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The Calculus topic has the highest number of suggested teaching hours of the five syllabus topics: 28 hours for SL (just one hour more than the Statistics & Probability topic at SL) and 55 hours for HL (4 hours more than the Geometry & Trigonometry topic at HL). For many students, calculus is often the most challenging part of the course. I think this is mostly due to the fact that most students will not have previously studied any calculus and that calculus involves a great deal of conceptual understanding, not just learning algebraic methods.

In my opinion, considerable thought should be given to when you schedule to teach the Calculus topic. Of course, not all of the syllabus content in the Calculus topic needs to be taught one after another without interruption - however, it can work well that way (look at my Analysis & Approaches teaching plan v5). One of the factors affecting your decision on when to schedule the teaching of Calculus syllabus content is whether you think it would be helpful for your students to have completed (or nearly completed) the Calculus content before they complete their mathematics internal assessment task (the Exploration). It would be virtually impossible to teach all of the Statistics & Probability syllabus content and also all of the Calculus syllabus content before your students write their Exploration. Although a bit over-simplified, one of the scheduling decisions that needs to be made is whether to teach Calculus before Stats & Probability, or teach Stats & Probability before Calculus. Either option can work out fine, but you (and your school colleagues) should carefully discuss these two options and the various factors at your school that might affect this key course planning decision.

key syllabus changes compared to the previous Maths HL-SL syllabusses:.
∗ No formal definition of derivative from first principles in SL
∗ No volumes of revolution in SL
∗ The following content was in previous Maths HL Calculus option topic:
   HL 5.18: 1^st order differential equations; numerical solution using Euler’s method; separation of variables method; homogeneous  differential equations; linear differential equations and integrating factor method
   HL 5.19: Maclaurin series; use of simple substitution, products, integration and differentiation to obtain other series; Maclaurin series developed from differential equations

Teaching materials

AA_SL_5.4(8)_diff_calc4_v1 
Exercise set with 4 questions. GDC allowed on all questions. Worked solutions included. Syllabus content: equations of tangents & normals; differentiation of \({x^n}\), chain rule, product rule; maximum and minimum points, points of inflexion.

AA_HL_5.4(14)_diff_calc6_v1 
Exercise set with 11 questions (1-6 no GDC, 7-11 GDC allowed). Worked solutions available below. Syllabus content:  chain rule; product rule; quotient rule; tangent lines; implicit differentiation; points of inflexion; related rates; optimization

AA_HL_5.4(14)_diff_calc6_SOL_KEY_v1 
Worked solutions for HL_diff_calc6 exercise set above.

AA_SL_Quiz_2_diff_calc_v1 
SL differential calculus quiz with 5 questions. GDC allowed on all questions. Content: equation of normal, optimization, points of inflexion, finding maxima & minima, applying 1st and 2nd derivative tests. Worked solutions available below.

AA_SL_Quiz_2_diff_calc_SOL_KEY_v1 
Worked solutions for SL differential calculus quiz above

AA_HL_Quiz_2_diff_calc_v1 
HL differential calculus quiz with 6 questions. GDC allowed on all questions. Content: equation of normal, derivative from first principles, optimization, points of inflexion, finding maxima & minima, applying 1st and 2nd derivative tests. Worked solutions available below.

AA_HL_Quiz_2_diff_calc_SOL_KEY_v1 
Worked solutions for HL differential calculus quiz above

AA_HL_Test1_diff_calc_v1  
First HL test on differential calculus; syllabus content covered: chain rule; product rule; quotient rule; finding maxima & minima; points of inflexion; derivative from first principles; optimization; worked solutions available below

AA_HL_Test1_diff_calc_SOL_KEY_v1  
worked solutions for first HL differential calculus test above

AA_HL_Test2_diff_calc_v1  
2nd HL test on differential calculus; syllabus content covered: chain rule; product rule; quotient rule; finding maxima & minima; points of inflexion; implicit differentiation; related rates; optimization; worked solutions available below

AA_HL_Test2_diff_calc_SOL_KEY_v1  
worked solutions for 2nd HL differential calculus test above

AA_SL_Test1_integral_calculus_v1 
First SL test on integral calculus - syllabus content: indefinite & definite integrals; area under a curve; area between two curves; kinematic problems - displacement, velocity & acceleration; total distance travelled; worked solutions below

AA_SL_Test1_integral_calculus_SOL_KEY_v1 
worked solutions for first SL integral calculus test above

AA_SL_Test2_integral_calculus_v1 
Second SL test on integral calculus - syllabus content: integration by inspection or substitution of the form \(\int {f\left( {g\left( x \right)} \right)} g'\left( x \right)dx\); area under a curve; area between two curves, total distance travelled; definite integrals using technology; worked solutions below

AA_SL_Test2_integral_calculus_SOL_KEY_v1 
worked solutions for second SL integral calculus test above

AA_HL_Test1_integral_calculus_v1 
First HL test on integral calculus - syllabus content: definite integrals using technology; areas between a curve and x-axis; kinematic problems; integration by inspection; areas between curves;  integration by substitution; integration by parts; volumes of revolution about the x-axis; worked solutions available below

AA_HL_Test1_integral_calc_SOL_KEY_v1 
worked solutions for first HL integral calculus test above

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