Grade 11 Equations and inequalities

Quadratic equations by every method, quadratic inequalities, linear-quadratic systems and nature of roots.

Gr 11 Term 1 - Equations and inequalitiesTerm 1 - 3 weeks (CAPS)

Practise Equations and inequalities in the app →

What gets asked

• Solve a quadratic equation by factorising or by the quadratic formula.
• Complete the square on a quadratic expression.
• Solve a quadratic inequality and give the interval.
• Solve a pair of equations where one is a line and one is a parabola.
• Use the discriminant to describe the nature of the roots.

You must be able to

• Write the equation as equal to zero before factorising.
• Halve the middle coefficient, square it, and balance what you added.
• Find the roots first, then test the sign between and beyond them.
• Substitute the linear equation into the quadratic one, never the other way.
• Compute $b^2-4ac$ and read its sign before talking about the roots.

Traps that cost marks

• Setting each factor equal to the number on the right, as in $(x-2)(x+1)=4$ giving $x-2=4$. Factors split only against zero. Move the 4 across first so the right side is 0.
• Keeping only the positive square root when unwrapping $(x+3{)}^2=16$. A square has two roots: $x+3=4$ or $x+3=-4$.
• Answering a quadratic inequality with just the two roots. The roots are the boundary. The answer is an interval, chosen by testing the sign.

Worked example