Mathematics GR 12 Exam Guidelines 2021 Eng hlayiso.com

Downloaded from hlayiso.com MATHEMATICS EXAMINATION GUIDELINES GRADE 12 2021 These guidelines consist of 16 pages. Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics 2 DBE/2021 Examination Guidelines CONTENTS Page Chapter 1: Introduction 3 Chapter 2: Assessment in Grade 12 2.1 Format of question papers for Grade 12 4 2.2 Weighting of topics per paper for Grade 12 4 2.3 Weighting of cognitive levels 5 Chapter 3: Elaboration of Content for Grade 12 (CAPS) 6 Chapter 4: Acceptable reasons: Euclidean Geometry 4.1 Acceptable Reasons: Euclidean Geometry (ENGLISH) 9 4.2 Aanvaarbare redes: Euklidiese Meetkunde (AFRIKAANS) 12 Chapter 5: Information sheet 15 Chapter 6: Guidelines for marking 16 Chapter 7: Conclusion 16 . Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics 3 DBE/2020 Examination Guidelines 1. INTRODUCTION The Curriculum and Assessment Policy Statement (CAPS) for Mathematics outlines the nature and purpose of the subject Mathematics. This guides the philosophy underlying the teaching and assessment of the subject in Grade 12. The purpose of these Examination Guidelines is to:  Provide clarity on the depth and scope of the content to be assessed in the Grade 12 National Senior Certificate Examination in Mathematics  Assist teachers to adequately prepare learners for the examinations This document deals with the final Grade 12 external examinations. It does not deal in any depth with the school-based assessment (SBA), performance assessment tasks (PATs) or final external practical examinations as these are clarified in a separate PAT document which is updated annually. These guidelines should be read in conjunction with:  The National Curriculum Statement (NCS) Curriculum and Assessment Policy Statement (CAPS): Mathematics  The National Protocol of Assessment: An addendum to the policy document, the National Senior Certificate: A qualification at Level 4 on the National Qualifications Framework (NQF), regarding the National Protocol for Assessment (Grades R–12)  National policy pertaining to the programme and promotion requirements of the National Curriculum Statement, Grades R to 12 Included in this document is a list of Euclidean Geometry reasons, both in English and Afrikaans, which should be used as a guideline when teaching learners Euclidean Geometry. The Information Sheet for Paper 1 and 2 is included in this document. Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics 4 DBE/2021 Examination Guidelines 2. ASSESSMENT IN GRADE 12 All candidates will write two external papers as prescribed. 2.1 Format of Question Papers for Grade 12 Paper Topics Duration Total Date Marking Patterns and sequences Finance, growth and decay Functions and graphs 1 3 hours 150 October/November Externally Algebra, equations and inequalities Differential Calculus Probability Euclidean Geometry Analytical Geometry 2 3 hours 150 October/November Externally Statistics and regression Trigonometry Questions in both Papers 1 and 2 will assess performance at different cognitive levels with an emphasis on process skills, critical thinking, scientific reasoning and strategies to investigate and solve problems in a variety of contexts. An Information Sheet is included on p. 15. 2.2 Weighting of Topics per Paper for Grade 12 PAPER 1 MARKS PAPER 2 MARKS Algebra, Equations and Inequalities 25 Statistics and Regression 20 Number Patterns 25 Analytical Geometry 40 Functions and Graphs 35 Trigonometry 50 Finance, Growth and Decay 15 Euclidean Geometry 40 Differential Calculus 35 Counting Principle and Probability 15 TOTAL 150 TOTAL 150 Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics 5 DBE/2021 Examination Guidelines 2.3 Weighting of Cognitive Levels Papers 1 and 2 will include questions across four cognitive levels. The distribution of cognitive levels in the papers is given below. Approximate Number of Cognitive Level Description of Skills to be Demonstrated Weighting Marks in a 150-mark Paper  Recall  Identification of correct formula on the information sheet (no changing of the subject)  Use of mathematical facts Knowledge 20% 30 marks  Appropriate use of mathematical vocabulary  Algorithms  Estimation and appropriate rounding of numbers  Proofs of prescribed theorems and derivation of formulae  Perform well-known procedures  Simple applications and calculations which Routine might involve few steps 35% 52–53 marks Procedures  Derivation from given information may be involved  Identification and use (after changing the subject) of correct formula  Generally similar to those encountered in class  Problems involve complex calculations and/or higher-order reasoning  There is often not an obvious route to the solution  Problems need not be based on a real-world Complex context 30% 45 marks Procedures  Could involve making significant connections between different representations  Require conceptual understanding  Learners are expected to solve problems by integrating different topics.  Non-routine problems (which are not necessarily difficult)  Problems are mainly unfamiliar  Higher-order reasoning and processes are Problem involved 15% 22–23 marks Solving  Might require the ability to break the problem down into its constituent parts  Interpreting and extrapolating from solutions obtained by solving problems based in unfamiliar contexts. Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics 6 DBE/2021 Examination Guidelines 3. ELABORATION OF CONTENT/TOPICS The purpose of the clarification of the topics is to give guidance to the teacher in terms of depth of content necessary for examination purposes. Integration of topics is encouraged as learners should understand Mathematics as a holistic discipline. Thus questions integrating various topics can be asked. FUNCTIONS 1. Candidates must be able to use and interpret functional notation. In the teaching process learners must be able to understand how f (x) has been transformed to generate f ( x) ,  f (x) , f ( x  a) f ( x)  a , af (x) and x  f ( y) where a  R . 2. Trigonometric functions will ONLY be examined in PAPER 2. NUMBER PATTERNS, SEQUENCES AND SERIES 1. The sequence of first differences of a quadratic number pattern is linear. Therefore, knowledge of linear patterns can be tested in the context of quadratic number patterns. 2. Recursive patterns will not be examined explicitly. 3. Links must be clearly established between patterns done in earlier grades. FINANCE, GROWTH AND DECAY 1. Understand the difference between nominal and effective interest rates and convert fluently between them for the following compounding periods: monthly, quarterly and half-yearly or semi-annually. 2. With the exception of calculating i in the Fv and Pv formulae, candidates are expected to calculate the value of any of the other variables. 3. Pyramid schemes will NOT be examined in the examination. ALGEBRA 1. Solving quadratic equations by completing the square will NOT be examined. 2. Solving quadratic equations using the substitution method (k-method) is examinable. 3. Equations involving surds that lead to a quadratic equation are examinable. 4. Solution of non-quadratic inequalities should be seen in the context of functions. 5. Nature of the roots will be tested intuitively with the solution of quadratic equations and in all the prescribed functions. Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics 7 DBE/2021 Examination Guidelines DIFFERENTIAL CALCULUS dy 1. The following notations for differentiation can be used: f (x) , D x , or y  . dx 2. In respect of cubic functions, candidates are expected to be able to:  Determine the equation of a cubic function from a given graph.  Discuss the nature of stationary points including local maximum, local minimum and points of inflection.  Apply knowledge of transformations on a given function to obtain its image. 3. Candidates are expected to be able to draw and interpret the graph of the derivative of a function. 4. Surface area and volume will be examined in the context of optimisation. 5. Candidates must know the formulae for the surface area and volume of the right prisms. These formulae will NOT be provided on the formula sheet 6. If the optimisation question is based on the surface area and/or volume of the cone, sphere and/or pyramid, a list of the relevant formulae will be provided in that question. Candidates will be expected to select the correct formula from this list. PROBABILITY 1. Dependent events are examinable but conditional probabilities are not part of the syllabus. 2. Dependent events in which an object is not replaced are examinable. 3. Questions that require the learner to count the different number of ways that objects may be arranged in a circle and/or the use of combinations are not in the spirit of the curriculum. 4. In respect of word arrangements, letters that are repeated in the word can be treated as the same (indistinguishable) or different (distinguishable). The question will be specific in this regard. EUCLIDEAN GEOMETRY AND MEASUREMENT 1. Measurement can be tested in the context of optimisation in calculus and two- and three-dimensional trigonometry. 2. Composite shapes could be formed by combining a maximum of TWO of the stated shapes. 3. The following proofs of theorems are examinable:  The line drawn from the centre of a circle perpendicular to a chord bisects the chord;  The line drawn from the centre of a circle that bisects a chord is perpendicular to the 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);  The opposite angles of a cyclic quadrilateral are supplementary;  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;  A line drawn parallel to one side of a triangle divides the other two sides proportionally;  Equiangular triangles are similar. Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics 8 DBE/2021 Examination Guidelines 4. Corollaries derived from the theorems and axioms are necessary in solving riders:  Angles in a semi-circle  Equal chords subtend equal angles at the circumference  Equal chords subtend equal angles at the centre  In equal circles, equal chords subtend equal angles at the circumference  In equal circles, equal chords subtend equal angles at the centre.  The exterior angle of a cyclic quadrilateral is equal to the interior opposite angle of the quadrilateral.  If the exterior angle of a quadrilateral is equal to the interior opposite angle of the quadrilateral, then the quadrilateral is cyclic.  Tangents drawn from a common point outside the circle are equal in length. 5. The theory of quadrilaterals will be integrated into questions in the examination. 6. Concurrency theory is excluded. TRIGONOMETRY 1. The reciprocal ratios cosec , sec  and cot  can be used by candidates in the answering of problems but will not be explicitly tested. 2. The focus of trigonometric graphs is on the relationships, simplification and determining points of intersection by solving equations, although characteristics of the graphs should not be excluded. ANALYTICAL GEOMETRY 1. Prove the properties of polygons by using analytical methods. 2. The concept of collinearity must be understood. 3. Candidates are expected to be able to integrate Euclidean Geometry axioms and theorems into Analytical Geometry problems. 4. The length of a tangent from a point outside the circle should be calculated. 5. Concepts involved with concurrency will not be examined. STATISTICS 1. Candidates should be encouraged to use the calculator to calculate standard deviation, variance and the equation of the least squares regression line. 2. The interpretation of standard deviation in terms of normal distribution is not examinable. 3. Candidates are expected to identify outliers intuitively in both the scatter plot as well as the box and whisker diagram. In the case of the box and whisker diagram, observations that lie outside the interval (lower quartile – 1,5 IQR; upper quartile + 1,5 IQR) are considered to be outliers. However, candidates will not be penalised if they did not make use of this formula in identifying outliers. Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics 9 DBE/2021 Examination Guidelines 4. ACCEPTABLE REASONS: EUCLIDEAN GEOMETRY In order to have some kind of uniformity, the use of the following shortened versions of the theorem statements is encouraged. 4.1 ACCEPTABLE REASONS: EUCLIDEAN GEOMETRY (ENGLISH) 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 adj s supp form a straight line. The adjacent angles in a revolution add up to 360. 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 alt s = parallel. If the corresponding angles between two lines are equal, then the lines corresp s = are parallel. If the co-interior angles between two lines are supplementary, then the coint s supp lines are parallel. TRIANGLES The interior angles of a triangle are supplementary.  sum in  OR sum of s in ∆ OR Int s  The exterior angle of a triangle is equal to the sum of the interior ext  of  opposite angles. 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 Pythagoras OR sum of the squares of the other two sides. Theorem of Pythagoras If the square of the longest side in a triangle is equal to the sum of the Converse Pythagoras squares of the other two sides then the triangle is right-angled. OR Converse Theorem of Pythagoras If three sides of one triangle are respectively equal to three sides of SSS another triangle, the triangles are congruent. If two sides and an included angle of one triangle are respectively SAS OR SS equal to two sides and an included angle of another triangle, the triangles are congruent. If two angles and one side of one triangle are respectively equal to two AAS OR S angles and the corresponding side in another triangle, the triangles are congruent. If in two right-angled triangles, the hypotenuse and one side of one RHS OR 90°HS triangle are respectively equal to the hypotenuse and one side of the other, the triangles are congruent Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics 10 DBE/2021 Examination Guidelines THEOREM STATEMENT ACCEPTABLE REASON(S) The line segment joining the midpoints of two sides of a triangle is Midpt Theorem parallel to the third side and equal to half the length of the third side The line drawn from the midpoint of one side of a triangle, parallel to line through midpt || to 2nd side another side, bisects the third side. A line drawn parallel to one side of a triangle divides the other two line || one side of  sides proportionally. OR prop theorem; name || lines If a line divides two sides of a triangle in the same proportion, then the line divides two sides of ∆ in prop line is parallel to the third side. If two triangles are equiangular, then the corresponding sides are in ||| s OR equiangular ∆s proportion (and consequently the triangles are similar). If the corresponding sides of two triangles are proportional, then the Sides of ∆ in prop triangles are equiangular (and consequently the triangles are similar). If triangles (or parallelograms) are on the same base (or on bases of same base; same height OR equal length) and between the same parallel lines, then the triangles (or equal bases; equal height parallelograms) have equal areas. CIRCLES The tangent to a circle is perpendicular to the radius/diameter of the tan  radius circle at the point of contact. tan  diameter If a line is drawn perpendicular to a radius/diameter at the point where line  radius OR the radius/diameter meets the circle, then the line is a tangent to the converse tan  radius OR circle. converse tan  diameter The line drawn from the centre of a circle to the midpoint of a chord is line from centre to midpt of chord perpendicular to the chord. The line drawn from the centre of a circle perpendicular to a chord line from centre  to chord bisects the chord. The perpendicular bisector of a chord passes through the centre of the perp bisector of chord circle; The angle subtended by an arc at the centre of a circle is double the  at centre = 2 × at circumference size of the angle subtended by the same arc at the circle (on the same side of the chord as the centre) The angle subtended by the diameter at the circumference of the circle s in semi-circle OR is 90. diameter subtends right angle OR 1  in  2 If the angle subtended by a chord at the circumference of the circle is chord subtends 90 OR 90, then the chord is a diameter. converse s in semi-circle Angles subtended by a chord of the circle, on the same side of the s in the same seg chord, are equal If a line segment joining two points subtends equal angles at two points line subtends equal s OR on the same side of the line segment, then the four points are concyclic. 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 equal circles; equal chords; equal s of the circles. Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics 11 DBE/2021 Examination Guidelines THEOREM STATEMENT ACCEPTABLE REASON(S) Equal chords in equal circles subtend equal angles at the centre of the equal circles; equal chords; equal s circles. 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 opp s quad supp OR quadrilateral is cyclic. converse opp s of cyclic quad The exterior angle of a cyclic quadrilateral is equal to the interior ext  of cyclic quad opposite angle. If the exterior angle of a quadrilateral is equal to the interior opposite ext  = int opp  OR angle of the quadrilateral, then the quadrilateral is cyclic. converse ext  of cyclic quad Two tangents drawn to a circle from the same point outside the circle Tans from common pt OR are equal in length Tans from same pt The angle between the tangent to a circle and the chord drawn from the tan chord theorem point of contact is equal to the angle in the alternate segment. If a line is drawn through the end-point of a chord, making with the converse tan chord theorem OR chord an angle equal to an angle in the alternate segment, then the line  between line and chord is a tangent to the circle. 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 opp sides of quad are || quadrilateral is a parallelogram. 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 opp sides of quad are = is a parallelogram. 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 opp s of quad are = OR is a parallelogram. 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 diags of quad bisect each other quadrilateral is a parallelogram. OR converse diags of a parm If one pair of opposite sides of a quadrilateral are equal and parallel, pair of opp sides = and || then the quadrilateral is a parallelogram. 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 Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics 12 DBE/2021 Examination Guidelines 4.2 ACCEPTABLE REASONS: EUCLIDEAN GEOMETRY (AFRIKAANS) STELLING AANVAARBARE REDE LYNE Aangrensende hoeke op 'n reguitlyn is supplementêr. e op reguit lyn As aangrensende hoeke supplementêr is, lê die buitenste bene van die aangr. e suppl. hoeke in 'n reguitlyn. Die som van die aangrensende hoeke om 'n punt is 360 . e om 'n punt OF e in 'n omw Regoorstaande hoeke is gelyk. regoorst. e As AB || CD, dan is die verwissellende hoeke gelyk verw. e ; AB || CD As AB || CD, dan is die ooreenkomstige hoeke gelyk. ooreenk. e ; AB || CD As AB || CD, dan is die ko-binnehoeke supplementêr. ko-binne e ; AB || CD As die verwissellende hoeke tussen twee lyne gelyk is, dan is die lyne verw. e = ewewydig. As die ooreenkomstige hoeke tussen twee lyne gelyk is, dan is die lyne ooreenk. e = ewewydig. As die ko-binnehoeke tussen twee lyne supplementêr is, dan is die lyne ko-binne e suppl. ewewydig. DRIEHOEKE Die binnehoeke van 'n driehoek is supplementêr.  som van  OF som van e in  OF binne e Die buitehoek van 'n driehoek is gelyk aan die som van die twee buite  van teenoorstaande binnehoeke. Die hoeke teenoor die gelyke sye van 'n gelykbenige driehoek, is e teenoor gelyke sye gelyk. Die sye teenoor die gelyke sye van 'n gelykbenige driehoek, is gelyk. sye teenoor gelyke e In 'n reghoekige driehoek is die vierkant op die skuinssy gelyk aan die Pythagoras OF Stelling van som van die vierkante op die ander twee sye. Pythagoras As die vierkant op een sy van 'n driehoek gelyk is aan die som van die Omgekeerde Pythagoras vierkante op die ander twee sye, dan is die driehoek reghoekig. OF Omgekeerde stelling: Pythagoras As drie sye van een driehoek onderskeidelik gelyk is aan drie sye van SSS 'n ander driehoek, dan is die driehoeke kongruent. As twee sye en 'n ingeslote hoek van een driehoek onderskeidelik SHS OF SS gelyk is aan twee sye en 'n ingeslote hoek van 'n ander driehoek, dan is die twee driehoeke kongruent. As twee hoeke en 'n sy van een driehoek onderskeidelik gelyk is aan HHS OF S twee hoeke en 'n ooreenstemmende sy van 'n ander driehoek, dan is die twee driehoeke kongruent. As die skuinssy en 'n reghoeksy van 'n reghoekige driehoek RHS OF 90°HS onderskeidelik gelyk is aan die skuinssy en 'n reghoeksy van 'n ander reghoekige driehoek, dan is die twee driehoeke kongruent. Die lynstuk wat die middelpunte van twee sye van 'n driehoek verbind, Midpt.-stelling is ewewydig aan en gelyk aan die helfte van die derde sy. Die lynstuk wat van die middelpunt van een sy van 'n driehoek lyn deur midpt || 2de sy ewewydig aan die tweede sy getrek word, halveer die derde sy. Die lyn ewewydig aan een sy van 'n driehoek verdeel die ander twee lyn || een sy van OF sye in eweredige dele. eweredige stelling; noem || lyne Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics 13 DBE/2021 Examination Guidelines STELLING AANVAARBARE REDE As 'n lyn twee sye van 'n driehoek in eweredige dele verdeel, is die lyn lyn verdeel twee sye van ewewydig aan die derde sy. eweredig As twee driehoeke gelykhoekig is, is hulle ooreenstemmende sye ||| e OF gelykhoekige e eweredig (en is driehoeke dus gelykvormig). e As die ooreenstemmende sye van twee driehoeke eweredig is, is die Sye van eweredig driehoeke gelykhoekig (en is driehoeke dus gelykvormig). Driehoeke (of parallelogramme) op dieselfde basis en tussen dieselfde dieselfde basis ; dieselfde hoogte ewewydige lyne is gelyk in oppervlakte. OF gelyke basis ; gelyke hoogte SIRKELS 'n Raaklyn aan 'n sirkel is loodreg op die radius/middellyn van die raaklyn  radius sirkel by die raakpunt. raaklyn  middellyn As 'n lyn loodreg getrek word na die radius/middellyn by die punt Lyn  Radius OF waar die radius/middellyn die sirkel ontmoet, dan is die lyn 'n raaklyn omgekeerde raaklyn  radius OF aan die sirkel. omgekeerde raaklyn  middellyn Die lynstuk wat die middelpunt van 'n sirkel met die middelpunt van 'n lyn vanuit midpt na midpt van koord verbind, is loodreg op die koord. koord Die loodlyn uit die middelpunt van 'n sirkel na 'n koord, halveer die lyn vanuit midpt  op koord koord. Die middelloodlyn van 'n koord gaan deur die middelpunt van die middelloodlyn van koord sirkel. Die hoek wat 'n koord by die middelpunt van 'n sirkel onderspan, is Midpts = 2 x Omtreks dubbel die hoek wat dit by enige punt op die omtrek onderspan (aan dieselfde kant van die koord as die midpt). Die omtrekshoek wat deur die middellyn onderspan word, is 90°.  in halwe sirkel OF middellyn onderspan regte hoek OF  in  As 'n koord van 'n sirkel 'n regte hoek by die omtrek onderspan, dan is Koord onderspan 90 OF die koord 'n middellyn. omgekeerde  in halwe sirkel Hoeke onderspan deur 'n koord van 'n sirkel, aan dieselfde kant van die e in dieselfde segment koord, is gelyk. As 'n lynstuk wat twee punte verbind, gelyke hoeke by twee ander Lynstuk onderspan gelyke e OF punte aan dieselfde kant van die lynstuk onderspan, dan is die vier omgekeerde e in dieselfde punte konsiklies (d.w.s. hulle lê op die omtrek van 'n sirkel). segment Gelyke koorde onderspan gelyke omtrekshoeke. gelyke koorde; gelyke e Gelyke koorde onderspan gelyke middelpuntshoeke. gelyke koorde; gelyke e Gelyke koorde in gelyke sirkels onderspan gelyke omtrekshoeke. gelyke sirkels; gelyke koorde ; gelyke e Gelyke koorde in gelyke sirkels onderspan gelyke middelpuntshoeke. gelyke sirkels; gelyke koorde ; gelyke e Die teenoorstaande hoeke van 'n koordvierhoek is supplementêr. teenoorst. e van kvh As die teenoorstaande hoeke van 'n vierhoek supplementêr is, dan is teenoorst. e van vierhoek is supp die vierhoek 'n koordevierhoek. OF omgekeerde teenoorst e koordevierhoek Die buitehoek van 'n koordevierhoek is gelyk aan die teenoorstaande buite van kvh binnehoek. Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics 14 DBE/2021 Examination Guidelines STELLING AANVAARBARE REDE As die buitehoek van 'n vierhoek gelyk is aan die teenoorstaande buite van vierhoek = teenoorst. binnehoek, dan is die vierhoek 'n koordevierhoek. binne  OF omgekeerde buite  koordevierhoek Twee raaklyn wat vanaf dieselfde punt buite 'n sirkel na 'n sirkel Raaklyne vanuit gemeensk. Punt getrek word, is ewe lank. OF raaklyne vanaf dieselfde punt Die hoek wat gevorm word tussen 'n raaklyn aan 'n sirkel en 'n koord raaklyn koord stelling wat vanuit die raakpunt getrek word, is gelyk aan die hoek in die oorstaande segment. As 'n lyn deur die eindpunt van 'n koord 'n hoek met die koord vorm  tussen lyn en koord OF wat gelyk is aan die hoek in die oorstaande segment, dan is die lyn 'n omgekeerde raaklyn koord stelling raaklyn aan die sirkel. VIERHOEKE Die som van die binnehoeke van 'n vierhoek is 360. som van e in vierhoek Die teenoorstaande sye van 'n parallelogram is ewewydig. teenoorst. sye van ||m As die teenoorstaande sye van 'n vierhoek ewewydig is, dan is die teenoorst sye van vierh is || vierhoek 'n parallelogram. Die teenoorstaande sye van 'n parallelogram is gelyk in lengte. teenoorst. sye van ||m As die teenoorstaande sye van 'n vierhoek gelyk is, dan is die vierhoek teenoorst sye van vierh = OF 'n parallelogram. omgekeerde teenoorst sye van ||m Die teenoorstaande hoeke van 'n parallelogram is gelyk. teenoorst. e van ||m As die teenoorstaande hoeke van 'n vierhoek gelyk is, dan is die teenoorst. e van vierh = OF vierhoek 'n parallelogram. omgekeerde teenoorst. e van ||m Die hoeklyne van 'n parallelogram halveer mekaar. hoeklyne van ||m As die hoeklyne van 'n vierhoek mekaar halveer, dan is die vierhoek 'n hoeklyne van vierh halveer mekaar parallelogram. OF omgekeerde hoeklyne van ||m As een paar teenoorstaande sye van 'n vierhoek gelyk en ewewydig is, teenoorst. sye = en || dan is die vierhoek 'n parallelogram. Die hoeklyne van 'n parallelogram halveer die oppervlakte van die hoeklyn van ||m halveer opp parallelogram. Die hoeklyne van 'n ruit halveer mekaar reghoekig. hoeklyne van ruit Die hoeklyne van 'n ruit halveer die teenoorstaande binnehoeke. hoeklyne van ruit Al vier sye van 'n ruit is gelyk. sye van ruit Al vier sye van 'n vierkant is gelyk. sye van vierkant Die hoeklyne van 'n reghoek is ewe lank. hoeklyne van reghoek Die hoeklyne van 'n vlieër sny mekaar reghoekig. hoeklyne van vlieër Die een hoeklyn van 'n vlieër halveer die ander hoeklyn. hoeklyne van vlieër Een hoeklyn van 'n vlieër halveer die teenoorstaande binnehoeke hoeklyne van vlieër Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics 15 DBE/2021 Examination Guidelines 5. INFORMATION SHEET  b  b 2  4ac x 2a A  P(1  ni) A  P(1  ni) A  P(1  i) n A  P(1  i) n Tn  a  (n  1)d Sn  n 2a  (n  1)d  2 Tn  ar n1 ar n  1 ; S  a Sn  r 1 ; 1  r  1 r 1 1 r F  x 1  i   1 n  P  x 1  1  i  n  i i f ( x  h)  f ( x ) f ' ( x)  lim h 0 h  x  x2 y1  y 2  d  ( x 2  x1 ) 2  ( y 2  y1 ) 2 M  1 ;   2 2  y 2  y1 y  mx  c y  y1  m( x  x1 ) m m  tan x 2  x1 x  a 2   y  b2  r 2 a b c 1 In ABC:   a 2  b 2  c 2  2bc. cos A area ABC  ab. sin C sin A sin B sin C 2 sin     sin  . cos   cos  .sin  sin     sin  . cos   cos  .sin  cos     cos  . cos   sin  . sin  cos     cos  . cos   sin  . sin  cos 2   sin 2   cos 2  1  2 sin 2  sin 2  2 sin  . cos  2 cos 2   1  n 2 x  x  x  i x   2 i 1 n n n( A) P( A)  P(A or B) = P(A) + P(B) – P(A and B) nS  yˆ  a  bx b  x  x ( y  y ) (x  x) 2 Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics 16 DBE/2021 Examination Guidelines 6. GENERAL GUIDELINES FOR MARKING  If a learner makes more than one attempt at answering a question and does not cancel any of them out, only the first attempt will be marked irrespective of which of the attempt(s) may be the correct answer.  Consistent Accuracy marking regarding calculations will be followed in the following cases: - Subquestion to subquestion: When a certain variable is incorrectly calculated in one subquestion and needs to be substituted into another subquestion, full marks can be awarded for the subsequent subquestions provided the methods used are correct and the calculations are correct. - Assuming values/answers in order to solve a problem is unacceptable. 7. CONCLUSION This Examination Guidelines document is meant to articulate the assessment aspirations espoused in the CAPS document. It is therefore not a substitute for the CAPS document which teachers should teach to. Qualitative curriculum coverage as enunciated in the CAPS cannot be over-emphasised. Copyright reserved