LVL: FREE 15H_EST Level 2

Numerical Foundations

A comprehensive journey through the building blocks of mathematics. From understanding the concept of zero and negative numbers to mastering fractions, percentages, and dimensional analysis. This path ensures you never stumble on basic arithmetic or estimation again.

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Numerical Foundations

Curriculum

1Part 1

Natural numbers and the decimal system

2General Concepts

The concept of zero and introduction to negative numbers

The number line and coordinate axis

Absolute value

Addition and subtraction of integers

3Part 2

Multiplication and division of integers

4General Concepts

Order of operations (PEMDAS/BODMAS)

Laws of arithmetic (commutative, associative, distributive)

Even and odd numbers

Divisibility rules (for 2, 3, 5, 9, 10)

5Part 3

Prime and composite numbers (Sieve of Eratosthenes)

6General Concepts

Greatest Common Divisor (GCD) and Least Common Multiple (LCM)

Orders of magnitude

Scientific notation: aimes10na imes 10^naimes10n

Approximation and estimation

7Part 4

Rounding errors and their accumulation

8General Concepts

Meaning of a fraction: numerator, denominator, parts

Proper, improper fractions, and mixed numbers

Fundamental property of fractions and simplifying

Addition, subtraction, multiplication, and division of fractions

9Part 5

Positional notation of decimals

10General Concepts

Rounding and comparing decimals

Arithmetic with decimals

Conversion between decimals and common fractions

Concept of ratio and scale

11Part 6

Fundamental property of proportions and solving proportion equations

12General Concepts

What is a percent (1% as one-hundredth)

Finding the percent of a number and a number by its percent

Applied problems: discounts, taxes, simple interest

Basic operations: AND, OR, NOT

13Part 7

Truth tables

14General Concepts

Basic structure of statements (If A, then B; necessity and sufficiency)

Concept of dimensionality (length, mass, time, speed)

Conversion of units

Verifying formulas using dimensional analysis

15Part 8

Translating text into mathematical expressions

16General Concepts

Variables as models of the real world

Checking the answer for physical/logical adequacy

Scientific notation: $a imes 10^n$