Enter symbolic math answers

Updated 29 Aug 2024

Some questions ask you to enter a symbolic math answer without also entering a unit. You can answer these questions on a computer, tablet, or smartphone. (Alternate instructions for Value with Units answer boxes)

These instructions apply to entering symbolic math answers.

  • Toolbar for these questions on a computer:

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  • Toolbar for these questions on a mobile device:

 

Enter answers on a computer

Enter answers on mobile device*
(tablet or smartphone)

Toolbar

  • Use the Templates menu for math formats like exponent and fraction.
  • Use the Symbols menu for Greek letter, hbar, and EMF symbols.
  • Mastering Engineering only: Choose Slope/Displacement menu and Vector button, as needed.
  • To undo, redo, and reset the answer box to its original state: Use toolbar buttons.
  • To view or print keyboard shortcuts or Help topic: Click buttons on the right.
  • To begin, tap in an answer box for the toolbar to appear below.
  • Choose buttons from the Letters, Numeric, Templates, and Symbols menus to compose your answer.
  • Mastering Engineering only: Choose Slope/Displacement menu and Vector button, as needed.
  • To undo, redo, and reset the answer box to its original state: Use toolbar buttons on the right.

Keyboard for letters and numbers

  • Use your physical keyboard to enter letters, numbers, and other characters.
  • For more details, see next section "Enter Symbolic math answers".
  • Choose either the Letters menu or the Numeric menu for alphanumeric characters and some math symbols.
  • To switch between lowercase and uppercase keys: Choose the arrow button from the Letters menu.

Keyboard shortcuts for special formats (like subscript)
  • It can be faster to use keyboard shortcuts instead of the Templates menu to insert special formats.
  • For keyboard shortcuts that begin with \ (backslash), choose \ from the Letters menu.

Cursor control in your answer

  • Use your keyboard arrow keys (, , , ) to move the cursor in your answer or between Value and Units answer boxes.
  • It can be easier to use arrow keys instead of a mouse or other input device to reposition your cursor.
  • Use your finger or other input device to position the cursor in an answer or in the other answer box.
  • For finer cursor control on a phone: Enlarge your view of the answer box before moving the cursor.
  • If cursor control on your phone is challenging: Consider using your computer or a tablet.


Enter symbolic math answers

Follow these guidelines when entering symbolic math answers.

  • Enter * for the multiplication operator. Do NOT use the letter x. Enter multiplication explicitly, that is, type 2*a*b, not 2ab. Use scientific notation, not e (which Mastering evaluates as the constant 2.718...) or E. For example, enter 1.23*10^5 instead of 1.23e+5 or 1.23E+5.

  • Use commas only as separators between multiple expressions within a single answer box, such as "1999,2009". Do NOT use commas in any large number, such as 32000.

  • No spaces. The answer box does not allow you to enter spaces.

  • Order of evaluation for grading is provided below.
    1. The deepest nested terms in parentheses are evaluated first.
    2. Exponents are evaluated next. Exponents are always evaluated from right to left. For example, 3^2^2 is evaluated as 3^(2^2), but 3/2/2 is evaluated as (3/2)/2.
    3. Multiplication and division are evaluated next, from left to right.
    4. Addition and subtraction are evaluated last, from left to right.

    Also, if a question asks for several answers in a particular order, such as numeric order, your answers must be in that order. Mastering uses string matching to grade such answers.

  • Parentheses to distinguish some subscripts and exponents: Add parentheses around a subscript or exponent when it’s immediately followed by another subscript or exponent that should NOT be applied to the earlier subscript or exponent. For example, enter 2*(v_0)^2 instead of 2*v_0^2, if you want to square v_0, where _ means 0 is a subscript of v.

    See also the section below about how to “Discontinue entering special format values (like exponent) in your answer”.

See also previous section for notes about order of evaluation and using parentheses for some subscripts and exponents.

To enter...

Choose this from the  Templates menu:

Or, enter this keyboard shortcut:

Examples/Notes

Instead of pressing or below, you can also reposition your cursor.

Exponent

(Superscript)

exponent (superscript) template format

^
(caret)

To enter , either:

  • Enter x^32
  • Enter x, choose exponent (superscript) template format, and enter 3

 

Subscript

subscript template format

_
(underbar)

To enter , either:

  • Enter T_i
  • Enter T, choose subscript template format, and enter i

Fraction

fraction template format

/

To enter , either:

  • Enter 2/3 or /23
  • Choose fraction template format, enter 2 , press , and enter 3

To move between the top and bottom parts of a fraction: Use the arrow keys from your computer keyboard or reposition your cursor using an input device.

Square root

square root template format

\sqrt


To enter square root of x + y, either:

  • Enter \sqrtx+y
  • Choose square root template format and enter x+y

Nth root

nth root template format

\nrt

To enter 3rd root of a, either:

  • Enter \nrt3chem_ee_r_arrow_smalla
  • Choose nth root template format , enter a, press left arrow keyleft arrow key, and then enter 3

Vector

nth root template format

 

Mastering Engineering:Choose vec button from toolbar.

\vec

To enter math_ee_vec_sample, either:

  • Enter \vecF
  • Choose nth root template format and enter F
    Mastering Engineering: Choose vec button from toolbar and enter F

Unit vector

(This option is not applicable for Mastering Engineering)

unit vector template format (non-engineering)

\hat

To specify unit vector of u, either:

  • Enter \hatu
  • Choose unit vector template format (non-engineering) and enter u

Absolute value

absolute value template format

|

 

This shortcut inserts both absolute value signs.

To enter math_ee_abs_sample, either:

  • Enter |y
  • Choose absolute value template format and type y

Polar form complex number

(Available in Mastering Engineering only.)

polar form complex number template format

cis

To enter 20polar form symbol30, either:

  • Type 20cis(30)
  • Choose polar form complex number template format, enter 20right arrow key30

Complex conjugate

(Available in Mastering Engineering only.)

complex conjugate template format

conj

To enter (2+3j)*, either:

  • Type conj(2+3j)
  • Choose complex conjugate template format and enter 2+3j

Scientific notation

* (asterisk for multiplication dot)

^
(caret for exponent)

To enter 5.2*103, either:

  • Enter 5.2*10^3
  • Choose  , enter 5.2, and enter 3 in the exponent format.

To edit the provided "10": Press the right arrow key to position your cursor, and then delete or add digits using your keyboard. You can also delete by choosing Delete.

 

To enter...

Choose this format from the Symbols menu

Or, enter this keyboard shortcut

alpha

alpha symbol (lowercase Greek letter)

\alpha

beta

beta symbol (lowercase Greek letter)

\beta

gamma

gamma symbol (lowercase Greek letter)

\gamma

Delta, delta

Delta symbol (uppercase Greek letter), delta symbol (lowercase Greek letter)

\Delta, \delta

epsilon

epsilon symbol (lowercase Greek letter)

\epsilon

eta

eta symbol (Greek lowercase letter)

\eta

theta

theta symbol (lowercase Greek letter)

\theta

kappa

kappa symbol (lowercase Greek letter)

\kappa

lambda

lambda symbol (lowercase Greek letter)

\lambda

mu

mu symbol (lowercase Greek letter)

\mu

nu

nu (lowercase Greek letter)

\nu

pi

pi symbol (lowercase Greek letter)

\pi

rho

rho symbol (lowercase Greek letter)

\rho

Sigma, sigma

Sigma symbol (uppercase Greek letter), sigma symbol (lowercase Greek letter)

\Sigma, \sigma

tau

tau symbol (lowercase Greek letter)

\tau

phi

phi symbol (lowercase Greek letter)

\phi

chi

chi symbol (lowercase Greek letter)

\chi

Psi, psi

Psi symbol (uppercase Greek character), psi symbol (lowercase Greek letter)

\Psi, \psi

Omega, omega

Omega symbol (uppercase Greek letter), omega symbol (lowercase Greek letter)

\Omega, \omega

EMF

EMF symbol

\EMF

hbar

hbar symbol

\hbar

 

Displacement arrows

Select the Slope/Displacement menu from the toolbar, and then choose the appropriate displacement arrow. (You can't get these symbols from your keyboard.)

  • Left displacement
  • Right displacement
  • Upward displacement
  • Downward displacement
  • Clockwise slope
  • Counterclockwise slope


Vector

Select Vector from the toolbar and enter any alphanumeric character to express the vector. (Your vector entry appears in bold).

Enter special functions

Answer using radians unless a question specifies to answer in degrees.


Work with or edit symbolic answers

The way to move the cursor in an answer depends on whether you're working with a physical or virtual keyboard.

  • Computer users: Use your keyboard arrow keys (, , , ) to move the cursor in your answer. Note that the left and right arrow keys can move the cursor vertically within an expression. You can also use a mouse or other input device to reposition your cursor in an answer, but using the arrow keys may be easier.
  • Smartphone and tablet users without a physical keyboard: Use your finger or other input device to position the cursor in your answer. For finer cursor control on a phone, enlarge your view of the answer box before moving the cursor. If moving the cursor on your phone is a challenge: Consider completing the question on your computer or tablet.

 

When you finish entering a value in a special format (for example, the numerator of a fraction), you need to move the cursor outside of the format area. The way you do this depends on whether you're working with a physical or virtual keyboard.

  • Computer users: Use your keyboard arrow keys (, , , ) to move outside of a special format area in your answer. You can also use a mouse or other input device to reposition your cursor within or outside of a special format, but using the arrow keys may be easier.
  • Smartphone and tablet users without a physical keyboard: Use your finger or other input device to position your cursor outside of any special format area. For finer cursor control on a phone, enlarge your view of the answer box before moving the cursor. If moving the cursor on your phone is a challenge: Consider completing the question on a computer or tablet.

 

Edit

Instructions

Undo

  • Select  undo to undo your previous actions in reverse order—one action per click (or tap/touch, on a mobile device).
  • Alternatively, press Ctrl+Z (Windows) or Command-Z (Mac OS) from your computer keyboard.

Redo

  • Select  redo to redo the previous action.
  • Alternatively, press Ctrl+Y (Windows) or Command-Y (Mac OS) from your computer keyboard.

Reset

  • Select  reset to clear your workspace.
  • If you want to start over: This is the easiest way!

Delete

  •  Delete button: Deletes individual characters from right to left. You can also use the Delete key on your computer keyboard.
    For a specially formatted expression, such as a fraction: Press Delete once to select the item, and then press Delete again to delete it.
  • Backspace key (on a keyboard): Deletes individual characters from right to left.
    For a specially formatted expression, such as a fraction: Press Backspace once to select the item, and then press Backspace again to delete it.
  • Keyboard shortcut to cut: You can use standard keyboard shortcuts (Ctrl+X for Windows, Command-X for Mac OS) to cut an answer or parts of an answer. See Step 1 below for details about selecting characters.

Copy and paste

These instructions apply when using a computer.

  1. Select the part of the expression you want to copy.

    2. To select individual characters or specially formatted expressions (such as a fraction): Drag your input device or hold down the Shift key and press either the left or right arrow key. Continue to press the arrow key for each additional character or format.

  2. Copy using a standard keyboard shortcut: Ctrl+C (Windows) or Command-C (Mac OS).
  3. Paste using a standard keyboard shortcut: Ctrl+V (Windows) and Command-V (Mac OS).


More about symbolic math answers

Open the Introduction to Mastering assignment and select the Introduction to Symbolic Answers item. This assignment provides practice items for different kinds of questions. You can usually return to this assignment anytime during the course, even after its due date. If you completed this assignment, you can usually rework its items for practice.

Select  Help from the toolbar then choose Enter symbolic math (no Units answer box) on the page that opens.

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Select  Keyboard shortcuts for instructions on answering with your keyboard.