Writing Mathematical Formulas in OPTIMATH

Many questions in OPTIMATH assignments ask you to type in a mathematical formula or expression. You can type in formulas using standard mathematical notation, using the same type of notation as you would use on a calculator. Thus, the computer will understand formulas like:

x^2-2*x+1 2*sqrt(x) (x^2+1)*e^(-x^2) 3*sin(4/x)

Operations: Just like on a calculator, use +, -, *, and / for addition, subtraction, multiplication, and division, and use the caret symbol ^ for exponents. However, the use of the asterisk * for multiplication is optional, so expressions with a number and letter together, such as 2x, will be graded correctly.

Use of parentheses:The most common mistake people make is to forget to put in enough parentheses to make it clear what they mean. For example, if you meant to type 1/(x+1) and instead entered 1/x+1, the system would interpret that as(1/x) + 1 and grade it as incorrect. In addition, you should always place the argument of a function in parentheses. For example, you should type sqrt(3x), not sqrt 3x.

Warning: The older TI calculators (82, 85, and 86) will allow you to enter sqrt 3x and sin x/2 without parentheses. This is not standard mathematical notation, and in fact the newer TI calculators (83, 89, and 92) use the standard convention and force you to put arguments of functions in parentheses, just as you should in OPTIMATH.

Variable Names: You can use any letter for a variable name, but you should always use the same letter that is used in the question. If the question asks you to expand (t+1)^2, then the answer x^2+2x+1 will be graded as incorrect.

Warning: The system is also case sensitive. So if the question asks for (t+1)^2, then the answer T^2+2T+1 will be graded as incorrect (but t^2+2t+1 will be okay). Take care with letters like x and X or v and V that your variables are the same case as the variable in the question.

Mathematical functions and constants: Use the letter e for 2.718... (so that the exponential function is e^x), and write pi for 3.14....

The square root function is sqrt(x) (or you can just type x^(1/2) or x^0.5 instead). For other roots, use rational exponents. The names for trigonometric functions (sin, cos, etc.) are just what you would expect. Trigonometric functions are all set to work in radians. The inverse trig functions are arcsin(x), arccos(x), and arctan(x).

The exponential function can be entered using either e^x or exp(x). The natural logarithm function is ln(x), and the common logarithm is log(x).


Summary of operations, numbers, and functions:

Arithmetic
+ addition
- subtraction
* multiplication
/ division
^ exponentiation
Numbers and Constants
e 2.71828...
pi 3.14159...
i complex number i
Trig Functions
sin sine
cos cosine
tan tangent
sec secant
csc cosecant
cot cotangent
arcsin
or asin
inverse sine
arccos
or acos
inverse cosine
arctan
or atan
inverse tangent
Other Functions
sqrt square root
abs absolute value
ln natural logarithm
log common logarithm
e^x or exp   exponential function
cis   cis(x)=cos(x)+i*sin(x)
fact   factorial: fact(n)=n!
sinh, cosh,
tanh, coth,
sech, csch
  hyperbolic functions
asinh, acosh,
atanh, acoth,
asech, acsch
  inverse hyperbolic functions