenues were $33,300. Which pair of equations can be
used to determine the number of double room, d, and the number of single room, s, in the hotel?
a.
b.
c.
d.
Solve the system of equations.
3. 6x – 6y = –6
–4x + 18y = 116
a. (7, 8)
c. (9, 1)
b. (8, 7)
d. (–9, –1)
_____4. A manufacturer makes both volleyballs and basketballs. Each volleyball requires 2 minutes on the forming
machine, and each basketball requires 1 minute. Each volleyball requires 1 minute on the inflating machine, and each
basketball requires 1.5 minutes. If the forming machine runs for 40 minutes and inflating machine runs for 25 minutes, the
following system of equations can be used to determine the number of volleyballs and basketballs produced.
a. Solve the system of equations..
b. Include a demonstration of how to solve the system of equations given in the problem.
Graph the system of equations. Then determine whether the system has no solution, one solution, or
infinitely many solutions. If the system has one solution, name it.
_____5. –x + y =1
-6x -6 = y/2
a.
one solution; (0, -1)
b. One solution (-1, 0)
b. infinitely many
d. no solution
Solve the system of equations.
____6. –31 = x – 6y
3x – 12 = 3y
a. (11, 7)
b. (6, 9)
c. (–7, –11)
d. infinitely many solutions
Determine the best method to solve the system of equations. Then solve the system.
_____7.
a.
substitution;
b.
elimination using multiplication; no solution
c.
substitution;
d.
elimination using multiplication; infinitely many solutions
____8 . Dakota’s math test grade was 7 points less than his science test grade. The sum of the grades was 183%.
What did Dakota get on his math test?
a. 83%
b. 88%
c. 93%
d. 95%
The following table shows car sales at a local car dealership for the first seven days of October.
Day
Sales
1
3
2
4
3
6
4
7
5
9
6
10
7
12
9 . Write the ordered pairs that represent the car sales for the first week of October.
a. (1, 3), (2, 4), (3, 6), (4, 7), (5, 9), (6, 10), (7, 12)
b. (3, 1), (4, 2), (6, 3), (7, 4), (9, 5), (10, 6), (12, 7)
c. (1, 3), (2, 4), (3, 6), (4, 7), (6, 10), (7, 12)
d. (1, 4), (2, 4), (3, 6), (4, 6), (5, 9), (6, 10), (7, 12)
Indicate the answer choice that best completes the statement or answers the question.
_____10. Which relation is a function?
a.
b.
c.
d.
Express the relation shown in each table, mapping, or graph as a set of ordered pairs. Then determine
the domain and range.
11.
________________________________________________________________________________________
Indicate the answer choice that best completes the statement or anwsers the question.
Sove the system of inequalities by graphing.
_____12.
a.
b.
c.
d.
__
____13. The difference between Rosa’s age and her father’s age is less than 35. Rosa’s father is more
than three times
her age. Which of the following are possible ages for Rosa and her father?
a. 5 and 40
b. 7 and 28
c. 10 and 30
d. 14 and 38
The sum of two positive integers is less than 80 and their difference is more than 10.
14. List three pairs of integers which are solutions.
a. 50 and 30, 40 and 35, 45 and 30
b. 50 and 24, 35 and 21, 18 and 2
c. 60 and 5, 44 and 34, 35 and 30
d. 60 and 20, 45 and 35, 36 and 22
Graph each inequality. Pick correct graph.
_____15.
a.
b.
c.
d.
______16. Use the graph below to determine the number of solutions. Use the graph to determine the
number of solutions the system has.
4.
a. infinitely many
c. one
b. two
d. no solution
______17. In this example data, x is years since 1990 and y is the number of people in thousands
using email or letters as the main method of communicating written information. See next page also.
e-mail
letters
a. Explain how graphs can be used to compare the number of people using letters to the
number of people using emails.
b. Include an estimate of the year in which the number of people writing letters equaled
the number of people using email. Then determine if your solution is reasonable for
this problem.
18. Carmen can buy bottles of paint for $2.00 each and boxes of colored pencils for $3.50 each. She
can spend no more than $42 on art supplies.
a.Write an inequality that shows how many bottles of paint, x, and boxes of colored pencils, y,
Carmen can buy.
b.Graph the inequality on a coordinate grid.
c.Name three different solutions to the inequality.
_____19. The circumference of a circle is given by the formula
the radius. Find r.
, where r is the measure of
a. r = 2πC
b. r = 2π+C
c. r = (2π)/C
d. r = C/(2π)
20. What is the radius of a right circular cone with a volume of 590 cubic inches and a height
of 15 inches? Round your answer to the nearest hundredth.
a. 6.13 inches
b. 6 inches
c. 6.13 square inches
d. 8.67 inches
The equation of a line containing the points (a, 0) and (0, b) is given by the formula
21 ____ Solve the equation for x.
a.
b.
c.
d.
22. Write an equation and solve for the variable specified.
Seven fourths of a number, u, equals one half minus one sixth of another number, v. Solve for v.