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Math 060 Test 1 Sample Test
Summer 2015
1.
2.
3.
4.
If x = 6, find y if y = 5x – 7
Is (-2, 3) a solution to the equation y = - x – 1?
Find the x and y intercepts of y = + 1
Write the equation for the following problem and find the solution:
Seven minus six times a number is the same as twelve minus seven times the number.
5. Solve the following equation for y: 4y + 3(y – 2) = 2 (y + 4) – 2(y – 7)
6. Solve the following equation for w:
=
7. Solve the following equation for y: - 0.4x + 0.8 y = - 0.2
8. The area of a trapezoid is A = h(a + b). Solve for a.
9. On a map, 2 cm represents 250 mi. If the route you need to follow measures 6 cm on the
map, how many miles will you be traveling?
10. Your favorite pancake recipes calls for three eggs and two cups of flour. When you go to
the refrigerator, you find that your roommate has used some of your eggs and that you
only have two left. If you make the recipe with only two eggs, how much flour will you
need?
11. A distributor has a gasohol tank that holds 15,000 gallons. It already has 9,000 gallons of
gasohol that contains 6% ethanol. How much pure alcohol must be added to the mixture
to produce a mix that is 10% ethanol?
12. Find the slope of the line passing through each given pair of points.
a)
b)
(−7, 3) and (15, 3)
( 2, −2 ) and ( 5, 2 )
c)
( 2a + 1, b − 1) and (2 − 5, + 5) d)
( 7, −3) and ( 7, − 8)
13. Find the equation of the line passing through the given pair of points. Write your answer
in slope-intercept form if possible.
a)
b) − , and , − ( −2,1) and ( 4, −2 )
c)
(−2, 1) and (−2, −2)
d)
( 7, 4 ) and ( 9, 4 )
14. Determine whether the given pair of lines is parallel, perpendicular, or neither.
3
5 x + 9 y = 27
y = x−2
a)
b)
2
10 y = 18 x + 50
6x − 4 y = 7
7 y + 4x = 2
c)
d)
= −2
7 y − 4x = 3
= −2
15. Find the equation of the line that passes through the point ( −9,7 ) and is perpendicular to
the line 3 + 5 = −10. Write your answer in slope-intercept form.
16. Find the equation of the line that passes through the point (2, −3) and is parallel to the
line −5 + 6 = 12. Write your answer in slope-intercept form.
 1
17. Find the equation of the line that passes through the point  6,  and is perpendicular to
 2
the line x = −4 .
18. Determine whether each ordered pair is a solution of the system of equations.
2x + 5 y = 0
(a) (3, −1)
(b) (5, −2)
x − 3 y = 11
19. Solve the system of equations by graphing. Write the point of intersection as an ordered
pair. x + y = -1, y = 3x - 5
20. Solve the systems of equations using substitution.
3 x + y = 10
5x − 2 y = 7
a)
b)
y = 3x − 4
x = 2y +8
21. Solve the systems of equations using elimination (addition).
2x + 3y = 2
−4 x + 9 y = 7
a)
b)
5x + 7 y = 0
2x − 3 y = − 5
22. Solve the system of equations using any method. Write the solution as an ordered pair, or
state that there is no solution or infinitely many solutions.
x − 2y = 0
y = − 2x + 3
b)
a.
3 x + 5 y = −11
y = 5 x − 11
x y
+ = −2
0.25 x + 0.10 y = 3.70
2
4
c)
d)
x+
y = 25
3x y
+ = −6
2 5
23. Find two numbers whose sum is 82 and whose difference is 16.
24. A baker wants to mix a 60% sugar solution with a 30% sugar solution to obtain 10 quarts
of a 51% sugar solution. How much of the 30% solution will the baker use?
25. Hilda invested part of her $25000 in savings bonds at 7% simple interest and the rest in
stocks at 8% simple interest. If she receives $1900 a year in interest, how much did she
invest in each account?
26. Tickets to a theatre cost $8 for students and $10 for nonstudents. They sold 390 tickets
and made $3270. How many student tickets were sold?
27. The perimeter of a rectangular garden is 650 meters. If the length is 75 meters more than
the width, what are the dimensions of the garden?
Answers: 1) 23; 2) no; 3) y: (0, 1), x: (-3, 0); 4) 7 – 6x = 12 – 7x; 5) 4; 6) -10; 7) y = 8) - b ; 9) 750 mi; 10) cups; 11) 400 gal; 12) 4/3, 0, -2/3, undef. 13) y= -x/2,
y = -x + 1/15, x = -2, y = 4 14) perp, par., neither, perp 15) y = 5/3x + 22
16) y = 5x/6 – 14/3 17) y = 1/2 18) no, yes 19) (1, -2) 20) (4, -2), (1, -1) 21) (-14,
10), ( -4, -1) 22) (-2, -1), (2,-1), (-4, 0), (8, 17) 23) 33 and 49 24) 3 qts.
25) $10,000 bonds, $15000 stocks 26) 315 27) 125m by 200m