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 |
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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 150-mark 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 co-interior angles are supplementary. | co-int ∠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 co-interior 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 right-angled 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 right-angled. | 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 right-angled 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 semi-circle 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 semi-circle |
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 end-point 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 right-angles. | 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 |