| Curriculum Map 2006-2007 | |||
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The Dwight School |
| Period | Content | Purpose/ Objectives | Activities & Resources | Areas of Interaction | Assessments | |
| LINEAR RELATIONS AND FUNCTIONS : | Distance and slope formulae. Parallel and perpendicular lines. Solving systems of equations. Concept of a function. Composition of functions. Inverses of functions. Matrices: order. Identities and inverses. Solving equations by a matrix method. Transformation matrices: rotation, reflection, dilation. |
To review and consolidate knowledge of functions and of co-ordinate geometry |
Using the graphing calculator. |
Homo faber: historical development of co-ordinate geometry. |
Summative: end of topic test |
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| LINEAR PROGRAMMING : | Inequalities. Graphical representation of inequalities Linear programming, finding feasible regions. |
To see how linear programming techniques can be used to solve problems in industry and elsewhere |
Specimen problems |
Homo Faber: how businesses uses linear programming. |
Formative: Summative end of topic test |
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| GRAPHS AND DERIVATIVES : | Odd and even functions and their graphs. Graphs of rational functions. Absolute value functions. Finding derivatives from first principles and by the power rule. Critical points. The equation of the tangent to a curve. |
To extend knowledge of types of graphs. To introduce methods of finding rates of change, using the slope of a curve as an example. |
Classwork and assigned homework. |
Homo Faber: Newton and Leibnitz and the development of calculus. Environment: examples of rates of change. |
Formative:finding derivatives from first principles. Summative: Quizzes and end of topic test. |
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| POLYNOMIAL AND RATIONAL FUNCTIONS : | Finding the roots of quadratics. Use of the discriminant. Graphs of the inverses of functions. The factor and remainder theorems. The rational roots theorem. Solving radical equations. |
To acquire further equation solving techniques. |
Graphing calculator Problem sets. |
Environment: Examples of the occurence of these equations |
Formative:Homework assignments. Summative: End of topic test. |
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| COMPLEX NUMBERS : | Changing to and from polar form and rectangular form. Graphs of polar equations. Complex numbers in rectangular and polar form. The Argand Diagram. Operations on complex numbers. Finding the complex roots of an equation. Finding the complex roots of an equation. Complex solutions of equations. |
To introduce a new way of writing equations. To explore the concept of an imaginary number. |
Problem sets. Graphing calculator. |
Homo Faber: the history of complex number theory |
Summative: end of topic test |
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| PROBABILITY AND STATISTICS : | Permutations and combinations. The fundamental counting principle. Probability: independent and conditional events. Mean, median, mode, variance and standard deviation. |
To investigate different problems involving arrangements or choice. To tackle various problems in probability. To see why averages and standard deviation are important statistical concepts. |
Graphing calculator. Statistical data. |
Homo Faber: Pascal and probability. Environment: predicting future events using statistics and probability. ATL: learning to be aware that probability can be counter-intuitive. Health and social education: probability and the dangers of gambling. |
Formative: Quizzes or assignments. Summative:End of topic test. |
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| TRIGONOMETRIC FUNCTIONS AND IDENTITIES : | Review of basic trigonometry: sine and cosine rules. Area of a triangle. Trigonometric functions and their graphs. Inverse trigonometric functions. The unit circle. Area of sectors. Length of arc. Radian measure. Trigonometric identities and their proofs. Solving trigonometric equations. |
To extend knowledge and understanding of trigonometry. To introduce trigonometric identities and learn methods of solving trigonometric equations. |
Textbook problem sets. Worksheets. |
Homo Faber: The history of trigonometry. Environment: the application of trigonometry to surveying, optics, simple harmonic motion and other areas. |
Summative: end of topic test. |
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| TRIGONOMETRY and CONICS : | Completion of work on trigonometry (see March entry). Introduction to conics: circles, ellipses, hyperbolae,parabolae. |
Consolidation of work on trigonometry. Recognition of conics from their equations. Learning to write the equation of a conic. Seeing how conics are found in nature: comets, planetary orbits.The path of a projectile. Radio antennae, car headlights. Telescope design. |
Textbook problem sets. Worksheets. |
Homo faber: telescope design, satellite dishes. Environment: planetary orbits. |
Summative: end of topic tests. |
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| SEQUENCES AND SERIES : | Arithmetic sequences. Geometric sequences. Finding the nth term and the sum of n terms of a sequence. Using sigma notation. Expanding binomials. The Fibonacci sequence |
To become familiar with different types of sequences and their descriptions and properties. To introduce the Fibonacci sequence and show its link to the Golden Number |
Problem sets. |
Homo Faber: Fibonacci and his sequence. Environment: Sequences in ther natural world. Simple and compound interest. |
Formative: quizzes Summative: end of topic test |
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| FINAL EXAMINATION : | Final examination. |
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FINAL EXAM. |
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