LVL: FREE 25H_EST Level 4

Algebraic Thinking

Algebra is the engine under the hood of every advanced quantitative model. In this comprehensive path, we deep-dive into equations, inequalities, polynomials, and the intricate behavior of functions. By the end of this course, you will understand the structural language of the mathematical universe.

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Algebraic Thinking

Curriculum

1Part 1

Variables and algebraic expressions

2General Concepts

Simplifying expressions and combining like terms

Expanding brackets

What is a root of an equation. Equivalent transformations

Solving linear equations with one variable

3Part 2

Absolute value equations (basics)

4General Concepts

Word problems leading to linear equations

Graphical meaning of a system of two equations

Substitution method

Elimination method (addition/subtraction)

5Part 3

Intervals and strict/non-strict inequality signs

6General Concepts

Solving linear inequalities

Systems of linear inequalities

Properties of exponents with natural and integer powers

Addition and subtraction of polynomials

7Part 4

Multiplication of polynomials (monomial by polynomial, binomial by binomial)

8General Concepts

Special product formulas (square of a sum/difference, difference of squares)

Factoring out the greatest common factor (GCF)

Factoring by grouping

Factoring quadratic trinomials

9Part 5

Incomplete quadratic equations

10General Concepts

Quadratic formula, Discriminant, and Vieta's formulas

Concept of a function: domain and range

Cartesian coordinate system

Linear function and its graph (y=kx+by = kx + by=kx+b)

11Part 6

Quadratic function and parabola (y=ax2+bx+cy = ax^2 + bx + cy=ax2+bx+c)

12General Concepts

Composition of functions (f(g(x))f(g(x))f(g(x)))

Inverse functions (f−1(x)f^{-1}(x)f−1(x))

Graph transformations (translations, stretches, reflections)

Even and odd functions (symmetry)

Linear function and its graph ( $y = kx + b$ )

Quadratic function and parabola ( $y = ax^2 + bx + c$ )

Composition of functions ( $f(g(x))$ )

Inverse functions ( $f^{-1}(x)$ )