Merced College; Don Power

 

Lab 3: Typing Math Expressions on a Computer/Calculator          NAME________________

 

The purpose of this lab is to practice the placement of parentheses in algebraic expressions.

We will use the computer program MAPLE 10 CLASSIC WORKSHEET for this lab, because MAPLE will translate an expression that you type (using parentheses) into standard algebraic notation.

 

Before starting, there are several things you need to know:

  1. MAPLE’s multiplication symbol is an asterisk, and you must always include it (it is never understood”) This can be subtle and tricky:
    For example, 3x+1 will be typed as 3*x+1, and 4(x+5) is typed as 4*(x+5);
  2. Exponents are typed using the ^ symbol.  For example, x2 is typed as x^2;
  3. You need to type a semicolon (;) at the end of each MAPLE command.
  4. Always compare the MAPLE output with your input.  If it is wrong, go back and fix your input.
  5. MAPLE may simplify or rearrange your input.  As long as it is equivalent to the input, it is OK.
    For example, (10*x+12)/2; gives an output of 5x + 6
  6. You normally need parentheses around:
    a.  Entire numerator of a fraction unless it is a single number or letter.  See the previous example.
    b.  Entire denominator of a fraction unless it is a single number or letter.
          Example   is typed as 4 / (2*x);
    c.  Entire exponent, unless it is a single number or letter.
          Example:  25x is typed as 2^(5*x);
    d.  Entire radicand, where radicals are involved, unless it is a single number or letter.
          Example:   is typed as sqrt(3*x+4); or (3*x+4)^(1/2);
  7. Do not insert parentheses unless you really need them.  Extra parentheses are confusing.

 

First, open the computer program MAPLE 10 CLASSIC WORKSHEET.  Your screen should look something like this (although this was from a previous version of MAPLE)

 

The symbol > is the prompt and the vertical bar is the cursor.

 

EXAMPLE:  Type  using MAPLE.

Notice the asterisks, the semicolon, the parentheses for the numerator, and the parentheses for the denominator.

 

            The result is slightly rearranged, but it is equivalent to the input -- except for the typographical error in the denominator.

Did MAPLE give you what you wanted?
      If not, move the cursor back to the expression you typed and edit it until it is correct.

(In this case, change the "x" to a "c")
      Press ENTER  (The cursor may be anywhere in the expression when you press ENTER).

 

 

 

 

ASSIGNMENT:  Type the following expressions using MAPLE:

 

1.           Remember to enclose the numerator in parentheses.
                        Also remember the multiplication symbol * between the 3 and the x.

 

2.         Use the caret symbol ^ for the exponent.

                        Think!  What would happen if you didn't parentheses around the 5-3x2?

                        Think!  What would happen if you didn't parentheses around the 4*z?

 

3.     To get π, type Pi (it must be capitalized).

                  All functions require parentheses, so type sin(Pi/6); (with the entire  in parentheses)

                  Your answer should be 1/2.

                  Experiment:  What happens if you type p as pi instead of Pi?

Try checking with a calculator in radian mode:  find p/6 (using the p key), then find the sine of than number with the "sin" key.

 

4.         This is a special notation that means that you square the result of sin(p/6)

                        I suggest you first type sin(Pi/6), then insert another parenthesis around the whole expression, and then type in the exponent:  ^2

That is, type:  (sin ())^2.
      If you do not get 1/4, your parentheses are probably wrong.

 

Now that you did it the hard way, I can tell you that Maple (and many calculators) let you omit the extra parentheses; you just have to type the exponent outside the parenthesis, like this:   sin(p/6)^2

 

5.     There are two ways to show square roots:  use sqrt(  )  for this radical.
                              Close the square root after the 9, not after the 3x.

 

6.              This time, do not type "sqrt" for the radical (although that would work).

Instead, use the rational exponent 1/2 for the radical:  type  (5*x-3)^(1/2)
Notice that the 1/2 has to be in parentheses to get the order of operations right.

 

7.     For radicals other than square roots, use rational exponents; so enter

                              Remember that the entire exponent must be inside ______________ (like the                                         previous problem).

 

8.     Expect MAPLE to simplify this one for you.

 

9.     If you do this correctly, MAPLE will simplify it , and you will not get a fraction.

 

10.    Expect MAPLE to simplify the coefficients.  You'll need three *'s here.

But no machine is perfect:  MAPLE may give you unnecessary absolute value brackets, and you won’t be able to get rid of them.

 

11.    Toughie!  Notice that MAPLE simplifies this part way.

                        You might try

                              a.  typing the fraction (x-1) / (x2-3x+2) on one line,

                              b.  typing the second fraction  x / (x-2) on a second line,

                              c.  typing the blank framework for a fraction on a third line:     (   ) / (   );

                              d.  and then copying and pasting the fractions (from a and b) into the framework.

 

12.  After getting a correct result for #11, surround the entire expression with an extra set of parentheses, and then type the word factor in front of it.  Now the result should be fully simplified.

 

13.  Select Insert..Text Input, and type your name.

 

Print your worksheet and turn it in.

 

Return to:  Merced College; Don Power               Updated 07/12/06 by Don Power