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Worksheet · PDF

Optimisation

AI SL · Topic 5 · AI SL 5.7

50-question AI SL 5.7 worksheet with labelled geometry diagrams, function graphs, data tables and a derivative sign table. Student questions pages 1-9; answer key and solution outlines pages 10-11. Uses first-derivative signs, graphs and endpoint comparisons; no second-derivative test or kinematics.

Worksheet · PDF

Geometric Sequences & Series

AA SL · AA HL · Topic 1 · SL 1.3

Shared AA SL/HL worksheet on SL 1.3 finite geometric sequences and series, including nth terms, common ratio, finite sums, partial sums, threshold problems, growth/decay and applications, with an additional AA HL challenge section. Infinite geometric series are excluded.

Worksheet · PDF

Infinite Geometric Series

AA SL · AA HL · Topic 1 · SL 1.8

Shared AA SL/HL worksheet on SL 1.8 infinite convergent geometric series, using |r|<1 and building on SL 1.3. Includes 50 core questions plus a 10-question AA HL-exclusive challenge section.

Worksheet · PDF

Sequences & Series Complete Practice

AA SL · AA HL · Topic 1 · SL 1.2; SL 1.3; SL 1.8

Comprehensive AA SL/HL sequences and series practice covering SL 1.2, SL 1.3 and SL 1.8, with 100 shared questions plus 20 AA HL-exclusive challenges.

Worksheet · PDF

Binomial Theorem

AA SL · AA HL · Topic 1 · SL 1.9

Shared AA SL/HL worksheet on finite positive-integer binomial expansions, coefficients and Pascal’s triangle.

Worksheet · PDF

Transformations of Graphs

AA SL · AA HL · Topic 2 · AA SL 2.11; AA HL 2.11

60 questions on translations, reflections, stretches, point mappings, sketches, domain, range and asymptotes. Includes 50 shared questions and 10 HL challenges on combined inputs f(ax + b), with answers and illustrated solutions.

Worksheet · PDF

Binomial Distribution

AA SL · AA HL · Topic 4 · SL 4.8

Shared AA SL/HL worksheet on recognizing and using binomial models, probabilities, mean and variance.

Worksheet · PDF

Introduction to Integration

AA SL · AA HL · Topic 5 · SL 5.5

60-question AA SL/HL worksheet with 50 shared questions and 10 HL-exclusive challenges, 7 graphs, 2 tables and 15 marked GDC tasks. Shared questions pages 1-6; HL-only questions pages 7-8; checked answer key and solution outlines pages 9-11. Revised 27 September 2026.

Worksheet · PDF

Differentiation & Optimisation Practice

AA SL · AA HL · Topic 5 · SL 5.6–5.8

Cumulative AA SL/HL calculus practice spanning derivative rules, second derivatives, extrema, concavity and optimisation.

Worksheet · PDF

Maxima, Minima, Optimisation & Inflexion

AA SL · AA HL · Topic 5 · SL 5.8

60-question AA SL/HL 5.8 worksheet: 50 shared questions plus 10 final HL-exclusive challenges. Includes derivative tests, concavity, horizontal and non-horizontal inflexion, optimisation models, original diagrams, sketch axes and number-line sign tables. Student questions pages 1-8; answer key and solution outlines pages 9-12.

Worksheet · PDF

Implicit Differentiation, Related Rates & Optimisation

AA HL · Topic 5 · AHL 5.14

50 AA HL 5.14 questions with nine student diagrams and a variation table. Includes worked solutions and justification of constrained optima. Student questions pages 1–10; answers pages 11–15.

Worksheet · PDF

Advanced Integration

AA HL · Topic 5 · AHL 5.16

50 questions covering substitution, integration by parts, repeated and cyclic integration, and mixed applications. Includes nine coordinate diagrams, method selection and worked solution outlines. Student questions pages 1–9; answers pages 10–13.

Worksheet · PDF

Differential Equations

AA HL · Topic 5 · AHL 5.18

50 questions on Euler’s method, separable and logistic equations, homogeneous substitution and integrating factors, with model graphs, Euler tables and worked solutions.

Worksheet · PDF

Maclaurin Series

AA HL · Topic 5 · AHL 5.19

50 questions on the five standard Maclaurin expansions, series manipulation, limits and series from differential equations, with comparison graphs, shaded integrals and worked solutions.

Worksheet · PDF

Differentiation: the Power Rule

AI SL · Topic 5 · AI SL 5.3

AI SL power-rule practice with 50 questions, four graphs and answer-key solution outlines. Differentiate sums of integer powers, find gradients, determine coefficients and interpret rates in context. Student pages 1-7; answers 8-10.

Worksheet · PDF

Differentiation: the Power Rule

AA SL · AA HL · Topic 5 · SL 5.3

AA SL/HL power-rule worksheet with 50 shared questions and 10 HL-exclusive challenges, five graphs and solution outlines. Shared questions pages 1-7; HL challenge pages 8-9; answers pages 10-13.

Worksheet · PDF

Tangents and Normals

AI SL · Topic 5 · AI SL 5.4

AI SL 5.4 worksheet with 50 questions, six mathematical diagrams and worked answer outlines. Includes a tangent crossing a curve, tangent/normal identification, a horizontal tangent and vertical normal, intersecting tangents, a tangential path and an intercept triangle. Student pages 1-7; answers pages 8-11.

Worksheet · PDF

Tangents and Normals

AA SL · AA HL · Topic 5 · SL 5.4

AA SL/HL tangents and normals worksheet with 50 shared questions and 10 HL-only challenges, 12 diagrams, six marked GDC tasks and worked solution outlines. Shared questions pages 1-8; HL-only questions pages 9-10; answers pages 11-13.

Worksheet · PDF

Stationary Points

AI SL · Topic 5 · AI SL 5.6

50-question AI SL worksheet with 6 graphs, 4 data tables and 3 sign tables. Student questions pages 1-7; answer key and solution outlines pages 8-9. Focuses on first-derivative signs, technology and local versus domain-wide extrema; no second-derivative test required.

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.