#### Differentiation

16 Powerpoints presentation for the following topics: Limits and convergence Basic rules for derivative The equations of tangent and normal lines Basic rules of derivatives The derivative of e^x and the derivative of ln x The product rule The quotient rule The chain rule for composite functions The second derivative and higher order derivatives Rate of change Velocity and acceleration functions Relative and global extrema Concavity Sketching a graph Optimisation problems

#### Topic 2: Functions and equations (IB Standard level)

Including all the Power point presentations for the Topic 2 -Functions and equations, based on the IB Mathematics SL Syllabus. The sub topics are: Introducing functions The Domain and the Range Function Notation Composite functions Inverse functions Transforming functions Solving quadratic equations The quadratic formula Roots of quadratic equations Quadratic graphs y=ax2+bx+c Quadratic graphs y=a(x-h)2+k Quadratic graphs y=a(x-p)(x-q) Finding the equation of a quadratic function from a graph The reciprocal function Rational functions Exponential functions Transformations of Exponential functions Logarithmic functions Applications of exponential and logarithmic functions

#### Length of arc and area of a sector

Power Point presentation, 5 slides, Explaining with examples how to calculate the length of arc and the area of a sector, given the angle measures in radians. For a preview of the power point copy the following link on your browser: https://drive.google.com/file/d/0B8z00qLZV7OlOTRNRllfRUZvV0k/view?usp=sharing

Power Point presentation, 11 slides, Explaining what radians are and how to use radians to measure angles, use examples to convert radians into degrees and viceversa. For a preview of the power point copy the following link on your browser: https://drive.google.com/file/d/0B8z00qLZV7OlMVFRT202ZjlyNWM/view?usp=sharing

#### Topic 1: Algebra (Mathematics IB Standard level)

Including all the Power point presentations for the Topic 1 - Algebra based on the IB Mathematics SL Syllabus. The sub topics are: Patterns and Sequences Arithmetic sequences Geometric sequences Sigma notation Arithmetic series Geometric series Convergent series and sums to infinity Applications of geometric and arithmetic patterns Exponents Solving exponential equations Properties of logarithms Laws of logarithms Change of base Exponential and logarithmic equations Pascal triangle Binomial expansion

#### Integration of sine and cosine functions

Power Point presentation, 11 slides, Explaining how to find the indefinite integral of the sine, and cosine functions and how to evaluate the definite integral of the same functions; use some examples to show how to integrate trigonometric functions, based on Mathematics IB Standard level Syllabus. For a preview of the power point copy the following link on your browser: https://drive.google.com/file/d/0B8z00qLZV7Olb1FMa3hMZ1Bva0E/view?usp=sharing

#### Maxima, minima and inflexion points of trigonometric functions

Power Point presentation, 7 slides, Explaining how to use the first and second derivatives of trigonometric functions to make the sketch of the function , based on Mathematics IB Standard level Syllabus. For a preview of the power point copy the following link in your browser: https://drive.google.com/file/d/0B8z00qLZV7OlTWRmSEJGWDhMc00/view?usp=sharing

#### Derivatives of sine, cosine and tangent functions

Power Point presentation, 11 slides, Explaining the derivative of the sine, cosine and tangent functions and use some examples to show how to differentiate trigonometric functions, based on Mathematics IB Standard level Syllabus. For a preview of the power point copy the following link on your browser: https://drive.google.com/file/d/0B8z00qLZV7OlTUh0a2dnNmJBUDg/view?usp=sharing

#### Rate of change

Power Point presentation, 13 slides, Explaining the meaning of rate of change and how to use differentiation to solve and interpret problems on rate of change, based on IB Mathematical Studies Syllabus. For a preview of the power point copy the following link on your browser: https://drive.google.com/file/d/0B8z00qLZV7OlWERHWkFjOGlTYkk/view?usp=sharing

#### Linear inequality regions

Power Point presentation, 11 slides, Explaining how to use the coordinate grid to find the solution set of a linear inequality, and how to describe a region on the cartesian plane using inequalities. For a preview of the power point copy the following link on your browser: https://drive.google.com/file/d/0B8z00qLZV7OleU55MG14NE02Y0E/view?usp=sharing

#### Solving problems using definite integration

Power Point presentation, 8 slides, Explaining how to use definite integration to solve problems related to linear motion and to find the cuulative effect of any varying rate of change, based on IB Standard Level Syllabus. For a preview of the power point copy the following link on your browser: https://drive.google.com/file/d/0B8z00qLZV7OlYmZTYkRNWFBMN2M/view?usp=sharing

#### Integration

Power point presentations: Antiderivative and the definite integral Integration of f(x) = 1/x; f(x) = e^x and compositions with the linear function ax + b Integrating by substitution The fundamental theorem of calculus Area under the curve, Properties of definite integrals Integration - Area between two curves Integration - Volume of revolution Solving problems using definite integration Integration of sine and cosine

#### The fundamental theorem of calculus

Power Point presentation, 9 slides, Explaining the fundamental theorem of calculus and use some examples to show how to use it to find the area under a curve, based on IB Standard Level Syllabus. For a preview of the power point copy the following link on your browser: https://drive.google.com/file/d/0B8z00qLZV7OlQnFnQWd4Ul9Bb2s/view?usp=sharing

#### Integration - Volume of revolution

Power Point presentation, 12 slides, Explaining how to calculate the volume of a shape generated by rotating a curve around the x-axis, using definite integrals , based on IB Standard Level Syllabus. For a preview of the power point copy the following link on your browser: https://drive.google.com/file/d/0B8z00qLZV7OlTnRvWVRSdWUtMVU/view?usp=sharing

#### Integration - Area between two curves

Power Point presentation, 15 slides, Explaining how to calculate the area between two curves using integrals and how to use the Graphic display calculator to find the area, based on IB Standard Level Syllabus. For a preview of the power point copy the following link on your browser: https://drive.google.com/file/d/0B8z00qLZV7OlMzI0eFo1WDk4T1E/view?usp=sharing

#### Area under the curve, Properties of definite integrals

Power Point presentation, 28 slides, Explaining how the area under any graph can be calculated using integrals defined from one point to another; State other properties of definite integrals and show some worked examples how to use theses properties, based on IB Standard Level Syllabus. For a preview of the power point copy the following link on your browser: https://drive.google.com/file/d/0B8z00qLZV7OlYWIyYzlfOTN4ejA/view?usp=sharing

#### Inverse normal distribution IBSL

Power Point presentation, 15 slides, Explaining how to find the value in a data that has a given cumulative probability, also to find either the mean or the standard deviation given cumulative probabilities, based on IB Mathematical Standard level Syllabus. For a preview of the power point copy the following link on your browser: https://drive.google.com/file/d/0B8z00qLZV7OlVGFCUFJPNVpfc28/view?usp=sharing

#### Graphs of sine, cosine and tangent functions (circular functions)

Power Point presentation, 35 slides, Explaining how to draw the sine graph, cosine graph and tangent graph, and how to solve equations using the graphs on a GDC, based on Mathematics IB Standard level Syllabus. For a preview of the power point copy the following link on your browser: https://drive.google.com/file/d/0B8z00qLZV7OleW10U1pTX1FpOTA/view?usp=sharing

#### Expected values and variance of the binomial distribution

Power Point presentation, 6 slides, Explaining how to calculate the expected values in a binomial distribution, which is the mean and how to calculate the Variance and standard deviation, based on Mathematics IB Standard level Syllabus. For a preview of the power point copy the following link on your browser: https://drive.google.com/file/d/0B8z00qLZV7OlSjhvcmxid3pXZzQ/view?usp=sharing

#### Probability distributions, IBSL

Presentations for IB Standard level Mathematics covering the following objectives: Concept of discrete random variables and their probability distributions. Expected value for dicrete data. Binomial distribution and its mean and variance. Normal distribution, Standardization of normal variables, and inverse normal calculations

#### Trigonometric identities

Power Point presentation, 12 slides, Explaining the following identities: Pythagorean identity, double angle identity for cosine, the double angle identity for sine, based on Mathematics IB Standard level Syllabus. For a preview of the power point copy the following link on your browser: https://drive.google.com/file/d/0B8z00qLZV7OldTJSaHNmQjFqb0U/view?usp=sharing