Lesson-1.1.1- The functions a^x and log b^x (where b is a natural number greater than one). - Alai Academy

Chapter-1. Logarithmic Functions and Indices.

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Lesson-1.1.1- The functions a^x and log b^x (where b is a natural number greater than one).

Lesson-1.1.2- Use and properties of indices and logarithms, including change of base.

Lesson-1.1.3- Simple manipulation of surds.

Lesson-1.1.4- Rationalizing the Denominator.

Chapter-2. The Quadratic Function.

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Lesson-2.1.1- The manipulation of quadratic expressions.

Lesson-2.1.2- The roots of a quadratic equation.

Lesson-2.1.3- Simple examples involving functions of the roots of a quadratic equation.

Chapter-3. Identities and inequalities.

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Lesson-3.1.1- Simple algebraic division.

Lesson-3.1.2- The factor and remainder theorems.

Lesson-3.1.3- Solutions of equations, extended to include the simultaneous solution of one linear and one quadratic equation in two variables.

Lesson-3.1.4- Simple inequalities, linear and quadratic.

Lesson-3.1.5- The graphical representation of linear inequalities in two variables.

Chapter-4. Graphs

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Lesson-4.1.1- Graphs of polynomials and rational functions with linear denominators.

Lesson-4.1.2- The solution of equations and transcendental functions by graphical methods.

Chapter-5. Series

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Lesson-5.1.1- Use of the ∑ notation

Lesson-5.1.2- Knowledge of the general term of an arithmetic series is required.

Lesson-5.1.3- Use of the sum to n terms of an arithmetic series is required.

Lesson-5.1.4- Knowledge of the general term of a geometric series is required.

Lesson-5.1.5- Use of the sum to n terms of a finite geometric series is required.

Lesson-5.1.6- Use of the sum to infinity of a convergent geometric series, including the use of r < 1 is required.

Lesson-5.1.7- Proofs of the above are not required.

Chapter-6. The Binomial Series.

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Lesson-6.1.1- Use of the binomial series (1 + x)^n

Chapter-7. Scalar and Vector Quantities

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Lesson-7.1.1- The addition and subtraction of coplanar vectors and the multiplication of a vector by a scalar.

Lesson-7.1.2- Components and resolved parts of a vector.

Lesson-7.1.3- Magnitude of a vector.

Lesson-7.1.4- Position vector.

Lesson-7.1.5- Unit vector.

Lesson-7.1.6- Use of vectors to establish simple properties of geometrical figures.

Chapter-8. Rectangular Cartesian Coordinates.

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Lesson-8.1.1- The distance between two points.

Lesson-8.1.2- The point dividing a line in a given ratio.

Lesson-8.1.3- Gradient of a straight line joining two points.

Lesson-8.1.4- The straight line and its equation.

Lesson-8.1.5- The condition for two lines to be parallel or to be perpendicular.

Chapter-9. Calculus

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Lesson-9.1.1- Differentiation and integration of sums of multiples of powers of x (excluding integration of 1 x ),sin ,cos ,e^ax

Lesson-9.1.2- Differentiation of a product, quotient and simple cases of a function of a function.

Lesson-9.1.3- Applications to simple linear kinematics and to determination of areas and volumes.

Lesson-9.1.4- Stationary points and turning points.

Lesson-9.1.5- Maxima and Minima

Lesson-9.1.6- The equations of tangents and normals to the curve y = f(x).

Lesson-9.1.7- Application of calculus to rates of change and connected rates of change.

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