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) |
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:
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