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Objectives |
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Algebra 1a |
Laws of indices for all rational exponents. |
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Use and manipulation of surds. |
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Assessment 1a % Grade |
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Algebra 1b |
Algebraic manipulation of polynomials, including expanding brackets and collecting like terms, and factorisation. |
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Quadratic functions and their graphs. |
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The discriminant of a quadratic function. |
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Completing the square. Solution of quadratic equations. |
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Assessment 1b % Grade |
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Algebra 2 |
Solution of linear and quadratic inequalities. |
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Simultaneous equations (analytical solution by substitution) |
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Graphs of functions; sketching curves defined by simple equations. |
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Geometrical interpretation of algebraic solution of equations. Use of intersection points of graphs of functions to solve equations. |
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Knowledge of the effect of simple transformations on the graph of as represented by , , , |
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Assessment 2 % Grade |
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Co-ordinate
geometry in the (x,y) plane
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Equation of a straight line in forms , and |
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Conditions for straight lines to be parallel or perpendicular |
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Assessment 3 % Grade |
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Sequences and series |
Sequences, including those given by a formula for the nth term and those generated by a simple relation in the form |
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Arithmetic series (incl. formula for sum of first n natural numbers) |
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Understanding of Σ notation. |
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Assessment 4 % Grade |
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Differentiation |
The derivative of as the gradient of the tangent to the graph of at a point; the gradient of the tangent as a limit; interpretation as a rate of change. Second order derivatives. |
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Differentiation of and related sums and differences. |
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Applications of differentiation to gradients, tangents and normals. |
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Assessment 5 % Grade |
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Integration |
Indefinite integration as the reverse of differentiation |
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Integration of |
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Assessment 6 % Grade |
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Mock |
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