# Basic Math Syntax in the System

## Writing Mathematical Expressions

The basic syntax for entering mathematical formulas or expressions in the system enables you to quickly enter expressions using 2-D notation. You can type formulas using standard mathematical notation (similar to that used for a graphing calculator) and, in general, the system correctly interprets it.

For example, the following formula is acceptable.

(x^2-2x+1) 2sin(x) (x^2+1)e^(-x^2)

Note: If a product includes one or more variables, always use an asterisk "*". For example, specify 2*\$A.

For a Maple question, you must always include an asterisk (*).

(x^2-2*x+1)*2*sin(x)*(x^2+1)*e^(-x^2)

The most common mistake is to forget parentheses "()". For example, the expression:

1/(x+1)

is different from:

1/x+1

which the system interprets as:

(1/x) + 1

Alternatively, you can use MathML expressions, which are supported for both display and content within the system.

## Variable Names

You can use any letter for a variable name.

Note: The grading system is case sensitive with respect to variable names. So if the correct answer is:

(t+1)^2

then the response

T^2 + 2T +1

t^2 + 2t +1

is correct.

Note: Be certain that the case of letters like x and X or v and V in answers match the case of the variables in questions.

## Operator and Function Syntax

For:

• Multiplication, use an asterisk "*". Alternatively, simply write:

• Two letters with a space (for example, x  y)

• A letter and a number with or without a space (for example, 2x or 2 x). Note that two letters without a space represents a single variable name.

• For Maple-graded questions, you must include an asterisk *, for example 2*x and not 2x, x*y and not xy, or  x*y and not x  y, which will be marked incorrect.

• Exponentiation, use the caret "^".

• Euler's Constant, 2.718..., use the letter e. (The exponential function is e^x.)  For Maple-graded questions, use the exp function: exp(1).

• Scientific notation, use the upper case letter E. (For example, 0.78 is 7.8E-2.)

• The trigonometric constant, 3.141..., use pi in Text Mode. For Maple-graded questions, use Pi. In the Symbol Editor Mode, enter ALT-P for pi or select it from the palette.

• Common mathematical functions, use the standard abbreviated names (for example, sin, cos, and tan).

• The arguments of trigonometric functions, remember they are measured in radians.

• The square root function, use sqrt(x). (Alternatively, use x^(1/2) or x^0.5.)  In 2-D Text Entry Mode the square root function is sqrt(x). (Alternatively, you can enter x^(1/2) or x^0.5.) In Symbol Mode, use the keyboard shortcut # for square root, or pick the symbol from the Tools Palette.

• The inverse trigonometric functions, use the standard abbreviated names (arcsin(x), arccos(x), and arctan(x)).

Note: The variable e should not be assigned as a global variable in Maple code. It can be used, however, as a local variable.