Number facts and everyday arithmetic: divisibility, primes, factors, HCF and LCM, irrational numbers, fractions, ratio and proportion, percentages, profit and loss, and simple and compound interest. This is the base for board exams and for the quantitative sections of aptitude tests.
10 reference pages
Quick tests to check whether a number is divisible by 2 through 12, with worked examples.
Squares from 1 to 30 and cubes from 1 to 20, with last-digit patterns, mental squaring shortcuts, and how to find square and cube roots of perfect powers.
Practice questions on adding fractions and mixed numbers, with worked solutions.
Percentages: combining scores correctly, mental shortcuts, increase and decrease, successive changes, reverse percentages, percentage points, worked examples and common mistakes.
Finding HCF using Euclid's division algorithm and prime factorization, plus verifying LCM x HCF = product of two numbers, with worked examples.
Proving a number is irrational by contradiction, and telling whether a fraction has a terminating or repeating decimal expansion, with worked examples.
Simplifying ratios, dividing in a given ratio, combining ratios, testing a proportion, mean and fourth proportionals, and direct vs inverse proportion, with worked examples.
Simple and compound interest: the formulas, year-by-year compounding, and solved examples on part-year interest, finding the principal or time, quarterly compounding, changing rates and population growth.
Prime numbers up to 100, why 0 and 1 aren't prime, checking primality up to the square root, prime factorization and distinct prime factors, twin and co-primes, and common mistakes.
Reading bar graphs for GATE General Aptitude: percentage change, averages, ratios and shares from one chart, with fully worked answers and common mistakes.