Download NOTE: In addition to the problems below, please study the two

MATD 0370 ELEMENTARY ALGEBRA REVIEW FOR TEST 2 (New Material From: 3.1, 4.1, 4.2, 5.1, and 5.2)
NOTE: In addition to the problems below, please study the two handouts Exercise Sets 3.1
and 4.1 posted at http://www.austincc.edu/jbickham/handouts.
1.
Find the coordinates of the point S.
2.
Find the coordinates of the point U.
3.
In what quadrant does the point (–1, 3) lie?
4.
Graph on an xy–coordinate system: 2x – 3y = 8
5.
Graph on an xy–coordinate system:
6.
Graph on an xy–coordinate system: y = –6
7.
Graph on an xy–coordinate system: x = 0
8.
Graph the vertical line through the point (3.5, 1.7) and find the equation of this vertical line.
9.
Graph the line y =
3
x – 3 using a table of values.
2
10.
Graph the line y =
3
x – 3 using the slope and y–intercept.
2
11.
Find the x-intercept and y-intercept of the line x – y = 5.
12.
Find the x-intercept and y-intercept of the line 7x + 2y = –12.
13.
What is the slope of any horizontal line?
2
3
x+ y=1
5
5
MATD 0370 ELEMENTARY ALGEBRA REVIEW FOR TEST 2 (New Material From: 3.1, 4.1, 4.2, 5.1, and 5.2)
14.
What is the slope of any vertical line?
15.
Find the slope and y-intercept of the line 5x + 3y = –6.
16.
Find the slope of the line that contains the points (1, 3) and (–8, –3).
17.
Find the slope of the line that contains the points (–5, –8) and (–7, 2).
18.
Find the equation of the line which passes through the point (–1, –3) and has a slope of –4. Write your
final equation in slope–intercept form.
19.
2
Find the equation of the line which passes through the point (–4, 6) and has a slope of 3 . Write your
final equation in slope–intercept form.
20.
Find the equations of the horizontal line and vertical line that pass through the point (–3, 1).
21.
Find the equation of the line which passes through the points (1, –5) and (–1, 3). Write your final
equation in slope–intercept form.
22.
Find the equation of the line which passes through the points (4, 2) and (–2, –7). Write your final
equation in slope–intercept form.
23.
Solve for x: 3x + 7 = 6x – 4
24.
Solve the system of equations by graphing. If there is no solution or more than one solution, state this.
6x – 3y = 12
y = 2x – 4
25.
Solve the system of equations by graphing. If there is no solution or more than one solution, state this.
x–y=6
2x – 2y = –6
26.
Solve the system of equations by graphing. If there is no solution or more than one solution, state this.
2x + y = 10
3x + 2y = 18
27.
Solve the system of equations by using the substitution method. If there is no solution or more than one
solution, state this.
x = 3y + 5
4x – 12y = 20
28.
Solve the system of equations by using the substitution method. If there is no solution or more than one
solution, state this.
4y – x = 27
2x + 7y = 21
29.
Solve the system of equations by using the substitution method. If there is no solution or more than one
solution, state this.
4x + y = –2
3y – 2x = –13
30.
Solve the system of equations by using the elimination method. If there is no solution or more than one
solution, state this.
2x – 10y = 1
3x – 15y = 4
MATD 0370 ELEMENTARY ALGEBRA REVIEW FOR TEST 2 (New Material From: 3.1, 4.1, 4.2, 5.1, and 5.2)
31.
Solve the system of equations by using the elimination method. If there is no solution or more than one
solution, state this.
4x + 5y = 3
6x – 3y = 15
32.
Solve the system of equations by using the elimination method. If there is no solution or more than one
solution, state this.
5x – 4y = 2
11x + 2y = 8
33.
Evaluate: x2 – y2 – z2 if x = –5, y = 6, and z = –4
34.
Two angles are supplementary. One angle is 52° more than three times the other. Find the angles.
(Hint: supplementary angles have a sum of 180°.)
35.
The sum of two numbers is 21. Half the larger number plus twice the smaller number is 12. What are
the numbers?
36.
Ling had a total of $1482 in her checking account and her savings account. Her savings account paid 4%
in simple interest and her checking account paid 2.5% in simple interest. If she earned $51.42 in interest
for the year, how was her money divided between the two accounts?
37.
Ben has a total of 49 bills, consisting of $5 bills and $10 bills. If the total value of the bills is $350, how
many of each does he have?
38.
Alan needs 250 ml of a solution that is 45% alcohol. If he has a solution that is 50% alcohol and
purified water (which is 0% alcohol), how much of each should he mix together?
39.
Jose wants 8 pounds of a dried fruit mixture that he can sell for $3.75 per pound. If he has dried peaches
that cost $4.50 per pound and dried apples that cost $3.25 per pound, how much of each should he use?
40.
LaKeshia wants 400 ml of a solution that is 11% HCl. If she has only 8% HCl and 16% HCl, how much of
each should she mix together?
41.
Darcy has 23 fewer quarters than dimes. Altogether the coins are worth $17.35. How many of each does
she have?
42.
Two angles are complementary. One angle is 24° less than twice the other. Find the angles.
(Hint: complementary angles have a sum of 90°.)
MATD 0370 ELEMENTARY ALGEBRA REVIEW FOR TEST 2 (New Material From: 3.1, 4.1, 4.2, 5.1, and 5.2)
ANSWERS:
1.
(–4, 0)
2.
(4, –5)
3.
Quadrant II
4.
5.
6.
7.
MATD 0370 ELEMENTARY ALGEBRA REVIEW FOR TEST 2 (New Material From: 3.1, 4.1, 4.2, 5.1, and 5.2)
ANSWERS (CONTINUED):
8.
Equation of Vertical Line: x = 3.5
9.
y=
3
x–3
2
Table Of Values (Answers May Vary):
x
–2
0
2
y
–6
–3
0
10.
y=
slope:
3
x–3
2
3
2
y–intercept: (0, –3)
11.
x-intercept: (5, 0), y-intercept: (0, –5)
12.
x-intercept: ( –
12
7
13.
slope: 0
14.
slope: undefined
, 0), y-intercept: (0, –6)
MATD 0370 ELEMENTARY ALGEBRA REVIEW FOR TEST 2 (New Material From: 3.1, 4.1, 4.2, 5.1, and 5.2)
ANSWERS (CONTINUED):
5
15.
slope: m = –
3
y-intercept: (0, –2)
16.
2
3
17.
–5
18.
y = –4x – 7
19.
y=
20.
Horizontal Line: y = 1
Vertical Line: x = –3
21.
y = –4x – 1
22.
23.
2
26
x+
3
3
3
x–4
2
11
x=
3
y=
24.
Infinitely Many Solutions (Same Line - All points on the line are solutions.)
25.
No Solution (Parallel Lines - They share no common points.)
26.
x = 2 and y = 6, or (2, 6)
MATD 0370 ELEMENTARY ALGEBRA REVIEW FOR TEST 2 (New Material From: 3.1, 4.1, 4.2, 5.1, and 5.2)
ANSWERS (CONTINUED):
27.
Infinitely Many Solutions (Same Line - All points on the line are solutions.)
28.
x = –7 and y = 5, or (–7, 5)
29.
1
1
x = 2 and y = –4, or ( 2 , –4)
30.
No Solution (Parallel Lines - They share no common points.)
31.
x = 2 and y = –1, or (2, –1)
32.
2
1
2 1
x = 3 and y = 3 , or ( 3 , 3 )
33.
–27
34.
The angles are 32° and 148°.
35.
The numbers are 1 and 20.
36.
Ling began the year with $524 in her checking account and $958 in her savings account.
37.
Ben has 28 $5 bills and 21 $10 bills.
38.
Alan should mix 225 ml of the 50% alcohol and 25 ml of the purified water.
39.
Jose should mix 3.2 pounds of dried peaches and 4.8 pounds of dried apples.
40.
LaKeshia should mix 250 ml of 8% HCl and 150 ml of 16% HCl.
41.
Darcy has 43 quarters and 66 dimes.
42.
The angles are 38° and 52°.