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Student questions pages 1-7; checked answer key and solution outlines pages 8-9. Revised 27 September 2026.", "question_count": 50, "question_structure": "15 short-response; 15 extended-response; 20 original IB-style; answer key and solution outlines", "worksheet_scope": "Single AI SL 5.5 syllabus section with modelling applications", "search_text": "introduction to integration ai sl calculus ai sl 5.5 ai sl 5.5; ai sl 5.3 (supporting derivative checks) ai sl 5.5; sl 5.5; 5.5; applications and interpretation sl 5.5; introduction to integration; antidifferentiation; definite integrals; area single ai sl 5.5 syllabus section with modelling applications gdc permitted throughout; 19 marked questions require numerical integration or numerical equation solving 15 short-response; 15 extended-response; 20 original ib-style; answer key and solution outlines integration; anti-differentiation; antidifferentiation; antiderivatives; integer powers; negative powers; power rule for integration; boundary conditions; initial conditions; constant of integration; definite integrals; area under a curve; area above the x-axis; gdc; calculator; accumulated change; rate of change; water flow; production cost; solar energy; units; mathematical modelling 50-question ai sl worksheet on antiderivatives, boundary conditions, definite integrals and area above the x-axis, with 6 graphs, 4 tables and 19 marked gdc tasks. student questions pages 1-7; checked answer key and solution outlines pages 8-9. revised 27 september 2026. ai-sl-5-5 introduction to integration ai sl 5 calculus ai sl 5.5 ai sl 5.5; ai sl 5.3 (supporting derivative checks) ai sl 5.5; sl 5.5; 5.5; applications and interpretation sl 5.5; introduction to integration; antidifferentiation; definite integrals; area single ai sl 5.5 syllabus section with modelling applications gdc permitted throughout; 19 marked questions require numerical integration or numerical equation solving 50 15 short-response; 15 extended-response; 20 original ib-style; answer key and solution outlines integration; anti-differentiation; antidifferentiation; antiderivatives; integer powers; negative powers; power rule for integration; boundary conditions; initial conditions; constant of integration; definite integrals; area under a curve; area above the x-axis; gdc; calculator; accumulated change; rate of change; water flow; production cost; solar energy; units; mathematical modelling 50-question ai sl worksheet on antiderivatives, boundary conditions, definite integrals and area above the x-axis, with 6 graphs, 4 tables and 19 marked gdc tasks. student questions pages 1-7; checked answer key and solution outlines pages 8-9. revised 27 september 2026. ib-ai-sl-5-5-antidifferentiation-definite-integrals-area-worksheet ai-sl-5-5-antidifferentiation-definite-integrals-area ib mathematics ib maths worksheet practice answer key solutions ib mathematics ib maths worksheet practice answer key solutions", "syllabus_codes": [ "AI SL 5.5", "AI SL 5.3 (supporting derivative checks)" ], "search_codes": [ "AI SL 5.5", "AI SL 5.3 (supporting derivative checks)", "ai sl 5.5", "sl 5.5", "5.5", "applications and interpretation sl 5.5", "introduction to integration", "antidifferentiation", "definite integrals", "area" ], "calculator_guidance": "GDC permitted throughout; 19 marked questions require numerical integration or numerical equation solving", "last_verified": "2026-09-29" }, { "id": "ai-sl-5-7", "title": "Optimisation", "courses": [ "AI SL" ], "syllabus_code": "AI SL 5.7", "topic_number": 5, "topic_name": "Calculus", "lesson_name": "Optimisation", "keywords": [ "optimisation", "optimization", "maximum", "minimum", "modelling", "profit", "revenue", "cost", "surface area", "volume", "perimeter", "fencing", "open box", "cylinder", "poster", "gutter", "shortest distance", "constraints", "feasible domain", "endpoints", "integer solutions", "GDC", "first derivative", "stationary points", "ai sl 5.7", "sl 5.7", "5.7", "applications and interpretation sl 5.7", "IB Mathematics", "IB Maths", "worksheet", "practice" ], "resource_type": "Worksheet", "calculator": "calculator", "pdf_path": "/downloads/worksheets/ib-ai-sl-5-7-optimisation-worksheet.pdf", "date_updated": "2026-09-27", "answers_included": true, "status": "published", "description": "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. 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Includes 50 core questions plus a 10-question AA HL-exclusive challenge section.", "question_count": 60, "question_structure": "15 short-response; 15 extended-response; 20 original IB-style Paper 1; 10 AA HL-only challenge", "worksheet_scope": "SL 1.8 with supporting SL 1.3 + AA HL challenge", "search_text": "infinite geometric series aa sl & hl number and algebra sl 1.8 sl 1.8; sl 1.3 aa sl 1.8; aa hl 1.8; sl 1.8; infinite geometric series; sum to infinity; geometric sequences; geometric series; sl 1.3 sl 1.8 with supporting sl 1.3 + aa hl challenge primarily non-calculator / paper 1; gdc on marked threshold question 15 short-response; 15 extended-response; 20 original ib-style paper 1; 10 aa hl-only challenge infinite geometric series; convergent geometric series; sum to infinity; s_infinity; modulus; absolute value; common ratio; |r|<1; finite geometric series; partial sums; tails; remainder; recurring decimals; bouncing ball; self-similar patterns; sl 1.3 shared aa sl/hl worksheet on sl 1.8 sum of infinite convergent geometric sequences, explicitly using |r|<1 and building on sl 1.3 finite geometric sequences and series. the exam-style and aa hl-exclusive sections are original sister questions informed by the uploaded aa sl, aa hl and sl 1.8-specific past-paper sets. includes 50 core questions plus a 10-question aa hl-exclusive challenge section. aa-sl-hl-1-8 infinite geometric series aa sl & hl number and algebra sl 1.8 sl 1.8 sl 1.3 aa sl 1.8 aa hl 1.8 infinite geometric series sum to infinity geometric sequences geometric series convergent geometric series s_infinity modulus absolute value common ratio |r|<1 finite geometric series partial sums tails remainder recurring decimals bouncing ball self-similar patterns shared aa sl hl worksheet 15 short response 15 extended response 20 ib style paper 1 10 aa hl challenge ib mathematics ib maths worksheet practice answer key solutions", "syllabus_codes": [ "SL 1.8", "SL 1.3" ], "search_codes": [ "SL 1.8", "SL 1.3", "aa sl 1.8", "aa hl 1.8", "sl 1.8", "infinite geometric series", "sum to infinity", "geometric sequences", "geometric series", "sl 1.3" ], "calculator_guidance": "Primarily non-calculator / Paper 1; 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30 extended-response; 40 original IB-style Paper 1; 20 AA HL-only challenge", "worksheet_scope": "Comprehensive mixed-topic review + AA HL challenge", "search_text": "sequences & series complete practice aa sl & hl number and algebra sl 1.2; sl 1.3; sl 1.8 sl 1.2; sl 1.3; sl 1.8 aa sl 1.2; aa hl 1.2; aa sl 1.3; aa hl 1.3; aa sl 1.8; aa hl 1.8; arithmetic sequences; arithmetic series; geometric sequences; geometric series; infinite geometric series; sequences and series review comprehensive mixed-topic review + aa hl challenge primarily non-calculator / paper 1; gdc on marked threshold/model questions 30 short-response; 30 extended-response; 40 original ib-style paper 1; 20 aa hl-only challenge arithmetic sequences; arithmetic series; nth term; common difference; sigma notation; finite sums; geometric sequences; common ratio; finite geometric series; sum to infinity; convergence; |r|<1; partial sums; tails; remainder; recurring decimals; growth; decay; bouncing ball; modelling; thresholds comprehensive shared aa sl/hl worksheet covering all sequence-and-series content in sl 1.2, sl 1.3 and sl 1.8. contains 100 shared questions plus 20 aa hl-exclusive challenges. exam-style questions are original sister questions informed by the uploaded aa sl, aa hl and sl 1.8-specific past-paper sets. aa-sl-hl sequences series complete practice aa sl hl number algebra sl 1.2 sl 1.3 sl 1.8 arithmetic sequences arithmetic series geometric sequences geometric series infinite geometric series nth term common difference common ratio finite sums sum to infinity convergence modulus sigma notation partial sums tails remainder recurring decimals growth decay bouncing ball modelling thresholds 100 shared 20 hl challenge ib mathematics ib maths worksheet practice answer key solutions", "syllabus_codes": [ "SL 1.2", "SL 1.3", "SL 1.8" ], "search_codes": [ "SL 1.2; 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15 extended-response; 20 IB-style Paper 1; 10 AA HL challenge", "worksheet_scope": "Single shared SL syllabus section", "search_text": "binomial theorem aa sl & hl number and algebra sl 1.9 sl 1.9 aa sl 1.9; aa hl 1.9; sl 1.9; analysis and approaches sl 1.9; analysis and approaches hl 1.9 single shared sl syllabus section mixed; paper 1 focus 15 short-response; 15 extended-response; 20 ib-style paper 1; 10 aa hl challenge binomial theorem; finite binomial expansion; pascal triangle; combinations; ncr; coefficients; terms; middle term; sum of coefficients; positive integer powers shared aa sl/hl worksheet on finite positive-integer binomial expansions, coefficients and pascal’s triangle. aa-sl-hl-1-9 binomial theorem aa sl & hl number and algebra sl 1.9 sl 1.9 aa sl 1.9; aa hl 1.9; sl 1.9; analysis and approaches sl 1.9; analysis and approaches hl 1.9 binomial theorem; finite binomial expansion; pascal triangle; combinations; ncr; coefficients; terms; middle term; sum of coefficients; positive integer powers shared aa sl/hl worksheet on finite positive-integer binomial expansions, coefficients and pascal’s triangle. aa-sl-hl-1-9-binomial-theorem ib mathematics ib maths worksheet practice answer key solutions", "syllabus_codes": [ "SL 1.9" ], "search_codes": [ "SL 1.9", "aa sl 1.9", "aa hl 1.9", "sl 1.9", "analysis and approaches sl 1.9", "analysis and approaches hl 1.9" ], "calculator_guidance": "Mixed; 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concave down; change of concavity 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. ib-aa-sl-hl-5-7-second-derivative-worksheet aa-sl-hl-5-7-second-derivative ib mathematics ib maths worksheet practice answer key solutions ib mathematics ib maths worksheet practice answer key solutions", "syllabus_codes": [ "SL 5.7", "SL 5.8 (concave-up and concave-down terminology)", "SL 5.6 (supporting differentiation rules)", "SL 5.2 and SL 5.4 (supporting gradients and tangents)" ], "search_codes": [ "SL 5.7", "SL 5.8 (concave-up and concave-down terminology)", "SL 5.6 (supporting differentiation rules)", "SL 5.2 and SL 5.4 (supporting gradients and tangents)", "aa sl 5.7", "aa hl 5.7", "sl 5.7", "5.7", "analysis and approaches sl 5.7", "analysis and approaches hl 5.7", "second derivative", "concavity", "concave up", "concave down" ], "calculator_guidance": "Non-calculator / Paper 1 on unmarked questions; 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hl-only questions pages 7–8; answer key and solution outlines pages 9–11. ib-aa-sl-hl-5-10-integration-and-substitution-worksheet aa-sl-hl-5-10-integration-and-substitution active 2026-09-27 ib mathematics ib maths worksheet practice answer key solutions ib mathematics ib maths worksheet practice answer key solutions", "syllabus_codes": [ "SL 5.10", "SL 5.5 (initial conditions)", "SL 5.8 (linked stationary-point reasoning)", "SL 5.1 (limiting behaviour)" ], "search_codes": [ "SL 5.10", "SL 5.5 (initial conditions)", "SL 5.8 (linked stationary-point reasoning)", "SL 5.1 (limiting behaviour)", "aa sl 5.10", "aa hl 5.10", "sl 5.10", "5.10", "analysis and approaches sl 5.10", "analysis and approaches hl 5.10", "standard integrals", "integration by substitution", "reverse chain rule" ], "calculator_guidance": "Non-calculator unless marked GDC; 4 shared GDC tasks (29, 30, 47, 50); Paper 1 and Paper 2 styles", "last_verified": "2026-09-29" }, { "id": "aa-sl-hl-5-11", "title": "Definite Integrals and Areas", "courses": [ "AA SL", "AA HL" ], "syllabus_code": "SL 5.11", "topic_number": 5, "topic_name": "Calculus", "lesson_name": "Definite Integrals and Areas", "keywords": [ "definite integrals", "antiderivatives", "evaluation at bounds", "reversed limits", "signed area", "total area", "x-axis", "area below axis", "area between curves", "upper minus lower", "intersections", "split intervals", "absolute value", "substitution", "symmetry", "odd functions", "even functions", "parameters", "equal areas", "optimization", "shaded graphs", "GDC", "HL challenge", "aa sl 5.11", "aa hl 5.11", "sl 5.11", "5.11", "analysis and approaches sl 5.11", "analysis and approaches hl 5.11", "IB Mathematics", "IB Maths", "worksheet", "practice" ], "resource_type": "Worksheet", "calculator": "non-calculator", "pdf_path": "/downloads/worksheets/ib-aa-sl-hl-5-11-definite-integrals-and-areas-worksheet.pdf", "date_updated": "2026-09-27", "answers_included": true, "status": "published", "description": "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. 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15 extended-response; 20 original ib-style; 10 aa hl-exclusive challenges; answer key and solution outlines definite integrals; antiderivatives; evaluation at bounds; reversed limits; signed area; total area; x-axis; area below axis; area between curves; upper minus lower; intersections; split intervals; absolute value; substitution; symmetry; odd functions; even functions; parameters; equal areas; optimization; shaded graphs; gdc; hl challenge 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. aa-sl-hl-5-11 definite integrals and areas aa sl & hl 5 calculus sl 5.11 sl 5.11; sl 5.10 (integration methods); sl 5.5 (technology); sl 5.4 (linked tangents); sl 5.8 (linked optimization) aa sl 5.11; 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hl-only questions pages 10–12; answer key pages 13–15. ib-aa-sl-hl-5-11-definite-integrals-and-areas-worksheet aa-sl-hl-5-11-definite-integrals-and-areas active 2026-09-27 ib mathematics ib maths worksheet practice answer key solutions ib mathematics ib maths worksheet practice answer key solutions", "syllabus_codes": [ "SL 5.11", "SL 5.10 (integration methods)", "SL 5.5 (technology)", "SL 5.4 (linked tangents)", "SL 5.8 (linked optimization)" ], "search_codes": [ "SL 5.11", "SL 5.10 (integration methods)", "SL 5.5 (technology)", "SL 5.4 (linked tangents)", "SL 5.8 (linked optimization)", "aa sl 5.11", "aa hl 5.11", "sl 5.11", "5.11", "analysis and approaches sl 5.11", "analysis and approaches hl 5.11", "definite integrals", "signed area", "area between curves" ], "calculator_guidance": "Non-calculator unless marked GDC; 4 shared GDC tasks (29, 30, 47, 50) and 1 HL GDC task (60); Paper 1 and Paper 2 styles", "last_verified": "2026-09-29" }, { "id": "aa-hl-5-12", "title": "Limits, First Principles and Higher Derivatives", "courses": [ "AA HL" ], "syllabus_code": "AHL 5.12", "topic_number": 5, "topic_name": "Calculus", "lesson_name": "Limits, First Principles and Higher Derivatives", "keywords": [ "limits", "convergence", "divergence", "continuity", "differentiability", "corner", "removable discontinuity", "derivative definition", "first principles", "polynomial", "difference quotient", "secant", "tangent", "higher derivatives", "nth derivative", "derivative notation", "repeated differentiation", "derivative patterns", "factorial", "initial conditions", "GDC", "aa hl 5.12", "ahl 5.12", "5.12", "analysis and approaches hl 5.12", "IB Mathematics", "IB Maths", "worksheet", "practice" ], "resource_type": "Worksheet", "calculator": "non-calculator", "pdf_path": "/downloads/worksheets/ib-aa-hl-5-12-limits-first-principles-higher-derivatives-worksheet.pdf", "date_updated": "2026-09-27", "answers_included": true, "status": "published", "description": "50-question AA HL AHL 5.12 worksheet with five graphs and worked solutions. 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divergence; continuity; differentiability; corner; removable discontinuity; derivative definition; first principles; polynomial; difference quotient; secant; tangent; higher derivatives; nth derivative; derivative notation; repeated differentiation; derivative patterns; factorial; initial conditions; gdc 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. aa-hl-5-12 limits, first principles and higher derivatives aa hl 5 calculus ahl 5.12 ahl 5.12; sl 5.4 (tangents); sl 5.5 (reconstruction); sl 5.6 (standard differentiation); sl 5.8 (linked extrema) aa hl 5.12; ahl 5.12; 5.12; analysis and approaches hl 5.12; first principles; higher derivatives; limits aa hl-only ahl 5.12; informal continuity and differentiability; polynomial first principles; 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60 extended-response; 40 original paper 1-style; 40 original paper 2-style; complete syllabus index and solution outlines limits; gradients; rates of change; increasing; decreasing; power rule; tangents; normals; antiderivatives; initial conditions; chain rule; product rule; quotient rule; exponential; logarithm; trigonometric derivative; rational powers; second derivative; concave up; concave down; inflexion; stationary points; maxima; minima; optimization; kinematics; velocity; acceleration; total distance; standard integrals; substitution; definite integral; signed area; areas between curves; numerical roots; gdc; exam preparation 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. aa-sl-topic-5-calculus-200-question-revision complete calculus revision — 200 questions aa sl 5 calculus aa sl topic 5 sl 5.1; 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15 extended-response; 20 original IB-style; 10 AA HL-exclusive challenges; worked answer key", "worksheet_scope": "Shared SL 1.2 with 10 AA HL-exclusive challenges deepening arithmetic sequences and series; no additional AHL methods", "search_text": "arithmetic sequences and series aa sl & hl number and algebra sl 1.2 sl 1.2 aa sl 1.2; aa hl 1.2; sl 1.2; 1.2; analysis and approaches sl 1.2; analysis and approaches hl 1.2; arithmetic sequences; arithmetic series shared sl 1.2 with 10 aa hl-exclusive challenges deepening arithmetic sequences and series; no additional ahl methods non-calculator unless marked gdc; technology questions 30, 40, 43 and 49 15 short-response; 15 extended-response; 20 original ib-style; 10 aa hl-exclusive challenges; worked answer key arithmetic sequence; arithmetic series; common difference; first term; nth term; partial sums; sigma notation; simple interest; discrete graph; modelling; approximate data; salary; savings; seating; integer thresholds; cumulative total; 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capacity limit; changing ratio; gdc 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. ai-sl-1-3 geometric sequences and series ai sl 1 number and algebra sl 1.3 sl 1.3; sl 1.2 (comparison in question 48) ai sl 1.3; sl 1.3; 1.3; applications and interpretation sl 1.3; geometric sequences; geometric series ai sl 1.3: geometric terms, finite sums, sigma notation and applications; question 48 revisits arithmetic sequences; sl-only gdc permitted throughout; 27 technology-focused questions marked 50 15 short-response; 15 extended-response; 20 original ib-style questions with mark allocations; worked answer key geometric sequence; geometric series; common ratio; nth term; finite sum; sigma notation; percentage growth; percentage decay; negative ratio; 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Student questions pages 1–8; answers pages 9–13.", "question_count": 50, "question_structure": "15 short-response; 15 extended-response; 20 original IB Paper 1-style questions with marks; solution outlines", "worksheet_scope": "AA HL only: limits at finite points and infinity, l'Hôpital's rule, repeated use and Maclaurin-series limits", "search_text": "limits and l'hôpital's rule aa hl calculus ahl 5.13 ahl 5.13 aa hl 5.13; ahl 5.13; 5.13; analysis and approaches hl 5.13 aa hl only: limits at finite points and infinity, l'hôpital's rule, repeated use and maclaurin-series limits non-calculator / paper 1 15 short-response; 15 extended-response; 20 original ib paper 1-style questions with marks; solution outlines limits; l'hôpital's rule; l'hopital's rule; indeterminate forms; zero over zero; infinity over infinity; repeated differentiation; maclaurin series; exponential limits; logarithmic limits; trigonometric limits; one-sided limits; continuity; removable discontinuity; horizontal asymptotes; growth rates; parameters; error analysis 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. aa-hl-5-13 limits and l'hôpital's rule aa hl 5 calculus ahl 5.13 ahl 5.13 aa hl 5.13; ahl 5.13; 5.13; analysis and approaches hl 5.13 aa hl only: limits at finite points and infinity, l'hôpital's rule, repeated use and maclaurin-series limits non-calculator / paper 1 50 15 short-response; 15 extended-response; 20 original ib paper 1-style questions with marks; solution outlines limits; l'hôpital's rule; l'hopital's rule; indeterminate forms; zero over zero; infinity over infinity; repeated differentiation; maclaurin series; exponential limits; logarithmic limits; trigonometric limits; one-sided limits; continuity; removable discontinuity; horizontal asymptotes; growth rates; parameters; error analysis 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. ib-aa-hl-5-13-limits-lhopitals-rule-worksheet aa-hl-5-13-limits-lhopitals-rule active 2026-09-28 ib mathematics ib maths worksheet practice answer key solutions ib mathematics ib maths worksheet practice answer key solutions" }, { "id": "aa-hl-5-15", "title": "Further Derivatives and Antiderivatives", "courses": [ "AA HL" ], "syllabus_code": "AHL 5.15", "syllabus_codes": [ "AHL 5.15", "AHL 1.11 (supporting partial fractions)" ], "search_codes": [ "AHL 5.15", "AHL 1.11 (supporting partial fractions)", "aa hl 5.15", "ahl 5.15", "5.15", "analysis and approaches hl 5.15", "ahl 1.11" ], "topic_number": 5, "topic_name": "Calculus", "lesson_name": "Further Derivatives and Antiderivatives", "keywords": [ "further derivatives", "antiderivatives", "trigonometric derivatives", "tangent", "secant", "cosecant", "cotangent", "exponential derivatives", "logarithmic derivatives", "inverse trigonometric functions", "arcsin", "arccos", "arctan", "linear composites", "chain rule", "partial fractions", "repeated linear factors", "completing the square", "indefinite integrals", "definite integrals", "families of curves", "tangents and normals", "shaded area", "domain", "constants of integration", "aa hl 5.15", "ahl 5.15", "5.15", "analysis and approaches hl 5.15", "ahl 1.11", "IB Mathematics", "IB Maths", "worksheet", "practice" ], "resource_type": "Worksheet", "calculator": "non-calculator", "calculator_guidance": "Non-calculator / Paper 1", "pdf_path": "/downloads/worksheets/ib-aa-hl-5-15-further-derivatives-antiderivatives-worksheet.pdf", "date_updated": "2026-09-28", "last_verified": "2026-09-29", "answers_included": true, "status": "published", "description": "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. 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Student questions pages 1–11; answers pages 12–14.", "question_count": 50, "question_structure": "15 short-response; 15 extended-response; 20 original IB Paper 1-style questions with marks; solution outlines", "worksheet_scope": "AA HL only: area enclosed by a curve and the y-axis; volumes of revolution about the x-axis or y-axis, including disks and washers", "search_text": "areas and volumes of revolution aa hl calculus ahl 5.17 ahl 5.17 aa hl 5.17; ahl 5.17; 5.17; analysis and approaches hl 5.17 aa hl only: area enclosed by a curve and the y-axis; volumes of revolution about the x-axis or y-axis, including disks and washers non-calculator / paper 1 15 short-response; 15 extended-response; 20 original ib paper 1-style questions with marks; solution outlines area relative to the y-axis; integration with respect to y; volumes of revolution; x-axis rotation; y-axis rotation; disk method; washer method; inner radius; outer radius; horizontal slices; vertical slices; change of variable; inverse functions; signed area; total area; hollow solids; sphere; ellipse; container capacity; scaling; parameters; overlapping solids; error analysis 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. aa-hl-5-17 areas and volumes of revolution aa hl 5 calculus ahl 5.17 ahl 5.17 aa hl 5.17; ahl 5.17; 5.17; analysis and approaches hl 5.17 aa hl only: area enclosed by a curve and the y-axis; volumes of revolution about the x-axis or y-axis, including disks and washers non-calculator / paper 1 50 15 short-response; 15 extended-response; 20 original ib paper 1-style questions with marks; solution outlines area relative to the y-axis; integration with respect to y; volumes of revolution; x-axis rotation; y-axis rotation; disk method; washer method; inner radius; outer radius; horizontal slices; vertical slices; change of variable; inverse functions; signed area; total area; hollow solids; sphere; ellipse; container capacity; scaling; parameters; overlapping solids; error analysis 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. ib-aa-hl-5-17-areas-volumes-revolution-worksheet aa-hl-5-17-areas-volumes-revolution active 2026-09-28 ib mathematics ib maths worksheet practice answer key solutions ib mathematics ib maths worksheet practice answer key solutions" }, { "id": "aa-sl-hl-2-2", "title": "Functions, Domain, Range and Inverses", "courses": [ "AA SL", "AA HL" ], "syllabus_code": "AA SL 2.2; AA HL 2.2", "syllabus_codes": [ "AA SL 2.2", "AA HL 2.2", "AHL 2.14 (HL extension)" ], "search_codes": [ "AA SL 2.2", "AA HL 2.2", "SL 2.2", "2.2", "AHL 2.14 (HL extension)" ], "topic_number": 2, "topic_name": "Functions", "lesson_name": "Functions, Domain, Range and Inverses", "keywords": [ "function notation", "functions", "input", "output", "domain", "range", "interval notation", "mapping diagrams", "one-to-one", "many-to-one", "inverse functions", "reflection", "graphs", "mathematical models", "piecewise functions", "parent functions" ], "resource_type": "Worksheet", "calculator": "mixed: calculator and non-calculator", "calculator_guidance": "GDC required for Q27–30, Q48–50 and Q60, each labelled. 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Includes 50 shared questions and 10 HL challenges, with marked calculator questions and answers.", "question_count": 60, "question_structure": "15 short-response; 15 extended-response; 20 original IB-style; 10 HL-exclusive challenges; answer key and solution outlines", "last_verified": "2026-10-03", "search_text": "functions, domain, range and inverses aa sl aa hl aa sl 2.2; aa hl 2.2 aa sl 2.2 aa hl 2.2 ahl 2.14 (hl extension) aa sl 2.2 aa hl 2.2 sl 2.2 2.2 ahl 2.14 (hl extension) functions function notation functions input output domain range interval notation mapping diagrams one-to-one many-to-one inverse functions reflection graphs mathematical models piecewise functions parent functions 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. gdc required for q27–30, q48–50 and q60, each labelled. all other questions are non-calculator. ib mathematics ib maths worksheet practice answer key solutions" }, { "id": "aa-sl-hl-2-5", "title": "Composite and Inverse Functions", "courses": [ "AA SL", "AA HL" ], "syllabus_code": "AA SL 2.5; AA HL 2.5", "syllabus_codes": [ "AA SL 2.5", "AA HL 2.5", "AA SL 2.2 (supporting inverse graphs)", "AA HL 2.2 (supporting inverse graphs)" ], "search_codes": [ "AA SL 2.5", "AA HL 2.5", "SL 2.5", "2.5", "AA SL 2.2 (supporting inverse graphs)", "AA HL 2.2 (supporting inverse graphs)" ], "topic_number": 2, "topic_name": "Functions", "lesson_name": "Composite and Inverse Functions", "keywords": [ "composite functions", "composition", "order of composition", "inverse functions", "identity functions", "domain", "range", "restricted domain", "one-to-one", "inverse graphs", "reflection", "fixed points", "function notation" ], "resource_type": "Worksheet", "calculator": "mixed: calculator and non-calculator", "calculator_guidance": "GDC only for Q25, Q26 and Q28. All other questions, including the IB-style section, are non-calculator.", "pdf_path": "/downloads/worksheets/ib-aa-sl-hl-2-5-composite-and-inverse-functions-worksheet.pdf", "date_updated": "2026-10-03", "answers_included": true, "status": "published", "description": "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.", "question_count": 60, "question_structure": "15 short-response; 15 extended-response; 20 original IB-style; 10 HL-exclusive challenges; answer key and solution outlines", "last_verified": "2026-10-03", "search_text": "composite and inverse functions aa sl aa hl aa sl 2.5; aa hl 2.5 aa sl 2.5 aa hl 2.5 aa sl 2.2 (supporting inverse graphs) aa hl 2.2 (supporting inverse graphs) aa sl 2.5 aa hl 2.5 sl 2.5 2.5 aa sl 2.2 (supporting inverse graphs) aa hl 2.2 (supporting inverse graphs) functions composite functions composition order of composition inverse functions identity functions domain range restricted domain one-to-one inverse graphs reflection fixed points function notation 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. gdc only for q25, q26 and q28. all other questions, including the ib-style section, are non-calculator. ib mathematics ib maths worksheet practice answer key solutions" }, { "id": "aa-hl-1-10-binomial-series", "title": "Binomial Series: Fractional and Negative Indices", "courses": [ "AA HL" ], "syllabus_code": "AHL 1.10", "syllabus_codes": [ "AHL 1.10 (fractional and negative indices)", "AHL 5.19 (supporting binomial Maclaurin series)" ], "search_codes": [ "AA HL 1.10", "AHL 1.10", "1.10", "AHL 1.10 (fractional and negative indices)", "AHL 5.19 (supporting binomial Maclaurin series)" ], "topic_number": 1, "topic_name": "Number and Algebra", "lesson_name": "Binomial Series: Fractional and Negative Indices", "keywords": [ "binomial series", "binomial expansion", "extended binomial theorem", "fractional indices", "negative indices", "rational powers", "rational exponents", "Maclaurin series", "coefficients", "validity restrictions", "numerical approximations", "rational approximations", "matching coefficients", "unknown parameters", "products of series", "even and odd powers", "polynomial approximation", "truncation error" ], "resource_type": "Worksheet", "calculator": "non-calculator", "calculator_guidance": "Non-calculator throughout (Paper 1 style).", "pdf_path": "/downloads/worksheets/ib-aa-hl-1-10-binomial-series-worksheet.pdf", "date_updated": "2026-10-01", "answers_included": true, "status": "published", "description": "50 questions on fractional and negative binomial expansions, validity restrictions, approximations and coefficient problems. Includes a comparison graph, answers and solution outlines.", "question_count": 50, "question_structure": "15 short-response; 15 extended-response; 20 original IB Paper 1-style questions with marks; answer key and solution outlines", "last_verified": "2026-10-03", "search_text": "binomial series: fractional and negative indices aa hl ahl 1.10 ahl 1.10 (fractional and negative indices) ahl 5.19 (supporting binomial maclaurin series) aa hl 1.10 ahl 1.10 1.10 ahl 1.10 (fractional and negative indices) ahl 5.19 (supporting binomial maclaurin series) number and algebra binomial series binomial expansion extended binomial theorem fractional indices negative indices rational powers rational exponents maclaurin series coefficients validity restrictions numerical approximations rational approximations matching coefficients unknown parameters products of series even and odd powers polynomial approximation truncation error 50 questions on fractional and negative binomial expansions, validity restrictions, approximations and coefficient problems. includes a comparison graph, answers and solution outlines. non-calculator throughout (paper 1 style). ib mathematics ib maths worksheet practice answer key solutions" } ]