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Curriculum: 

Final objectives of the third grade of mainstream secondary education - ASO

Core Curriculum main page - Third grade mainstream secondary education

MATHEMATICS

1 General final objectives

The pupils are able to:

1 understand and use the language of mathematics;

2 analyse mathematical information, represent it in diagrams and structure it;

3 analyse simple mathematical problems (making a distinction between data and the question, explore the relevance of the data and make links between them) and translate this into an appropriate mathematical context;

4 tackle mathematical problems in a planned way (if necessary, by dividing them hierarchically into sub-problems);

5 in solving mathematical problems, critically reflect on the solution process and the final result;

6 give examples of real problems which can be solved with the help of mathematics;

7 use ICT in a functional way to solve mathematical problems;

8 give examples of the role of mathematics in art;

9 use the knowledge, insights and skills acquired in mathematics to explore, interpret and explain problems in the real world;

10 obtain information on the part played by mathematics in further education of their choice and their preparation for this.

The pupils:

11 * demonstrate a sense of accuracy in their use and application of mathematics;

12 * develop self-regulation with regard to the acquisition and processing of mathematical information and the solution of problems;

13 * focus on cooperation to increase their own potential.

2 Real functions

The pupils

14 can read on a graph:

  • any symmetries;
  • increases, decreases, constants;
  • the sign;
  • any zero values;
  • any extremal values.

The pupils are able to:

15 in polynomial functions

  • use the derivative as a standard for the instantaneous variable;
  • with the help of an intuitive understanding of limits, draw the link between:
    • the concept of the derivative;
    • the concept of difference quotients;
    • the slope of the tangent line.

16 calculate the derivative from the functions f(x) = x, f(x) = x2, f(x) = x3, and generalize the answer that is obtained into functions f(x) = xn, in which n is a natural number;

17 apply the rule of sum and product in order to determine the derivative of a polynomial function;

18 in polynomial functions, use the derivative to study the curve and to look up or verify extremal values and make the link between the derivative and the special character of the graph;

19 recognise the concept of the derivative in situations outside mathematics;

20 in a simple problem which can be described in terms of determining extremal values of a polynomial function, choose a variable, draw up the function rule and determine the extremal values;

21 give a explanation of the expression ab, with a>0 and b a rational number;

22 draw the graph of the function f(x) = ax (if necessary with help of ICT), and read off the domain, range, special values, increases, decreases and asymptotic behaviour;

23 for suitable domains, establish the link between the functions f(x)=x² and f(x) = wortelteken , f(x)=x³ and f(x)= ³wortelteken, and by analog between the functions f(x)=xn and f(x)= nwortelteken and between the functions f(x)=ax and f(x)=alog(x).

24 calculate the third variable in the equation ab = c, when the two others have been given (if necessary with use of ICT);

25 examine linear and exponential growth processes and with exponential growth solve concrete problems in which the calculations must be carried out with regard to the initial value, growth factor and growth percentage;

26 establish the link between degrees and radians;

27 draw the graph of the function f(x) = sinx , based on the trigonometric unit circle;

28 for the function f(x) = sinx, read the domain, range, periodicity, increases/decreases and extremal values on the graph;

29 draw the graphs of the functions f(x) = a sin (bx + c) and interpret a, b and c on this;

30 solve equations of the form sinx = k on the graph;

31 to solve a problem which makes use of functional relationships which have been studied, draw up a function rule, an equation or an inequality;

32 use tables and graphs for functions that have been studied to interpret function rules, equations and inequalities.

3  Statistics

The pupils are able to:

33 make use of a normal distribution curve as a model for a continuous random variable for data with a bell-shaped frequency distribution in significant situations, and use the mean and the standard deviation of the given data as an estimate for the mean and the standard deviation of this normal distribution;

34 interpret the mean and the standard deviation of a normal distribution curve on a graph;

35 indicate the relationship between a normal distribution curve and the standard normal distribution on a graph;

36 in a normal distribution, interpret the relative frequency of a collection of data with values between two given limits, with values larger than a given limit or with values smaller than a given limit, as the surface area of a particular area.

Attitudes have been indicated by * in the margin, for checking by the inspectorate.

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