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.
13 reference pages
Quick tests to check whether a number is divisible by 2 through 12, with worked examples.
A quick-reference table of squares from 1 to 30 and cubes from 1 to 20.
Common percentage calculation shortcuts and mental math tricks with worked examples.
Practice questions on adding fractions and mixed numbers, with worked solutions.
What percentage means, how to compute a combined percentage across subjects, with a worked example.
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.
What a ratio is and how to simplify one to its lowest terms, with a worked real-world example.
How to check whether four numbers are in proportion, and how to solve for a missing term, with worked examples.
How to calculate profit and loss percent, and work backwards from a selling price or discount to find the cost price, with worked examples.
The simple interest and compound interest formulas, why compound interest grows faster, and worked examples for both.
The formula for counting how many divisors a number has from its prime factorization, with worked examples.
What a prime number is, why 0 and 1 are neither prime nor composite, and what twin primes are, with a worked example checking a number for primality.