Mathematics grade 12 exam guidelines 2022 pdf download – Examination Guidelines for Grade 12 South Africa 2022/2023

• 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.

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

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.

• 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.
• Trigonometric functions will ONLY be examined in PAPER 2.

  NUMBER PATTERNS, SEQUENCES AND SERIES

• 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.
• Recursive patterns will not be examined explicitly.
• Links must be clearly established between patterns done in earlier grades.
  
  FINANCE, GROWTH AND DECAY
• 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.
• 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.
• Pyramid schemes will NOT be examined in the examination.

  ALGEBRA

• Solving quadratic equations by completing the square will NOT be examined.
• Solving quadratic equations using the substitution method (k-method) is examinable.
• Equations involving surds that lead to a quadratic equation are examinable.
• Solution of non-quadratic inequalities should be seen in the context of functions.
• Nature of the roots will be tested intuitively with the solution of quadratic equations and in all theprescribed functions.

  DIFFERENTIAL CALCULUS

• The following notations for differentiation c an be used: f ‘(x) , x D_x ,dy or y ‘
  dx
• 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.
• Candidates are expected to be able to draw and interpret the graph of the derivative of a function.
• Surface area and volume will be examined in the context of optimisation.
• 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
• 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

• Dependent events are examinable but conditional probabilities are not part of the syllabus.
• Dependent events in which an object is not replaced are examinable.
• 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.
• 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

• Measurement can be tested in the context of optimisation in calculus and two- and three-dimensional trigonometry.
• Composite shapes could be formed by combining a maximum of TWO of the stated shapes.
• 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.
• 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.
• The theory of quadrilaterals will be integrated into questions in the examination.
• Concurrency theory is excluded.

  TRIGONOMETRY

• The reciprocal ratios cosec θ, sec θ and cot θ can be used by candidates in the answering of problems but will not be explicitly tested.
• 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

• Prove the properties of polygons by using analytical methods.
• The concept of collinearity must be understood.
• Candidates are expected to be able to integrate Euclidean Geometry axioms and theorems into Analytical Geometry problems.
• The length of a tangent from a point outside the circle should be calculated.
• Concepts involved with concurrency will not be examined.

  STATISTICS

• Candidates should be encouraged to use the calculator to calculate standard deviation, variance and the equation of the least squares regression line.
• The interpretation of standard deviation in terms of normal distribution is not examinable.
• 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.

• 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.