Level 3 Integration Walkthrough
2022 NCEA Level 3 Integration Question 1(b)
2022 Paper
Question
The graph of the function \(y=f(x)\) below is symmetrical about the \(y\)-axis. The shaded areas are given.
The diagram is shown in its initial state. JavaScript adds any interactive controls and later walkthrough visuals.
First walkthrough idea
Focus to try first
Use the graph's symmetry, then count regions above the axis as positive and below the axis as negative.
Step 1
Use the symmetry
The graph is even-looking about the \(y\)-axis, so each shaded region has a matching partner on the other side.
Show the first step’s working
The central shaded region labelled \(4.4\) appears on both sides of the \(y\)-axis.
The lower shaded region labelled \(1.2\) also appears on both sides of the \(y\)-axis.
Walkthrough overview
What this question practises
This 2022 walkthrough is part of AS91579 — Apply integration methods in solving problems.
Method: Using symmetry and signed area on a graph with no formula.
This is Question 1(b) from the 2022 NCEA Level 3 Integration paper for AS91579 — Apply integration 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 AS91579.
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Learning summary
Review the method, not only the answer
This walkthrough helps you practise using symmetry and signed area on a graph with no formula. Use the hints to plan the method, then repeat the question without hints and check each step.
Common mistake to avoid
Check intersections, signs, and whether the question asks for signed area or total geometric area.