KIST DP Course Descriptions

Transcription

1 Grade: 11 Unit Number: 1 Unit Title: Algebra Sequence and Series; Exponents and Logarithms; The Binomial Theorem Deductive vs. Inductive reasoning Mathematics begins with axioms and uses deductive reasoning to derive theorems. The aim of this unit is to introduce students to some basic concepts and applications in Algebra. Students will first develop knowedge of arithmetic and geometric sequence and series. Secondly, knowledge of exponents and logarithms from MYP 5 Math will be reviewed and used to solve equations and problems of application, e.g. compound interest and population growth. Finally, students will explore patterns of binomial expansion and develop an understanding of the Binomial Theorem. The main summative assessment of this unit will be a test comprised of past paper Arithmetic and geometric sequences and series; sums of arithmetic and geometric series; sums of finite and infinite geometric series Sigma notation Laws of exponents; laws of logarithms Change of base Examples of applications, compound interest and population growth The binomial theorem: expansion of

2 Grade: 11 Unit Number: 2 Unit Title: Functions Approximate Duration: 2 months Functions; Graphs of Functions LP Link: Communicator Patterns Characterizing mathematics as a search for abstract patterns. The aim of this unit is to explore the notion of function as a unifying theme in mathematics, and to apply functional methods to a variety of mathematical situations. Students will first be introduced to the concept of a function, and related topics. Secondly, the graphs of various types of functions will be explored, including graphs unfamiliar functions. Students will analyze graphs of functions in terms of their key features, learn patterns of transformation of functions, and find solutions of equations graphically. Extensive use of a graphic display calculator and graphic software will be made in both the development and application of this topic. The main summative assessment of this unit will be a test comprised of past paper The concept of a function f : x f ( x) ; domain, range Composite functions f g ; inverse functions f 1 The graph of a function; its equation y=f(x); function graphing skills; the use of a GDC to graph functions; investigate the key features of graphs; find the solutions of equations graphically Transformations of graphs: translations, stretches, reflections in the axes Families of functions and their graphs: The reciprocal function, 0 ; The quadratic function ; The function, 0; The exponential function ; the logarithmic function ln,0

3 Grade: 11 Unit Number: 3 Unit Title: Trigonometry The Circle; Trigonometric Identities; Trigonometric Functions and Equations Ways of knowing A priori and a posteriori knowledge The aim of this unit is to learn the fundamentals of trigonometry and to apply this knowledge to a variety of mathematical situations. At the start of the unit, students will practice finding the length of an arc and area of a sector. Then they will review the use of trigonometric rules to find unknown lengths, angles, and areas of triangles. After this, students will analyze graphs of trigonometric functions in the same manner that they analyzed graphs of other functions in Unit 2. Finally, students will use basic trigonometric identities to manipulate trigonometric expressions and solve equations. The main summative assessment of this unit will be a test comprised of past paper The circle: radian measure; length of an arc; area of a sector Definition of sin and cos ; definition of tan as Solution of triangles using the sine rule: formula for the area of a triangle: sin ; the identity sin cos 1, cosine rule: 2 cos ; The trigonometric (circular) functions sin, cos, and tan ; transformations Double angle formulae Solution of trigonometric equations in a finite interval.

4 Grade: 11 Unit Number: 4 Unit Title: Matrices Matrix Algebra; the Determinant and Inverse Matrices; Systems of Linear Equations Applied mathematics the usefulness of mathematics and algorithms The aim of this unit is to provide an elementary introduction to matrices, a fundamental concept of linear algebra. Students will beging with learning the terminology of matrices, and the conventions of matrix algebra, including multiplication of matrices. Students will then learn about the determinant of a square matrix and its relation to inverse matrices. Finally, students will learn to solve systems of linear equations using inverse matrices. Use of a graphic display calculator will be allowed and required for handling some complex matrix operations, such as finding the inverse of a 3x3 Matrix.The main summative assessment of this unit will be a test comprised of past paper Definition of a matrix: the terms element, row, column, and order Algebra of matrices: equality; addition; subtraction; multiplication by a scalar; multiplication of matrices; identity and zero matrices Determinant of a square matrix; calculation of 2x2 and 3x3 determinants; the inverse of a 2x2 matrix, condition for the existence of the inverse of a matrix Solution of systems of linear equations using inverse matrices (a maximum of three equations with three unknowns)

5 Grade: 11 Unit Number: 5 Unit Title: Vectors Approximate Duration: 2 months Matrix Algebra; the Determinant and Inverse Matrices; Systems of Linear Equations Platonism vs. formalism Is mathematics discovered or invented? The aim of this unit is to provide an elementary introduction to vectors. This includes both algebraic and geometric approaches. Students will first be introduced to the concept of a vector as a displacement in a plane and in three dimensions. Students will then learn the algebraic properties of vectors, including the scalar product (also known as the "dot product'). They will solve problems involving parallel and perpendicular vectors, and finding the angle between two vectors. At the end of the unit, students will learn how to represent parametric equations with vectors, and to solve problems such as finding where lines intersect. The main summative assessment of this unit will be a test comprised of past paper Vectors as displacements in a plane and in three dimensions Components of a vector; column representation Algebraic and geometric approaches to the following topics: the sum and difference of two vectors; the zero vector; negative vectors; multiplication by a scalar; the magnitude of a vector, unit vectors; base vectors; position vectors The scalar product of two vectors cos ; ; perpendicular vectors; parallel vectors; the angle between two vectors Representation of a line as ; distinguishing between coincident and parallel lines; infding points where lines meet