What is covered in Grade 11 Mathematics Equations & Inequalities?

Solve quadratic, surd and literal equations. Solve quadratic inequalities. Determine the nature of roots using the discriminant.

Is Grade 11 Equations & Inequalities tested in Paper 1 or Paper 2?

Grade 11 Mathematics Equations & Inequalities is assessed in Paper 1 of the end-of-year examinations, as per the CAPS Mathematics curriculum guidelines.

When is Equations & Inequalities taught in Grade 11 Mathematics?

Equations & Inequalities is taught in Term 1 of Grade 11 according to the CAPS Annual Teaching Plan (ATP) for Mathematics in South Africa.

Is Grade 11 Mathematics Equations & Inequalities on the CAPS curriculum?

Yes. Equations & Inequalities is part of the official CAPS Mathematics curriculum for Grade 11, Term 1 in South Africa. The content on MathSciBuddy follows the Annual Teaching Plan (ATP) set by the Department of Basic Education.

Is this Grade 11 Mathematics study material free?

Yes. All chapter notes, definitions, formulas, and worked examples on MathSciBuddy are completely free to read. No account or subscription is needed to access CAPS-aligned study notes.

Grade 11 Mathematics

Grade 11 · Term 1Mathematics

Equations & Inequalities

We extend solving to quadratic inequalities, absolute value equations, and nature-of-roots analysis using the discriminant.

Week 3

2.1 Quadratic Inequalities & Nature of Roots

Solve quadratic inequalities using sign analysis or sketch
Apply the discriminant to determine the nature of the roots of $ax^2+bx+c=0$
Find values of $k$ for specific root conditions

🌍

Real-World Connection

A rocket's trajectory satisfies $h(t)=-5t^2+20t>0$ while in the air. Solving this quadratic inequality tells you the time interval when the rocket is above the ground — critical for launch timing.

Definition

Discriminant & Nature of Roots

For $ax^2+bx+c=0$ : $\Delta=b^2-4ac$ . If $\Delta>0$ : two distinct real roots. If $\Delta=0$ : one repeated real root. If $\Delta<0$ : no real roots. If $\Delta>0$ and a perfect square: two rational roots.

\Delta = b^2-4ac

Property / Rule

Solving Quadratic Inequalities

Step 1: Rearrange so one side is 0. Step 2: Factorise or find roots. Step 3: Use a sign table or parabola sketch. Step 4: Read off the interval(s) satisfying the inequality.

(x-p)(x-q)>0\Rightarrow x<p\text{ or }x>q\quad(p<q)

💡 Tip

Draw a rough sketch of the parabola — it's the fastest way to read off the solution of a quadratic inequality. Upward parabola is positive OUTSIDE the roots.

Worked Examples

Worked Example

Solve a quadratic inequality

Problem

Solve: x^2-x-6 < 0

Worked Example

Nature of roots using discriminant

Problem

k

Activity — 8 Questions

CAPS Cognitive Level Distribution

L1 · Knowledge2 Q

L2 · Routine Procedures2 Q

L3 · Complex Procedures2 Q

L4 · Problem Solving2 Q

L1 · Knowledge1 mark

State the nature of the roots if

\Delta=0

L1 · Knowledge2 marks

Calculate

\Delta

for

2x^2+3x-5=0

L2 · Routine Procedures3 marks

Solve

x^2-5x+4>0

L2 · Routine Procedures4 marks

Solve

-x^2+3x+10\geq0

L3 · Complex Procedures3 marks

Find

k

such that

x^2+kx+9=0

has equal roots.

L3 · Complex Procedures5 marks

Solve

(x-2)(x+1)\leq8

L4 · Problem Solving4 marks

Prove that

x^2+4x+6>0

for all real

x

L4 · Problem Solving5 marks

For what values of

p

does

px^2+4x+p^2=0

have two distinct real roots?

Exponents & Surds

Number Patterns