How good are you at math? Equations.

C

cynicallywired

CAG Veteran
I was bored and decided to see how fast I could answer all of these. Try your luck and post your times, IF YOU DARE. :D

1. Which of the following pairs of numbers contain like fractions?
A. 6/7 and 15/7
B. 3/2 and 2/3
C. 5/6 and 10/12
D. 31/2 and 43/4


2. 7 1/5 – 6 2/5 = ?
A. 13 3/5
B. 1 4/5
C. 4/5
D. 1 1/5


3. What is the sum of 2/5 and 2/4?
A. 8/20
B. 9/10
C. 10/20
D. 6/7


4. What is the least common denominator of 3/4, 4/5, 2/3?
A. 20
B. 15
C. 12
D. 60


5. What is the product of 3 2/3 and 14 2/5?
A. 52 4/15
B. 54
C. 52 4/5
D. 42 4/5


6. Divide 6/13 by 6/12 .
A. 12/13
B. 1/12
C. 13/12
D. 9/16


7. Jane is making a suit which requires 2 5/8 yards for the jacket and 1 3/4 yards for the skirt. What is the total amount of material she needs?
A. 4 yards
B. 3 2/3 yards
C. 3 1/2 yards
D. 4 3/8 yards


8. Which of the following is an example of a proper fraction?
A. 15/2
B. 4/17
C. 6/6
D. 11/10


9. A bus on a regular schedule takes 3 1/4 hours to reach its destination. The express bus takes 2 1/2 hours to make the same trip. How much travel time can be saved by taking the express?
A. 5 3/4 hours
B. 1 1/4 hours
C. 3/4 hour
D. 2 hours


10. Ralph spends 15 1/3 hours per month playing tennis. How many hours does he play tennis in a year? (There are twelve months in a year.)
A. 164
B. 184
C. 182 2/3
D. 164 1/3


11. What is the reciprocal of 6/5?
A. 12/10
B. 1 1/5
C. 1
D. 5/6


12. A family spends 1/10 of its annual income for housing, 1/4 for food and clothing, 1/5 for general expenses, and 2/15 for entertainment. What fractional part of their income is spent on these items altogether?
A. 1/7
B. 11/12
C. 6/41
D. 41/60


13. What is the fraction 18/24 reduced to its lowest terms?
A. 3/4
B. 9/12
C. 18/24
D. 24/18


14. 7/8 = ?/48
A. 6
B. 13
C. 42
D. 1


15. A chef prepared five chocolate tortes for a dinner party. The guests consumed 2 5/16 tortes. How many tortes are left?
A. 2 11/16
B. 3 11/16
C. 2 9/16
D. 3 9/16


16. Write 10 5/12 as an equivalent improper fraction.
A. 10 12/5
B. 120/12
C. 125/12
D. 12/125


17. Simone has 5 employees in her flower shop. Each employee works
6 4/15 hours per day. How many hours, in total, do the 5 employees work per day?
A. 30
B. 28
C. 31 1/3
D. 30 2/3


18. 15 ÷ 6 2/3 = ?
A. 100 1/4
B. 2 1/4
C. 100
D. 2 3/4


19. What is the difference between 126 1/4 and 78 2/3?
A. 58 5/12
B. 57 7/12
C. 48 1/3
D. 47 7/12


20. 4/15 of the 315 members of a book club are male. How many female members are there in the club?
A. 84
B. 131
C. 174
D. 231

Answer example.

1. A
2. B
3. C
Ect... Good luck!
 
[quote name='Strell']Here I was expected Calculus equations.[/QUOTE]
:lol: Honestly, this stuff is freshman year of HS.
 
[quote name='Rich']:lol: Honestly, this stuff is freshman year of HS.[/QUOTE]

Dude, fractions are like 4th grade - maybe 3rd. What busted high school did you go to?
 
adding fractions and stuff was definitely middle school for me... anyone who did this stuff in elementary school was probably in those wacky "gifted" programs.
 
[quote name='javeryh']Dude, fractions are like 4th grade - maybe 3rd. What busted high school did you go to?[/QUOTE]

It's 3rd, at least it was for me. First year of HS was Geometry and Algebra 2.
 
[quote name='eldad9']come on, somebody must be desperate enough for acceptance to do all of these...[/QUOTE]

Yeah, now someone's gonna post their answers...:lol:
 
[quote name='Rich']:lol: Honestly, this stuff is freshman year of HS.[/QUOTE]

What HS did you go to? I was doing this in 3rd grade
 
just answer all C. you'll get at least a C grade. but you'd probably deserve an F if you couldn't even pull out a calculator and do it on that.
 
[quote name='sblymnlcrymnl']It's 3rd, at least it was for me. First year of HS was Geometry and Algebra 2.[/QUOTE]

Adding fractions usually requires a pretty decent knowledge of multiplication and divison, especially distributive rules. I definately don't remember having knowledge of those things at that point, especially because my fourth grade teacher used to have games of boys vs. girls for doing multiplication flash cards (man, I wish my professors would have done shit like that for us now, "Quick! Who can solve this second order non-homogeneous differential equation!")
 
[quote name='sblymnlcrymnl']It's 3rd, at least it was for me. First year of HS was Geometry and Algebra 2.[/QUOTE]

Agreed.
 
[quote name='RacinReaver']Adding fractions usually requires a pretty decent knowledge of multiplication and divison, especially distributive rules. I definately don't remember having knowledge of those things at that point, especially because my fourth grade teacher used to have games of boys vs. girls for doing multiplication flash cards (man, I wish my professors would have done shit like that for us now, "Quick! Who can solve this second order non-homogeneous differential equation!")[/QUOTE]

Did you ride to school on the short bus? Multiplication flash cards was so 2nd grade... :lol:
 
You guys are no fun. :(

1. C
2. C
3. B
4. D
5. C
6. A
7. D
8. B
9. C
10. B
11. D
12. D
13. A
14. C
15. A
16. C
17. C
18. B
19. D
20. D

2 mins with my trusty sidekick: calculator
 
[quote name='Kaijufan']I always hated it when math teachers told me that fractions are friends.[/QUOTE]

The type of friends that use you, backstab you, and ditch you. Totally right.
 
[quote name='cynicallywired']The type of friends that use you, backstab you, and ditch you. Totally right.[/QUOTE]

Huh... sounds like half the members on CAG now doesn't it...
 
Ok, cynicallywired. People put up with your game. I want full documentation of the solutions of this set of problems.

1a.Find the general solution of y3(dy/dx) = (y^4 + 3) cos x

1b.Find the general solution of (tan x)(dy/dx) = y

2a.Solve the initial value problem

dy/dx = 4x-y/x-6y ; y(1) = 1

2b.Solve the initial value problem

(x2 + 1) dy/dx + 3x^3y = 6x exp(-3/2x^2); y(0) = 5

3.Find the general solution of dy/dx + 5xy = y ln yx by substituting v = ln y


4a.Show that the substitution v = ax + by + c transforms the diferential equation
dy/dx = F(ax + by + c) into a separable equation.

4b.Using (a) or otherwise, and the general solution of dy/dx = x^2 + y^2 + 2xy + 4x + 4y + 4

5.Suppose that you discover in your attic an overdue 18.03 textbook on which your
grandfather owed a fine of 5 cents 100 years ago. If an overdue fine grows exponentially
at a 5% annual rate compounded continuously, how much would you have to pay if you
return the book today? (hint: think of this problem as continuously compounded interest)

6.A tank contains 1000 liters (L) of a solution consisting of 50 kg salt dissolved in water.
Pure water is pumped into the tank at the rate of 5 L/s, and the mixture - kept uniform
by stirring - is pumped out at the same rate. How long will it be until only 3 kg of salt
remains in the tank?


7. This problem concerns a water tank
in the shape of an inverted cone of height 1 m. The opening angle of the cone is 90
degrees. so the radius at the top is also 1 m. The cone is initially full of water. At t=0
a small hole is cut horizontally across the cone 1 cm. above the apex, so the hole has
radius 1 cm. The water begins to drain. How long will it take for all the water to drain
from the tank? Hint: sensible numerical approximations can simplify things. Use g=980
cm/(sec)2. The answer is t=900 sec. to a close approximation.
8b. What is the volume of the conical tank? What is the radius of a cylindrical tank of
height 1 m. with same volume as the cone? If initially full, how long does the cylindrical
tank take to drain through a hole of radius 1 cm. in its base?

8.Early one morning it began to snow at a constant rate. At 7 A.M. a snowplow set of
to clear a road. By 8 A.M. it had travelled 2 miles, but it took two more hours (until 10
A.M.) for the snowplow to go an additional 2 miles.
a.Let t = 0 when it began to snow and let x denote the distance travelled by the snowplow
at time t. Assuming that the snowplow clears snow from the road at a constant rate (in
cubic feet per hour, say), show that k dx
dt = 1
t where k is a constant.
b.What time did it start snowing?

9. An advanced technology rocket expels fuel such that the total mass is m(t), a smooth
decreasing function of time. At time t, the velocity of the escaping fuel is u(t) (relative
to the rocket and directed opposite to its course), another given positive function. Both
functions m(t) and u(t) are controlled from "Mission Control Center" on the ground. As
a generalization of what was done in class, use the conservation of mass and momentum
laws to derive the diferential equation for the velocity:
m(t) (dv(t)/dt) = -u(t) (dm(t)/dt)

Show that, for constant u(t) = u0, the solution to this ODE is v(t) = v(0) + u0 ln(m(0)/m(t))
 
[quote name='JSweeney']Ok, cynicallywired. People put up with your game. I want full documentation of the solutions of this set of problems.

1a.Find the general solution of y3(dy/dx) = (y^4 + 3) cos x

1b.Find the general solution of (tan x)(dy/dx) = y

2a.Solve the initial value problem

dy/dx = 4x-y/x-6y ; y(1) = 1

2b.Solve the initial value problem

(x2 + 1) dy/dx + 3x^3y = 6x exp(-3/2x^2); y(0) = 5

3.Find the general solution of dy/dx + 5xy = y ln yx by substituting v = ln y


4a.Show that the substitution v = ax + by + c transforms the diferential equation
dy/dx = F(ax + by + c) into a separable equation.

4b.Using (a) or otherwise, and the general solution of dy/dx = x^2 + y^2 + 2xy + 4x + 4y + 4

5.Suppose that you discover in your attic an overdue 18.03 textbook on which your
grandfather owed a fine of 5 cents 100 years ago. If an overdue fine grows exponentially
at a 5% annual rate compounded continuously, how much would you have to pay if you
return the book today? (hint: think of this problem as continuously compounded interest)

6.A tank contains 1000 liters (L) of a solution consisting of 50 kg salt dissolved in water.
Pure water is pumped into the tank at the rate of 5 L/s, and the mixture - kept uniform
by stirring - is pumped out at the same rate. How long will it be until only 3 kg of salt
remains in the tank?


7. This problem concerns a water tank
in the shape of an inverted cone of height 1 m. The opening angle of the cone is 90
degrees. so the radius at the top is also 1 m. The cone is initially full of water. At t=0
a small hole is cut horizontally across the cone 1 cm. above the apex, so the hole has
radius 1 cm. The water begins to drain. How long will it take for all the water to drain
from the tank? Hint: sensible numerical approximations can simplify things. Use g=980
cm/(sec)2. The answer is t=900 sec. to a close approximation.
8b. What is the volume of the conical tank? What is the radius of a cylindrical tank of
height 1 m. with same volume as the cone? If initially full, how long does the cylindrical
tank take to drain through a hole of radius 1 cm. in its base?

8.Early one morning it began to snow at a constant rate. At 7 A.M. a snowplow set of
to clear a road. By 8 A.M. it had travelled 2 miles, but it took two more hours (until 10
A.M.) for the snowplow to go an additional 2 miles.
a.Let t = 0 when it began to snow and let x denote the distance travelled by the snowplow
at time t. Assuming that the snowplow clears snow from the road at a constant rate (in
cubic feet per hour, say), show that k dx
dt = 1
t where k is a constant.
b.What time did it start snowing?

9. An advanced technology rocket expels fuel such that the total mass is m(t), a smooth
decreasing function of time. At time t, the velocity of the escaping fuel is u(t) (relative
to the rocket and directed opposite to its course), another given positive function. Both
functions m(t) and u(t) are controlled from "Mission Control Center" on the ground. As
a generalization of what was done in class, use the conservation of mass and momentum
laws to derive the diferential equation for the velocity:
m(t) (dv(t)/dt) = -u(t) (dm(t)/dt)

Show that, for constant u(t) = u0, the solution to this ODE is v(t) = v(0) + u0 ln(m(0)/m(t))[/QUOTE]

I can't believe how much math I've forgotten since I graduated college. I used to be able to do all of this stuff pretty easily - oh well, it's not like I need to know it anymore...
 
[quote name='cynicallywired']You guys are no fun. :(

1. C
2. C
3. B
4. D
5. C
6. A
7. D
8. B
9. C
10. B
11. D
12. D
13. A
14. C
15. A
16. C
17. C
18. B
19. D
20. D

2 mins with my trusty sidekick: calculator
 
[quote name='Jrunt20x']What grade or school do you go to? If you're in like 2nd grade or live in Compton then it's ok, but honestly I learned this stuff when I was 7 years old.[/QUOTE]


whoa whoa whoa. let's not talk shit on compton just because some gangsters came out of there. just because they come from a bad neighborhood doesn't mean they're dumb. haven't those mexican immigrants that beat MIT at robot making taught you anything?
 
Your right 2poor. Sorry about my compton comments. I know plenty of chill people from there. I just said that cause I thought it would help get the point across that his school sucks.
 
A grade calculator helps a lot to students in their acedemic math activities or grade calculator helps students by providing a clear and immediate way to understand their academic performance. It allows them to input their grades and assignments to calculate current averages and predict final grades. This tool aids in identifying areas needing improvement and setting realistic goals, thereby enhancing academic planning and motivation
 
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