## ALISON – Project Maths – Higher Level

MODULE 1 Counting And Probability Complete

```Learn more about counting and probability.
```

Arrangements And Selections Topic Completed
Expected Value Topic Completed
Probability Of Simple Events Topic Completed
Probability Of Compound Events Topic Completed
Independent Events Topic Completed
Probability Using Tree Diagrams Topic Completed
Probability Trees With And Without Replacement Topic Completed
Reverse Probability – Bayes’ Theorem Topic Completed
Bayes’ Theorem And Medical Testing Topic Completed
Probability Patterns Of Discrete Variables Topic Completed
Comparing Distributions Topic Completed
The Binomial Distribution Topic Completed
A Problem Using Binomial Distribution Topic Completed
Bernoulli Trials And The Binomial Formula Topic Completed
The Normal Distribution Topic Completed
Using Excel To Calculate Binomial Probabilities Topic Completed
Using Excel To Find The Mean Of A Binomial Distribution Topic Completed

MODULE 2 Statistics Complete

```Learn more about statistics.
```

Cumulative Frequency And The Ogive Topic Completed
Cumulative Frequency, Quartiles And The Inter-Quartile Range Topic Completed
Mean Of Grouped Frequency Tables Topic Completed
Constructing A Stem And Leaf Diagram Topic Completed
Comparative Stem And Leaf Diagram Topic Completed
Histograms – Understanding That Area Gives Frequency Topic Completed
Introduction To Sampling Techniques Topic Completed
Random Stratified Sampling Topic Completed
Statistical Correlation Topic Completed
Measuring Correlation – Pearson’s Correlation Coefficient Topic Completed
Using Excel To Calculate Pearson’s Correlation Coefficient Topic Completed
Using Excel To Find Pearson’s Correlation Coefficient, Using The Inbuilt Function Topic Completed
Regression Lines And Their Equation Topic Completed
The Meaning Of The Coefficients In The Equation Of The Regression Line Topic Completed
Using Excel To Calculate The Equation Of The Regression Line Topic Completed
Using Excel To Find The Equation Of The Regression Line, Using Inbuilt Function Topic Completed

MODULE 3 Synthetic Geometry Complete

```Learn more about synthetic geometry.
```

Properties Of Shapes Topic Completed
Geometric Reasoning – Part 1 Topic Completed
Geometric Reasoning – Part 2 Topic Completed
Geometric Reasoning – Part 3 Topic Completed
Geometric Reasoning – Part 4 Topic Completed
Proof Of Theorem 11 Topic Completed
Proof Of Theorem 12 Topic Completed
Proof Of Theorem 13 Topic Completed

MODULE 4 Coordinate Geometry Complete

```Learn more about coordinate geometry.
```

Geometry With Coordinates Topic Completed
Equation Of A Straight Line Topic Completed
Parallel Lines Topic Completed
Perpendicular Lines Topic Completed
The Graphs Of Y=Kx^N Topic Completed
Translation Of Functions Topic Completed
Reflection Of Functions Topic Completed
Stretching Functions Topic Completed
General Transformation Of Functions Topic Completed
Equation Of A Circle 1 – Centre (0,0) Topic Completed
Equation Of A Circle 2 – Centre Not (0,0) Topic Completed
Equation Of A Circle 3 Topic Completed
Diameter Of A Circle Topic Completed
Tangent And Normal To A Circle Topic Completed
Touching Circles Topic Completed
Prove That A Line Is A Tangent To A Circle Topic Completed
Distance From A Point To A Line Topic Completed
Angle Between Two Lines Topic Completed
Dividing A Line Segment In A Given Ratio Topic Completed

MODULE 5 Trigonometry Complete

```Learn more about trigonometry.
```

Finding Angles With Sine Ratio Topic Completed
Finding Sides With The Sine Ratio Topic Completed
Finding Angles With The Cosine Ratio Topic Completed
Finding Sides With The Cosine Ratio Topic Completed
Finding Angles With The Tangent Ratio Topic Completed
Finding Sides With The Tangent Ratio Topic Completed
Finding A Missing Side With The Sine Rule Topic Completed
Finding A Missing Angle With The Sine Rule Topic Completed
Problem Solving With The Cosine Rule Topic Completed
Using Radians To Find Area Of Sector Topic Completed
Sketching And Matching Trigonometric Functions Topic Completed
Graphing Trigonometric Functions. Y = Sinx – Calculator Work – In Degrees Topic Completed
Graphing Trigonometric Functions. Y = 3sin2x – Calculator Work – In Radians Topic Completed
Introducing The Unit Circle Topic Completed
The Unit Circle – Drawing Sine And Cosine Topic Completed
Comparing Degrees To Radians On The Unit Circle Topic Completed
Solving Trigonometric Equations Topic Completed
Proving The Sine Rule Topic Completed
Proving The Cosine Rule Topic Completed
Proving Trigonometric Identity – (Sin Squared + Cos Squared = 1) Topic Completed
Finding Areas With Trigonometry Topic Completed
3-D Trigonometry – The Cuboid Topic Completed
3-D Trigonometry – Rectangular Based Pyramid Topic Completed
Area Of A Segment Topic Completed

MODULE 6 Number Systems Complete

```Learn more about number systems.
```

Large Numbers In Standard Form Topic Completed
Changing Decimals To Standard Fom Topic Completed
Changing Large Numbers From Standard Form Topic Completed
Changing Small Numbers From Standard Form Topic Completed
Adding And Multiplying Simple Powers Topic Completed
Working With Indices Topic Completed
Negative Indices Topic Completed
Fractional Indices, Numerator Of 1 Topic Completed
Index Power Equal To 0 Topic Completed
Positive Fractional Indices All Types Topic Completed
Negative Fractional Indices Topic Completed
Writing Index Numbers As A Power Of 2 Topic Completed
Manipulating Complex Numbers And The Complex Conjugate Topic Completed
The Argand Diagram And Modulus Topic Completed
The Meaning Of I Topic Completed
Patterns With Imaginary Numbers Topic Completed
Rational Or Irrational Topic Completed
Root 2 Is Irrational – Proof By Contradiction Topic Completed
Finding The Cube Roots Of 8 Topic Completed
Changing The Base Of Logarithms Topic Completed
Logarithmic Equations Topic Completed
Limits Of Sequences Topic Completed
Arithmetic Series Topic Completed
Geometric Series Topic Completed
Infinite Geometric Series – Part 1 Topic Completed
Infinite Geometric Series – Part 2 Topic Completed
Deriving Amortisation Formula From Geometric Series Topic Completed
The Sum Of The First N Natural Numbers – Proof By Induction Topic Completed
Proof By Induction Applied To A Geometric Series Topic Completed
Further Proof By Induction – Multiples Of 3 Topic Completed
Further Proof By Induction – Factorials And Powers Topic Completed

MODULE 7 Arithmetic – Financial Maths Complete

```Learn more about arithmetic using financial maths.
```

Profit, Markup And Margin Topic Completed
Calculating Profit With Special Offers Topic Completed
Percentage Loss – Part 1 Topic Completed
Percentage Loss – Part 2 Topic Completed
Simple Interest – Calculating The Interest Topic Completed
Simple Interest – Calculating The Rate Topic Completed
Simple Interest – Calculating The Principal Topic Completed
Simple Interest – Calculating The Period Topic Completed
Percentage Changes Using Multipliers Topic Completed
Reverse Percentages And VAT Topic Completed
Introducing Compound Interest Topic Completed
Compound Interest And Annual Equivalent Rate Topic Completed
Compound Interest APR With Credit Cards Topic Completed
Depreciation Topic Completed
Calculating APR Topic Completed
Calculating Monthly Interest From APR – 2 Methods Topic Completed
Income Tax, USC And PRSI Topic Completed
Net Pay/Take Home Pay Topic Completed
Present Value – Working Out Future Value Topic Completed
Present Value – Working Out Present Value Topic Completed
Present Value – Harder Example Topic Completed
Present Value And Amortisation Problem Topic Completed
Completing An Amortization Schedule Topic Completed
Savings And Amortization Topic Completed

MODULE 8 Length, Area And Volume Complete

```Learn more about length, area and volume.
```

Circumference Of A Circle Topic Completed
Area Of A Circle Topic Completed
Finding Radius And Diameter Of A Circle From Its Perimeter Topic Completed
Finding Radius And Diameter From Area Of Circle Topic Completed
Area Of Trapezium Topic Completed
Area Of Acute Angled Triangles Topic Completed
Area Of Obtuse Angled Triangles Topic Completed
Area Of Parallelogram Topic Completed
Area Of Rectangles Topic Completed
Area Compound Shapes (Rectangles) Topic Completed
Area Of Compound Shapes Topic Completed
Area Of Compound Shapes (Triangles) Topic Completed
Volume And Surface Area Topic Completed
Sectors And Arcs Topic Completed
Area Of A Segment Topic Completed
Volume Of Compound Solid

MODULE 9 Complex Numbers Complete

```Learn more about complex numbers.
```

Manipulating Complex Numbers And The Complex Conjugate Topic Completed
The Argand Diagram And Modulus Topic Completed
The Meaning Of I Topic Completed
Patterns With Imaginary Numbers Topic Completed
Writing Complex Numbers In Polar Form Topic Completed
Multiplying And Dividing In Polar Form (Proof) Topic Completed
Multiplying And Dividing In Polar Form (Example) Topic Completed
Proof Of De Moivre’s Theorem Topic Completed
Complex Numbers When Solving Quadratic Equations Topic Completed
Cubic Equations With Complex Roots Topic Completed
Finding The Cube Roots Of 8 Topic Completed

MODULE 10 Expressions And Formulae Complete

```Learn more about expressions and formulae.
```

Factorising – Difference Of Two Squares Topic Completed
Expanding Brackets (Grid Method) Topic Completed
Expanding Brackets (FOIL Method) Topic Completed
Expanding Any Two Brackets Topic Completed
Rearranging Simple Formulae Topic Completed
Rearranging Simple Formulae – 2 Steps Topic Completed
Rearranging Formulae With Squares And Square Roots Topic Completed
Rearranging Formulae New Subject Appearing Twice Topic Completed
Simplifying Surds Topic Completed
Further Calculations With Surds Topic Completed
Completing The Square Topic Completed
General Completing The Square Topic Completed
Binomial Expansion Topic Completed

MODULE 11 Solving Equations Complete

```Learn more about solving equations.
```

Equations With Linear Functions In The Denominator Topic Completed
Quadratic Equations Using The Formula Topic Completed
Quadratic Equations Non Unitary X Squared Topic Completed
Quadratic Equations Both Brackets The Same Sign Topic Completed
Quadratic Equations Brackets With Different Signs Topic Completed
Quadratic Equations That Have To Be Rearranged Topic Completed
Solving Simultaneous Equations Graphically Topic Completed
Simultaneous Equations Both Negative Signs Topic Completed
Simultaneous Equations Negative And Positive Signs Topic Completed
Simultaneous Equations Both Positive Topic Completed
Use Of The Discriminant Topic Completed
Equations With Indices Topic Completed
Logarithmic Equations Topic Completed
Solving Exponential Equations Topic Completed
From Roots To Functions Topic Completed
Non-Linear Simultaneous Equations Topic Completed
Factor Theorem – Part 1 Topic Completed
Factor Theorem – Part 2 Topic Completed
The Remainder Theorem Topic Completed
General Remainder And Factor Theorem Topic Completed
Finding Roots Of Cubic Equation Topic Completed
Modulus Equations Topic Completed
Using Graphs To Solve Modulus Equations Topic Completed

MODULE 12 Inequalities Complete

```Learn more about inequalities.
```

Finding Inequalities From Shaded Regions Topic Completed
Solving Linear Inequalities With Fractions Topic Completed
Solving Quadratic Inequalities – Method 1 Topic Completed
Solving Quadratic Inequalities – Method 2 Topic Completed
Solving Quadratic Inequalities – Method 3 Topic Completed
Non-Unitary X^2 – Trial And Error Method Topic Completed
Non-Unitary X^2 – Algebra Method Topic Completed
Non-Unitary X^2 – Graphical Method Topic Completed
Special Cases (Use SQI DoTS) Topic Completed
Rational Functions Topic Completed
Modulus Equations Topic Completed
Using Graphs To Solve Modulus Equations Topic Completed
Modulus Inequalities Topic Completed
Modulus Function On A Graph Topic Completed
Graphical Solution Of Modulus Inequalities Topic Completed

MODULE 13 Functions Complete

```Learn more about functions.
```

Plotting Quadratic Graphs From Table Of Values Topic Completed
Plotting Cubic Graphs From Table Of Values Topic Completed
Plotting Reciprocal Graphs From Table Of Values Topic Completed
Plotting Exponential Graphs From Table Of Values Topic Completed
Matching Equations And Sketches Topic Completed
Sketching Parabola Using Completing The Square Topic Completed
Completing The Square And Sketching The Full Method Topic Completed
Matching Functions And Graphs – Quadratic / Exponential Topic Completed
Translation Of Functions Using F(X-A) Topic Completed
Translating Of Functions Using F(X)+A Topic Completed
Sketching Functions In X Direction Topic Completed
Sketching Functions In The Y Direction Topic Completed
The Discriminant Topic Completed
Inverse And Bijective Functions Topic Completed

MODULE 14 Calculus – Differentiation Complete

```Learn more about differentiation.
```

Basic Differentiation Of Y = X^N Topic Completed
Differentiation Of Polynomials Topic Completed
Equation Of A Tangent Topic Completed
Equation Of A Normal Topic Completed
Harder Questions On Normals Topic Completed
General Differentiation Of X^N Topic Completed
Second Derivative Topic Completed
Differentiation Of Tangents Topic Completed
Using Different Variables Topic Completed
Differentiating Products And Quotients Topic Completed
The Chain Rule Topic Completed
The Product Rule Topic Completed
The Quotient Rule Topic Completed
Differentiation Of Logarithms Topic Completed
Differentiation Of Y = Sinx Topic Completed
Differentiation Of Y = Cosx Topic Completed
Differentiation And Rates Of Change Topic Completed
Rate Of Change – Example 1 Topic Completed
Rate Of Change – Example 2 Topic Completed
Differentiation And Turning Points Topic Completed
Differentiation And Matching Graphs Topic Completed
Applications Of Differentiation 1 (Displacement / Velocity / Acceleration) Topic Completed
Applications Of Differentiation 2 (Voltage / Current) Topic Completed
Maximum Volume Of Box Topic Completed
Exploring Relationships Between Graphs Of Cubic Functions And Their Differentials Topic Completed
Exploring Relationships Between Graphs Of Trigonometric Functions And Their Differentials Topic Completed
Exploring Relationships Between Graphs Of Exponential Functions And Their Differentials Topic Completed
Inverse Functions Differentiated Topic Completed

MODULE 15 Calculus – Integration Complete

```Learn more about integration.
```

Basic Integration Topic Completed
The Integral Sign Topic Completed
Harder Integration Topic Completed
Definite Integration Topic Completed
Area Between Lines Topic Completed
Basic Differential Equations Topic Completed
Integration Of Trig Functions (Y=Cos4x) Topic Completed
Integration Of Exponentials Topic Completed
Introducing The Trapezoidal Rule Topic Completed
Trapezoidal Rule Into Integration Topic Completed
Finding The Area Between A Quadratic Function And A Straight Line Topic Completed