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Worksheet · PDF

Differentiation Rules

AA SL · AA HL · Topic 5 · SL 5.6

60-question AA SL/HL worksheet with 50 shared questions and 10 HL-exclusive challenges, 5 graphs and 4 function-value tables. Shared questions pages 1-6; HL-only questions pages 7-8; answer key and solution outlines pages 9-11.

Worksheet · PDF

The Second Derivative

AA SL · AA HL · Topic 5 · SL 5.7

60-question AA SL/HL 5.7 worksheet with 50 shared questions and 10 final HL-exclusive challenges. Explicit concave-up and concave-down questions accompany increasing/decreasing-gradient reasoning across all sections. Includes 9 supplied graphs, 3 sketch grids, 4 data tables and a worked second-derivative sign table. Shared questions pages 1-7; HL-only questions pages 8-9; answer key and solution outlines pages 10-12.

Worksheet · PDF

The Trapezoidal Rule

AI SL · Topic 5 · SL 5.8

50-question AI SL 5.8 worksheet on equal-width trapezoidal approximation from tables and functions. Includes original diagrams, contextual areas and accumulation, missing ordinates, error interpretation and measurement bounds. Student questions pages 1-8; answer key and solution outlines pages 9-10.

Worksheet · PDF

Complete Calculus Revision — 200 Questions

AI SL · Topic 5 · AI SL Topic 5

200-question full AI SL calculus revision pack covering SL 5.1–5.8. Progresses from core fluency to linked applications and original IB-style exam preparation. Includes graphs, sign tables, contextual data and solution outlines. GDC permitted throughout. Student questions pages 1–23; answers pages 24–31.

Worksheet · PDF

Kinematics

AA SL · AA HL · Topic 5 · SL 5.9

60-question AA SL/HL 5.9 worksheet with 50 shared questions and 10 final HL-exclusive challenges. Includes polynomial, exponential and trigonometric motion, velocity graphs, total distance, initial conditions, parameters and linked reasoning. Shared questions pages 1–7; HL questions pages 7–8; answers pages 9–11.

Worksheet · PDF

Integration and Substitution

AA SL · AA HL · Topic 5 · SL 5.10

60-question AA SL/HL 5.10 worksheet covering standard indefinite integrals, linear composites and reverse-chain-rule substitution. Includes initial conditions, error correction, graph interpretation, contextual applications, nested substitutions and parameter challenges. Shared questions pages 1–6; HL-only questions pages 7–8; answer key and solution outlines pages 9–11.

Worksheet · PDF

Definite Integrals and Areas

AA SL · AA HL · Topic 5 · SL 5.11

60-question AA SL/HL 5.11 worksheet covering analytical and technological evaluation of definite integrals, areas above and below the x-axis, and areas between curves. Includes 21 shaded graphs, two tables, parameter problems, equal-area conditions and full solution outlines. Shared questions pages 1–10; HL-only questions pages 10–12; answer key pages 13–15.

Worksheet · PDF

Limits, First Principles and Higher Derivatives

AA HL · Topic 5 · AHL 5.12

50-question AA HL AHL 5.12 worksheet with five graphs and worked solutions. First-principles differentiation is restricted to polynomials. Continuity and differentiability are explored informally rather than tested formally in exam-style questions. Student questions pages 1–6; answers pages 7–8.

Worksheet · PDF

Complete Calculus Revision — 200 Questions

AA SL · Topic 5 · AA SL Topic 5

200-question AA SL revision pack covering the entirety of SL 5.1–5.11. Includes 60 short and 60 extended questions, 40 Paper 1-style and 40 calculator-enabled Paper 2-style questions, 37 student visuals, revision map, complete syllabus index and full solution outlines. Overview page 1; student questions pages 2–27; answers pages 28–35.

Worksheet · PDF

Arithmetic Sequences and Series

AI SL · Topic 1 · SL 1.2

50 original questions aligned to AI SL 1.2, with contextual modelling, simple interest, diagrams, tables and worked solutions. Student questions pages 1–7; answers pages 8–9.

Worksheet · PDF

Arithmetic Sequences and Series

AA SL · AA HL · Topic 1 · SL 1.2

60 original questions aligned to AA SL/HL 1.2, including ten HL-exclusive challenges, diagrams, tables, proof and parameter problems, and worked solutions. Shared questions pages 1–7; HL challenges pages 7–8; answers pages 9–11.

Worksheet · PDF

Geometric Sequences and Series

AI SL · Topic 1 · SL 1.3

50 original AI SL 1.3 questions covering geometric terms and finite sums, sigma notation and growth and decay applications. Includes tables, a discrete graph, tile and square diagrams, a bouncing-ball diagram, a direction diagram and worked solutions. Student questions pages 1–7; answers pages 8–10.

Worksheet · PDF

Limits and l'Hôpital's Rule

AA HL · Topic 5 · AHL 5.13

50 original AA HL 5.13 questions with three coordinate diagrams, a derivative-value table and solution outlines. Student questions pages 1–8; answers pages 9–13.

Worksheet · PDF

Further Derivatives and Antiderivatives

AA HL · Topic 5 · AHL 5.15

50 original AA HL 5.15 questions with eight student graphs/sets of axes, a solution sign table and completed sketch, and worked answer outlines. Student questions pages 1–9; answers pages 10–13.

Worksheet · PDF

Areas and Volumes of Revolution

AA HL · Topic 5 · AHL 5.17

50 AA HL 5.17 questions with 15 coordinate diagrams, one washer cross-section and worked solution outlines. Student questions pages 1–11; answers pages 12–14.

Worksheet · PDF

Binomial Series: Fractional and Negative Indices

AA HL · Topic 1 · AHL 1.10

50 original questions on fractional and negative binomial expansions, with validity restrictions, approximations and coefficient problems. Includes a comparison graph and solution outlines. Student questions pages 1–9; answers pages 10–13.

Worksheet · PDF

Key Features of Graphs

AI SL · Topic 2 · SL 2.4

50 gradually scaffolded questions for less confident AI SL students, with labelled graphs, calculator reminders, contextual applications and solution outlines. Student questions pages 1–11; answers pages 12–17.

Worksheet · PDF

Advanced Integration — Worksheet 2: Powers of Sine and Cosine

AA HL · Topic 5 · AHL 5.16

Second 50-question worksheet for AHL 5.16, extending the first with substantial practice on powers of sine and cosine and further substitution, integration by parts, repeated and cyclic parts. Includes a guided sin^2(x) cos^4(x) example, mixed-method problems, three coordinate diagrams and worked solutions. Student questions pages 1–10; answers pages 11–19.

Worksheet · PDF

Financial Mathematics: Compound Interest, Depreciation and Inflation

AA SL · AA HL · Topic 1 · SL 1.4

60 questions aligned with the latest AA 1.4 handout: u0 and Sn conventions, compound interest, annual depreciation, inflation and TI-Nspire CX Finance Solver. Includes 50 shared questions, 10 HL challenges and solution outlines. 13 pages: questions 1–10, answers 11–13.

Worksheet · PDF

Functions, Domain, Range and Inverses

AA SL · AA HL · Topic 2 · AA SL 2.2; AA HL 2.2

60 questions on function notation, domain and range, graphs, mathematical models and inverse representations. Includes 50 shared questions and 10 HL challenges, with marked calculator questions and answers.

Worksheet · PDF

Composite and Inverse Functions

AA SL · AA HL · Topic 2 · AA SL 2.5; AA HL 2.5

60 questions on composition, domain and range, inverse functions and identity functions. Includes 50 shared questions and 10 HL challenges, with diagrams, clearly marked GDC tasks and answers.

Worksheet · PDF

Standard Form

AA SL · AA HL · Topic 1 · SL 1.1

50 questions on writing, comparing and calculating with standard form, with answers.

Worksheet · PDF

Laws of Exponents and Introduction to Logarithms

AA SL · AA HL · Topic 1 · SL 1.5

60 questions on integer exponent laws and logarithm definitions, with 50 shared SL/HL questions, 10 HL-exclusive challenges and answer outlines. GDC only for Q24-30. Strictly SL 1.5; logarithm laws and change of base are reserved for SL 1.7.

Worksheet · PDF

Rational Exponents and Logarithms

AA SL · AA HL · Topic 1 · SL 1.7

60 questions on rational powers, logarithm laws, change of base and exponential equations. Includes 50 shared questions, 10 HL challenges and solution outlines. Only Q24-26 require a GDC. Latest 16-page edition.