Welcome to Quickmath Solvers!

### Q: How does QuickMath work ?

QuickMath is an automated service which enables anyone with access to the internet to get solutions to all sorts of common mathematical problems within a couple of seconds.

This is how it works.

First, you decide what kind of question you want to ask. QuickMath currently has seven sections containing sixteen commands which cover many of the problems faced by school and university students. More commands will be introduced soon. You can choose the command you wish to use from the menu in the top left corner of each page.

Once you are on the page for the command you want, simply type your problem into the form provided and submit it. It will then be sent off to QuickMath's server.

When your question arrives at QuickMath, it is automatically processed by Mathematica, an extremely powerful computer algebra package. After the answer has been calculated, a page containing the solution is created on the fly and returned to your browser. The whole process should take no more than a couple of seconds.

This is a free service, so ask as many questions as you like.

### Q: How do I type math into my computer ?

#### How do I type math into my computer?

About the only thing you have to learn in order to use QuickMath is how to type mathematical expressions and equations into your computer.

First, you need to know what the allowable characters are.

#### Allowable characters

Here is a comprehensive list of all the characters accepted by QuickMath.

a b c d e f g h i j k l m n o p q r s t u v w x y z
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
1 2 3 4 5 6 7 8 9 0
+ - * / ^ = | ( )
<space> <carriage return> or <newline>

Not all of these characters will be accepted by all commands. For instance, an expression entered in the algebra section cannot contain the equals symbol, since then it would be an equation which can only be used in the equations section.

#### Basic operations

The most common types of operations you'll use in your questions are multiplication, division, addition, subtraction and powers.

#### Multiplication

You can multiply two things together in several ways :

• Use the * symbol (<shift>8 on most keyboards), e.g. 2*x or a*b.

• Use a space, e.g. 2 x or a b.

• Use nothing, e.g. 2x or ab.

Caution : Because QuickMath has been programmed to interpret adjacent characters as a product, you can only use single letters for your variable names. For example, if you entered 2*fred, this would be interpreted as 2*f*r*e*d rather than as two times the single variable ' fred '.

Examples of multiplication

#### Division

To divide two things, use the / symbol (usually on the same key as the ? symbol). For example, for " x divided by 3 " you would type x/3.

Caution : If you want to enter a fraction and there are two or more terms or factors in the numerator or the denominator (the top and bottom parts of the fraction), make sure you enclose them in brackets. This way, you will ensure that QuickMath interprets your question correctly.

Examples of division

To add two things, use the + symbol. See the multiplication and division examples above.

#### Subtraction

To subtract one thing from another, use the - symbol. See the multiplication and division examples above.

#### Powers

To raise something to a power, use the ^ symbol (<shift>6 on most keyboards). See the multiplication and division examples above.

#### Functions

You can use all the functions you would normally come across in most textbooks, including trigonometric, logarithmic and exponential functions. To see a list of typical functions as they would be written in a textbook, along with the way they need to be entered for QuickMath, just select the type of function you want from the list below.

Is there a function missing that you would like to see included? If so, just send your suggestion to contact form and we'll do what we can to add your function to those already supported by QuickMath.

#### Constants

The three constants that QuickMath knows are pi, e (Euler's constant) and i (the square-root of -1). These names are reserved, in both uppercase and lowercase forms, so you should never use them as your own variable names.

If you think QuickMath should support other constants, just send your suggestion to contact form .

### Q: How do I use matrix solutions in other calculations ?

Anytime you do a calculation in QuickMath which generates a matrix solution, this solution will be given in two forms : a 'natural' form, which mimics the row and column form you would normally use when writing a matrix out by hand, and an 'input' form, which is suitable for re-use in another QuickMath matrix calculation.

The input form is already in the proper format required for the entry of matrices into QuickMath, so if you wish to re-use that result in another calculation, simply copy it and paste it wherever it is needed. This allows you to do complicated multi-step calculations without having to re-type the intermediate solutions.

### Q: How do I enter matrices ?

Matrices need to be entered one row at a time. Each row should begin on a new line, and elements within each row need to be separated by commas. Always make sure you have the same number of elements in each row, otherwise QuickMath will return an error.

As an example, the matrix

1 2 3
4 5 6
7 8 9

would be entered in QuickMath by typing in the following three lines :

1,2,3
4,5,6
7,8,9

Notice that each row begins on a new line and that the three items in each row are separated by commas. Matrices in QuickMath can be as complicated as you like. They can contain numbers only, as in the above example, or they can involve complicated mathematical expressions using pro-numerals and functions.

When you are entering matrices, the rows and columns do not have to line up - as long as each row is on a new line and elements are separated with commas, QuickMath will know what you mean.

### Q: How do I enter cube roots, fourth roots, etc ?

One of the index laws says that the nth root of x can be written as

x1/n

In QuickMath, this would be entered as

x^(1/n)

For instance, if you wanted to enter the fourth root of x + y, you would type

(x + y)^(1/4)

Notice that the power is enclosed in brackets.

### Q: How do I enter radicals/square roots ?

To find the square root of something, use the sqrt function. For example, the square root of 2 would be entered as

sqrt(2)

whilst the square root of a + b would be entered as

sqrt(a + b)

As with all functions, be sure to always use brackets.

### Q: How do I enter powers ?

To raise something to a power, use the ^ symbol, which is shift 6 on most keyboards. For example, the expression

ab

would be entered as

a^b

If either the base or the power contains more than one term or factor, use brackets. So the expression

(a + b)xy

would be entered as

(a + b) ^ (x y)

### Q: How do I divide fractions ?

Before you enter a quotient of two fractions, make sure you know how to enter fractions properly.

Whenever you are dividing one fraction by another (or indeed a fraction by anything else) make sure you enclose each fraction in a set of brackets. So the expression

```
a + b
-----
cd
------
x
-
y

```

should be entered as

((a + b) / (c d)) / (x / y)

Notice that each fraction has another set of brackets around it.

### Q: How do I multiply fractions ?

Before you enter a product of two fractions, make sure you know how to enter fractions properly.

Whenever you are multiplying two fractions by one another (or indeed one fraction by anything else) make sure you enclose each fraction in a set of brackets. So the expression

```
a + b   x
----- * -
cd     y

```

should be entered as

((a + b) / (c d)) * (x / y)

Notice that each fraction has another set of brackets around it.

### Q: How do I enter fractions ?

One of the biggest problems people have using QuickMath is knowing how to enter fractions properly. This section will explain precisely how to enter fractions so that they are interpreted correctly by QuickMath.

```		a
-
b
```

Since this fraction has just one term in the numerator and the denominator, it can be entered as :

a / b

Here is a fraction with two terms in the numerator :

```
a + b
-----
c

```

Now that there is more than a single term in the numerator, we have to start using brackets in order to indicate that both a and b are in the numerator. This is how this fraction should be entered into QuickMath :

(a + b) / c

The next step is a fraction which contains two terms in both the numerator and the denominator :

```
a + b
-----
c + d

```

Of course, now both the a + b and the c + d must be enclosed by brackets :

(a + b) / (c + d)

The same goes if you have a fraction with more than a single factor in either the numerator of the denominator. For instance, the fraction

```
ab
--
cd

```

should be entered as

(a b) / (c d)

So the moral of the story is that whenever you enter a fraction with more than a single term or a single factor in the numerator or denominator, you need to use brackets. If in doubt, always put brackets around the entire numerator and the entire denominator.

### Q: What is an equation ?

An equation consists of two expressions, one on each side of an equals symbol (=). You need to enter an equation whenever you use a command from the equations section, but not in the algebra or calculus sections. These sections require an expression only.

### Q: I sent my question, but I got a timeout message.

Each question to QuickMath is allocated 15 seconds of CPU time. This is plenty for most calculations, but occasionally your time will run out before the question is answered. When this happens, you will receive a timeout message. Try breaking your question up into smaller parts if possible and re-submitting it.

### Q: Who runs QuickMath and why?

My name is Ben Langton, and I created and operate QuickMath. I hold a PhD from the University of Sydney, Australia, in the field of exact solutions of the Einstein field equations (general relativity). Amongst other things, I am interested in mathematics and programming, so I created QuickMath as a means of combining my skills in these areas to produce a site unlike any other currently available on the internet.

### Q: Is QuickMath an alternative to math tutoring ?

QuickMath on its own is not an viable alternative to math tutoring. As a supplement to tutoring, however, it can be extremely useful. Consider these points . . .