Download Math 060 Test 1 Sample Test Summer 2015 1. If x = 6, find y if y = 5x

Math 060 Test 1 Sample Test
Summer 2015
1. If x = 6, find y if y = 5x – 7
y = 5(6) – 7 = 30 – 7 = 23
2. Is (-2, 3) a solution to the equation y = - x – 1?
Does 3 = -(-2) – 1 = 2 – 1? NO
3. Find the x and y intercepts of y = + 1
If x = 0, y = 1, if y = 0, x = -3; (0,1) is y intercept, (-3, 0) is x intercept
4. 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.
Let the number be n. 7 – 6(n) = 12 – 7(n)
7-6n = 12 -7n becomes n = 5
5. Solve the following equation for y: 4y + 3(y – 2) = 2 (y + 4) – 2(y – 7)
Distribute: 4y + 3y – 6 = 2y + 8 – 2y +14
7y – 6 = 0 + 22, y = 4; checking 4(4) +3(2) = 2(8) – 2(-3), 22 = 22
6. Solve the following equation for w: = Clear fraction: 5w + 5 = 3w – 15, 2w = -20, w = -10; checking -9/3 = -15/5 = -3
7. Solve the following equation for y: - 0.4x + 0.8 y = - 0.2
Multiply by 10 to clear decimal: -4x + 8y = -2; 8y = 4x – 2 or y = x/2 – ¼
8. The area of a trapezoid is A = h(a + b). Solve for a.
Multiply both sides by 2/h, 2A/h = a+b; therefore a = 2A/h – b
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?
250mi/2cm = x mi/6cm; The proportion/ratio is 250/2 = 125/1, x = 125(6) = 750 mi
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?
2 C flour/3 eggs is the proportion; 2 C/ 3 = x C/2, x = 4/3 C flour
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?
Original
Added
Total
Gallons
9000
x
9000+x
% sol
6
100
10
Gal Alcohol
540
x
540+x
0.1(9000+x) = 540+x
9000 + x = 5400 + 10x
9x = 3600
x= 400
12. Find the slope of the line passing through each given pair of points.
a)
( 2, −2 ) and ( 5, 2 ) [ 2-(-2)}]/[5-2]=4/3 b) (−7, 3) and (15, 3) 0
c)
( 2a + 1, b − 1) and (2 − 5, + 5) d)
( 7, −3) and ( 7, − 8)
[b+5-(b-1)]/[2a – 5 –(2a + 1)] = 4/(-6) = -2/3
Undefined
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 )
m= - ½ , y = -1/2x
m= -1, y = -x +1/15
(−2, 1) and (−2, −2)
d)
c)
( 7, 4 ) and ( 9, 4 )
m is undefined, x = -2
m = 0, y = 4
14. Determine whether the given pair of lines is parallel, perpendicular, or neither.
3
5 x + 9 y = 27
y = x−2
b)
a)
2
10 y = 18 x + 50
6x − 4 y = 7
Slopes: -5/9, 9/5, perp
slopes: 3/2, 3/2, par
c)
7 y + 4x = 2
7 y − 4x = 3
Slopes: -4/7, 4/7, neither
d)
= −2
= −2
slopes 0, undefined, perp
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.
slope is -3/5 so perp slope is 5/3; y = 5/3x + b; put in (-9, 7) and get 7 = -15 + b; b = 22
y = 5/3x + 22
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.
slope is 5/6, so need y = 5/6x + b; -3 = 10/6 + b, b = -14/3; y = 5/6x – 14/3
 1
17. Find the equation of the line that passes through the point  6,  and is perpendicular to
 2
the line x = −4 .
Must be a line of the for y = constant; here y = ½
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
a. 2(6) – 5 ≠0, no b. 2(5) + 5(-2) = 0, 5 -3(-2) = 11, yes
19. Solve the system of equations by graphing. Write the point of intersection as an ordered
pair. x + y = -1, y = 3x – 5
(1, -2)
20. Solve the systems of equations using substitution.
3 x + y = 10
5x − 2 y = 7
a)
b)
y = 3x − 4
x = 2y +8
nd
st
subs 2 into 1 : 6y + 24 + y = 10
subs 2nd into 1st: 5x – 6x + 8 = 7
7y = -14, y = -2, x = 2(-2)+8 = 4
-x = -1, x=1 and y = -1
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
st
nd
mult 1 by 5, 2 by -2
mult 2nd by 2
10x + 15y = 10
-4x + 9y = 7
-10x – 14y = 0
4x – 6y = -10
y = 10, x = -14
3y = -7, y = -1, x = -4
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
a.
b)
3 x + 5 y = −11
y = 5 x − 11
st
Mult 1 by -3 and add
Subtract 1st from 2nd
11y = -11
7x = 14, x = 2
y = -1, x = -2
y = -1
x y
+ = −2
2
4
d)
c)
3x y
+ = −6
2 5
clear fractions; mult 1st by 4, 2nd by 10
2x + y = -8
15x + 2y = -60; mult 1st by -2 and add
11x = -44, x = 4, y = 0
0.25 x + 0.10 y = 3.70
x+
y = 25
mult 1st by 100 2nd times 10, subt
25x + 10y = 370
10x + 10y = 250
15x = 120, x = 8, y = 17
23. Find two numbers whose sum is 82 and whose difference is 16.
n+m=82, n-m=16, 2n = 98, n = 49, m = 33
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?
Name
sixty
thirty
fifty one
Amt
10-x
x
10
%
60
30
51
Sugar
0.6(10-x)
0.3x
5.1
5.1 = 6-0.6x + 0.3x
5.1 = 6-0.3x
0.9 = 0.3x
x =3
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?
Name
savings
stocks
total
Amt
x
25-x
25
%
7
8
earn
0.07x
0.08(25-x)
1.9
190 = 7x + 200 - 8x
x = 10
10,000 savings, 15,000 stocks
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?
Name
students
non
total
Num
x
390-x
390
each
8
19
earn
8x
10(390-x)
3270
3270=8x + 10(390-x)
3270=8x + 3900-10x
630=2x
x=315 stud
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?
P = 2L + 2W, L = W + 75
P = 2(W+75) + 2W = 4W + 150 = 650, 4W = 500, W = 125, L = 200
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