Small practice
brighter futures.
Checking sign-in status
Menu

Calculus practice

Drawing and Identifying Slope Fields worksheets

Draw exact direction fields or recover a degree-at-most-two differential equation from 49 slope segments and six exact readings.

Ready-made English PDF · fixed settings

Worksheet · LetterWorksheet · A4
Customize worksheet ↓
With answer key

Customization below makes a separate PDF.

First page of the drawing and identifying slope fields worksheets printable worksheetOpen full-size sample (first page)

Fixed English ready-made files. Custom settings below apply only to the configured PDF.

Ready to print

Start with a ready-made worksheet

Sketch a direction field or identify its polynomial differential equation using the six exact slope readings.

Download the practice pages alone, or include a separate answer key or teacher model. Longer activities may use more than one page.

US Letter

Student worksheetWorksheet with answers

A4

Student worksheetWorksheet with answers
Customize this worksheet

Paper sizes and printing help · More calculus activities

Read local directions

Each short segment is centered at a lattice point and has slope F(x,y). The axes use equal scale, so horizontal, rising, falling, and steep directions remain visually honest.

Learning objective

What this activity builds

Connect dy/dx = F(x,y) to local segment directions and use exact sampled slopes to identify a bounded polynomial field.

Worked example

If F(0,0)=1 and F(1,0)=3, what do the field segments show?

The segment at (0,0) has slope 1 and the segment at (1,0) has slope 3.

A slope field records the derivative at each point. Exact readings supplement the picture so identification does not depend on visual guessing.

Teaching notes

Make the practice count

  • Keep every short segment centered at its lattice point.
  • Positive slopes rise left-to-right; negative slopes fall; zero slopes are horizontal.
  • In identify mode, use the declared basis x^2, xy, y^2, x, y, 1 and all six readings.

Make it yours

Customize the practice

Choose your options, update the preview, then download the exact same pages.

Choose 4 or 8 free-response tasks. Sketch mode supplies equations and blank lattice grids; identify mode supplies complete fields, six exact readings, and a blank equation response.

Worksheet settings

Page note and reproducible seed

The same settings and seed make the same questions. Shared links include your page note; leave personal information out.

Configured PDF · Drawing and Identifying Slope Fields · US Letter

Preview ready. Download includes these exact pages.

2 student pages
Enlarged pages scroll. PDF size stays the same.
Math SheetNameScoreTeacherDateDrawing and Identifying Slope FieldsSketch the direction field for each differential equation at all 49 marked lattice points.A slope field shows local tangent directions, not a solution curve.1.dydx=-2-3-3-2-2-1-1112233xy2.dydx=-2·y-3-3-2-2-1-1112233xy3.dydx=-2·x2-2·x·y-1·y2+2·x-2·y+1-3-3-2-2-1-1112233xy4.dydx=x-2·y-2-3-3-2-2-1-1112233xymath-sheet.comPage 1 of 2
Math SheetNameScoreTeacherDateDrawing and Identifying Slope FieldsSketch the direction field for each differential equation at all 49 marked lattice points.A slope field shows local tangent directions, not a solution curve.5.dydx=-1·x·y-3-3-2-2-1-1112233xy6.dydx=-1·y2+1-3-3-2-2-1-1112233xy7.dydx=x-3-3-2-2-1-1112233xy8.dydx=-1·x2-1·x-3-3-2-2-1-1112233xymath-sheet.comPage 2 of 2

A useful next step

Related activities

First page preview: Solving Separable Equations worksheets

Calculus

Solving Separable Equations worksheets

Solve genuinely y-dependent first-order separable equations with exact implicit solutions, connected-domain restrictions, and restored equilibrium solutions.

Preview and download