Writing Mathematical Formulas
Many questions in these tests ask you to type in a mathematical formula or expression. You can type in formulas using standard mathematical notation and, if it looks right, the computer should understand it. You should use the same type of notation as you would use on a calculator. Thus, the computer will understand formulas like:
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 wrong. In addition, you should always place the argument of a function in parentheses. For example, you should type sqrt(3x), not sqrt 3x (this would be interpreted as (sqrt(3))*x. For another example, you should type sin(x/2), not sin x/2 (this would be interpreted as (sin(x))/2).
x^2-2x+1 2sin(x) (x^2+1)e^(-x^2)
Warning: The lower level TI calculators (86 and below) will allow you to enter sqrt 3x and sin x/2 without parentheses. This is not standard mathematical notation, and in fact the higher level TI calculators (89 and 92) use the standard convention and force you to put arguments of function in parentheses, just as you should on MapleTA.
So what can you do to prevent making accidental errors like this?
Answer: Use the Preview Button! Beside every question that you need to enter a formula into you'll see a button marked Preview. Once you've typed in your answer, press the button and the computer will display what it thinks you entered, in standard mathematical layout. It'll be really easy to spot any mistakes you made! (Please be patient the first time you press the button - the computer may be a little slow as it has to download a large file. But it'll run fast after the first experience.)
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 for (t+1)^2 then the answer (x^2 + 2x +1) will be graded wrong.
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 wrong (but t^2 + 2t +1 will be OK). 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.
Hints: You can type an asterisk (ie "*") for multiplication, or just write two letters or a letter and a number together (like "2x").Use the caret, "^" for exponentiation, and the letter "e" for 2.718... (so that the exponential function is "e^x"). Write pi for 3.14....
The names for common mathematical functions (sin, cos, etc.) are just what you would expect. The square root function is sqrt(x) (or you can just type "x^(1/2)" or "x^0.5" instead). The inverse trig functions are arcsin(x), arccos(x), and arctan(x). Trigonometric functions are all set to work in radians.
The functions and operations you can use:
Arithmetic + Addition - Subtraction * Multiplication / Division ^ Exponentiation
Numbers e 2.71828... pi 3.14159... 2.9E8 Scientific notation: 290,000,000
Trig Functions sin Sine cos Cosine tan Tangent arcsin Inverse sine arccos Inverse cosine arctan Inverse tangent sec Secant csc Cosecant cot Cotangent
Functions sqrt Square root log Logarithm base 10 ln Natural logarithm abs Absolute value function Important: Different types of questions require different forms of answer
Below each answer box there is an instruction that tells you in what form you should give your answer. These are
- This question accepts numbers in decimal form or scientific notation.
- This question accepts numbers or formulas.
- This question accepts equations. E.g. y-2 = 5(x-4)+1.
- This question accepts answers that are in a form like "(-1,3)" or "(3,7,3z)".
The entries can be numbers or formulas.- This question accepts lists of terms, separated by commas ","
The entries can be numbers or formulas.
The entriesmust be given in the correct order.- This question accepts lists of numbers or formulas separated by semicolons.
E.g. "2; 4; 6" or "x+1; x-1".
The order of the list doesn't matter but be sure to separate the terms with semicolons.You must pay attention to these instructions!!! For example, numbers are just that: 1, 3.4, 0.048875, etc. Formulas contain math operators: 1/2, sqrt(2), (x-y)/12, etc. Equations will always contain an equals sign (and nothing else will have an equals sign). So if you are asked to find the value of x, and you are asked for a number or formula, then 12/7 is correct, while x=12/7 is incorrect.
Be sure to mind the difference between commas and semicolons.