Grade 11 Gradient and Differentiation Practice

Revision activities / Core Mathematics study practice

Learning focus: Calculus. This original Grade 11 Core Mathematics exercise gives you a task, a suggested response and a follow-up challenge. It is classroom practice, not an official assessment paper.

Understand the idea

Differentiation gives a function describing the instantaneous rate of change. For a power xⁿ, its derivative is nxⁿ⁻¹ where the power rule applies.

Try the activity

For y = 3x² + 2x − 5, find dy/dx and the gradient when x = 2.

Attempt your response before opening the guidance. Show the steps, textual evidence or reasons that support your answer; a final answer alone may hide a misunderstanding.

Follow-up challenge

Calculate the gradient at x = −1. Explain why the derivative and the original function have different values at the same x.

Review your work

• Did you answer the question actually asked?
• Can you explain the method or evidence in your own words?
• What would you change if one condition in the task changed?

Use the suggested response to identify one correction, then attempt the task again without copying it. For an open-ended question, other well-supported answers may be reasonable. Ask your teacher to check interpretations or language forms where needed.

Continue Core Mathematics practice

• Linear Equation Word Problems
• Scale Drawing and Area Practice
• Mean Median and Probability Practice

Back to the subject guide · Check available member notes and downloads

Match this activity to the learning outcomes and sequence in your school’s current Grade 11 curriculum-design collection. This activity is a focused learning example, not a complete curriculum map.