Additional / Further Maths Revision Cards

Build confidence with 118 revision cards, each breaking a skill into clear steps. Study the worked examples, try five questions, then check your answers.

Explore the available skills. More topics are being added.

Search card titles, sections and categories. Try factorising, graphs or integration

118 cards · 118 available

Algebra and proof43 available · 2 coming soon

Notation and simplifying

2 cards
Multiplying algebraic termsAdditional / Further MathsOpen Card
Dividing algebraic termsAdditional / Further MathsOpen Card

Expanding expressions

4 cards
Expanding two bracketsUsing arrowsAdditional / Further MathsOpen Card
Expanding two bracketsUsing the grid methodAdditional / Further MathsOpen Card
Expanding three bracketsUsing arrowsAdditional / Further MathsOpen Card
Expanding three bracketsUsing the grid methodAdditional / Further MathsOpen Card

Factorising expressions

5 cards
Factorising quadraticsIn the form Additional / Further MathsOpen Card
Difference of two squaresAdditional / Further MathsOpen Card
Factorising quadraticsIn the form Additional / Further MathsOpen Card
Factorising quadraticsIn the form Additional / Further MathsOpen Card
Factorising a common factorAdditional / Further MathsOpen Card

Index laws

7 cards
Multiplying powers with the same baseAdditional / Further MathsOpen Card
Dividing powers with the same baseAdditional / Further MathsOpen Card
A power raised to a powerAdditional / Further MathsOpen Card
Powers of products and quotientsAdditional / Further MathsOpen Card
Zero exponentsAdditional / Further MathsOpen Card
Negative indicesAdditional / Further MathsOpen Card
Combining index lawsAdditional / Further MathsOpen Card

Surds and fractional indices

4 cards
Simplifying square rootsAdditional / Further MathsOpen Card
Adding and subtracting surdsAdditional / Further MathsOpen Card
Fractional indices and rootsAdditional / Further MathsOpen Card
Evaluating fractional powersAdditional / Further MathsOpen Card

Linear equations and inequalities

5 cards
Solving equationsWith fractionsAdditional / Further MathsOpen Card
Solving equationsWith one bracketAdditional / Further MathsOpen Card
Solving equationsWith several bracketsAdditional / Further MathsOpen Card
Solving equationsWith unknowns on both sidesAdditional / Further MathsOpen Card
Solving linear inequalitiesAdditional / Further MathsOpen Card

Quadratic equations

4 cards
The quadratic formulaAdditional / Further MathsOpen Card
Solving quadratics by factorisingAdditional / Further MathsOpen Card
Solving quadratics by completing the squareAdditional / Further MathsOpen Card
Classifying quadratic roots with the discriminantAdditional / Further MathsOpen Card

Rearranging formulas

2 cards
Rearranging a formulaone occurrenceAdditional / Further MathsOpen Card
Rearranging a formularepeated occurrencesAdditional / Further MathsOpen Card

Simultaneous equations

3 cards
Solving simultaneous equationsby eliminationAdditional / Further MathsOpen Card
Solving simultaneous equationsby substitutionAdditional / Further MathsOpen Card
Solving simultaneous equationswith three unknownsAdditional / Further MathsOpen Card

Completing the square

2 cards
Completing the squareIn the form Additional / Further MathsOpen Card
Completing the squareIn the form Additional / Further MathsOpen Card

Inequalities

3 cards
Plotting inequalities on a number lineAdditional / Further MathsOpen Card
Compound inequalitiesAdditional / Further MathsOpen Card
Solving compound inequalitiesWith unknowns in all three partsAdditional / Further MathsOpen Card

Absolute value and modulus

2 cards
Absolute valueAdditional / Further MathsOpen Card
Solving absolute value / modulus equationsAdditional / Further MathsOpen Card
Functions14 available · 2 coming soon

Division and theorems

3 cards
Using the factor theoremAdditional / Further MathsOpen Card
Polynomial long division by or Additional / Further MathsOpen Card
Using the remainder theoremAdditional / Further MathsOpen Card

Quadratic functions

3 cards
Vertex of a quadraticFrom completed-square formAdditional / Further MathsOpen Card
Axis of symmetry of a quadraticAdditional / Further MathsOpen Card
Constructing a quadratic from zeros and a pointAdditional / Further MathsOpen Card

Function notation and representations

4 cards
Evaluating function notationAdditional / Further MathsOpen Card
Substituting an expression into a functionAdditional / Further MathsOpen Card
Reading a function tableAdditional / Further MathsOpen Card
Reading a function value from a graphAdditional / Further MathsOpen Card

Zeros and factors

3 cards
Finding real zeros by factorisingAdditional / Further MathsOpen Card
Solving equations that are quadratic in Additional / Further MathsOpen Card
Solving equations that are quadratic in By substitutionAdditional / Further MathsOpen Card

Piecewise functions

1 card
Evaluating piecewise functionsAdditional / Further MathsOpen Card
Exponentials and logarithms2 available · 1 coming soon

Exponential prerequisites

2 cards
Evaluating exponential functionsAdditional / Further MathsOpen Card
Constructing an exponential modelAdditional / Further MathsOpen Card
Sequences and binomial expansion2 available · 4 coming soon

Binomial expansion

2 cards
Positive-integer binomial expansionAdditional / Further MathsOpen Card
Binomial coefficients and specified termsAdditional / Further MathsOpen Card
Coordinate geometry and vectors7 available · 3 coming soon

Coordinate geometry

7 cards
Gradient between two pointsAdditional / Further MathsOpen Card
Midpoint of a line segmentAdditional / Further MathsOpen Card
Distance between two pointsAdditional / Further MathsOpen Card
Equation of a line from a point and gradientAdditional / Further MathsOpen Card
Equations of parallel linesAdditional / Further MathsOpen Card
Equations of perpendicular linesAdditional / Further MathsOpen Card
Intercepts of a linear functionAdditional / Further MathsOpen Card
Trigonometry6 available · 3 coming soon

Right-angled trigonometry

3 cards
Choosing sine, cosine or tangentAdditional / Further MathsOpen Card
Finding a side using trigonometryAdditional / Further MathsOpen Card
Finding an angle using inverse trigonometryAdditional / Further MathsOpen Card

Right-triangle trigonometry

1 card
Modelling an angle of elevationAdditional / Further MathsOpen Card

Pythagoras’ theorem

2 cards
Pythagoras - finding the hypotenuseAdditional / Further MathsOpen Card
Pythagoras - finding a shorter sideAdditional / Further MathsOpen Card
Calculus44 available · 2 coming soon

Differentiation

20 cards
The power ruleAdditional / Further MathsOpen Card
Differentiating polynomialsAdditional / Further MathsOpen Card
Differentiating negative powersAdditional / Further MathsOpen Card
The second derivativeAdditional / Further MathsOpen Card
Gradient at a pointAdditional / Further MathsOpen Card
Equation of a tangentAdditional / Further MathsOpen Card
Equation of a normalAdditional / Further MathsOpen Card
Finding stationary pointsAdditional / Further MathsOpen Card
Classifying stationary pointsAdditional / Further MathsOpen Card
Differentiating fractional powersAdditional / Further MathsOpen Card
Differentiating sineAdditional / Further MathsOpen Card
Differentiating cosineAdditional / Further MathsOpen Card
Differentiating exponentialsAdditional / Further MathsOpen Card
Differentiating natural logarithmsAdditional / Further MathsOpen Card
The chain rule - notationAdditional / Further MathsOpen Card
The chain rule - notationAdditional / Further MathsOpen Card
The product rule - notationAdditional / Further MathsOpen Card
The product rule - notationAdditional / Further MathsOpen Card
The quotient rule - notationAdditional / Further MathsOpen Card
The quotient rule - notationAdditional / Further MathsOpen Card

Integration

24 cards
Integration as reverse differentiationAdditional / Further MathsOpen Card
The integration power ruleAdditional / Further MathsOpen Card
Integrating polynomialsAdditional / Further MathsOpen Card
Integrating negative powersAdditional / Further MathsOpen Card
Integrating fractional powersAdditional / Further MathsOpen Card
Simplifying before integrationAdditional / Further MathsOpen Card
Integrating powers of linear expressionsAdditional / Further MathsOpen Card
Integrating reciprocals and logarithmsAdditional / Further MathsOpen Card
Integrating sineAdditional / Further MathsOpen Card
Integrating cosineAdditional / Further MathsOpen Card
Integrating secant squaredAdditional / Further MathsOpen Card
Integrating exponentialsAdditional / Further MathsOpen Card
Integration using a given derivativeAdditional / Further MathsOpen Card
Finding the constant of integrationAdditional / Further MathsOpen Card
Evaluating definite integralsAdditional / Further MathsOpen Card
Signed area and definite integralsAdditional / Further MathsOpen Card
Area above the horizontal axisAdditional / Further MathsOpen Card
Area below the horizontal axisAdditional / Further MathsOpen Card
Area on both sides of the axisAdditional / Further MathsOpen Card
Area between a line and a curveAdditional / Further MathsOpen Card
Area between two curvesAdditional / Further MathsOpen Card
Finding an unknown integration limitAdditional / Further MathsOpen Card
Volume of revolution about the -axisAdditional / Further MathsOpen Card
Volume of revolution about the -axisAdditional / Further MathsOpen Card