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Skills available for South Africa grade 11 maths curriculum

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National Curriculum Statement (CAPS) National Curriculum Statement (CAPS)

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11.1 Functions

11.1.a Extend Grade 10 work on the relationships between variables in terms of numerical, graphical, verbal and symbolic representations of functions and convert flexibly between these representations (tables, graphs, words and formulae). Include linear and quadratic polynomial functions, exponential functions, some rational functions and trigonometric functions.
11.1.b Generate as many graphs as necessary, initially by means of point-by-point plotting, supported by available technology, to make and test conjectures and hence generalise the effects of the parameter which results in a horizontal shift and that which results in a horizontal stretch and/or reflection about the y-axis.
11.1.c Problem solving and graph work involving the prescribed functions. Average gradient between two points.

11.2 Number Patterns, Sequences and Series

11.2.a Investigate number patterns leading to those where there is a constant second difference between consecutive terms, and the general term is therefore quadratic.

11.3 Finance, Growth and Decay

11.3.a Use simple and compound decay formulae A = P(1 + in) and A = P(1- i)ⁿ to solve problems (including straight line depreciation and depreciation on a reducing balance). Link to work on functions.
- Describe linear and exponential growth and decay (11-L.10)
- Exponential growth and decay: word problems (11-L.11)
11.3.b The effect of different periods of compounding growth and decay (including effective and nominal interest rates).
- Compound interest (10-B.2)
- Exponential growth and decay: word problems (11-L.11)

11.4 Algebra

11.4.a Take note that there exist numbers other than those on the real number line, the so-called nonreal numbers. It is possible to square certain nonreal numbers and obtain negative real numbers as answers.
- Introduction to complex numbers (11-C.1)
11.4.b Nature of roots.
- Using the discriminant (11-E.11)
11.4.a Apply the laws of exponents to expressions involving rational exponents.
11.4.b Add, subtract, multiply and divide simple surds.
11.4.c Revise factorisation.
11.4.d Solve:
- 11.4.d.1 quadratic equations;
- 11.4.d.2 quadratic inequalities in one variable and interpret the solution graphically; and
  - Graph solutions to quadratic inequalities (11-E.12)
  - Solve quadratic inequalities (11-E.13)
- 11.4.d.3 equations in two unknowns, one of which is linear the other quadratic, algebraically or graphically.
  - Solve nonlinear simultaneous equations (11-B.11)

11.5 Differential Calculus

11.9 Analytical Geometry

11.9.a Use a Cartesian co-ordinate system to derive and apply:
- 11.9.a.1 the equation of a line through two given points;
  - Write the equation of a linear function (11-A.8)
- 11.9.a.2 the equation of a line through one point and parallel or perpendicular to a given line; and
  - Write the equation of a linear function (11-A.8)
- 11.9.a.3 the inclination of a line.

11.10. Statistics

11.10.a Represent measures of central tendency and dispersion in univariate numerical data by:
- 11.10.a.1 using ogives; and
- 11.10.a.2 calculating the variance and standard deviation of sets of data manually (for small sets of data) and using calculators (for larger sets of data) and representing results graphically.
  - Variance and standard deviation (11-Y.4)
11.10.b Represent Skewed data in box and whisker diagrams, and frequency polygons. Identify outliers.
- Interpret box-and-whisker plots (11-Y.2)

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11.1 Functions

11.1.c Problem solving and graph work involving the prescribed functions. Average gradient between two points.

11.2 Number Patterns, Sequences and Series

11.2.a Investigate number patterns leading to those where there is a constant second difference between consecutive terms, and the general term is therefore quadratic.

11.3 Finance, Growth and Decay

11.3.a Use simple and compound decay formulae A = P(1 + in) and A = P(1- i)n to solve problems (including straight line depreciation and depreciation on a reducing balance). Link to work on functions.

11.3.b The effect of different periods of compounding growth and decay (including effective and nominal interest rates).

11.4 Algebra

11.4.a Take note that there exist numbers other than those on the real number line, the so-called nonreal numbers. It is possible to square certain nonreal numbers and obtain negative real numbers as answers.

11.4.b Nature of roots.

11.4.a Apply the laws of exponents to expressions involving rational exponents.

11.4.b Add, subtract, multiply and divide simple surds.

11.4.c Revise factorisation.

11.4.d Solve:

11.4.d.1 quadratic equations;

11.4.d.2 quadratic inequalities in one variable and interpret the solution graphically; and

11.4.d.3 equations in two unknowns, one of which is linear the other quadratic, algebraically or graphically.

11.5 Differential Calculus

11.6 Probability

11.6.a Dependent and independent events.

11.6.b Venn diagrams or contingency tables and tree diagrams as aids to solving probability problems (where events are not necessarily independent).

11.7 Euclidean Geometry and Measurement

11.7.a Investigate and prove theorems of the geometry of circles assuming results from earlier grades, together with one other result concerning tangents and radii of circles.

11.7.b Solve circle geometry problems, providing reasons for statements when required.

11.7.c Prove riders.

11.7.a Revise Grade 10 work.

11.8 Trigonometry

11.8.a Derive and use the identities: tan θ = sin θ/cos θ and sin² θ + sin² θ = 1.

11.8.b Derive the reduction formulae.

11.8.c Determine the general solution and / or specific solutions of trigonometric equations.

11.8.d Establish the sine, cosine and area rules.

11.8.a Solve problems in 2-dimensions.

11.9 Analytical Geometry

11.9.a Use a Cartesian co-ordinate system to derive and apply:

11.9.a.1 the equation of a line through two given points;

11.9.a.2 the equation of a line through one point and parallel or perpendicular to a given line; and

11.9.a.3 the inclination of a line.

11.10. Statistics

11.10.a Represent measures of central tendency and dispersion in univariate numerical data by:

11.10.a.1 using ogives; and

11.10.a.2 calculating the variance and standard deviation of sets of data manually (for small sets of data) and using calculators (for larger sets of data) and representing results graphically.

11.10.b Represent Skewed data in box and whisker diagrams, and frequency polygons. Identify outliers.

11.3.a Use simple and compound decay formulae A = P(1 + in) and A = P(1- i)ⁿ to solve problems (including straight line depreciation and depreciation on a reducing balance). Link to work on functions.