hello everyone,
i have been going through various threads on nairaland and sincerely i am impressed by how young nigerian are helping each other.Seun you know you have acheived a fit that's a dream for many.keep it up bro.
By a way of introduction i recently graduated from O.A.U ile ife chemical engineering with a first class(i said that humbly) and iam currently serving in an oil company in ikoyi.
i humbly want to contribute my own quota on this site and since mathematics is my strenght i decided to do something along that line
if anyone has any maths question,assignment , from secondary school level to university,gmat,gre and sat maths questions, Kindly bring it on .

All the maths whiz in the house come on let's make this thread exciting

1. The famous Pythagorean Theorem, which states that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse, is actually a special case of what theorem/law?

2. This theorem, considered a fundamental theorem in mathematics, links two branches of calculus: differential calculus and integral calculus. This is known as the,

3. Limits - everyone's favourite! This rule/theorem uses derivatives to calculate limits of indeterminate forms (that of the form 0/0 or infinity/infinity). This is known as,

4. The indefinite integral of e^(x^2) is one of the many very special integrals. What makes it so special, in terms of numerical integration?

5. Again, limits - my old friend. This theorem can be quite useful if you're not familiar with l'Hôpital's Rule. It states that if a function is bounded by two other functions and those two functions approach the same limit at a point, the function that is in between must also approach that very same limit. This is known as the,

6. Hyperbolic Functions - very interesting functions you learn about early in university calculus. One of the most famous applications of hyperbolic functions is to describe the shape of a hanging wire. The shape of the curve is given by the following equation: y = c + a cosh(x/a), where one can see the use of the hyperbolic function: cosh (hyperbolic cosine). What is the equation called?

7. A very important thing to do, especially in mathematics, is to read your question(s) carefully. With that said, check out this integral:
"the integral with limits from -1 to 1 of (1/x) dx."
What, if anything, is wrong with this integral?

8. In linear algebra, there is such a thing called mapping, using linear transformations. There are two properties that a transformation must hold in order to be linear:
1. Additivity: f(x + y) = f(x) + f(y)
2. Homogeneity: f(cx) = c f(x), where c is a constant
An additional property (although sometimes not reliable) is that f(0) = 0.
Knowing all this, which of the following transformations is linear?

9. When doing matrix row operations on a set of linear equations, you happen to get a row that looks like this:
[0 0 0 , 0 | x ], where x is any non-zero number
You would classify this system as being,

10. Here is an equation:
(x,y,z) = (1,2,5) + t1(2,0,0) + t2(0,1,-2)
What does this equation represent?

jamb,gce,ssce and any kind of exams too are welcome as long as it is mathematics

answer the ones above genius.

i see u cant answer them,

hello Dr holiness_m
Thanx for your tym Dr how is Uk today

Boy i like your questions they are giving me a run for my claims
1.cosine rule

2.It's actually called fundamental law of calculus:states that differentiation and integration are inverse operations

3.L'hospital rule
4.Dr , to numerically integrate a function we need to know the limits.and most function can be numerically integrated if we know btween the limits we are integrating it

7.

well - your claims of being good in mathematics is hereby faulted.

of course i dare not argue with a doc but just do the correction so that me and other great nigerian students can learn.
Thank you so very much in advance
7 ln(-1) does not exist

10. That's an equation of a plane

5.Squeeze theorem/sandwich theorem/pinching theorem

6. Jefferson National Expansion Memorial /the Gateway Arch

Holiness_M:

well - your claims of being good in mathematics is hereby faulted.

Am waiting to see your answers, then,

education is the first step to human freedom from all global atrocities.

lovemajek,
i concur 100% with what you said
"education is the first step to human freedom from all global atrocities"
Thanks for your post

naijacute,
Thank you so very much i sincerely appreciate.

Holiness_m,
i actually use the cafe that's why i've not been on for quite sometime.

for question 8 ,
which transformation are you talking about.You gave homogeneity and additivity as 2 conditions for linearity of a transformation and f(0)=0
but you said "which of the following transformations is linear? "
you suppose to give me the transformations whose linearity i would test.
or may be i'm missing something there.

i really want to say a big thank you for the questions,you 've definitely made me a better mathematics student.For me learning never stops.

I had first class as well, and i don't see it as a big deal.

Holiness_M - my answers below:

1. Cosine Law.
The Pythagorean Theorem is just a modified version of the Cosine Law that applies only to right triangles. The Cosine Law, c^2 = a^2 + b^2 - 2ab cosC, will yield the Pythagorean Theorem, when C = 90 degrees. Since cos90 = 0, the term "2ab cosC" disappears and you're left with the Pythagorean Theorem.

2. Fundamental Theorem of Calculus
The Fundamental Theorem of Calculus is a remarkable discovery as it shows that integration and differentiation are related; it shows that the two processes are inverses (that is, one process is the inverse of the other and vice-versa).

3. L'Hôpital's Rule
e.g. lim x -> 1 of (x - 1)/(x^2 - 1).
Instead of factoring to cancel the x - 1 term in the numerator, simply take the derivative of the numerator and the denominator, and you will get:
lim x -> 1 of 1/2x, which equals 1/2. Try it with factoring and cancelling and you will get the same answer!
L'Hôpital's Rule is generally used for more complicated functions where it is not possible to cancel terms. It also has applications to the limits of indeterminate products, differences and powers - check it out!

4. It cannot be integrated using elementary functions (numerical integraton).
The problem with integrating e^(x^2) is finding an antiderivative. Using common elementary functions, it is not possible, so mathematicians rely on analytical integration to approximate the integral of e^(x^2). Mathematicians can also use computers to compute the integrals.
There are other integrals that cannot be evaluted using elementary functions, such as (e^x)/x, sin(x^2), et cetera.

5. Squeeze, Pinching or Sandwich Theorem
Example. Say you have three functions: f(x), g(x) and h(x), where g(x) is greater than or equal to f(x) and h(x) is greater than or equal to g(x). If f(x) and h(x) approach the point 0 as x approaches 0, then by the theorem, g(x) must also approach the point 0 as x approaches 0.

6. Catenary Equation.
The catenary states that when a chain or cable is hung, it (the chain/cable) is steepest near the point(s) of suspension, because this is where most of the weight of the chain/cable is pulling down, thanks to gravity.

7. The function has a discontinuity within the given limits.
The differential is in the question: dx. It simply means integrate with respect to the variable 'x'.
The antiderivative of 1/x does in fact exist; it is ln |x| + C (where C is the integration constant).
The problem stems from the fact that in the interval [-1,1] for 1/x, there is a discontinuity at x = 0, which is in the given interval. Because there is a discontinuity in the function, its definite integral cannot be calculated. If you did calculate it (tsk, tsk), you would get an answer of ln 1 - ln |-1| = ln 1 - ln 1 = 0. However, you CANNOT do that.
On that note, when doing definite integrals, be sure to check your limits of integration to see if there are any discontinuities within the limits.

8. T(x,y) = (2x + y, x - y).
In order for a transformation to be deemed non-linear, it just has to fail one of the two main properties: additivity or homogeneity. For T(x,y) = (x + 1, y), I will show how it fails using homogeneity:
T(x,y) = (x + 1, y) - Take any vector, say u, to be u = (1,2) and a constant c = 2.
For the transformation to be linear, T(cu) = cT(u)
T(cu): cu is the same as 2(1,2) which will give a new vector, (2,4). Using x = 2 and y = 4, we plug it into the transformation equation T(x,y) which gives us (2+1, 4) = (3,4)
cT(u): instead of multiplying the vector by the constant first, we use the original vector (1,2), put it into the tranformation equation and then multiply by the constant. Doing that, we get T(x,y) = (1+1, 2) = (2,2). Now multiply by 2, and you get (4,4).
Because the two results are not equal, this system fails the property of homogeneity, and is therefore, not linear.
I encourage you to try it out with the others!

9. Inconsistent.
Having a row [0 0 0 ,  0 | x ], where x is any non-zero number, means the system is inconsistent, because you're saying that nothing is equal to a specific value, which is not possible (e.g. 0x = 5; not possible to evaluate).
If you have the row [0 0 0 ,  0 | 0], this is entirely possible because you're saying nothing equals nothing (e.g. 0x = 0, x = 0); having a row like this would mean that your system is consistent and will have a unique solution of infinitely many solutions (when you have one or more free variables).

10. A plane passing through the point (1,2,5), parallel to the vectors (2,0,0) and (0,1,-2)
When analyzing these types of equations, the point will never have a variable attached to it (in this case, the variables are t1 and t2).
Also, with a line, you will only be given one vector; with a plane, you will be given two or more vectors. The vectors will have a variable attached to it (in this case, t1 and t2).


Are these correct @ Holiness_M?

Hello labiyemmy,

nice one i guess you save the day.congratulation on your first class.
You are the whiz we've been waiting for.

now i can give my answers too.

Very interesting thread!

Anybody up for stochastic processes?

I'll be posting some questions soon.

someone said something that life is for the bold and i have found it to be so true.
i think we need not wait for anyone let's just bring them on.Questions ,answers,criticism,contributions, as far as it is mathematics.
only let's be objective.
don't be afraid to be wrong because most people that we listen to today are not all correct but they unlike many have one thing : gutz

from today i like to start posting some mathematics tips on a daily basis.

the difference btween a number and it's mirror image is always divisible by 9

e.g1
122 is a mirror image of 221 .
the difference is 221-122=99
99/9=11
e.g2
25 is a mirror of 52
52-25=27
27/9=3

i'll be ready to answer your quetion on this and anyother thing
but remember keep it restrictd to maths
thank you in advance

1. These are the marks gained in a quiz, out of 10 possible points, by ten people: 10 9 8 7 5 5 4 3 2 2. What is the modal mark?

5 and 2
5
2
10



2. One card is drawn at random from an ordinary pack of playing cards. What is the probability that it does not belong to the suit of clubs?

40/52 = 10/13
13/52 = 1/4
39/52 = 3/4
26/52 = 1/2



3. What will be the base of a triangle when the area of the triangle is 36 cm^2, the perpendicular height is 0.36 metres and the slant height is 6 cm?

0.2 m
0.012 m
12 cm
2 cm



4. Three men build a wall in 10 days. How long would it take 2 men?

7 days
6 days and 6 hours
15 days
60 days



5. Jack has 3/5 of 1/2 of 1/2 of a minute to answer 3 simple addition problems. How many seconds does he have?

Answer: (Type the number only (In figures or in words))



6. The area of one of the faces of a cube is 196 cm^2. Find its volume.

2744 cm^2
117649 cm^2
117649 cm^3
2744 cm^3



7. One angle of a triangle measures 72 degrees. The other two angles measure 2y degrees and 1y degrees. What type of a triangle is this?

Obtuse angled
Scalene
Isosceles
Equilateral



8. How many lines of symmetry does a regular pentagon have?

3
0
5
1



9. What is the perimeter of a regular heptagon measuring 2.5 m on a side?

20 m
17.5 m^2
0.0175 km
17500 cm



10. 1 litre is equal to 1000 cubic centimetres. If Jill is going to be fed with 11 millilitres of cough syrup every day for a week for her cough, how many cubic centimetres of cough syrup will she drink?

77 cm^3
0.011 cm^3
0.077 cm^3
11 cm^3

1. i'll choose 5 &2


3. 2cm

4. 3men build in 10 days
1 man build in 30 days working @ the same rate
2 men builds in 30/2=15 days
5. he has 9 secs to answer the 3 questions
3secs to answer 1 question

6 2744cm^3

7 isosceles triangle


8 5 lines of symmetry

9 Heptagon is a 7- sided polygon
1 side is 2.5m hence 7 sides is 7*2.5=17.5m
convert to km by dividing by 1000
hence perimeter=0.0175km

10 1 cm^3 = 1 milliliter
11 ml for a week=77ml
=77cm^3

note it's not 17.5 m^2 that would be an area

9

Given Pythagoras's rule:

X^2+y^2= z^2 is true

for 9 + 16 = 25

Can someone prove that this is not true:

X^n+y^n = z^n

for n >2

this is all so nice

keep it up!

@ebam,

The proof you want is a proof of the famous Fermat's Last Theorem (see http://en.wikipedia.org/wiki/Fermat's_last_theorem). Andrew Wiles (http://en.wikipedia.org/wiki/Andrew_Wiles) proved that in 1994. An overview of the proof (for non-specialists) can be found here: http://www.ams.org/notices/199507/faltings.pdf

Fermat's Last Theorem states that:
no nontrivial integer solutions exist for the equation: x^n + y^n = z^n if n is an integer greater than two.

Problem:
Three of every four trucks on the road are followed by a car, while only one of every five cars is followed by a truck. What fraction of vehicles on the road are trucks?
_{(Essentials of Stochastic Processes (2001), page 91, problem 9.13)}

@labiyemmy:

2. One card is drawn at random from an ordinary pack of playing cards. What is the probability that it does not belong to the suit of clubs?

40/52 = 10/13
13/52 = 1/4
39/52 = 3/4
26/52 = 1/2

@edusegzy

I see you skipped #2. I don't blame you jare, this is one of those questions where Anglo-American bias is evident. Knowledge of their type of playing cards is necessary to solve it.

The standard Anglo-American playing card is divided into 4 suits :
1. Clubs
2. Diamonds
3. Hearts
4. Spades

Each suit has 13 cards: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, and King.

This gives a total of 4*13 = 52.

So, using a random pick to choose a card x:
P( x not element of suit of clubs) = (52-13)/52 = 39/52 = 3/4.

i can see this thread is full of senior ogas

lai-lai
come on if you have any question i mean any maths questions(e.g you can ask a question as simple as 2+2) do bring it oni promise if nobody would answer i will.And remember nobody can even see your face.
Thank you in advance lai-lai

RichyBlack
I am so thrilled and honoured to have you contribute on this thread.I've been following your post,you are such a great person.
Thanx for saving the day on that number2
i actually worked it on my own and got the same answer as yours and was trying to post it but my connection was having a little problem.
Once again thank you so very much.
i look forward to reading more of you on this thread.

@ poster simple MTH 423 qusetion:
What's the major difference between Partial Differential Equation PDE and Ordinar Differential Equation ODE

watch out for the result of my questions.


1. These are the marks gained in a quiz, out of 10 possible points, by ten people: 10 9 8 7 5 5 4 3 2 2. What is the modal mark?


The correct answer is 5 and 2.

Now that was easy! The mode of a set of numbers is the number that occurs most frequently. In this case ( 10 9 8 7 5 5 4 3 2 2 ), 5 and 2 occur most frequently.



2. One card is drawn at random from an ordinary pack of playing cards. What is the probability that it does not belong to the suit of clubs?

The correct answer is 39/52 = 3/4.

There are 13 cards which are clubs, therefore the number of cards that are not clubs is 52-13, or 39. Therefore the probability that it does not belong to the suit of clubs is 39/52 or 3/4 (simplified).


3. What will be the base of a triangle when the area of the triangle is 36 cm^2, the perpendicular height is 0.36 metres and the slant height is 6 cm?

We know that the formula for finding the area of a triangle is:
A = 1/2 * b * h (where A is area, b is the base and h is the perpendicular height)
0.36 metres = 36 centimetres.
Now we can plug in the numbers:
36 = 1/2 * b * 36
36 = 18b
36/18 = b
b = 2.
Check: If the base is 2 cm and the perpendicular height is 36 cm, then the area is 1/2 * 2* 36 = 36 cm^2. Notice that we do not need the slant height.



4. Three men build a wall in 10 days. How long would it take 2 men?

The correct answer is 15 days.

Three men build a wall in 10 days. Therefore 1 man takes 3*10 days or 30 days (This is a question involving inverse proportion). 2 men take 30/2 days or 15 days to build a wall.
Check:
1 man takes 30 days to build a wall.
2 men take 15 days to build a wall.
3 men take 10 days to build a wall.
Therefore, the more men, the less time.


5. Jack has 3/5 of 1/2 of 1/2 of a minute to answer 3 simple addition problems. How many seconds does he have?

We all know that the word "of" in mathematics means "multiply" and a minute consists of 60 seconds. Therefore:

3/5 * 1/2 * 1/2 * 60
= 3/5 * 1/2 * 30
= 3/5 * 15
= 9 seconds.


6. The area of one of the faces of a cube is 196 cm^2. Find its volume.

The correct answer is 2744 cm^3.

A cube consists of six faces which are all squares. The formula for finding the area of a face of a cube (a square) is l^2 (or length squared). To find the length of one side of a square when the area is given, we find the square root of the area. The square root of 196 is 14.
Now, we can find the volume of the cube. The formula is V = l^3 (or length cubed). Therefore:
V = l^3
V = 14^3
V = 2744 cm^3.



7. One angle of a triangle measures 72 degrees. The other two angles measure 2y degrees and 1y degrees. What type of a triangle is this?

To know the type of triangle, first you add all the angles given:
72+ 2y+ 1y = 180 (The angles of a triangle add up to 180 degrees)
72 + 3y = 180
3y= 180- 72
3y = 108
y = 108/3
y = 36
Now we know that the value of y is 36 degrees. The value of 2y will be 36*2 degrees, or 72 degrees. Therefore the angles of the triangle are 72 degrees, 72 degrees and 36 degrees. This tells us that the triangle is isosceles.



8. How many lines of symmetry does a regular pentagon have?

The correct answer is 5.

A regular pentagon is a polygon with all its five sides and angles equal. And did you know that, a regular hexagon has 6 lines of symmetry, a regular heptagon has 7 lines of symmetry, a regular octagon has 8 lines of symmetry and so on? The number of sides the polygon consists of is equal to the number of lines of symmetry it has!


9. What is the perimeter of a regular heptagon measuring 2.5 m on a side?

The correct answer is 0.0175 km.

A regular heptagon has seven sides. If one side measures 2.5 m, then the perimeter of the heptagon (the distance around the heptagon) is 2.5 * 7 = 17.5 m = 17.5 / 1000 = 0.0175 km (1 km = 1000 m, therefore 1 m is 1/1000 of a kilometre). m^2 (metre squared) is a unit of area, not of perimeter.



10. 1 litre is equal to 1000 cubic centimetres. If Jill is going to be fed with 11 millilitres of cough syrup every day for a week for her cough, how many cubic centimetres of cough syrup will she drink?

If 1 litre = 1000 cm^3, then 1000 ml = 1000 cm^3 which means 1 ml = 1 cm^3. If Jill is given 11 millilitres of cough syrup every day for a week, she will drink 77 millilitres of cough syrup in a week (11*7; there are 7 days in a week). And as 1 ml = 1 cm^3, 77 ml = 77 cm^3!