Grade 12 Mathematics – Term 2 – The School of Mathematics

About Course

This Grade 12 Mathematics Term 2 course develops similarity-based Euclidean geometry, circle analytical geometry and differential calculus.

Learners prove theorems, solve riders, work with circles and tangents, differentiate functions, analyse cubic graphs and solve optimisation and rate-of-change problems.

Course Content

Similarity and Proportionality Theorems
Prove proportional division, the midpoint theorem, equiangular similarity, side-proportion similarity and Pythagoras using similar triangles.

Euclidean Geometry Riders
Apply similarity, proportionality and earlier circle-geometry results to formal proofs and riders.

Straight-Line Analytical Geometry
Revise equations of lines, parallel and perpendicular gradients and inclination.

Circles and Tangents in Analytical Geometry
Use the standard circle equation and determine equations of tangents to circles.

Polynomials and Factor Theorem
Factorise cubic polynomials and apply the remainder and factor theorems.

Limits and First-Principles Differentiation
Develop the limit concept and determine derivatives from first principles.

Differentiation Rules and Tangents
Apply the power, sum, difference and constant-multiple rules and determine tangent equations.

Second Derivative and Cubic Graphs
Use first and second derivatives to determine stationary points, concavity and inflection points and sketch cubic functions.

Optimisation and Rates of Change
Solve practical optimisation, motion and rate-of-change problems.

Term 2 Assignment and June Examination
Complete the assignment, revise Terms 1 and 2 and prepare for the June examination or control test.

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Grade 12 Mathematics – Term 2

About Course

What Will You Learn?

Course Content

Similarity and Proportionality Theorems
<p>Prove proportional division, the midpoint theorem, equiangular similarity, side-proportion similarity and Pythagoras using similar triangles.</p>

Euclidean Geometry Riders
<p>Apply similarity, proportionality and earlier circle-geometry results to formal proofs and riders.</p>

Straight-Line Analytical Geometry
<p>Revise equations of lines, parallel and perpendicular gradients and inclination.</p>

Circles and Tangents in Analytical Geometry
<p>Use the standard circle equation and determine equations of tangents to circles.</p>

Polynomials and Factor Theorem
<p>Factorise cubic polynomials and apply the remainder and factor theorems.</p>

Limits and First-Principles Differentiation
<p>Develop the limit concept and determine derivatives from first principles.</p>

Differentiation Rules and Tangents
<p>Apply the power, sum, difference and constant-multiple rules and determine tangent equations.</p>

Second Derivative and Cubic Graphs
<p>Use first and second derivatives to determine stationary points, concavity and inflection points and sketch cubic functions.</p>

Optimisation and Rates of Change
<p>Solve practical optimisation, motion and rate-of-change problems.</p>

Term 2 Assignment and June Examination
<p>Complete the assignment, revise Terms 1 and 2 and prepare for the June examination or control test.</p>

About Course

What Will You Learn?

Course Content

Similarity and Proportionality Theorems <p>Prove proportional division, the midpoint theorem, equiangular similarity, side-proportion similarity and Pythagoras using similar triangles.</p>

Euclidean Geometry Riders <p>Apply similarity, proportionality and earlier circle-geometry results to formal proofs and riders.</p>

Straight-Line Analytical Geometry <p>Revise equations of lines, parallel and perpendicular gradients and inclination.</p>

Circles and Tangents in Analytical Geometry <p>Use the standard circle equation and determine equations of tangents to circles.</p>

Polynomials and Factor Theorem <p>Factorise cubic polynomials and apply the remainder and factor theorems.</p>

Limits and First-Principles Differentiation <p>Develop the limit concept and determine derivatives from first principles.</p>

Differentiation Rules and Tangents <p>Apply the power, sum, difference and constant-multiple rules and determine tangent equations.</p>

Second Derivative and Cubic Graphs <p>Use first and second derivatives to determine stationary points, concavity and inflection points and sketch cubic functions.</p>

Optimisation and Rates of Change <p>Solve practical optimisation, motion and rate-of-change problems.</p>

Term 2 Assignment and June Examination <p>Complete the assignment, revise Terms 1 and 2 and prepare for the June examination or control test.</p>

Student Ratings & Reviews

Similarity and Proportionality Theorems
<p>Prove proportional division, the midpoint theorem, equiangular similarity, side-proportion similarity and Pythagoras using similar triangles.</p>

Euclidean Geometry Riders
<p>Apply similarity, proportionality and earlier circle-geometry results to formal proofs and riders.</p>

Straight-Line Analytical Geometry
<p>Revise equations of lines, parallel and perpendicular gradients and inclination.</p>

Circles and Tangents in Analytical Geometry
<p>Use the standard circle equation and determine equations of tangents to circles.</p>

Polynomials and Factor Theorem
<p>Factorise cubic polynomials and apply the remainder and factor theorems.</p>

Limits and First-Principles Differentiation
<p>Develop the limit concept and determine derivatives from first principles.</p>

Differentiation Rules and Tangents
<p>Apply the power, sum, difference and constant-multiple rules and determine tangent equations.</p>

Second Derivative and Cubic Graphs
<p>Use first and second derivatives to determine stationary points, concavity and inflection points and sketch cubic functions.</p>

Optimisation and Rates of Change
<p>Solve practical optimisation, motion and rate-of-change problems.</p>

Term 2 Assignment and June Examination
<p>Complete the assignment, revise Terms 1 and 2 and prepare for the June examination or control test.</p>