Mathematics Flashcards

Build your calculus foundation with this essential flashcard deck covering the core concepts of differential and integral calculus. Calculus is the mathematics of change and accumulation — it powers physics, engineering, economics, machine learning, and virtually every quantitative field. This deck covers limits and continuity, the definition of the derivative, all major differentiation rules (power, product, quotient, chain), derivatives of standard functions, the Fundamental Theorem of Calculus, indefinite and definite integrals, integration techniques, and applications including maxima/minima and area under a curve. Essential for AP Calculus AB/BC, A-Level Further Maths, and first-year university calculus.

Master geometry from basic angle relationships to 3D volume calculations with this comprehensive flashcard deck. Geometry is one of the oldest branches of mathematics and is heavily tested on the SAT, ACT, GCSE, A-Level, and state standardized exams. A strong geometry foundation is also essential for physics, architecture, engineering, and computer graphics. This deck covers all essential geometry formulas and theorems: angle types and relationships, triangle properties and congruence rules, the Pythagorean theorem, polygon properties, circle theorems, area and perimeter formulas, and 3D shape volumes and surface areas. Based on publicly available educational resources including OpenStax Geometry and CK-12.

Master algebra — the language of mathematics — with this essential flashcard deck. Algebra is the gateway to all higher mathematics, and every topic from geometry to calculus builds directly on algebraic thinking. This deck covers everything from the basics of linear equations to quadratic functions, factoring, exponent laws, logarithms, and systems of equations. Whether you are preparing for your GCSE, SAT, ACT, A-Level, or first-year university math course, this deck gives you the rules, formulas, and techniques you need to solve problems confidently and quickly. All content is based on publicly available educational resources including OpenStax Algebra and Khan Academy.

Master trigonometry with this comprehensive flashcard deck covering every key concept from basic SOH CAH TOA ratios to the unit circle, trigonometric identities, and the graphs of sine, cosine, and tangent. Trigonometry is essential for physics, engineering, architecture, and navigation — and it is a major component of the SAT, ACT, A-Level, AP Precalculus, and AP Calculus exams. This deck covers trigonometric ratios, exact values, the unit circle, solving triangles with the sine and cosine rules, amplitude and period of trig graphs, the Pythagorean identities, double angle formulas, inverse trigonometric functions, and general solutions. Based on publicly available resources including OpenStax Precalculus and CK-12.

Build a solid mathematical foundation with this number theory and fundamentals flashcard deck. These core concepts underpin all of mathematics and are essential for GCSE, SAT, AMC (American Mathematics Competition), and everyday mathematical reasoning. This deck covers prime and composite numbers, factors and multiples, HCF and LCM, divisibility rules, fractions and decimals, percentages and ratios, indices and surds, set theory and Venn diagrams, types of numbers (natural, integer, rational, irrational, real), and basic proof techniques including proof by contradiction and mathematical induction. Based on publicly available educational resources including OpenStax Prealgebra and CK-12 Number Theory.

Master statistics and probability with this comprehensive flashcard deck covering every key concept from descriptive statistics to inferential analysis. Statistics is increasingly essential in every field — from medicine and economics to machine learning and social sciences — and it is a major component of AP Statistics, A-Level Mathematics, IB Mathematics, and undergraduate courses. This deck covers measures of central tendency and spread, probability rules, permutations and combinations, discrete and continuous probability distributions (including the normal distribution), hypothesis testing, confidence intervals, correlation and regression, and the central limit theorem. Based on publicly available resources including OpenStax Statistics and Khan Academy.

Twenty flashcards covering vector and matrix algebra. Includes vector magnitude, addition, the dot and cross products, unit vectors, matrix addition and multiplication, determinants, inverse matrices, and solving linear systems. Suited to A-Level Further Maths, AP Precalculus/Calculus and introductory linear algebra.

Twenty flashcards covering discrete mathematics foundations. Includes set operations, propositional logic and truth tables, logical equivalences, permutations and combinations, basic graph theory terminology, and proof by induction. Suited to computer science coursework, A-Level Further Maths and discrete maths modules.

Sequences and series appear throughout A-Level and AP Precalculus, and this deck of 20 flashcards covers both the arithmetic and geometric cases in full. You'll learn the nth-term and sum formulas for arithmetic sequences, then the equivalent formulas for geometric sequences, including the special case of an infinite geometric series and the condition for it to converge. The deck also introduces sigma notation, recursive versus explicit formulas, and named sequences including Fibonacci and harmonic sequences, finishing with an introduction to convergence and divergence testing using the ratio test. A dedicated card explains why the harmonic series diverges despite its terms shrinking toward zero — a classic exam trick question. These flashcards pair each formula with a plain-English explanation, helping you understand not just how to calculate a sum but why the underlying pattern works.

Complex numbers extend the number system beyond the real numbers, and this deck of 18 flashcards builds up from the basics to more advanced applications. You'll start with the imaginary unit and basic arithmetic — addition, multiplication and division of complex numbers — then learn about the complex conjugate, modulus and argument. The deck introduces the Argand diagram for visualising complex numbers geometrically, before moving into polar and exponential form and De Moivre's theorem for raising complex numbers to a power. It finishes with how complex roots arise from quadratics with negative discriminants, the fundamental theorem of algebra, and real-world applications in electrical engineering and quantum mechanics. Suited to A-Level Further Maths and AP Precalculus, this deck is especially useful for students who find the geometric interpretation of complex numbers clicks better than the pure algebra alone.

Coordinate geometry connects algebra and geometry, and this deck of 20 flashcards covers everything from basic line formulas through to the full family of conic sections. You'll start with the distance and midpoint formulas and the rules for parallel and perpendicular gradients, then move into the equation of a circle before tackling parabolas, ellipses and hyperbolas in their standard forms. The deck explains what defines each conic geometrically — for example, how an ellipse is defined by the sum of distances to two foci — along with eccentricity, which tells you how "stretched" a conic is. It finishes with practical skills like finding line-circle intersections and converting a quadratic to vertex form. Suited to A-Level and AP Precalculus, this deck is especially useful for connecting the algebraic equations to the shapes they represent, which is where many students lose marks in exams.

Differential equations describe how quantities change, and they show up in nearly every branch of science and engineering — this deck of 20 flashcards introduces the essential concepts for a first encounter with the topic. You'll learn what a differential equation represents, the difference between a general and particular solution, and how to solve simple equations using separation of variables. The deck covers exponential growth and decay models, Newton's law of cooling, and the logistic growth equation, before introducing slope fields and Euler's method for approximating solutions numerically. It finishes with linear first-order equations and integrating factors. Suited to A-Level Further Maths and AP Calculus BC, this deck focuses on connecting each equation type to a real-world model — population growth, radioactive decay, cooling — so the abstract algebra has a concrete meaning you can visualise.

Linear algebra underlies everything from computer graphics to machine learning, and mastering its core vocabulary is the first step to fluency. This deck walks through matrices and vectors, key operations like addition, multiplication, and transposition, and important properties such as determinants, rank, and invertibility. You'll also review vector spaces, linear independence, bases, and the concept of eigenvalues and eigenvectors that appear throughout advanced math and engineering. Clear, exam-style definitions make this deck a solid refresher for college linear algebra courses or a quick primer before tackling data science and applied math topics.

Financial mathematics applies core math principles to real-world money problems, from savings growth to loan repayment. This deck covers simple and compound interest formulas, the difference between nominal and effective rates, and time-value-of-money concepts like present value, future value, and net present value. You'll also review practical terms such as amortization, annuities, APR, depreciation, and the Rule of 72 for quickly estimating investment doubling time. A great refresher for finance, economics, or business math students, or anyone wanting to better understand loans, investments, and interest.

Numerical methods provide practical tools for approximating solutions when exact analytical answers aren't feasible. This deck covers root-finding techniques like the bisection, Newton-Raphson, and secant methods, along with numerical integration approaches such as the trapezoidal rule and Simpson's rule. You'll also review error analysis concepts including round-off and truncation error, convergence and stability, and foundational tools like Euler's method, Gaussian elimination, and the Monte Carlo method. Ideal for engineering, computer science, or applied math students studying computational approximation techniques.

Exponents and logarithms are fundamental tools that appear throughout algebra, calculus, and science. This deck covers the core rules for multiplying, dividing, and raising powers, along with negative and fractional exponents. You'll also review logarithm properties, the natural logarithm, the change of base formula, and how exponential and logarithmic functions relate as inverses. A solid refresher for students working through algebra, precalculus, or any course involving exponential growth and decay.

Ratios, proportions, and percentages are everyday math skills used in finance, cooking, shopping, and countless other contexts. This deck covers how to simplify and compare ratios, solve proportions using cross-multiplication, and calculate percentage increase and decrease. You'll also review direct and inverse proportion, unit rates, and practical applications like discounts, markups, and map scales. A great refresher for middle school through early high school math, or anyone wanting to sharpen everyday numeracy skills.

Fractions and decimals are foundational math skills tested from elementary school through standardized tests. This deck covers simplifying fractions, adding and multiplying them, and converting between fractions and decimals. You'll also review terminating vs. repeating decimals, common denominators, and decimal place value. A must-have refresher deck for building strong numeracy fundamentals.