MATHEMATICS
EXAMINATION GUIDELINES
GRADE 12
2021
CONTENTS  Page 
Chapter 1: Introduction  3 
Chapter 2: Assessment in Grade 12 2.1 Format of question papers for Grade 12 2.2 Weighting of topics per paper for Grade 12 2.3 Weighting of cognitive levels 

Chapter 3: Elaboration of Content for Grade 12 (CAPS)  6 
Chapter 4: Acceptable reasons: Euclidean Geometry 4.1 Acceptable Reasons: Euclidean Geometry (ENGLISH) 4.2 Aanvaarbare redes: Euklidiese Meetkunde (AFRIKAANS) 1  9 12 
Chapter 5: Information sheet  15 
Chapter 6: Guidelines for marking  16 
Chapter 7: Conclusion  16 
Paper  Topics  Duration  Total  Date  Marking 
1  Patterns and sequences Finance, growth and decay Functions and graphs Algebra, equations and inequalities Differential Calculus Probability  3 hours  150  October/November  Externally 
2  Euclidean Geometry Analytical Geometry Statistics and regression Trigonometry  3 hours  150  October/November  Externally 
PAPER 1  MARKS  PAPER 2  MARKS 
Algebra, Equations and Inequalities Number Patterns Functions and Graphs Finance, Growth and Decay Differential Calculus Counting Principle and Probability  25 25 25 25 25 25  Statistics and Regression Analytical Geometry Trigonometry Euclidean Geometry  20 40 50 40 
TOTAL  150  TOTAL  150 
Cognitive Level  Description of Skills to be Demonstrated  Weighting  Approximate Number of Marks in a 150mark Paper 
Knowledge 
 20%  30 marks 
Routine Procedures 
 35%  52–53 marks 
Complex Procedures 
 30%  45 marks 
Problem Solving 
 15%  22–23 marks 
THEOREM STATEMENT  ACCEPTABLE REASON(S) 
LINES  
The adjacent angles on a straight line are supplementary.  ∠s on a str line 
If the adjacent angles are supplementary, the outer arms of these angles form a straight line.  adj ∠s supp 
The adjacent angles in a revolution add up to 360º  ∠s round a pt OR ∠s in a rev 
Vertically opposite angles are equal.  vert opp ∠s = 
If AB  CD, then the alternate angles are equal.  alt ∠s; AB  CD 
If AB  CD, then the corresponding angles are equal.  corresp ∠s; AB  CD 
If AB  CD, then the cointerior angles are supplementary.  coint ∠s; AB  CD 
If the alternate angles between two lines are equal, then the lines are parallel.  alt ∠s = 
If the corresponding angles between two lines are equal, then the lines are parallel.  corresp ∠s = 
If the cointerior angles between two lines are supplementary, then the lines are parallel.  coint ∠s supp 
TRIANGLES  
The interior angles of a triangle are supplementary.  ∠ sum in Δ OR sum of ∠s in Δ OR Int ∠s Δ 
The exterior angle of a triangle is equal to the sum of the interior opposite angles.  ext ∠ of Δ 
The angles opposite the equal sides in an isosceles triangle are equal.  ∠s opp equal sides 
The sides opposite the equal angles in an isosceles triangle are equal.  sides opp equal ∠s 
In a rightangled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.  Pythagoras OR Theorem of Pythagoras 
If the square of the longest side in a triangle is equal to the sum of the squares of the other two sides then the triangle is rightangled.  Converse Pythagoras OR Converse Theorem of Pythagoras 
If three sides of one triangle are respectively equal to three sides of another triangle, the triangles are congruent.  SSS 
If two sides and an included angle of one triangle are respectively equal to two sides and an included angle of another triangle, the triangles are congruent.  SAS OR S∠S 
If two angles and one side of one triangle are respectively equal to two angles and the corresponding side in another triangle, the triangles are congruent.  AAS OR ∠∠S 
If in two rightangled triangles, the hypotenuse and one side of one triangle are respectively equal to the hypotenuse and one side of the other, the triangles are congruent  RHS OR 90°HS 
THEOREM STATEMENT  ACCEPTABLE REASON(S) 
The line segment joining the midpoints of two sides of a triangle is parallel to the third side and equal to half the length of the third side  Midpt Theorem 
The line drawn from the midpoint of one side of a triangle, parallel to another side, bisects the third side.  line through midpt  to 2nd side 
A line drawn parallel to one side of a triangle divides the other two sides proportionally.  line  one side of Δ OR prop theorem; name  lines 
If a line divides two sides of a triangle in the same proportion, then the line is parallel to the third side.  line divides two sides of Δ in prop 
If two triangles are equiangular, then the corresponding sides are in proportion (and consequently the triangles are similar).   Δs OR equiangular Δs 
If the corresponding sides of two triangles are proportional, then the triangles are equiangular (and consequently the triangles are similar).  Sides of Δ in prop 
If triangles (or parallelograms) are on the same base (or on bases of equal length) and between the same parallel lines, then the triangles (or parallelograms) have equal areas.  same base; same height OR equal bases; equal height 
CIRCLES  
The tangent to a circle is perpendicular to the radius/diameter of the circle at the point of contact.  tan ⊥ radius tan ⊥ diameter 
If a line is drawn perpendicular to a radius/diameter at the point where the radius/diameter meets the circle, then the line is a tangent to the circle.  line ⊥ radius OR converse tan ⊥ radius OR converse tan ⊥ diameter 
The line drawn from the centre of a circle to the midpoint of a chord is perpendicular to the chord.  line from centre to midpt of chord 
The line drawn from the centre of a circle perpendicular to a chord bisects the chord.  line from centre ⊥ to chord 
The perpendicular bisector of a chord passes through the centre of the circle;  perp bisector of chord 
The angle subtended by an arc at the centre of a circle is double the size of the angle subtended by the same arc at the circle (on the same side of the chord as the centre)  ∠ at centre = 2 ×∠ at circumference 
The angle subtended by the diameter at the circumference of the circle is 90.  ∠s in semicircle OR diameter subtends right angle OR ∠ in ½ 
If the angle subtended by a chord at the circumference of the circle is 90º, then the chord is a diameter.  chord subtends 90º OR converse ∠s in semicircle 
Angles subtended by a chord of the circle, on the same side of the chord, are equal  ∠s in the same seg 
If a line segment joining two points subtends equal angles at two points on the same side of the line segment, then the four points are concyclic.  line subtends equal ∠s OR converse ∠s in the same seg 
Equal chords subtend equal angles at the circumference of the circle.  equal chords; equal ∠s 
Equal chords subtend equal angles at the centre of the circle.  equal chords; equal ∠s 
Equal chords in equal circles subtend equal angles at the circumference of the circles.  equal circles; equal chords; equal ∠s 
THEOREM STATEMENT  ACCEPTABLE REASON(S) 
Equal chords in equal circles subtend equal angles at the centre of the circles.  equal circles; equal chords; equal ∠s 
The opposite angles of a cyclic quadrilateral are supplementary  opp ∠s of cyclic quad 
If the opposite angles of a quadrilateral are supplementary then the quadrilateral is cyclic.  opp ∠s quad supp OR converse opp ∠s of cyclic quad 
The exterior angle of a cyclic quadrilateral is equal to the interior opposite angle.  ext ∠ of cyclic quad 
If the exterior angle of a quadrilateral is equal to the interior opposite angle of the quadrilateral, then the quadrilateral is cyclic.  ext ∠ = int opp ∠ OR converse ext ∠ of cyclic quad 
Two tangents drawn to a circle from the same point outside the circle are equal in length  Tans from common pt OR Tans from same pt 
The angle between the tangent to a circle and the chord drawn from the point of contact is equal to the angle in the alternate segment.  tan chord theorem 
If a line is drawn through the endpoint of a chord, making with the chord an angle equal to an angle in the alternate segment, then the line is a tangent to the circle.  converse tan chord theorem OR ∠ between line and chord 
QUADRILATERALS  
The interior angles of a quadrilateral add up to 360.  sum of ∠s in quad 
The opposite sides of a parallelogram are parallel.  opp sides of m 
If the opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram.  opp sides of quad are  
The opposite sides of a parallelogram are equal in length.  opp sides of m 
If the opposite sides of a quadrilateral are equal , then the quadrilateral is a parallelogram.  opp sides of quad are = OR converse opp sides of a parm 
The opposite angles of a parallelogram are equal.  opp ∠s of m 
If the opposite angles of a quadrilateral are equal then the quadrilateral is a parallelogram.  opp ∠s of quad are = OR converse opp angles of a parm 
The diagonals of a parallelogram bisect each other.  diag of m 
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.  diags of quad bisect each other OR converse diags of a parm 
If one pair of opposite sides of a quadrilateral are equal and parallel, then the quadrilateral is a parallelogram.  pair of opp sides = and  
The diagonals of a parallelogram bisect its area.  diag bisect area of m 
The diagonals of a rhombus bisect at right angles.  diags of rhombus 
The diagonals of a rhombus bisect the interior angles.  diags of rhombus 
All four sides of a rhombus are equal in length.  sides of rhombus 
All four sides of a square are equal in length.  sides of square 
The diagonals of a rectangle are equal in length.  diags of rect 
The diagonals of a kite intersect at rightangles.  diags of kite 
A diagonal of a kite bisects the other diagonal.  diag of kite 
A diagonal of a kite bisects the opposite angles  diag of kite 