Level 2 Calculus Walkthrough
2025 NCEA Level 2 Calculus Question 1(a)
2025 Paper — Differentiate and evaluate the gradient
Question
Use calculus to find the gradient of the function at \(x=-\frac{1}{2}\).
First walkthrough idea
Tip to try first
Differentiate each term separately using the power rule, and remember the derivative of a constant is 0.
Step 1
Identify the differentiation method
Reveal the explanation and working for this step.
Show the first step’s working
Differentiate the polynomial term by term using the power rule.
Key result
This is a polynomial, so differentiating term by term with the power rule is the cleanest start.
Walkthrough overview
What this question practises
This 2025 walkthrough is part of AS91262 — Apply calculus methods in solving problems.
Method: Using the power rule term by term and evaluating the gradient at a point.
This is Question 1(a) from the 2025 NCEA Level 2 Calculus paper for AS91262 — Apply calculus methods in solving problems. Use the guided hints to practise the method before revealing the full working.
Calc.nz is an independent learning resource. Compare questions, diagrams, and assessment information with the official NZQA resources for AS91262.
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Learning summary
Review the method, not only the answer
This walkthrough helps you practise using the power rule term by term and evaluating the gradient at a point. Use the hints to plan the method, then repeat the question without hints and check each step.
Common mistake to avoid
Check each step against the original condition, preserve signs and restrictions, and confirm that the final result answers the question asked.