AP Precalculus Revision Cards

Build confidence with 127 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 factoring quadratics or polynomial long division

127 cards · 127 available

Prerequisites79 available · 4 coming soon

Algebra prerequisites · Notation and simplifying

6 cards
Simplifying by collecting like termsPrerequisiteOpen Card
Multiplying algebraic termsPrerequisiteOpen Card
Dividing algebraic termsPrerequisiteOpen Card

Algebra prerequisites · Expanding expressions

7 cards
Expanding a single parenthesisUsing arrowsPrerequisiteOpen Card
Expanding a single parenthesisUsing the grid methodPrerequisiteOpen Card
Expanding two parenthesesUsing arrowsPrerequisiteOpen Card
Expanding two parenthesesUsing the grid methodPrerequisiteOpen Card
Expanding three parenthesesUsing arrowsPrerequisiteOpen Card
Expanding three parenthesesUsing the grid methodPrerequisiteOpen Card

Algebra prerequisites · Factoring expressions

5 cards
Factoring quadraticsIn the form PrerequisiteOpen Card
Difference of two squaresPrerequisiteOpen Card
Factoring quadraticsIn the form PrerequisiteOpen Card
Factoring quadraticsIn the form PrerequisiteOpen Card
Factoring a common factorPrerequisiteOpen Card

Algebra prerequisites · Completing the square

2 cards
Completing the squareIn the form PrerequisiteOpen Card
Completing the squareIn the form PrerequisiteOpen Card

Algebra prerequisites · Exponent rules

7 cards
Multiplying powers with the same basePrerequisiteOpen Card
Dividing powers with the same basePrerequisiteOpen Card
A power raised to a powerPrerequisiteOpen Card
Powers of products and quotientsPrerequisiteOpen Card

Algebra prerequisites · Radicals and rational exponents

4 cards
Simplifying square rootsPrerequisiteOpen Card
Adding and subtracting radicalsPrerequisiteOpen Card
Rational exponents and rootsPrerequisiteOpen Card
Evaluating rational powersPrerequisiteOpen Card

Equation prerequisites · Linear equations and inequalities

9 cards
Solving equationsWith fractionsPrerequisiteOpen Card
Solving equationsOne-step addition and subtractionPrerequisiteOpen Card
Solving equationsOne-step multiplication and divisionPrerequisiteOpen Card
Solving equationsWith one set of parenthesesPrerequisiteOpen Card
Solving equationsWith several sets of parenthesesPrerequisiteOpen Card
Solving equationsWith unknowns on both sidesPrerequisiteOpen Card
Solving linear inequalitiesPrerequisiteOpen Card
Solving equationsTwo-step equationsPrerequisiteOpen Card
When a linear equation has no solution or infinitely manyPrerequisiteOpen Card

Equation prerequisites · Inequalities

1 card
Solving compound inequalitiesWith unknowns in all three partsPrerequisiteOpen Card

Equation prerequisites · Quadratic equations

4 cards
Solving quadratics by factoringPrerequisiteOpen Card
Solving by completing the squareInteger solutionsPrerequisiteOpen Card
Solving by completing the squareIrrational real solutionsPrerequisiteOpen Card

Equation prerequisites · Rearranging formulas

2 cards
Rearranging a formulaone occurrencePrerequisiteOpen Card
Rearranging a formularepeated occurrencesPrerequisiteOpen Card

Equation prerequisites · Systems of equations

3 cards
Two-variable systemseliminationPrerequisiteOpen Card
Two-variable systemssubstitutionPrerequisiteOpen Card
Solving three-variable systemsPrerequisiteOpen Card

Function prerequisites · Linear functions

4 cards
Equation of a line from a point and slopePrerequisiteOpen Card
Equations of parallel linesPrerequisiteOpen Card
Equations of perpendicular linesPrerequisiteOpen Card
Intercepts of a linear functionPrerequisiteOpen Card

Function prerequisites · Quadratic functions

2 cards
Vertex of a quadraticFrom vertex formPrerequisiteOpen Card
Axis of symmetry of a quadraticPrerequisiteOpen Card

Function prerequisites · Function notation and representations

4 cards
Evaluating function notationPrerequisiteOpen Card
Substituting an expression into a functionPrerequisiteOpen Card
Reading a function tablePrerequisiteOpen Card
Reading a function value from a graphPrerequisiteOpen Card

Geometry prerequisites · Coordinate geometry

3 cards
Slope between two pointsPrerequisiteOpen Card
Midpoint of a line segmentPrerequisiteOpen Card
Distance between two pointsPrerequisiteOpen Card

Geometry prerequisites · Right-triangle trigonometry

8 cards
Choosing sine, cosine or tangentPrerequisiteOpen Card
Finding a side using trigonometryPrerequisiteOpen Card
Finding an angle using inverse trigonometryPrerequisiteOpen Card
Modeling an angle of elevationPrerequisiteOpen Card
Finding a length with the sine ratioPrerequisiteOpen Card
Finding a length with the cosine ratioPrerequisiteOpen Card
Finding a length with the tangent ratioPrerequisiteOpen Card
Repeated use of right-triangle trigonometryPrerequisiteOpen Card

Geometry prerequisites · Pythagorean theorem

3 cards
The Pythagorean theorem - finding the hypotenusePrerequisiteOpen Card
The Pythagorean theorem - finding a shorter sidePrerequisiteOpen Card
Repeated use of the Pythagorean theoremPrerequisiteOpen Card

Algebra prerequisites · Complex numbers

5 cards
Adding and subtracting complex numbersPrerequisiteOpen Card
Multiplying complex numbersPrerequisiteOpen Card
Dividing complex numbers using a conjugatePrerequisiteOpen Card
Solving by completing the squareNon-real complex solutionsPrerequisiteOpen Card
Algebra13 available

Sequences and repeated change

9 cards
Finding an arithmetic common differenceUnit 2Open Card
Writing an explicit arithmetic sequence ruleUnit 2Open Card
Writing a recursive arithmetic sequence ruleUnit 2Open Card
Finding a geometric common ratioUnit 2Open Card
Writing an explicit geometric sequence ruleUnit 2Open Card
Writing a recursive geometric sequence ruleUnit 2Open Card
Connecting sequence indexing to a function inputUnit 2Open Card
Distinguishing an explicit rule from a recursive ruleUnit 2Open Card
Comparing additive and multiplicative changesUnit 2Open Card

Equivalent exponential forms

4 cards
Rewriting an exponential with a different baseUnit 2Open Card
Rewriting an exponential to show an initial valueUnit 2Open Card
Rewriting an exponential to show a chosen growth intervalUnit 2Open Card
Moving a multiplier into an exponentUnit 2Open Card
Exponential and logarithmic functions4 available · 52 coming soon

Exponential functions and models

4 cards
Evaluating exponential functionsUnit 2Open Card
Reading exponential growth and decayUnit 2Open Card
Constructing an exponential modelUnit 2Open Card
Comparing two exponential modelsUnit 2Open Card
Functions and graphs10 available · 49 coming soon

Piecewise functions and models

2 cards
Evaluating piecewise functionsUnit 1Open Card
Constructing a piecewise modelUnit 1Open Card

Rates of change

2 cards
Average rate of change from a formulaUnit 1Open Card
Average rate of change from a tableUnit 1Open Card

Symmetry

1 card
Is a function odd, even or neither?Unit 1Open Card

Transformations of functions

5 cards
Transformations of - words to notationUnit 1Open Card
Transformations of - notation to graphsUnit 1Open Card
Polynomial functions21 available · 15 coming soon

Quadratics and polynomial zeros

5 cards
Classifying quadratic roots with the discriminantUnit 1Open Card
Constructing a quadratic from zeros and a pointUnit 1Open Card
Solving equations that are quadratic in Unit 1Open Card
Solving equations that are quadratic in Real and complex solutionsUnit 1Open Card
Solving equations that are quadratic in By substitutionUnit 1Open Card

Recognizing polynomial structure

3 cards
Finite differences and polynomial degreeUnit 1Open Card
Recognizing a polynomial functionUnit 1Open Card
Writing a polynomial in standard formUnit 1Open Card

Degree and leading coefficient

4 cards
Degree of an expanded polynomialUnit 1Open Card
Degree of a factored polynomialUnit 1Open Card
Leading coefficient of an expanded polynomialUnit 1Open Card
Leading coefficient of a factored polynomialUnit 1Open Card

Zeros and factors

3 cards
Finding real zeros by factoringUnit 1Open Card
Finding non-real complex zerosUnit 1Open Card
Multiplicity of a polynomial rootUnit 1Open Card

End behavior

1 card

Division and theorems

5 cards
Polynomial long division by or Unit 1Open Card
Synthetic divisionBy a linear divisorOptional methodOpen Card
Polynomial long division by a quadraticUnit 1Open Card