CURRICULUM SUMMARY – Septemberto December 2017

SUBJECT: MATHEMATICAL STUDIES SLYEAR GROUP: IB1TEACHER: AGATA PISKORZ

Week / Dates / Learning objectives / Activities (in brief)
1 / 4-8 September / COORDINATE GEOMETRY
Students willknow, understand and use:
  • formulae for the midpoint and a distance between two points of given coordinates
/ Introducing the course objectives.
Deriving the formulae.
Calculating coordinates of the midpoint and distanced between points.
Solving practical problems involving the distance or the midpoint of two points.
2 / 11 -15 September /
  • the gradient formula
  • equation of a line in two dimensions: the forms y = mx + c and ax + by + d = 0 .
  • parallel and perpendicular lines
  • points of intersection of lines
/ Calculating gradients between two points.
Using the gradient in a practical situations from real life eg. gradients of mountain roads.
Finding equation of a line through two given points.
Graphing lines.
Finding where lines meet.
3 / 18 - 22 September /
  • perpendicular bisectors
/ Solving practical problems involving the equation of a line.
Solving past paper problems. Solving revision sets from the student textbooks (Review set 13A-13D)
Writing a test. Feedback of the test.
4 / 25 -29 September / NUMBERS
Students will understand and use:
  • the exponential expression: , Q; rules of indices;
  • the index notation (scientific notation): where and Z; very large and very small numbers in scientific, economic and other applications; awareness and use of scientific mode on the GDC;
  • operations with numbers expressed in the form: where and Z;
  • decimals; decimal places; approximations; rounding off to a given number of decimal places or significant figures;
  • the absolute errors; percentage errors;
/ Revising rules of indices and scientific notation.
Using GDC (Graphic Display Calculator) for conversion between scientific and standard notation.
Rounding and estimating numbers.
Calculating errors.
Estimating and accuracy –homework investigation.
5 / 2 – 6 October /
  • System International (SI); other basic units of measurements;
  • conversion between different units.
/ Converting between different units .
Revision – solving problems at class and at home.
Writing a test.
Discussing results of the test.
6 / 9 – 13 October / SEQUENCES AND SERIES
Students will understand and use:
  • definition of a sequence, the general term ( n-th term ) of a sequence,
  • definition of arithmetic and geometric sequences, the formula for the n-th term of an arithmetic sequence,
/ Generating terms of a sequence using term-to-term and position-to-term definitions of the sequence.
Specifying sequences by using words, using an explicit formula (general term – n-th term formula).
Showing that a sequence is arithmetic.
7 / 16 – 20 October /
  • the formula for the n-th term of a geometric sequence
  • the sum of an arithmetic sequence -arithmetic series, the formula for the sum of the first n terms,
/ Showing that a sequence is geometric.
Finding the formula for the general term of an arithmetic or geometric sequence. Deriving the formula for the sum of an arithmetic series.
8 / 23 – 27 October /
  • the sum of an geometric sequence, geometric series,
/ Finding sums of the arithmetic and geometric series.
Using sequences to solve word problems.
Revision – solving problems at class and at home.
Writing a test;
Discussing results of the test.
30 October–
3 November / Mid-Term Break / Mid-Term Break
9 / 6 – 10 November / DESCRIPTIVE STATISTICS
Students will understand and use:
  • concept of population and sample; classification of data as discrete or continuous;
  • mean, mode, median for discrete data;
  • quartiles; Box and Whisker Plots (boxplots); parallel boxplots;
  • grouped discrete or continuous data – organization and display;
/ What is statistics, its methods and purposes – discussion.
Finding examples of different types of data.
Using the GDC to present data: tables; frequency tables (lists); graphs, diagrams, boxplots.
Summarizing data – calculations with and without the GDC;
10 / 13 -17 November /
  • mean, mode, median for grouped discrete or continuous data;
  • cumulative frequency
  • cumulative frequency tables for grouped discrete data and grouped continuous data; cumulative frequency curves percentiles from the cumulative frequency curves;
  • measures of dispersion; range, interquartile range, standard deviation;
/ Drawing and interpreting cumulative frequency diagrams.
Presenting situations where percentiles are used.
Calculating dispersion of the data.
Calculating variance and standard deviation.
11 / 20 – 24 November /
  • significance of the numerical value of standard deviation.
/ Finding out the significance of standard deviation – examples from real world.
Revision – solving problems at class and at home.
Writing a test;
Discussing results of the test.
12 / 27 November –
1 December / BIVARIATE STATISTICS
Students will understand and use:
  • scatter plot; correlation; Pearson’s correlation coefficient.
  • line of best fit; the least square regression line;
  • interpolation and extrapolation.
/ Describing correlation.
Using the equation for prediction purposes.
Mathematical and contextual interpretation of the regression line.
Analysing and interpreting data.
13 / 4 - 8 December / THETEST FOR INDEPENDENCE
  • independent variables;
  • the null hypothesis;
  • degrees of freedom, critical value;
/ Analysing contingency tables. Finding the expected contingency table. Finding number of degrees of freedom.
Calculating . Reading the critical value.
14 / 11 – 15 December /
  • the formal test for independence.
/ Performing the formal test for independence.
Revision – solving problems at class and at home.
Writing a test. Feedback of the test.
15 / 18 – 22 December / HALF – YEAR REVISION / Solving past paper problems.
Writing a half-year assessment test.