KIST DP Course Descriptions

Transcription

1 Grade: 11 Unit Number: 1 Unit Title: Number and Algebra Approximate Duration: 1 month Number Classification, Approximation, Error, Scientific Notation, Units of Measurement and Conversions LP Link: Communicator Do mathematical symbols have sense in the same way words have sense? Is zero different? Are these numbers created or discovered? The aim of this unit is to introduce students to some basic elements and concepts of mathematics. Students will start the unit by reviewing how numbers can be classified. They will then study how errors can result from rounding and also work with very large and very small numbers in scientific, economic, and other applications to become familiar using scientific notation. Students will work with SI (Systeme International) units and other basic units of measurement and practice converting between them. Finally, students will use a GDC to find solutions to pairs of linear equations in two variables and quadratic equations. Use of a GDC will be heavily integrated throughout this unit as well as the course. The main summative assessment of this unit will be a test comprised of past paper questions that assess student knowledge of the unit. Classifying numbers: natural numbers, integers, rational numbers, real numbers Approximation, decimal places, significant figures, percentage errors, estimation Scientific notation, expressing numbers and operations with numbers in the form SI (Systeme International) and other basic units of measurement Converting between different units k a 10

2 Grade: 11 Unit Number: 2 Unit Title: Sets, Logic and Probability Sets, Venn Diagrams, Probability, Symbolic Logic, Truth Tables LP Link: Thinker Can the probability of an event happening be truly zero? What is an improbable event? The aim of this unit is to develop understanding of some of the functions that can be applied to practical situations. Students will explore the concept of functions as mappings. The graphs of various types of functions, such as linear functions, quadratic functions, and exponential functions, will be explored and used to understand examples from real life situations. A GDC will be used extensively in this unit. The main summative assessment of this unit will be a test comprised of past paper questions that assess student knowledge of the unit. The concept of a function as a mapping; domain, range Linear functions and their graphs f : x mx c Graphs and properties of quadratic functions f ( x) ax 2 bx c ; symmetry, vertex, intercepts Graphs and properties of exponential functions f ( x) ka x c ; growth and decay Using a GDC to sketch and analyze simple, unfamiliar functions and equations involving combinations of functions

3 Grade: 11 Unit Number: 3 Unit Title: Geometry and Trigonometry Coordinate Geometry, Trigonometry, Geometric Shapes LP Link: Inquirer Descartes showed that geometric problems can be solved algebraically and vice versa. What does this tell us about mathematical representation and mathematical knowledge? The aims of this unit are to develop the ability to draw clear diagrams, to represent information given in two dimensions, and to develop the ability to apply geometric and trigonometric techniques to problem solving. Students will start the unit working with points and lines in coordinate space. Then, they will use equations of lines to determine points of intersection and whether sets of lines are parallel or perpendicular to each other. In the trigonometry component, students will use trigonometric ratios to solve problems and apply the sine and cosine rules. Finally, students will explore the geometry of three dimensional shapes. The main summative assessment of this unit will be a test comprised of past paper questions that assess student knowledge of the unit. Coordinates in two dimensions: points, lines, midpoints, distance between points Equation of a line in two dimensions y mx c and ax by d 0 Gradients, intercepts, points of intersetion of lines, parallel lines, perpendicular lines Right angled trigonometry; sine, cosine, tangent ratios Solution of triangles using the sine rule: formula for the area of a triangle: sin, cosine rule: 2cos; Geomtry of three dimensional shapes: cuboid, prism, pyramid, cylinder, sphere, hemisphere, cone

4 Grade: 11 Unit Number: 4 Unit Title: Descriptive Statistics Approximate Duration: 1 month Classification of Data, Cumulative Frequency, Measures of Central Tendancy, Measures of Dispersion LP Link: Communicator How is the validity of data incorporated into results? What are the dangers of bias in statistics? The aims of this unit are to introduce concepts that will prove useful in further studies of inferential statistics and to develop techniques to describe and analyze sets of data. Students will first learn how to classify data as discrete or continuous and study concepts for measuring central tendency such as mean, median and mode. They will then learn to measure the amount of spread in data using concepts such as range, interquatile range, and standard deviation. Throughout the unit, students will get an exposure to various ways to present data such as frequency histograms, box and whisker plots, and cumulative frequency tables. It is expected that most of the calculations required in this unit will be done on a GDC. The main summative assessment will be a test comprised of past paper questions that assess student knowledge of the unit. Discrete and continuous data Simple discrete data: frequency tables, frequency polygons Grouped discrete data and grouped continuous data: frequency histograms, stem and leaf diagrams, box and whisker plots Measures of central tendancy: mean, median, mode Measures of dispersion: range, interquartile range, standard deviation

5 Grade: 11 Unit Number: 5 Unit Title: Statistical Applications Normal Distribution, Expected Value, Correlation, Linear Regression, Tests for Independence LP Link: Inquirer Does correlation imply causation? The aims of this unit are to introduce concepts that will prove useful in further studies of inferential statistics and to develop techniques to describe and analyze sets of data. Students will investigate the nature of normal distribution and look into phenomena that follow these trends. We will investigate the correlation of scattered data and use statistical methods to quantify and communicate results. Finally, we will use the Chi squared test for independence to study the dependence of two data sets. It is expected that most of the calculations required in this unit will be done on a GDC. The main summative assessment will be a test comprised of past paper questions that assess student knowledge of the unit. Normal Distribution; probability calcuations Scatter diagrams; line of best fit by eye/passing through the mean point Linear regression; Pearson's product moment correlation coefficient 2 The test for independence