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Mathematics

The National Benchmark Test in Mathematics aims to assess a learners’ ability with respect to a number of mathematical topics, set out below.
 

It is not the intention of these tests to replicate the NSC. The MAT tests are explicitly designed to provide a snapshot of the mathematical competencies of test writers at a particular point in time.
 

The knowledge and skills assessed relate to school mathematical content that is relevant to Higher Education. The MAT tests attempt to determine how well relevant mathematical concepts have been understood and can be applied.
 

Tests will contain items at four different cognitive levels selected from the competence areas described below. Items are thus located within a matrix defined by the competence areas and four levels of difficulty.
 

These levels are roughly described in terms of knowing (Level 1), performing routine procedures (Level 2), performing complex procedures (Level 3) and reasoning, reflecting and problem solving (Level 4).
 

The fact that ‘problem solving’ is placed at Level 4 should not suggest that there is no problem solving at any other level, but rather that problem solving at this cognitive level requires greater insight than problem solving where routine procedures or more complex procedures are involved.

 

1. PROBLEM SOLVING AND MODELLING

1.1 Algebraic processes

  • Pattern recognition and generation.
  • Operations involving relationships such as ratios and percentages.
  • Modelling situations by making use of mathematical process skills.
  • Operations involving surds, logarithms and exponents, including financial calculations.
  • Calculations involving integers, rational and irrational numbers.
  • Algebraic manipulation.
 

1.2 Functions represented by graphs and equations

  • Identification of domain and range.
  • Properties of graphs, relationship between graphs and their equations or inequalities.
  • Graphs of functions and interpretations of transformations (rotations, translations, reflections) of functions; solution of related problems.
 

2. BASIC TRIGONOMETRY, INCLUDING GRAPHS OF TRIGONOMETRIC FUNCTIONS, PROBLEMS REQUIRING SOLUTIONS OF TRIGONOMETRIC EQUATIONS AND APPPLICATION OF TRIGONOMETRIC CONCEPTS

  • Characteristics and interpretations of trigonometric functions and their graphs (such as domain, range, period, amplitude), including transformations of trigonometric functions.
  • Problems involving the solution of trigonometric equations and the use of identities.
  • Application of area, sine and cosine rules problems.
  • Application of trigonometric concepts in solving problems, including two- and three-dimensional problems.
 

3. SPATIAL PERCEPTION INCLUDING ANGLES, SYMMETRIES, MEASUREMENTS, REPRESENTATIONS AND INTERPRETATION OF TWO-DIMENSIONAL AND THREE-DIMENSIONAL SHAPES

  • Transformations (including scale factor).
  • Properties of shapes (2D and 3D).
  • Perimeter, area, volume (modelling).
  • Analytic geometry (linking geometric and algebraic properties).
 

4. DATA HANDLING

  • Measurement (and related interpretations).
  • Representation (and related interpretations).
 

5. COMPETENT USE OF LOGICAL SKILLS IN MAKING DEDUCTIONS AND DETERMINING THE TRUTH OF GIVEN ASSERTIONS