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Grade 12 Mathematics: modules and lessons

Explore Grade 12 Mathematics: 25 modules and 280 lesson entries. Use the dorKk lesson guide to plan revision and catch-up study.

dorKk provides pre-recorded CAPS-aligned video lessons for self-paced study alongside schoolwork. Choose a module below, find the lesson that matches your classwork, and use the sequence to identify gaps. This guide lists lesson titles; access to the videos depends on your subscription. dorKk is not an online school.

Source: dorKk English lesson list dated 21 January 2026. Catalogue entries may differ from current app availability.

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Worked explanations

ALGEBRA & EQUATIONS

  1. 1.1.BASIC ALGEBRA; THE REAL NUMBER SYSTEM
  2. 1.2.POSITIONING A SURD BETWEEN TWO INTEGERS
  3. 1.3.ROUNDING REAL NUMBERS
  4. 1.4.INSTANTANEOUS VELOCITY AND SPEED
  5. 1.5.POLYNOMIALS; MULTIPLICATION OF A BINOMIAL BY A BINOMIAL
  6. 1.6.MULTIPLICATION OF A BINOMIAL BY A TRINOMIAL

FACTORISATION

  1. 2.1.COMMON FACTOR
  2. 2.2.DIFFERENCE OF SQUARES
  3. 2.3.GROUPING IN PAIRS
  4. 2.4.GROUPING 3 AND 1
  5. 2.5.TRINOMIALS
  6. 2.6.SUM AND DIFFERENCE OF CUBES
  7. 2.7.FACTOR AND REMAINDER THEOREM
  8. 2.8.FACTORISING THIRD DEGREE POLYNOMIALS

FRACTIONS

  1. 3.1.MULTIPLICATION AND DIVISION
  2. 3.2.ADDITION AND SUBTRACTION
  3. 3.3.MULTIPLICATION AND DIVISION FACTORISING
  4. 3.4.ADDITION AND SUBTRACTION FACTORISING (LCD)

EXPONENTS

  1. 4.1.EXPONENTIAL RULES AND
  2. 4.2.EXPONENTIAL EXPRESSIONS (MULTIPLY AND DIVIDE)
  3. 4.3.EXPONENTIAL EXPRESSIONS (ADD AND SUBTRACT)
  4. 4.4.EXPONENTIAL EQUATIONS (SIMPLE), UNKNOWN IN POWER
  5. 4.5.EXPONENTIAL EQUATIONS, UNKNOWN IN POWER FACTORISING
  6. 4.6.EXPONENTIAL EQUATIONS, UNKNOWN IN BASE
  7. 4.7.EXPONENTIAL EQUATIONS SAME BASE AND POWER DOUBLE THE OTHER
  8. 4.8.EXPONENTIAL EQUATIONS SAME BASE ONE POWER NEGATIVE OF THE OTHER
  9. 4.9.SURDS; LAWS, CONVERTING BETWEEN SURD AND EXPONENT FORM
  10. 4.10.SURD EXPRESSIONS; MULTIPLICATION AND DIVISION
  11. 4.11.SURD EXPRESSIONS; ADDITION AND SUBTRACTION
  12. 4.12.SURD EQUATIONS

EQUATIONS

  1. 5.1.SOLVING LINEAR EQUATIONS REVIEW
  2. 5.2.SOLVING LINEAR EQUATIONS WITH SINGLE TERM DENOMINATORS
  3. 5.3.SOLVING LINEAR EQUATIONS FACTORISE FOR LCD (RESTRICTIONS)
  4. 5.4.SOLVING QUADRATIC EQUATIONS THROUGH FACTORISING
  5. 5.5.SOLVING SIMULTANEOUS LINEAR EQUATIONS IN TWO UNKNOWNS; ELIMINATION
  6. 5.6.SOLVING SIMULTANEOUS LINEAR EQUATIONS IN TWO UNKNOWNS; SUBSTITUTION
  7. 5.7.SOLVING WORD PROBLEMS; LINEAR EQUATIONS (MONEY, NUMBER, ETC)
  8. 5.8.SOLVING WORD PROBLEMS; QUADRATIC EQUATIONS (AREA)
  9. 5.9.SOLVING WORD PROBLEMS; SIMULTANEOUS EQUATIONS (RATES)
  10. 5.10.SOLVING LITERAL EQUATIONS; CHANGING THE SUBJECT OF THE FORMULA
  11. 5.11.SOLVING QUADRATIC EQUATIONS BY SQUARING BOTH SIDES
  12. 5.12.SOLVING QUADRATIC EQUATIONS BY SQUARE ROOTING BOTH SIDES
  13. 5.13.SOLVING QUADRATIC EQUATIONS BY USING tHE K METHOD
  14. 5.14.SOLVING QUADRATIC EQUATIONS BY COMPLEATING THE SQUARE
  15. 5.15.SOLVING QUADRATIC EQUATIONS USING THE FORMULA
  16. 5.16.COMPLETING THE SQUARE
  17. 5.17.SOLVING SIMULTANEOUS EQUATIONS; ONE LINEAR ONE QUADRATIC IN TWO UNKNOWNS
  18. 5.18.SOLVING THIRD DEGREE EQUATIONS USING THE FACTOR AND REMAINDER THEOREMS
  19. 5.19.USING FACTOR THEOREM TO FIND VALUE OF COEFFICIANT IN THIRD DEGREE EQUATIONS
  20. 5.20.SOLVING EXPONENTIAL EQUATIONS BY ADAPTING TO LOGARITHMS

INEQUALITIES

  1. 6.1.LINEAR INEQUALITIES
  2. 6.2.INTERVAL NOTATION
  3. 6.3.QUADRATIC INEQUALITIES
  4. 6.4.INEQUALITIES INVOLVING FRACTIONS
  5. 6.5.INEQUALITIES INVOLVING ROOTS

NATURE OF ROOTS

  1. 7.1.NATURE OF ROOTS
  2. 7.2.DETERMINING THE NATURE OF ROOTS
  3. 7.3.FINDING THE VALUE OF AN UNKNOWN

FUNCTIONS

  1. 8.1.RELATIONS AND FUNCTIONS
  2. 8.2.TERMINOLOGY
  3. 8.3.AVERAGE GRADIENT
  4. 8.4.DEFINITION OF A FUNCTION
  5. 8.5.INVERSE FUNCTIONS
  6. 8.6.INVERSE FUNCTIONS AND DOMAIN RESTRICTIONS
  7. 8.7.CONCEPTS FOR FOCUS
  8. 8.8.NOTATION

STRAIGHT LINE

  1. 9.1.THE PARENT GRAPH
  2. 9.2.SKETCHING; TABLE METHOD
  3. 9.3.INVESTIGATING VERTICAL TRANSLATIONS
  4. 9.4.INVESTIGATING VERTICAL DILATIONS
  5. 9.5.SKETCHING GRADIENT INTERCEPT METHOD
  6. 9.6.SKETCHING DUAL INTERCEPT METHOD
  7. 9.7.WAYS TO FIND THE GRADIENT
  8. 9.8.DETERMINE THE EQUATION
  9. 9.9.GRAPH INTERPETATION

PARABOLA

  1. 10.1.THE PARENT GRAPH
  2. 10.2.INVESTIGATING VERTICAL TRANSLATIONS (SHIFTS)
  3. 10.3.INVESTIGATING VERTICAL DILATIONS (STRETCHES)
  4. 10.4.SKETCHING USING TURNING POINT AND INTERCEPTS
  5. 10.5.DETERMINING THE EQUATION
  6. 10.6.REVIEW OF GRADE 10
  7. 10.7.INVESTIGATING HORIZONTAL TRANSLATIONS (SHIFTS)
  8. 10.8.SKETCH COMBINATIONS USING TWO PARAMETER CHANGES
  9. 10.9.SKETCHING WITH A TURNING POINT FORM
  10. 10.10.DETERMINING THE EQUATION USING ROOTS AND ONE POINT
  11. 10.11.DETERMINING THE EQUATION USING VERTEX AND ONE POINT
  12. 10.12.GRAPH INTERPERTATION; STRAIGHT LINE AND PARABOLA
  13. 10.13.DETERMINING THE EQUATION OF THE INVERSE

HYPERBOLA

  1. 11.1.THE PARENT GRAPH
  2. 11.2.INVESTIGATING VERTICAL TRANSLATIONS (SHIFTS)
  3. 11.3.INVESTIGATING VERTICAL DILATIONS (STRETCHES)
  4. 11.4.SKETCHING
  5. 11.5.DETERMINING THE EQUATION
  6. 11.6.GRAPH INTERPETATION; STRAIGHT LINE AND HYPERBOLA
  7. 11.7.REVIEW GRADE 10
  8. 11.8.INVESTIGATING HORIZONTAL TRANSLATIONS (SHIFTS)
  9. 11.9.ASYMPTOTES AND LINES OF SYMMETRY
  10. 11.10.SKETCHING COMBINATIONS USING TWO OR MORE PARAMETER CHANGES
  11. 11.11.GRAPH INTERPRETATION; STRAIGHT LINE AND HYPERBOLA

EXPONENTIAL FUNCTIONS

  1. 12.1.PARENT GRAPHS
  2. 12.2.VERTICAL SHIFTS
  3. 12.3.VERTICAL DILATIONS
  4. 12.4.SKETCHING
  5. 12.5.FIND THE EQUATION
  6. 12.6.GRAPH INTERPRETATION
  7. 12.7.REVIEW OF GRADE 10
  8. 12.8.INVESTIGATING HORIZONTAL TRANSLATIONS (SHIFTS)
  9. 12.9.SKETCHING COMBINATIONS OF GRAPHS
  10. 12.10.GRAPH INTERPRETATION PART 1
  11. 12.11.GRAPH INTERPRETATION PART 2

LOGARITHMIC FUNCTIONS

  1. 13.1.LOGARITHMIC LAWS AND EXPRESSIONS
  2. 13.2.LOGARITHMIC LAWS SKETCHING FING AND EQUATION

FINANCE AND GROWTH

  1. 14.1.SIMPLE GROWTH REVIEW
  2. 14.2.SIMPLE GROWTH; CALCULATING INTEREST RATE, HIRE PURCHASE
  3. 14.3.COMPOUND GROWTH
  4. 14.4.IMPLICATIONS OF FLUCTUATING EXCHANGE RATES
  5. 14.5.SIMPLE DECAY
  6. 14.6.INTEREST AND SIMPLE DECAY
  7. 14.7.SIMPLE DECAY CALCULATING ANY VARIABLE
  8. 14.8.COMPOUND DEPRECIATION
  9. 14.9.COMPOUND DEPRECIATION; CALCULATING ANY VARIABLE
  10. 14.10.COMPOUND DEPRECIATION; REDUCING BALANCE DEPRECIATION
  11. 14.11.COMPOUND DEPRECIATION; DIFFERENT COMPOUNDINGS
  12. 14.12.NOMINAL AND EFFECTIVE INTEREST RATES
  13. 14.13.TIMELINES
  14. 14.14.CHANGING COMPOUNDING RATES
  15. 14.15.ANNUITIES; FUTURE VALUE ANNUITY
  16. 14.16.PRESENT VALUE ANNUITIES
  17. 14.17.PAYMENTS AT THE BEGINNING OF THE PERIOD
  18. 14.18.BALANCE OUTSTANDING ON PRESENT VALUE ANNUITIES
  19. 14.19.POSTPONED PAYMENTS
  20. 14.20.FINAL PAYMENT WITH REDUCED VALUE
  21. 14.21.SINKING FUNDS
  22. 14.22.PRESENT VALUE ANNUITIES BALANCE OUTSTANDING
  23. 14.23.FINDING N

NUMBERS AND PATTERNS

  1. 15.1.ARITHMETIC PATTERNS INTRODUCTION
  2. 15.2.ARITHMETIC PATTERNS THE GENERAL TERM
  3. 15.3.ARITHMETIC PATTERNS PROBLEM SOLVING
  4. 15.4.QUADRATIC SEQUENCES INVESTIGATION
  5. 15.5.QUADRATIC SEQUENCES THE GENERAL TERM 1
  6. 15.6.QUADRATIC SEQUENCES THE GENERAL TERM 2
  7. 15.7.QUADRATIC SEQUENCES PROBLEM SOLVING
  8. 15.8.ARITHMETIC SEQUENCES THE GENERAL TERM
  9. 15.9.ARITHMETIC SEQUENCE PROBLEM SOLVING (1)
  10. 15.10.ARITHMETIC SERIES THE SUM OF TERMS
  11. 15.11.ARITHMETIC SERIES PROBLEM SOLVING (2)
  12. 15.12.GEOMETRIC SEQUENCE THE GENERAL TERM
  13. 15.13.GEOMETRIC SEQUENCE PROBLEM SOLVING
  14. 15.14.GEOMETRIC SERIES THE SUM OF TERMS
  15. 15.15.GEOMETRIC SERIES PROBLEM SOLVING (2)
  16. 15.16.GEOMETRIC SERIES THE INFINITE SERIES

DIFFERENTIAL CALCULUS

  1. 16.1.INTRODUCTION TO LIMITS
  2. 16.2.GRADIENTS
  3. 16.3.GRADIENT AND THE DERIVATIVE
  4. 16.4.RULES FOR DIFFERENTIATION
  5. 16.5.SKETCHING A CUBE FUNCTION
  6. 16.6.MORE ABOUT SKETCHES OF CUBIC FUNCTIONS
  7. 16.7.APPLICATION OF DIFFERENTIAL CALCULUS

EUCLIDEAN GEOMETRY

  1. 17.1.PROPERTIES; LINES AND ANGLES
  2. 17.2.REVISE TRIANGLES AND QUADRILATERALS
  3. 17.3.SIMILAR AND CONGRUENT TRIANGLES
  4. 17.4.SPECIAL QUADRILATERALS AND THEIR PRORERTIES PART 1
  5. 17.5.SPECIAL QUADRILATERALS AND THEIR PRORERTIES PART 2
  6. 17.6.EXAMPLES; HOW TO PROVE THEOREMS ON PARALELLOGRAMS
  7. 17.7.CALCULATE THE INTERIOR ANGLES OF POLYGONS
  8. 17.8.THE MIDPOINT THEOREM
  9. 17.9.CIRCLE TERMINOLOGY AND LINE SEGMENT THROUGH CENTRE AND MIDPOINT
  10. 17.10.PERPENDICULAR BISECTOR OF A CHORD AND ANGLE AT CENTRE
  11. 17.11.OPPOSITE ANGLES OF CYCLIC QUADRILATERAL
  12. 17.12.PROVE A QUADRILATERAL IS CYCLIC, TANGENTS FROM THE SAME POINT, TAN CHORD

PROBABILITIY

  1. 18.1.VENN DIAGRAMS
  2. 18.2.TREE DIAGRAMS AND CONTINGENCY TABLES
  3. 18.3.INDEPENDENT AND DEPENDENT EVENTS
  4. 18.4.THE COUNTING PRINCIPLE
  5. 18.5.PERMUTATIONS AND COMBINATIONS

TRIGONOMETRY

  1. 19.1.INTRODUCTION
  2. 19.2.SIN COS AND TAN
  3. 19.3.RATIOS IN THE FIRST QUADRANT OF A CARTESIAN PLANE
  4. 19.4.SPECIAL ANGLES 30, 45, AND 60 DEGREES
  5. 19.5.SPECIAL ANGLES 0 AND 90 DEGREES
  6. 19.6.TRIGONOMETRIC RATIOS IN ALGEBRAIC EXPRESSIONS
  7. 19.7.USE A CALCULATOR TO FIND THE RATIO OF AN ANGLE
  8. 19.8.SIMPLE TRIGONOMETRIC EQUATIONS
  9. 19.9.FIND THE LENGTH OF ONE SIDE OF A TRIANGLE
  10. 19.10.FIND ONE OF THE ANGLES OF A TRIANGLE
  11. 19.11.DIRECTION AND BEARING
  12. 19.12.ANGLE OF ELEVATION AND DEPRESSION
  13. 19.13.ANGLES IN FOUR QUADRANTS OF THE CARTESIAN PLANE
  14. 19.14.COSEC, SEC AND COT

TRIGONOMETRIC GRAPHS

  1. 20.1.SINE AND COSINE GRAPHS
  2. 20.2.TAN GRAPH
  3. 20.3.PERIOD AND AMPLITUDE PART 1
  4. 20.4.PERIOD AND AMPLITUDE PART 2
  5. 20.5.VERTICAL SHIFTS
  6. 20.6.HORIZONTAL SHIFTS

TRIGONOMETRIC FUNCTIONS

  1. 21.1.INVESTIGATING VERTICAL TRANSLATIONS (SHIFTS)
  2. 21.2.INVESTIGATING VERTICAL DILATIONS (STRETCHES)
  3. 21.3.SKETCHING USING TURNING POINT AND INTERCEPTS

ANALYTICAL GEOMETRY

  1. 22.1.DISTANCE FORMULA
  2. 22.2.MIDPOINT FORMULA
  3. 22.3.GRADIENT FORMULA
  4. 22.4.GRADIENT OF HORIZONTAL AND VERTICAL LINES
  5. 22.5.PARALLEL AND PERPENDICULAR LINES
  6. 22.6.COLLINEAR POINTS
  7. 22.7.DEFINE ANGLE OF INCLINATION
  8. 22.8.CALCULATE THE INCLINATION OF A LINE WITH TAN AS GRADIENT
  9. 22.9.GRADIENT AND Y
  10. 22.10.GRADIENT AND ONE POINT
  11. 22.11.THROUGH ONE POINT AND PARALLEL OR PERPENDICULAR TO A GIVEN LINE
  12. 22.12.INTERSECTING LINES
  13. 22.13.PROVE THAT A QUADRILATERAL IS A PARM, RECTANGLE, RHOMBUS, ETC
  14. 22.14.FIND THE EQUATION OF A CIRCLE WITH CENTRE AT ORIGIN
  15. 22.15.FIND THE EQUATION OF A CIRCLE CENTRED OFF THE ORIGIN
  16. 22.16.SYMMETRICAL POINTS ON A CIRCLE
  17. 22.17.THE EQUATION OF A TANGENT TO A CIRCLE
  18. 22.18.PROVE A GIVEN STRAIGHT LINE A TANGENT
  19. 22.19.SOLVING PROBLEMS INVOLVING CIRCLES AND TANGENTS

IDENTITIES

  1. 23.1.THE QUOTIENT IDENTITY
  2. 23.2.THE SQUARE IDENTITY
  3. 23.3.IDENTITIES IN SOLVING TRIG EXPRESSIONS
  4. 23.4.PROOF IDENTITIES
  5. 23.5.UNDEFINED IDENTITIES
  6. 23.6.CAST RULE
  7. 23.7.TRIGNOMETRIC RATIOS (180 DEGREES)
  8. 23.8.TRIGONOMETRIC RATIOS
  9. 23.9.NEGATIVE ANGLES
  10. 23.10.ANGLES GREATER THAN 360 DEGREES
  11. 23.11.COFUNCTIONS 1
  12. 23.12.COFUNCTIONS 2
  13. 23.13.SIN, COS AND k360 DEGREES
  14. 23.14.GENERAL SOLUTION TAN
  15. 23.15.TRIG EQUATIONS; FINDING THETA IN A GIVEN INTERVAL
  16. 23.16.TRIG EQUATIONS; SPECIAL FORMS
  17. 23.17.AREA RULE
  18. 23.18.SINE RULE
  19. 23.19.COSINE RULE
  20. 23.20.USING THE SINE, COS AND AREA RULES TO CALCULATE DISTANCE AND ANGLES
  21. 23.21.COMPOUND ANGLES PROOF OF COS ALPHA MINUS BETA
  22. 23.22.COMPOUND ANGLE FORMULAE
  23. 23.23.DOUBLE ANGLE FORMULA 1
  24. 23.24.DOUBLE ANGLE FORMULA 2
  25. 23.25.USING DIAGRAMS TO SOLVE DOUBLE AND COMPOUND ANGLE PROBLEMS
  26. 23.26.EXPRESSIONS AND PROOF IDENTITIES INCLUDING DOUBLE AND COMPOUND ANGLES
  27. 23.27.UNDEFINED IDENTITIES DOUBLE AND COMPOUND ANGLES
  28. 23.28.EQUATIONS WITH DOUBLE AND COMPOUND ANGLES
  29. 23.29.DRAWING AND WORKING WITH GRAPHS OF COMPOUND ANGLES
  30. 23.30.FINDING HEIGHTS DISTANCES ANGLES AND AREAS IN THREE DIMENSIONS
  31. 23.31.COMPOUND ANGLES IN THREE DIMENSIONS
  32. 23.32.SINE COSINE AND TANGENT FUNCTIONS PARENT GRAPHS
  33. 23.33.AREA RULE PROOF
  34. 23.34.SINE RULE PROOF
  35. 23.35.COSINE RULE PROOF

STATISTICS

  1. 24.1.MEASURES OF CENTRAL TENDENCY
  2. 24.2.MEASURES OF DISPERSION
  3. 24.3.FIVE NUMBER SUMMARY; BOX AND WHISKER DIAGRAMS
  4. 24.4.CALCULATING MEASURES OF CENTRAL TENDENCY AND DISPERSION
  5. 24.5.WORKING WITH GROUPED DATA
  6. 24.6.STANDARD DEVIATION AND VARIANCE
  7. 24.7.SYMMETRICAL AND SKEWED DATA
  8. 24.8.IDENTIFICATION OF OUTLIERS
  9. 24.9.REPRESENTING DATA; FREQUENCY TABLES
  10. 24.10.REPRESENTING DATA; BAR GRAPHS
  11. 24.11.REPRESENTING DATA; STEM AND LEAF PLOTS
  12. 24.12.REPRESENTING DATA; HISTOGRAMS
  13. 24.13.REPRESENTING DATA; FREQUENCY POLYGONS
  14. 24.14.REPRESENTING DATA; OGIVES
  15. 24.15.REPRESENTING DATA; SCATTER PLOTS
  16. 24.16.LEAST SQUARES REGRESSION LINES
  17. 24.17.CORRELATION COEFFICIENT
  18. 24.18.CALCULATOR WORK

NOVEMBER EXAMINATION

  1. 25.1.DBE NOVEMBER 2023 PAPER 1 QUESTION 1 AND 2
  2. 25.2.DBE NOVEMBER 2023 PAPER 1 QUESTION 3 AND 4
  3. 25.3.DBE NOVEMBER 2023 PAPER 1 QUESTION 5 AND 6
  4. 25.4.DBE NOVEMBER 2023 PAPER 1 QUESTION 7 AND 8
  5. 25.5.DBE NOVEMBER 2023 PAPER 1 QUESTION 9 AND 10
  6. 25.6.DBE NOVEMBER 2023 PAPER 2 QUESTION 1 TO 3
  7. 25.7.DBE NOVEMBER 2023 PAPER 2 QUESTION 4 AND 5
  8. 25.8.DBE NOVEMBER 2023 PAPER 2 QUESTION 6 AND 7
  9. 25.9.DBE NOVEMBER 2023 PAPER 2 QUESTION 8 AND 9
  10. 25.10.DBE NOVEMBER 2023 PAPER 2 QUESTION 10

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