Further Maths A level Teaching and Learning Resources
Through our eLearning platform, we serve schools and colleges with Further Maths A level teaching and learning resources including Core Pure Maths 1 & 2, Further Statistics 1 & 2, and Further Mechanics 1 & 2 in a form of thoroughly structured online tutorials, homework, assessments, and more!
In-depth Tutorials
- Nearly all Maths topics are covered
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- Reduces the need for re-teaching
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GeoGebra Activities (our official partner)
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GeoGebra interactive elements for in-class teaching
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GeoGebra practice activities for your students
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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
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
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
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 for One Academic Year
for £250 Excl. VAT
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
3
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