Free Printable Derivative Graphs Worksheets for Grade 9

Derivative graphs are not a standard Grade 9 topic in most US curricula — they typically appear in pre-calculus or AP Calculus, usually in Grades 11 or 12. A Grade 9 student encountering this material is likely in an accelerated or advanced track. That context matters for instruction: these students may have strong algebra skills but limited experience thinking about slope as a dynamic, continuous quantity, so grounding derivative graphs in rate-of-change language they already know helps bridge the gap.

Because Grade 9 students are unlikely to have formal calculus background, lead with slope as the entry point. Have students calculate average rates of change over shrinking intervals on a polynomial function, then ask what value those rates seem to approach — that intuition is the derivative, even before the notation. Once they can describe slope behavior at different points on a curve, sketching the derivative graph becomes a matter of plotting those slope values, which connects to graphing skills they already have.

Start with simple polynomial functions where the slope behavior is easy to reason about — parabolas are ideal, since students can see that the slope goes from negative to zero to positive (or vice versa) and can sketch a linear derivative graph from that. Wayground's derivative graphs worksheets include problems on sketching f′ from f and identifying critical points and intervals of increase or decrease, which are the right building blocks at this level before moving to more complex functions.

The most persistent one is conflating the height of f with the value of f′ — students mark f′ as positive wherever f is above the x-axis rather than wherever f has a positive slope. At Grade 9, this confusion is especially common because students are still solidifying the idea that a derivative measures change, not position. A quick diagnostic: ask students to sketch f′ for a decreasing function that stays entirely above the x-axis. If they draw a positive f′, the height-vs-slope confusion is the issue to address.

The worksheets come with a complete answer key, making them practical for homework or independent practice without extra prep. You can assign them as a digital quiz on Wayground so students get immediate feedback, or print the PDF for paper-based work — a good option if you want students working through graphs by hand, which reinforces the visual reasoning these problems are designed to build.

Derivative graph problems are visually demanding, so font size and spacing matter more than on a typical algebra worksheet. Wayground lets you generate alternate versions of the same worksheet with larger font sizes or wider spacing, and apply a dyslexia-friendly font for students who need it. For students who find the multi-step analysis overwhelming, the reduced answer choices accommodation narrows the decision space so they can focus on reading the graph rather than managing too many options at once.