Presentation by Marina Nazarova International Baccalaureate Diploma Programme Mathematics. Name - Marina Nazarova I work at school № 9 Study at Perm Teacher Training University Work with DP Mathematics HL and SL Sphere of interests – Computer in Mathematical Studies.
by Marina Nazarova
The main aim:
IB DP overview
Command terms for lessons on mathematics
Assessment system and terminology
Presumed knowledge content
Maths SL themes
Maths HL themes
All topics in the core are compulsory. Students must study all the sub-topics in each of the topics in the syllabus as listed in guide. Students are also required to be familiar with the topics listed as presumed knowledge (PK).
Topic 1—Algebra 20 hrs
Topic 2—Functions and equations 26 hrs
Topic 3—Circular functions and trigonometry 22 hrs
Topic 4—Matrices 12 hrs
Topic 5—Vectors 22 hrs
Topic 6—Statistics and probability 40 hrs
There are two types of tasks:
• mathematical investigation
• mathematical modelling.
There are 3 examination papers, assest by external experts.
Studentsneed to be familiar with notation the IBO uses and the command terms, as these will be used withoutexplanation in the examination papers
Let’s demonstrate the way we studied the topic “Arithmetic and geometric sequences and series”.
Arithmetic sequences “Arithmetic and geometric sequences and series”.
An arithmetic sequence, sometimes known as an arithmetic progression, is one where the terms are separated by the same amount each time. This is known as the common difference and is denoted by d.Note that for a sequence to be arithmetic, a common difference must exist.
Consider the sequence 5, 7, 9, 11, 13, ... The first term is 5 and the common difference is 2. So we can say a = 5 and d = 2. Sequences can be defined in two ways, explicitly or implicitly. An implicit expression gives the result in relation to the previous term, whereas an explicit expression gives the result in terms of n. Although it is very easy to express sequences implicitly, it is usually more useful to find an explicit expression in terms of n.
u “Arithmetic and geometric sequences and series”.n = a + (n – 1) d
This is an example of command terms glossary “Arithmetic and geometric sequences and series”.
Write down “Arithmetic and geometric sequences and series”.Obtain the answer(s), usually by extracting information. Little or no calculation isrequired.
Working does not need to be shown.
CalculateObtain the answer(s) showing all relevant working. “Find” and “determine” can alsobe used.
Find Obtain the answer(s) showing all relevant working. “Calculate” and “determine” canalso be used.
DetermineObtain the answer(s) showing all relevant working. “Find” and “calculate” can also beused.
DifferentiateObtain the derivative of a function.
Integrate Obtain the integral of a function.
Solve Obtain the solution(s) or root(s) of an equation.
Draw “Arithmetic and geometric sequences and series”.Represent by means of a labelled, accurate diagram or graph, using a pencil. A ruler(straight edge) should be used for straight lines. Diagrams should be drawn to scale.
Graphs should have points correctly plotted (if appropriate) and joined in a straightline or smooth curve.
SketchRepresent by means of a diagram or graph, labelled if required. A sketch should givea general idea of the required shape of the diagram or graph. A sketch of a graph
should include relevant features such as intercepts, maxima, minima, points ofinflexion and asymptotes.
PlotMark the position of points on a diagram.
CompareDescribe the similarities and differences between two or more items.
Deduce “Arithmetic and geometric sequences and series”.Show a result using known information.
JustifyGive a valid reason for an answer or conclusion.
ProveUse a sequence of logical steps to obtain the required result in a formal way.
Show thatObtain the required result (possibly using information given) without the formality of
proof. “Show that” questions should not generally be “analysed” using a calculator.
Hence Use the preceding work to obtain the required result.
Hence orotherwiseIt is suggested that the preceding work is used, but other methods could also receive
Thank you for attention conference