1. Presented by: MA HENDRICKS
USAF CoP : Teaching and Learning of Mathematics
“Technical Mathematics”
UNISA (Pretoria)
Bamboo Auditorium
19 February 2019
Presented by: MA HENDRICKS

2. CAPS ( Curriculum and Assessment Policy Statement)
Comparison of the Aims , Structure , Content and Assessment of the Papers for
Technical Mathematics
&
Mathematics
CAPS ( Curriculum and Assessment Policy Statement)

3. TECHNICAL MATHEMATICS
CAPS DEFINITIONS
TECHNICAL MATHEMATICS
MATHEMATICS
Mathematics is a LANGUAGE that makes use of symbols and notations describing numerical , geometric and graphical representations.

4. TECHNICAL MATHEMATICS
CAPS DEFINITIONS
MATHEMATICS
TECHNICAL MATHEMATICS
It is a HUMAN ACTIVITY that involves observing, representing and investigating patterns and qualitative relationships in physical and social phenomena and between mathematical objects themselves

5. TECHNICAL MATHEMATICS
CAPS DEFINITIONS
MATHEMATICS
TECHNICAL MATHEMATICS
It helps to DEVELOP MENTAL PROCESSES that enhance logical and critical thinking , accuracy and problem solving that will contribute in decision making.

6. TECHNICAL MATHEMATICS.
CAPS DEFINITIONS
MATHEMATICS
TECHNICAL MATHEMATICS.
Mathematical problem solving enables us to understand the world (physical, social and economic) around us , and, most of all to teach us to think creatively.

7. TECHNICAL MATHEMATICS
CAPS DEFINITIONS
MATHEMATICS
TECHNICAL MATHEMATICS
The aim of Technical Mathematics is to APPLY the Science of Mathematics to the TECHNICAL FIELD
where the emphasis is
on APPLICATION
and
not on abstract ideas.

8. SPECIFIC AIMS DIFFERENCES TECHNICAL MATHEMATICS.
To provide the opportunity to develop in learners the ability to be methodical , to generalize ,
make conjectures
and try to justify
or prove them..
To provide the opportunity to develop in learners the ability to be methodical , to generalize and
to be skillful users of
the Science of
Mathematics

9. SPECIFIC AIMS (DIFFERENCES) TECHNICAL MATHEMATICS
To provide learners of Technical Schools an alternative and value adding substitute to Mathematical Literacy.
To support and sustain technical subjects at Technical Schools

10. SPECIFIC AIMS (DIFFERENCES) TECHNICAL MATHEMATICS
To provide a vocational route aligned with the expectations of labour in order to ensure direct access to learnership/ apprenticeship.
To create the opportunity for learners to further their studies at FET Colleges at an entrance level of N4 and thus creating an alternative route to access other HEI’s.

11. OVERVIEW ASSESSMENT COMMON STRUCTURE PAPER 1 SIMILAR CONTENT PAPER 2
DIFFERENCES
ASSESSMENT

12. STRUCTURE OF THE TWO PAPERS
TECHNICAL MATHEMATICS
Paper 1 1
Number Systems 2
Algebra 3
Functions & Graphs 4
Finance 5
Differential Calculus & Integration
MATHEMATICS
Paper 1 1
Algebra 2
Patterns & Sequences 3
Finance 4
Functions & Graphs 5
Differential Calculus 6
Probability & Counting Principle

13. STRUCTURE OF THE TWO PAPERS
TECHNICAL MATHEMATICS
Paper 2 1
Analytical Geometry 2
Trigonometry 3
Euclidean Geometry 4
Mensuration 5
Circles, Angles & Angular movement
MATHEMATICS
Paper 2 1
Statistics 2
Analytical Geometry 3
Trigonometry 4
Euclidean Geometry

14. STRUCTURE OF THE TWO PAPERS
COMMON
PAPER 2
PAPER 1
FOUR Topics
ALGEBRA
FUNCTIONS
FINANCE
DIFFERENTIAL CALCULUS
THREE Topics
ANALYTICAL GEOMETRY
TRIGONOMETRY
EUCLIDEAN GEOMETRY

15. DIFFERENCES Mathematics Mathematics STRUCTURE OF THE TWO PAPERS
Technical Mathematics
OTHER NUMBER SYSTEMS
- Binary numbers
- Complex Numbers
INTEGRATION
Technical Mathematics
CIRCLE (SECTORS /SEGMENTS)
RADIAN MEASURE
ANGULAR MOVEMENT
Mathematics
NUMBER PATTERNS
PROBABILITY
Mathematics
STATISTICS

16. CONTENT OF THE TWO PAPERS Technical Mathematics & Mathematics
SIMILAR
PAPER 1
ALGEBRA
Topics
Technical Mathematics & Mathematics 1
Linear Equations and Inequalities 2
Quadratic Equations and Inequalities 3
Simultaneous equations 4
Exponents/ Surds / exponential Equations 5
Logarithms to solve simple exponential equations 6
Remainder & Factor Theorem 7
Nature of roots of quadratic equations

19. CONTENT OF THE TWO PAPERS Technical Mathematics Additional Content
DIFFERENCES
PAPER 1
ALGEBRA
topics
Technical Mathematics Additional Content 1
Binary Number system 2
Complex Numbers 3
Equations involving complex numbers 4
Logarithmic equations 5
Scientific Notation 6
Real Life applications from Technical Field

20. CONTENT OF THE TWO PAPERS
SIMILAR
Functions
Graphs
Technical Mathematics & Mathematics 1
Linear / Quadratic/ Exponential functions 2
Hyperbolic Functions – Technical Mathematics simpler types 3
Cubic Functions – Technical Mathematics simpler types
DIFFERENCES
Functions
Graphs
Technical Mathematics Additional Content 1
Graphs of Circle / Semi-circle and Ellipse

25. CONTENT OF THE TWO PAPERS Technical Mathematics & Mathematics
SIMILAR
FINANCE
topics
Technical Mathematics & Mathematics 1
Simple & Compound Growth and Decay 2
Nominal & Effective rates 3
Real life applications
DIFFERENCES
FINANCE
topics
Mathematics ONLY 1
ANNUITIES – Future and Present Values

26. CONTENT OF THE TWO PAPERS Technical Mathematics & Mathematics
SIMILAR
PAPER 1
CALCULUS
topics
Technical Mathematics & Mathematics 1
First Principles **** 2
Differentiation Rules 3
Equation of tangents 4
Rates of change 5
Graphs of Cubic functions **** 6
Optimization
**** TECHNICAL MATHEMATICS –Simpler examples

31. CONTENT OF THE TWO PAPERS Technical Mathematics Additional Content
DIFFERENCES
PAPER 1
CALCULUS
topics
Technical Mathematics Additional Content 1
Calculus of Motion ( Displacement Formula) 2
Basic Integration 3
Definite Integral 4
Areas bounded by a curve and x-axis

32. CONTENT OF THE TWO PAPERS
DIFFERENCES
PAPER 1
SEQUENCES & SERIES
Mathematics ONLY 1
Quadratic sequences 2
General terms – Arithmetic & Geometric Sequences 3
Summation of Series & Convergence
PROBABILITY
Mathematics ONLY 1
Probability 2
Basic Counting Principle

33. CONTENT OF THE TWO PAPERS Technical Mathematics &
SIMILAR
PAPER 2
ANALYTICAL
GEOMETRY
Technical Mathematics &
Mathematics 1
Distance / Midpoint / Gradient 2
Angle of inclination 3
Equation of straight lines 4
Equation of circle with centre (0;0) 5
Equation of tangent to circle 6
Points of intersection

36. CONTENT OF THE TWO PAPERS Technical Mathematics ONLY
DIFFERENCES
PAPER 2
ANALYTICAL
GEOMETRY
Mathematics ONLY 1
Equation of circle with centre (a;b) and Applications
ANALYTICAL
GEOMETRY
Technical Mathematics ONLY 1
Equation of ellipse & semi-circle and plotting graph of ellipse and semi-circle

37. CONTENT OF THE TWO PAPERS Technical Mathematics & Mathematics
SIMILAR
TRIGONOMETRY
Technical Mathematics & Mathematics 1
Sine , Cosine & Tangent functions 2
Basic Sine , Cosine & Tangent Identities 3
Solution of trigonometric equations [0o ; 360o] 4
Graphs of trig functions 5
Reduction formulae 6
Application of Sine , Cosine and Area Rules in 2D & 3D
Technical Mathematics restricted to numerical examples .
PAPER 2

42. CONTENT OF THE TWO PAPERS Technical Mathematics ONLY
DIFFERENCES
TRIGONOMETRY
DEGREES & RADIANS
Technical Mathematics ONLY 1
Cosecant , Secant & Cotangent functions 2
Basic Cosecant , Secant & Cotangent Identities 3
2D & 3D problems restricted to numerical measurements only.
PAPER 2
TRIGONOMETRY
DEGREES only
Mathematics ONLY 1
Solution of trigonometric equations including negative angles. 2
General solutions of trigonometric equations 3
Proofs of Sine, Cosine and Area Rules examinable.

43. CONTENT OF THE TWO PAPERS
SIMILARITIES
PAPER 2
EUCLIDEAN
GEOMETRY
Technical Mathematics & Mathematics 1
Circle Theorems 2
Proportion and Similarity Theorems 3
Applications
DIFFERENCES
EUCLIDEAN
GEOMETRY
Technical Mathematics 1
Proofs of Theorems NOT EXAMINABLE 2
Riders restricted to Calculations only – No proofs

46. CONTENT OF THE TWO PAPERS Technical Mathematics ONLY
DIFFERENCES
PAPER 2
SHAPES
ANGULAR
MEASUREMENT
Technical Mathematics ONLY 1
Radian Measure 2
Arcs and Angles / Areas of Sectors and Segments of circle 3
Angular and Circumferential Velocity 4
Surface Areas & Volumes of Prisms, Cylinders, Cones & Spheres 5
Areas of irregular shapes using the
Mid-ordinate rule.

47. CONTENT OF THE TWO PAPERS
DIFFERENCES
PAPER 2
STATISTICS
Mathematics ONLY 1
Measures of central tendency ( Mean , Mode. Median) 2
Measures of dispersion (range , variance) 3
Lines of best fit , correlation 4
Box-whisker plots, scatter plots, ogives, frequency polygons, histograms 5
Frequency tables

48. ASSESSMENT OF THE TWO PAPERS TECHNICAL MATHEMATICS
WEIGHTING OF TOPICS
PAPER 1
TOPICS
TECHNICAL MATHEMATICS
MATHEMATICS
ALGEBRA
33,3%
16,6%
FUNCTIONS
23,4%
FINANCE
10%
CALCULUS
SEQUENCES & SERIES 0%
PROBABILITY

49. ASSESSMENT OF THE TWO PAPERS TECHNICAL MATHEMATICS
WEIGHTING OF TOPICS
PAPER 2
TOPICS
TECHNICAL MATHEMATICS
MATHEMATICS
ANALYTICAL GEOMETRY
17%
27%
TRIGONOMETRY
33%
EUCLIDEAN GEOMETRY
MENSURATION , CIRCLES, ANGLES , ANGULAR MOVEMENT
23% 0%
STATISTICS
13%

50. TOPICS WEIGHTING OF TAXONOMY LEVELS ASSESSMENT OF THE TWO PAPERS
DIFFERENCES
PAPER 1 & 2
TOPICS
TECHNICAL MATHEMATICS
2018 Exam Guidelines
MATHEMATICS
KNOWLEDGE
25%
20%
ROUTINE PROCEDURES
45%
35%
COMPLEX PROCEDURES
30%
PROBLEM SOLVING
10%
15%

51. TOPICS WEIGHTING OF TAXONOMY LEVELS
TECHNICAL MATHEMATICS NOV Paper
WEIGHTING OF TAXONOMY LEVELS
ANALYSIS DBE EXAMINING PANEL NOV 2018
PAPER 1 & 2
TOPICS
NORM
PAPER 1
PAPER 2
KNOWLEDGE
25%
23,3%
26,7%
ROUTINE PROCEDURES
45%
46,0%
43,3%
COMPLEX PROCEDURES
20%
22,6%
PROBLEM SOLVING
10%
7,4%

52. SOME ACCREDITATION RECOMMENDATIONS
FOR HEI’s
TECHNICAL MATHEMATICS:
TO BE EVALUATED THE SAME AS MATHEMATICS FOR
NON- MATHEMATICS PROGRAMMES
TO BE EVALUATED THE SAME AS MATHEMATICS FOR PROGRAMMES THAT REQUIRE MATHEMATICS FOR ENTRY, BUT VERY LITTLE PURE MATHEMATICS or SOME SERVICE MATHEMATICS MODULES IS TAUGHT.
e.g.
Business & Economic Sciences
Architecture / Building Sciences
Health Sciences
Biological Sciences

53. SOME ACCREDITATION RECOMMENDATIONS
TECHNICAL MATHEMATICS: PROGRAMMES WITH MATHEMATICS PRE-REQUISITE
PRE 2018 EXAMINATION GUIDELINES:
TO BE EVALUATED THE SAME AS MATHEMATICS FOR PROGRAMMES THAT REQUIRE MATHEMATICS FOR ENTRY
TO BE CONSIDERED EQUIVALENT TO MATHEMATICS FOR ACADEMIC ACCESS TO HE

54. SOME ACCREDITATION RECOMMENDATIONS
TECHNICAL MATHEMATICS: PROGRAMMES WITH MATHEMATICS PRE-REQUISITE
(SCIENCE / ENGINEERING/ )
POST EXAMINATION GUIDELINES:
(CHANGE OF TAXONOMY WEIGHTINGS)
TO BE EVALUATED AT ONE LEVEL LOWER AS MATHEMATICS FOR PROGRAMMES THAT REQUIRE MATHEMATICS FOR ENTRY

55. THANK YOU