CAT Quant Formulas: Free Formula Sheets for Every Chapter

Every CAT Quant chapter has a formula sheet: the identities, shortcuts and relationships the questions are built on, on one page. They are free, and they are ordered below by how often CAT has asked each chapter since 2017, so you revise in the order that matters.

Formula sheets by area

Arithmetic

About 8.2 questions in a 22-question section.

• Time & Work: Work as a rate: combinations, people joining and leaving, pipes and rosters.
• Averages: Two groups combined, someone joining or leaving, and squeezing one value to its limit.
• Time, Speed & Distance: D = S × T, relative speed, and the four applications: trains, boats, races and tracks.
• Mixtures & Alligation: Alligation, repeated remove-and-replace, and liquid moved between vessels.
• Percentages: Multiply, don't add, and always ask "per cent of what?"
• Simple & Compound Interest: Compounding, simple against compound, instalments, and a sum split across rates.
• Profit, Loss & Discount: CP, marked price and SP as multipliers, and the same-price trap.
• Ratio & Proportion: Think in parts: chain ratios, transfers that change a ratio, and whole-number answers.

Algebra

About 8.1 questions in a 22-question section.

• Quadratic & Polynomial Equations: Roots, the discriminant, symmetric expressions and quadratics in disguise.
• Progressions & Series: APs, GPs, recurrences and series that telescope.
• Inequalities & Modulus: Modulus equations, maxima and minima, and counting integer solutions.
• Exponents & Surds: One prime at a time, size comparisons, surds, and substitutions that turn quadratic.
• Logarithms: A log is an exponent: log equations, change of base, and inequalities with domains.
• Functions: Functional equations, composition, greatest-integer and min-max of two curves.
• Linear Equations: Words into equations, integer solutions, and how many solutions a system has.

Geometry

About 3.1 questions in a 22-question section.

• Quadrilaterals & Polygons: Regular hexagons and octagons, rhombus diagonals, trapeziums and polygon angles.
• Triangles: Right triangles with altitudes and incircles, centroids, area splits and hidden similarity.
• Circles: Curved areas, chords, angles in a circle, tangents and touching circles.
• Coordinate Geometry: Regions built from modulus, shapes from vertices, circles and shortest distances.
• Mensuration: Cubes, cylinders, cones cut parallel to the base, prisms and pyramids.

Number System

About 1.5 questions in a 22-question section.

• Factors & Multiples: Primes one at a time, counting divisors, and listing factor pairs.
• Digits & Number Properties: Digit-position puzzles, reversed numbers and digit sums of huge numbers.
• Remainders & Divisibility: Remainders of large powers, and the same remainder from several divisors.

Modern Maths

About 1 questions in a 22-question section.

• Permutation & Combination: Numbers from digits, handing out identical things, and selecting under conditions.
• Set Theory: Venn regions, and the largest or smallest possible overlap.

How to revise from a formula sheet

A formula sheet is for revision, not for learning. Read a line and ask yourself two things: where does this come from? and what question would make me reach for it? If you can't answer both, that line won't help you under time pressure. Go back to the concept.

The fastest check is a question you haven't seen before. If you can solve it from the sheet, the chapter is ready. If you can't, you know exactly what to fix.