Quantitative Aptitude Formulas and Shortcuts: All Formula Sheet for CA Foundation Maths

The first page deals with ratio, proportion, logs and indices. It defines antecedent and consequent. It gives the fourth proportional (b×c/a), the third proportional (b²/a) and the mean proportional (√ab). For a/b = c/d it lists invertendo, alternendo, componendo, dividendo, componendo-dividendo, addendo and subtrahendo. The laws of indices run from a^m × a^n = a^(m+n) to the m-th root as a^(1/m). The log section moves from B^P = N meaning log base B of N = P to the product, quotient and power rules and the change of base. It also covers log_b a × log_a b = 1 and the chain rule log_b a × log_c b = log_c a. The sets page covers the number of subsets (2^n) and proper subsets (2^n − 1), De Morgan's laws, and n(A∪B) for two and three sets. It also lists the power set, the Cartesian product, symmetric difference and the types of relations. Standard identities such as (a+b)³ and a³+b³+c³−3abc appear, along with the sum of n natural numbers, their squares and their cubes. The chapter numbers shown are Ch-1, Ch-7 and Ch-14, so the sheet seems to be arranged by chapter. Only the first 3 of 16 pages are previewed here.

Several notes on the sheet flag common MCQ traps. Every equal set is an equivalent set, but an equivalent set need not be equal. Every set is a subset of itself, and the empty set is a subset of every set. Every universal relation is reflexive. An identity relation is reflexive, but the converse is not true. A relation is an equivalence relation only when it is reflexive, symmetric and transitive. The sheet gives 'is equal to' and 'is parallel to' as examples. In logs, remember that log of 1 is 0 in any base and log_a a is 1. Also, log(ab/cd) splits into log a + log b − log c − log d. The sheet suggests converting a single log into index form when it looks difficult, as with log_2 8 = 3. For the mean, keep the three methods separate. The direct method uses Σfx/Σf. The short-cut method adds Σfu/Σf to the assumed mean A. The step deviation method multiplies by the class width h. The calculator tricks, such as the log 512 to base 2√2 and log 100 to base 0.1 examples, are worth practising until they become quick.

First, study each chapter from the ICAI study material so that you understand where each formula comes from. Then use this sheet as a one-glance recall tool. Cover the highlighted answers and try to write each result from memory, for example the proportion properties or n(A∪B∪C). Next, solve RTP and MTP questions on ratio, logs, sets and central tendency with the sheet beside you. Mark any formula you had to look up. Try the calculator tricks on past paper MCQs to check that they give the right answer in your own calculator. Where a trick fails, the sheet notes that a second division-based method can be used. In the final week, read the whole sheet once a day and attempt a timed set of past questions. This builds the speed that the objective paper needs.

The sheet is written for CA Foundation students taking the Quantitative Aptitude paper. It is especially useful for those who find it hard to keep track of the many small results in ratio, logarithms, indices and sets. It suits students who have already studied the chapters once and now need a compact revision aid before the exam. It also helps those who want to learn calculator shortcuts for log and root questions. Commerce students preparing for other aptitude tests that include ratio, logs, sets or averages may find the algebra and log sections helpful. However, the sheet does not cover logical reasoning topics in the preview pages. No attempt or syllabus year is mentioned, so check the topics against your current ICAI syllabus. The full 16-page note can be opened in the Studycaller app.

• Ratio and proportion properties
• Fourth third and mean proportion
• Invertendo alternendo componendo and dividendo
• Laws of indices
• Logarithm rules and change of base
• Calculator tricks for logs
• Sets subsets and power set
• De Morgan's laws and n(A∪B∪C)
• Types of relations and composite function
• Algebraic identities and sum of natural numbers
• Arithmetic mean: direct short-cut and step deviation methods

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