A-level Further Mathematics
Digital Learning Courseware
Our digital learning courseware for Further Mathematics A-level is a collection of thoroughly structured online tutorials, homework, assessments, and more!
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The Education Auditorium UK is an educational platform that is dedicated to providing interactive learning opportunities to inspiring students to achieve their full potential in Further Maths A-level. We offer a wide range of Maths Courseware that are tailored to individual learning needs of all abilities. From our extensive digital online tutorial videos to our practice questions and assessment builder, we have something to suit every learner and educator. We strive to provide a learning experience that is both engaging and rewarding.
Sample Playlist name: Adding and Subtracting Volumes
Courseware Name: Further Mathematics A-level
Subject: Core Pure Mathematics
Topic: Volumes of Revolution
In-depth Tutorials
- Nearly all Maths topics are covered
- Helpful for long-term retention
- Invaluable when it comes to exam revising
- Reduces the need for re-teaching
- Reduces the impact of students & teacher accidental absence
The Students Practice Page
- Students find their specific topics to practice
- Maths practice for long-term retention
- Reduces the teaching time for revising prior exams
- Reduces the impact of students & teacher accidental absence
Creating Students Homeworks
- Select from a large questions bank
- Create an assignment in less than 5 minutes
- All assignments are auto-graded
- Save Lecturers Time
Performance Report
- Displays student gradebook
- Provides students & class performance report
- Monitor the amount of student has practiced
- Highlights weak areas of individual students
- Gathers invaluable statistical information in different format to use for different purposes
Playlist name: Momentum as a Vector
Courseware Name: Further Mathematics A-level
Subject: Further Mechanics 1
Topic: Momentum and Impulse
The Benefits for Educators
Time & cost saving
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Using our questions bank, tutors can create & publish any homework & test to students in less than 5 minute
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All our homework and tests are auto-graded & automatically saved to the Student Grade Table
Eliminate the need for constant teaching & mitigate students & teachers absence
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Owing to our extensive library of curriculum aligned tutorial videos, it eliminates the need for constant re-teaching & it mitigates students & teachers absence
Other Benefits
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In-depth tutorials for the applied Mathematics modules which cover all the A-level Statistics & Mechanics topics
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Organising our tutorials in topic-format helps in eliminating overwhelming efforts needed by teachers during the short revision period before exams
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Our LMS provides you with a comprehensive reports for student & class performance
The Benefits for Students
Abundance of Auto-graded practice questions
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Abundance of auto-graded practice questions for each topics to improve long-term skill retention, boosting student engagement and skill mastery.
Extensive curriculum-based Tutorial
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A generous amount of comprehensive curriculum-based videos ensures long-term retention, increases student motivation and confidence
Other Benefits
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Owing to the topic-format & being digital materials, that gives the ability to less able students to re-learn & practice any lesson over & over at their own time & comprehension ability till the new ideas sink in well which reduces the performance gap between students
Playlist name: Second Order Differential Equations
Courseware Name: Further Mathematics A-level
Subject: Core Pure Mathematics
Topic: Second Order Differential Equations
TOC - Maths Digital Learning Courseware for A-level
Further Maths - Core Pure Mathematics 1
Chapter 1: Complex Numbers
1.1: Imaginary and Complex Numbers
1.2: Multiplying Complex Numbers
1.3: Complex Conjugation
1.4: Roots of Quadratic Equations
1.5: Solving Cubic and Quartic Equations
Chapter 2: Argand Diagrams
2.1: Argand Diagrams
2.2: Modulus and Argument
2.3: Modulus-Argument Form of Complex Numbers
2.4: Loci in the Argand Diagram
2.5: Regions in the Argand Diagram
Chapter 3: Series
3.1. Sums of natural numbers
3.2. Sums of squares and cubes
Chapter 4: Roots of Polynomials
4.1. Roots of quadratic equation
4.2. Roots of a cubic equation
4.3. Roots of quartic equation
4.4. Expressions relating to the roots of a polynomial
4.5. Linear transformation of roots
Chapter 5: Volumes of Revolution
5.1. Volumes of revolution around the x-axis
5.2. Volumes of revolution around the y-axis
5.3. Adding and subtracting volumes
5.4. Modelling with volumes of revolution
Chapter 6: Matrices
6.1: Introduction to matrices
6.2: Matrix multiplication
6.3: Determinants
6.4: Inverting 2x2 matrix
6.5: Inverting 3x3 matrix
6.6: Solving systems of equations using matrices
Chapter 7: Linear Transformations
7.1: Linear transformations in two dimension
7.2: Reflections and rotations
7.3: Enlargements and stretches
7.4: Successive transformations
7.5: Linear transformation in three dimensions
7.6: The inverse of a linear transformation
Chapter 8: Proof by Induction
8.1:.Proof by mathematical induction
8.2. Proving divisibility results
8.3. Proving statements involving matrices
Chapter 9: Vectors
9.1. Equation of a line in three dimensions
9.2. Equation of a plane in three dimensions
9.3. Scalar product
9.4. Calculating angles between lines and planes
9.5. Points of intersection
9.6. Finding perpendiculars
TOC - Maths Digital Learning Courseware for A-level
Further Maths - Core Pure Mathematics 2
Chapter 1: Complex Numbers
1.1. Exponential Form of Complex Numbers
1.2. Multiplying and Dividing Complex Numbers
1.3. De Moivre's Theorem
1.4. Trigonometric Identities
1.5. Sum of series
1.6. nth Roots of a Complex Number
1.7. Solving Geometric Problems
Chapter 2: Series
2.1. The Method of Differences
2.2. Higher Derivatives
2.3. Maclaurin Series
2.4. Series Expansions of Compound Functions
Chapter 3: Methods in Calculus
3.1 : Improper Integrals
3.2 : The Mean Value of a Function
3.3 : Differentiating Inverse Trigonometric Functions
3.4 : Integrating with Inverse Trigonometric Functions
3.5 : Integrating Using Partial Fractions
Chapter 4: Volumes in Revolution
4.1. Volumes of Revolution Around x - axis
4.2. Volumes of Revolution Around y-axis
4.3. Volumes of Revolution of Parametrically Defined Curves
4.4. Modelling with Volumes of Revolution
Chapter 5: Polar Coordinates
5.1. Polar Coordinates and Equations
5.2. Sketching Curves
5.3. Area Enclosed by a Polar Curve
5.4. Tangents to Polar Curves
Chapter 6: Hyperbolic Functions
6.1. Introduction of Hyperbolic Functions
6.2. Inverse Hyperbolic Functions
6.3. Identities and Equations
6.4. Differentiating Hyperbolic Functions
6.5. Integrating Hyperbolic Functions
Chapter 7: Methods in Differential Equations
7.1. First-Order Differential Equations (FODE's) - General Solution
7.2. FODE's - Sketching Members of the Family of Solution Curves
7.3. FODE's - Solving Exact Equation
7.4. FODE's - Solving FOE's Type by Multiplying by an Integrating Factor
7.5. Second-order Homogenous Differential Equations
7.6. Second-Order Non-Homogenous Differential Equations
7.7. Solving Second Order Differential Equations - Using boundary conditions
Chapter 8: Modelling with Differential Equations
8.1. Modelling with First-Order Differential Equations
8.2. Simple Harmonic Motion
8.3. Damped and Forced Harmonic Motion
8.4. Coupled First-Order Simultaneous Differential Equations
Playlist name: Residuals Linear Regression
Courseware Name: Further Mathematics A-level
Subject: Further Statistics
Topic: Residuals
TOC - Maths Digital Learning Courseware for A-level
Further Statistics 1
Chapter 1: Discrete random variables
1.1: Expected value of a discrete random variable
1.2: Variance of a discrete random variable
1.3: Expected value and variance of a function of X
1.4: Solving problems involving random variables
Chapter 2: Poisson distributions
2.1. The Poisson distribution
2.2. Modelling with the Poisson distribution
2.3. Adding Poisson distribution
2.4. Mean and variance of a Poisson distribution
2.5. Mean and variance of binomial distribution
2.6. Using the Poisson distribution to approximate the binomial distribution
Chapter 3: Geometric and negative binomial distributions
3.1: The geometric distribution
3.2: Mean and variance of a geometric distribution
3.3: The negative binomial distribution
3.4: Mean and variance of the negative binomial distribution
Chapter 4: Hypothesis testing
4.1. Testing for the mean of a Poisson distribution
4.2. Finding critical regions for Poisson distribution
4.3. Hypothesis testing for the parameter p of a geometric distribution
4.4. Finding critical regions for a geometric distribution
Chapter 5: Central limit theorem
5.1. The central limit theorem
5.2. Applying the central limit theorem to other distributions
Chapter 6: Chi-squared tests
6.1. Goodness of fit
6.2. Degrees of freedom and the chi-squared family of distributions
6.3. Testing a hypothesis
6.4. Testing the goodness of fit with discrete data
6.5. Using contingency tables
6.6. Apply goodness-of-fit tests to geometric distributions
Chapter 7: Probability generating functions
7.1. Probability generating functions
7.2. Probability generating functions of standard distributions
7.3. Mean and variance of a distribution
7.4. Sums of independent random variables
Chapter 8: Quality of tests
8.1: Type | and Type || errors
8.2: Finding Type | and Type || rrors using the normal distribution
8.3: Calculating the size and the power of a test
8.4: The power function
TOC - Maths Digital Learning Courseware for A-level
Further Statistics 2
Chapter 1: Linear regression
1.1. Least squares linear regression
1.2. Residuals
Chapter 2: Correlation
2.1. The product moment correlation coefficient
2.2. Spearman's rank correlation coefficient
2.3. Hypothesis testing for zero correlation
Chapter 3: Continuous distributions
3.1. Continuous random variables
3.2. The cumulative distribution function
3.3. Mean and variance of a continuous distribution
3.4. Mode, median, percentiles and skewness
3.5. The continuous uniform distribution
3.6. Modelling with the continuous uniform distribution
Chapter 4: Combinations of random variables
4.1. Combination of random variables
Chapter 5: Estimation, confidence intervals and tests using a normal distribution
5.1. Estimators, bias and standard error
5.2. Confidence intervals
5.3. Hypothesis testing for the difference between means
5.4. Use of large sample results for an unknown population
Chapter 6: Further hypothesis tests
6.1. Variance of a normal distribution
6.2. Hypothesis testing for the variance of a normal distribution
6.3. The F-distribution
6.4. The F-test
Chapter 7: Confidence intervals and tests using the t-distribution
7.1. Mean of a normal distribution with unknown variance
7.2. Hypothesis test for the mean of a normal distribution with unknown variance
7.3. The paired t-test
7.4. Difference between means of two independent normal distributions
7.5. Hypothesis test for the difference between means
Playlist name: Dynamics
Courseware Name: Further Mathematics A-level
Subject: Further Mechanics
Topic: Simple Harmonic Motion
TOC - Maths Digital Learning Courseware for A-level
Further Mechanics 1
Chapter 1 - Momentum and Impulse
1.1. Momentum in One Direction
1.2. Conservation of Momentum
1.3. Momentum as a Vector
Chapter 2 - Work, Energy, and Power
2.1. Work Done
2.2. Kinetic and Potential Energy
2.3. Conservation of Mechanical Energy and The Work-Energy Principle
2.4. Power
Chapter 3 - Elastic Strings and Springs
3.1. Hooke's Law and Equilibrium Problems
3.2. Hooke's Law and Dynamics Problem
3.3. Elastic Energy
Chapter 4 - Elastic Collisions in One Dimension
4.1: Direct Impact and Newtons Law of Restitution
4.2: Direct Collision With a Smooth Plane
4.3: Loss of Kinetic Energy
4.4: Successive Direct Impacts
Chapter 5 - Elastic Collisions in Two Dimensions
5.1. Oblique Impact With a Fixed Surface
5.2. Successive Oblique Impacts
5.3. Oblique Impact of a Smooth Spheres
TOC - Maths Digital Learning Courseware for A-level
Further Mechanics 2
Chapter 1 - Circular Motion
1.1. Angular Speed
1.2. Acceleration of an Object Moving on a Horizontal Circular Path
1.3. Three-Dimensional Problems With Objects Moving in Horizontal Circles
1.4. Objects Moving in Vertical Circles
1.5. Objects Not Constrained on a Circular Path
Chapter 2 - Centres of Mass of Plane Figures
2.1. Centres of Mass of a Set of Particles on a Straight Line
2.2. Centre of Mass of a Set of Particles Arranged in a Plane
2.3. Centres of Mass of Standard Uniform Plane Laminas
2.4. Centre of Mass of a Composite Lamina
2.5. Centre of Mass of a Framework
2.6. Lamina in Equilibrium
2.7. Frameworks in Equilibrium
2.8. Non-Uniform Composite Laminas and Framework
Chapter 3 - Further Centres of Mass
3.1. Using Calculus to Find Centres of Mass
3.2. Centre of Mass of a Uniform Body
3.3. Non-Uniform Bodies
3.4. Rigid Bodies in Equilibrium
3.5. Toppling and Sliding
Chapter 4 - Kinematics
4.1. Acceleration Varying With Time
4.2. Acceleration Varying With Displacement
4.3. Acceleration Varying With Velocity
Chapter 5 - Dynamics
5.1. Motion in a Straight Line With Variable Forces
5.2. Newtons Law of Gravitation
5.3. Simple Harmonic Motion
5.4. Horizontal Oscillation
5.5. Vertical Oscillation
Here's What's Included in the
A-level Further Maths Core Pure Digital Learning
Subscription Pack
1
A level Further Mathematics Core Pure
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Pure Core Mathematics 1 & 2, 82 Different Topics
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600+ Tutorial Videos
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100s of Interactive Practice Questions
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100s Auto-graded Homeworks & Assessments
*Common Features
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Gradebooks & Performance Reports
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Student-lecturer 2-way Messaging Capability from within each specific assignment
2
A level Further Statistics
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Statistics, 59 Different Topics
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450+ Tutorial Videos
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100s of Interactive Practice Questions
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100s Auto-graded Homeworks & Assessments
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All common features stated in column 1
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A-level Further Mechanics
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Mechanics, 52 Different Topics
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400+ Tutorial Videos
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100s of Interactive Practice Questions
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100s Auto-graded Homeworks & Assessments
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All common features stated in column