Non-Linear Inequalities in MYP Year 5 Standard Maths

Q: How do students lose marks on sign analysis questions?

By trying to 'cross-multiply' rational inequalities the way they would an equation. Multiplying (x-1)/(x+2) 0, students write 2 3.

Learn to solve quadratic and polynomial inequalities using sign diagrams in MYP Year 5 Standard Maths. Includes common errors and exam strategies.

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Non-Linear Inequalities

180 min100 marks

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Moving Beyond Linear Inequalities

Non-linear inequalities involve expressions where the variable appears with a power greater than one — most commonly quadratic. For example: x² − 3x − 4 > 0. Because the expression is not linear, the approach to solving it must account for how the sign of the expression changes across different intervals.

The Sign Diagram Method

A sign diagram (also called a sign chart) is the standard tool for solving non-linear inequalities in MYP Year 5.

Step-by-Step Process

Rearrange the inequality so one side equals zero.
Factorise the expression to identify its roots (critical values).
Plot the critical values on a number line to create intervals.
Test a value from each interval to determine whether the expression is positive or negative there.
Select the intervals that satisfy the original inequality.

For x² − 3x − 4 > 0, factorising gives (x − 4)(x + 1) > 0, with critical values at x = −1 and x = 4. Testing shows the expression is positive for x < −1 and x > 4.

Graphical Interpretation

Students may also be asked to read inequality solutions from a parabola sketch — identifying where the curve lies above or below the x-axis. This graphical approach reinforces algebraic reasoning and is frequently used in Criterion C tasks.

Common Errors

Treating the inequality like an equation and stopping after finding the roots without checking the sign in each interval
Incorrectly combining intervals (using 'and' when 'or' is needed, or vice versa)
Forgetting that inequality direction may affect which region is selected

Exam Context

Non-linear inequalities test students' ability to connect algebraic technique with logical reasoning — both assessed under Criterion A. In some tasks, the inequality is embedded in a modelling context, requiring students to interpret what the solution range means in the real world.

Frequently asked questions

Two main types: quadratic inequalities such as x^2 - 5x + 6 > 0, and simple rational inequalities like (x-1)/(x+2) <= 0. You factorise, find critical values (roots and where the denominator is zero), then use a sign chart to decide which intervals satisfy the inequality. Final answers are usually written in interval notation or as compound inequalities, and graphing on a number line is often required for full Criterion A marks.

By trying to 'cross-multiply' rational inequalities the way they would an equation. Multiplying (x-1)/(x+2) <= 0 by (x+2) is invalid because you don't know the sign of (x+2). Instead, find critical values from numerator and denominator, mark them on a number line (open circle if denominator is zero there), and test one number from each interval. With quadratics, after factorising (x-2)(x-3) > 0, students write 2 < x < 3 instead of the correct x < 2 or x > 3.

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