If you are taking IB Mathematics: Analysis and Approaches (AA), the formula booklet is your best friend during exams. However, walking into a test with 15 pages of formulas can be overwhelming if you don’t know what to look for.
The booklet is divided into five core topics: Number & Algebra, Functions, Geometry & Trigonometry, Statistics & Probability, and Calculus. Whether you are at Standard Level (SL) or Higher Level (HL), understanding which formulas are “high yield” is the key to saving time and reducing stress.
Let’s break down the most critical formulas from each topic.
Topic 1: Number & Algebra
Arithmetic Sequence
Formula: or
What it does: Finds any term or sum of terms in a sequence with a constant difference.
When to use:
- Loan repayments with fixed installments
- Saving money weekly/monthly in equal amounts
- Any pattern like 5, 9, 13, 17…
How to use: Identify (first term), (difference), and (term number). Plug into the formula.
Geometric Sequence
Formulas:
only if
What it does: Models repeated multiplication (growth/decay).
When to use:
- Population growth
- Radioactive decay
- Depreciation of car value
- Bank interest (but compound interest formula is better)
How to use: Find and common ratio . For the infinite sum, check.
Compound Interest
Formula:
What it does: Calculates future value of an investment/loan with compounding.
When to use: Any bank account, loan, or investment where interest compounds monthly, quarterly, etc.
How to use:
- = present value (initial)
- = annual interest rate (%)
- = compounding periods/year
- = years
⚠️ Don’t confuse it with a geometric sequence—this one handles intra-year compounding.
Logarithms & Exponentials
Formulas:
What it does: Converts between exponential and logarithmic forms; simplifies multiplication/division into addition/subtraction.
When to use:
- Solving for exponents (e.g., )
- Decibel scale (log)
- pH scale
- Richter scale
How to use: Identify the base. Use the rules to combine or split logs. To solve
rewrite as
.
Binomial Theorem
Formula:
What it does: Expands without multiplying manually.
When to use:
- Finding a specific term in a binomial expansion
- Probability (binomial distribution)
- Approximations in calculus
How to use: For term with , coefficient = . Remember: exponent of is , exponent of is .
Topic 2: Functions
Quadratic Axis of Symmetry
Formula:
What it does: Finds the vertical line through the vertex of a parabola.
When to use:
- Finding vertex coordinates
- Maximizing/minimizing quadratic functions (e.g., profit, projectile height)
How to use: Given , plug and into the formula.
Discriminant
Formula:
What it does: Tells you the nature of roots.
When to use:
- Before solving a quadratic
- Determining if a quadratic intersects the x-axis
How to interpret:
- : two real distinct roots
- : one repeated root (tangent)
- : no real roots (complex)
Sum & Product of Polynomial Roots
Formulas: Sum of roots = Product of roots =
What it does: Relates roots to coefficients without solving.
When to use:
- Forming a quadratic from its roots
- Checking roots quickly
- Symmetric root problems
How to use: For : sum = , product = . For higher degree, match terms.
Topic 3: Geometry & Trigonometry
Sine Rule
Formula:
When to use:
- AAS (two angles, one side)
- ASA (two angles, included side)
- SSA (ambiguous case — check)
How to use: Set up proportion with the side-angle pair you know. Solve for unknown.
Cosine Rule
Formulas:
When to use:
- SSS (all three sides)
- SAS (two sides, included angle)
How to use: First version: find side. Second version: find angle.
Area of a Triangle (Trig)
Formula:
When to use: You know two sides and the included angle (SAS).
How to use: Multiply: 0.5 × side a × side b × sine of the angle between them.
Arc Length & Sector Area
Formulas:
When to use: Any circle problem where the angle is in radians (convert if needed).
How to use: Ensure is in radians. Plug and solve.
Pythagorean & Double Angle Identities
Formulas:
When to use:
- Simplifying trig expressions
- Solving trig equations
- Integrating trig functions
How to use: Replace with etc. Use double angles to reduce powers.
Topic 4: Statistics & Probability
Mean from Grouped Data
Formula:
When to use: Data is grouped into intervals (e.g., 0–10, 10–20).
How to use: = midpoint of interval. Multiply by frequency, sum, divide by total frequency.
Conditional Probability
Formula:
When to use: Probability of A given that B has occurred.
How to use: Identify the reduced sample space (B). Find intersection over B’s probability.
Binomial Distribution
Formulas: Mean Variance
When to use: Fixed number of trials (), two outcomes (success/fail), constant probability (), independent trials.
How to use: Check BINS: Binary, Independent, Number fixed, Same probability.
Normal Distribution (Standardization)
Formula:
When to use: Finding probabilities for normal distributions using z-tables.
How to use: Convert raw score to z-score, then look up probability.
Bayes’ Theorem (HL only)
Formula:
When to use: Updating probability based on new evidence (medical tests, spam filters).
How to use: Draw a tree diagram first. Then plug into formula.
Topic 5: Calculus
Basic Derivatives (SL)
| Function | Derivative |
|---|
When to use: Finding slope of tangent, rates of change, optimization.
How to use: Apply power rule, trig rules, or exponential rules directly.
Chain, Product, Quotient Rules
- Chain:
*Use for composite functions like* *.*
- Product:
*Use for .*
- Quotient:
*Use for .*
Basic Integrals (SL)
When to use: Finding area under curve, reversing differentiation, solving differential equations.
How to use: Add 1 to power, divide by new power. Don’t forget for indefinite integrals.
Kinematics (SL)
- Acceleration:
- Displacement:
- Distance:
When to use: Motion problems (particle moving along a line).
How to use:
- Displacement = final position − initial position (can be negative)
- Distance = total path length (always positive — integrate absolute value of velocity)
Integration by Parts (HL only)
Formula:
When to use: Integrating products of functions, e.g., , . ,
How to choose and Use LIATE rule: Log → Inverse trig → Algebraic → Trig → Exponential (u = first in LIATE, dv = rest)
Final Tips: How to Master the Formula Booklet
- Don’t memorize — practice locating. Under exam pressure, you need to flip to the right page in seconds.
- Annotate your booklet. Write small reminders, such as “use for compound interest,” next to the formula.
- Practice without the booklet first, then with it.This builds both memory and lookup speed.
- Know what’s NOT in the booklet. E.g., unit circle, calculator commands, common derivatives/integrals — memorize those.
- For HL: Focus on the “HL only” sections (complex numbers, vectors, Bayes, Maclaurin, parts). They appear in Papers 2 and 3.
The Formula Booklet is not a textbook — it’s a tool. The more you understand *why* and *when* to use each formula, the less intimidating exams become.
Learning the All Round Way
Master essential IB Math AA formulas for SL and HL, decode the official formula booklet with clarity, apply key equations confidently, solve complex problems faster, and elevate your exam performance through detailed explanations and examples. If you find yourself needing more guidance, we invite you to connect with us at All Round Education Academy. Our dedicated team is here to support you in achieving your academic goals. For more information, please contact us at [email protected] or +852 6348 8744.