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Study guides, exam tips, and revision strategies for SAT, A-Level & IGCSE

AP Calculus Textbook

AP Calculus

Ch 1: Limits and Continuity

Limit evaluation, one-sided limits, Squeeze Theorem, continuity, and the Intermediate Value Theorem.

Textbook Chapter · AB & BC
AP Calculus

Ch 2: Differentiation Rules

Power rule, product & quotient rules, derivatives of trigonometric, exponential, and logarithmic functions.

Textbook Chapter · AB & BC
AP Calculus

Ch 3: Chain Rule & Implicit Differentiation

Chain rule, implicit differentiation, inverse function derivatives, and higher-order derivatives.

Textbook Chapter · AB & BC
AP Calculus

Ch 4: Applications of Derivatives

Related rates, optimization, linear approximation, extreme values, and the Mean Value Theorem.

Textbook Chapter · AB & BC
AP Calculus

Ch 5: Curve Sketching & L'Hôpital's Rule

Critical points, first/second derivative tests, concavity, inflection points, L'Hôpital's Rule, optimization.

Textbook Chapter · Interactive
AP Calculus

Ch 6: Integration & Fundamental Theorem

Antiderivatives, Riemann sums, FTC Parts 1 & 2, and u-substitution.

Textbook Chapter · AB & BC
AP Calculus

Ch 7: Techniques of Integration

Integration by parts, partial fractions, and improper integrals.

Textbook Chapter · AB & BC
AP Calculus

Ch 8: Applications of Integration

Area between curves, volumes of revolution, cross sections, arc length, and average value.

Textbook Chapter · AB & BC
AP Calculus

Ch 9: Differential Equations

Slope fields, Euler's method, separation of variables, exponential and logistic growth.

Textbook Chapter · AB & BC
AP Calculus

Ch 10: Parametric, Polar & Vectors

Parametric equations, polar coordinates, polar area, and vector-valued functions.

Textbook Chapter · BC Only
AP Calculus

Ch 11: Infinite Series & Taylor Series

Convergence tests, power series, Taylor and Maclaurin series, Lagrange error bound.

Textbook Chapter · BC Only

Precalculus Textbook

Precalculus

Ch 1: Functions & Their Graphs

Function notation, domain & range, transformations, compositions, and inverse functions with interactive Desmos graphs.

Textbook Chapter · Interactive
Precalculus

Ch 2: Polynomial Functions

End behavior, zeros and multiplicity, Rational Root Theorem, synthetic division, and graphing with interactive Desmos.

Textbook Chapter · Interactive
Precalculus

Ch 3: Rational Functions

Vertical and horizontal asymptotes, holes, oblique asymptotes, and graphing rational functions with Desmos.

Textbook Chapter · Interactive
Precalculus

Ch 4: Exponential & Logarithmic Functions

Exponential growth/decay, logarithmic properties, solving equations, and applications with interactive graphs.

Textbook Chapter · Interactive
Precalculus

Ch 5: Trigonometric Functions

Unit circle, graphs of sine, cosine, tangent, amplitude, period, phase shift with interactive Desmos sliders.

Textbook Chapter · Interactive
Precalculus

Ch 6: Trig Identities & Equations

Pythagorean, sum/difference, double-angle, half-angle formulas. Verifying identities and solving trig equations.

Textbook Chapter
Precalculus

Ch 7: Vectors & Polar Coordinates

Vector operations, dot product, polar coordinates, polar graphs (roses, limaçons) with interactive Desmos.

Textbook Chapter · Interactive
Precalculus

Ch 8: Conic Sections

Parabolas, ellipses, hyperbolas, eccentricity, rotation of axes, and applications with interactive Desmos explorer.

Textbook Chapter · Interactive
Precalculus

Ch 9: Sequences & Series

Arithmetic and geometric sequences, infinite series, sigma notation, mathematical induction, and Binomial Theorem.

Textbook Chapter
Precalculus

Ch 10: Introduction to Calculus

Limits, tangent lines, rates of change, derivative concept preview, and Riemann sum intuition with Desmos.

Textbook Chapter · Interactive

US Exams

SAT

15 SAT Math Tips and Strategies to Boost Your Score

Proven tips for time management, calculator usage, must-know formulas, and test-day strategies for the Digital SAT.

8 min read · Updated Feb 2026
SAT

Digital SAT Complete Guide: Format, Scoring & How to Prepare

Everything about the Digital SAT including format changes, adaptive testing, Desmos calculator, and preparation strategies.

10 min read · Updated Feb 2026

UK Exams

A-Level

A-Level Maths Past Papers: How to Use Them Effectively

4-phase revision strategy for CIE 9709, Edexcel, OCR, and AQA. Includes tips by exam board and common mistakes to avoid.

9 min read · Updated Feb 2026
IGCSE

IGCSE Maths Revision Guide: Tips, Topics & Past Paper Strategy

Complete revision guide for Cambridge 0580 and Edexcel 4MA1. Key topics, revision timeline, and past paper techniques.

8 min read · Updated Feb 2026