IB Math AA: Core Concepts & Applications

Front

Distinguish between an **equation** and an **identity**.

Back

An **equation** is true only for specific values of the variable (e.g., 2x = 4), whereas an **identity** is true for all permissible values of the variable (e.g., sin^2(x) + cos^2(x) = 1).

Front

What is the **Binomial Theorem** used for?

Back

It describes the algebraic expansion of powers of a binomial expression (a + b)^n. The coefficients of the terms correspond to the nth row of Pascal's Triangle.

Front

State the formula for the sum of a **finite geometric series**.

Back

S_n = a(r^n - 1) / (r - 1), where 'a' is the first term, 'r' is the common ratio (r ≠ 1), and 'n' is the number of terms.

Front

Explain the concept of **exponential growth** and **decay**.

Back

Models where the rate of change is proportional to the current value. Used for populations (growth) or radioactive half-life (decay). The general form is y = a(1 + r)^t or y = ae^(kt).

Front

Define the **modulus function** |x|.

Back

The modulus function outputs the non-negative value of x. Geometrically, it represents the distance of x from zero on the number line. |x| = x if x ≥ 0, and |x| = -x if x < 0.