MATH FOR COMPETITIONS : Number Systems

Sharpen speed and accuracy for math competitive exams with structured lessons, tricks, and practice—from theory to problems to quizzes—covering AMC, Accuplacer arithmetic ACT, SAT, SSC, CDL, and banking tests.

Explore prime numbers, composites, and the special case of one; learn coprime pairs, divisibility rules, arithmetic progression, inverses, and Euclid's division algorithm with dividend, divisor, quotient, and remainder.

Explore patterns for competition math, including difference of squares of consecutive natural numbers and the sum of first n odd numbers equals n^2, plus patterns for squares of ones.

Identify quick square-sum patterns, such as 1^2+2^2+2^2=3^2 and 4^2+5^2+20^2=21^2, and apply Vedic maths and column methods to find missing numbers.

Practice decimal handling and divisibility rules, find multiples for numbers like 16 and 18, and simplify nested square roots while solving sums and products.

Practice solving number systems questions by applying surd simplifications and identities, such as (a+b)(a−b)=a^2−b^2 and a^3+b^3, and tackle related word problems like mango distribution to solidify concepts.

Explore hcf and lcm in the number system, solve ratio-based problems, apply prime factorization, and practice simplification of surds for efficient competition math.

Introduce power surds and indices, and apply exponent rules for like bases, subtraction in division, negative exponents, and nth roots, then explore rationalizing cube roots with surds and related examples.

Explain power and index rules with solved examples, from matching bases to equal exponents and nested radicals. Show quick competition tricks for infinite series and root-based solutions.

Explore decimal fractions and repeating decimals, converting recurring patterns to fractions. Solve equations with decimals, align decimal places, and practice algebraic and fraction problems from number systems.