MAC 1105

Test 2 Review

andPractice Solutions

MAC 1105 Test 2 Review 2.1 – 2.3, 5.1, 5.4

• You will need to have your own graphing calculator for the test.

• You may not share calculators or use any type of communication device in place of a calculator.

• Tests cannot be made up for any reason other than an NWFSC event for which you must miss class. If you miss one test, your final exam score will be substituted. A second missed test is a zero.

Exam TopicsObjective Section Suggested Text Problems

1) Given two points, find the distance between the two points and the midpoint of the line segment connecting the two points.

2.1 p.293: 9, 11 (parts a and b)

2) Test an equation for symmetry. 2.2 p. 293: 25, 27, 29(symmetry)

3) Write the equation of a circle. 2.2 p. 293: 35

4) Find the slope of a line. 2.3 p.293: 9,11(part c)

5) Write a linear equation given two ordered pairs of data. 2.3 p. 295: 105 (part a)

6) Solve problems involving linear regression. 2.3 p. 295: 111(parts a and c)

7) Determine if the given ordered pair is a solution of the system of two equations.

5.1 p. 487: 7

8) Solve a system of two equations by substitution or elimination 5.1 p. 487: 57, 59, 61, 63

9) Work with applications of systems of two equations. 5.1 p. 489: 99

10) Graph a linear inequality. 5.4 p. 520: 13, 15, 17

11) Graph a system of two linear inequalities. 5.4 p. 521: 29, 31, 33

To Study for the Test:

• Complete all assigned homework. Remember that a score of at least 70% on each assignment gives you 10 bonus points on the test.

• Complete the practice test and check your solutions.• Set up a study system (note cards for example) for each

of the 11 objectives in the chart above.• Review your notes and applicable problem set questions

for each of the 11 objectives in the chart above.• Work the suggested text problems for each of the 11

objectives in the chart above.

Special Note

• It is entirely possible that the questions on the test may have additional parts that differ slightly from those in the practice test.

• To prepare for these additional parts, be sure you are familiar with your notes, your worksheets, and your homework.

• Objectives will remain unchanged.

1) Let P be the point and Q be the point

a) Find the distance between P and Q. Simplify the square root completely and do not give a decimal approximation.

1) Let P be the point and Q be the point

b) Find the midpoint of the line segment PQ.

2) Test the following equations for symmetry:

3) Write the equation of the circle with center and radius 7.

4) Find the slope of the line through the points and (4, 3).

m =

=

5) The relation between the cost of a diamond and its weight is linear. One diamond weighs 0.7 carat and costs $3543, while the other diamond weighs 0.8 carat and costs $4378. Write a linear

equation for the cost of a diamond.

6) Enter the following data into your calculator:

x 25 38 43 54 68 72 86

y 42 65 74 94 119 126 151

6a. Use the linear regression capabilities of your calculator to find an equation of the line of best fit: y = ax + b. Round each coefficient to two decimal places.

6b. Use the line of best fit you found in part a to predict what y value would correspond to an x

value of 115.

7) Write the letter of the ordered pair that solves the system.

TypoAnswer is none of the above.

8) Solve. Be sure to write your solution as an ordered pair.

9) Carol’s Candy Corral sells chocolate candy for $3 per pound. She sells vanilla candy for $5 per pound. Suppose she wants to create a mix of the two and sell it for $3.80 per pound. If she plans to make 100 pounds of the mix, how many pounds of each should she use?

Item Price per pound Number of pounds Revenue

Chocolate $3.00

Vanilla $5.00

Mix $3.80 100

10) Graph the linear inequality 3x + y > 4• Graph y = −3x + 4• Test (0,0) 3(0) + 0 > 4 no

11) Graph the solution set of the following system of two linear inequalities. Indicate the vertex of the system.

OR

OR

Vertex:

Graphed Lines:

Extra Test 2 Practice

1) Let P be the point and Q be the point

a) Find the distance between P and Q. Simplify the square root completely and do not give a decimal approximation.

5

1) Let P be the point and Q be the point

b) Find the midpoint of the line segment PQ.

2) Test the following equations for symmetry:

origin

2𝑐¿ 𝑥=1

𝑦 2+1

3) Write the equation of the circle with center and passing through the point (0, 7) .

4) Find the slope of the line through the points and ().

m =

=

5) The relation between the cost of tuition and the number of hours taken is linear. The cost of taking 15 hours is $1865. The cost of taking 18 hours is $2183. Write a linear equation that

relates the tuition cost to the hours taken.

6) Enter the following data into your calculator:

x 20 35 40 55 70 85 90

y 158 128 116 87 64 28 22

6a. Use the linear regression capabilities of your calculator to find an equation of the line of best fit: y = ax + b. Round each coefficient to two decimal places.

195.63

6b. Use the line of best fit you found in part a to predict what y value would correspond to an x

value of 167.

195.63

7) Write the letter of the ordered pair that solves the system.

8) Solve. Be sure to write your solution as an ordered pair.

9) Bill’s Bait Barn sells worms for $2 per pound and crickets for $2.50 per pound. If he wants to create a 100 pound mix and sell it for $2.15 per pound with no loss in revenue, how much of each kind of bait should be sold?

Item Price per pound Number of pounds

Revenue

Worms $2.00

Crickets $2.50

Mix $2.15 100 215

10) Graph the linear inequality:

Graph the following system.

:

: