Worked solutions.

Watch a problem solved, then try it yourself in the editor.

To use The Math App, watch a solution example, then choose one and work it in the editor. The Examples page explains each feature.

Geometry

Right triangle

Insert a Drawing after an equation. Copy equations onto a Drawing.
Square Root of both sides. Annotate with suggestions. Replace terms with values and solve for c.
Ctrl-R (Auto Calculate/Replace) and mark the answer. Copy the answer to the drawing.
Go back using Ctrl-D to re-add steps for clarity and group rows for hiding the details.

Step-by-step how-tos (4 short videos)

Step 1
- To Insert a Drawing after the selected row Right-Click the row and select the [Drawing] button.
- To insert a shape (Right Triangle) into the drawing, Right-Click the drawing and select the [Right Triangle] button.
- Adjust the size and location of the shape with the corner and center cursors.
Step 2
- To Square Root of both sides, Right-Click the equals sign of the desired row. This selects the whole row and opens the context menu.
- Selecting the [square-root] button will show the terms on both sides square-rooted.
- Paste the row in by touching the equation.
- Solve for c by Select-Delete which red-lines the terms.
- Copy/paste the given values for the terms using Ctrl-C/Ctrl-V. Use Select-Delete and Ctrl-D to clean up the equation.
Step 3
- To calculate the result, select the terms and use Ctrl-R which red-lines the terms and inserts the calculated result.
- Mark the answer (we use green here) by Right-Clicking the side and selecting the [Green] button.
- To copy the answer to the drawing, Right-Click on the answer row and touch the drawing to label the hypotenuse. Color that cell the same way as above.
Step 4
- Go back and show the cleaned up row. Touch the row to select it and Ctrl-D
  to duplicate the row and remove red-lined terms.
- For clarity select the rows showing the details then click the [Group] on the side button stack. Hide the rows by clicking the [B-] label. To show the group, click the [B+].

Physics

Conversion

Create and multiply an identity fraction using Intelligent Notes.
Duplicate an equation using Ctrl-D.
Edit the equation and cancel terms.
Duplicate an equation using Ctrl-D.
Calculate and Replace using Ctrl-R.
Duplicate an equation using Ctrl-D.
Color an equation side.

Step-by-step how-tos (2 short videos)

Step 1
- To create and multiply an identity fraction given an equation, Right-Click on the equals sign of the equation. This opens the context menu with the row selected (in blue).
- Select the [X/Y] and [(...)] buttons to create a fraction that equals one, in parentheses.
- Note that clicking the button again will flip the X/Y. When the proper units are in the numerator/denominator, click the right side of the equation to paste in (multiply) the fraction.
- Use Intelligent Notes by Right-Clicking in the note field. Suggestions based on previous usage will appear. Select the desired note, including the Arrow button if an arrow to the source is desired.
- Duplicate the equation using Ctrl-D for the next steps.
Step 2
- Edit the equation using Shift-Arrow-Delete to select and red-line the terms to be canceled.
- Duplicate the equation using Ctrl-D, which will drop the red-lined terms.
- Select the numerical terms using Shift-Home and use Ctrl-R to Calculate and Replace the terms.
- Duplicate the equation using Ctrl-D.
- Color an equation side by Right-Clicking the side and selecting the [Green] button. This will set the cell to green, which is used for the Answer.
This step’s video is a 3-second clip that is in the Wix trash. Check it is the right one.

Trigonometry

Unit circle

Label the angles of a unit circle in both degrees and radians.
Use the Keyboard's paste feature:
Opens a context menu with the chosen key if there is not a current Cursor.
Touch will then insert the key at that point which works well for labeling drawings.
Shift-Touch is used to paste multiple copies of various labels. Note that releasing the Shift on the last paste will clear the context menu.
Use Ctrl-C and Shift-Touch to paste multiple copies of various labels.

Chemistry

Specialty keyboard

Create and use identity equations using the Chemistry Keyboard.
Using Ctrl-D, Duplicate Row and Ctrl-R Integrated Calculator.
Use a term previously calculated and multiply it via paste.
Use Shift-Arrow-Delete to red-line and Ctrl-R to calculate the result.

Step-by-step how-tos (3 short videos)

Step 1
- Use the Right-Click context menu to select and paste 3 and 9.
- Open the Chemistry keyboard via the [Keyboard] button on the left of the top menu stack.
- Clicking the element, [CL] in this case, creates a series of keys using [CL]'s atomic numbers. Note that clicking the element again flips the fraction keys to get the desired numerator/denominator.
- Right-Click in the Notes field to open the Notes Context menu with suggestions based on previous steps.
- In this case click the [Arrow] button next to "Use this: 3" and again with "Use this: 9"
- This will insert arrows to the source of those numbers. This type of detail can greatly help students new to the material.
Step 2
- Use Ctrl-D to duplicate the row. Use Shift-Arrow-Delete to red-line the units that cancel.
- Use Ctrl-D again to duplicate the row dropping the red-lined terms.
- Select the numeric terms and use Ctrl-R (Auto Calculate/Replace) to calculate and red-line the terms and insert the result.
- Use Ctrl-D again to duplicate the row dropping the red-lined terms and Right-Click the side and select the [Green] button to mark the side as the partial answer.
Step 3
- Select the detailed work rows and click the [Group] button at the top of the side button stack.
  Then hide the group to focus on the second part of the solution.
- For the second part of the solution, duplicate the original question. Right-Click the green solution side above to select it, select the [(..)] button to wrap it in parentheses.
  Paste (multiply) it to the equation to cancel the mol terms.
  Use Shift-Arrow-Delete to red-line those units and Ctrl-D to duplicate and clean up the row.
- Select numeric terms using Shift-Home and use Ctrl-R to calculate and red-line the terms and insert the result.
- Right-Click and select the [Green] button to mark as answer.

Algebra

System of equations

Multiply to both sides from Selection. Use Intelligent Notes to add notes.
Calculate and Replace using Ctrl-R and Duplicate row using Ctrl-D.
Highlight an equation for later use.
Add 2 equations and solve by dividing both sides.
Copy rows, group and hide rows.
Replace terms with value.
Insert a Drawing, Grid and graph the 2 equations to verify the answers.

Step-by-step how-tos (5 short videos)

Step 1Step text missing on the live site (it reads “Usingial.”). Write this step.
Step 2This text is a copy of a Chemistry step on the live site. Write the System of equations version.
Step 3Step text missing on the live site (it reads “Select t”). Write this step.
Step 4Step text missing on the live site (it reads “Select t”). Write this step.
Step 5Step text missing on the live site (it reads “Select t”). Write this step.

Calculus

Integration by parts

This example has zero writing, so it eliminates mistakes that occur during transcription.
Use selection copy/paste to create the parts of the integration by parts example.
Use Font Colors to make it clear, both what should be done, and what was done to help with review.
Intelligent-Notes is used to add Note Shapes and comments to reference where terms originated.
Near the end there is a good example of using The Math App to factor complex equations with minimal errors.

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