5. Calculus
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.
∼ quick link ∼
downloadable exercise sets, quizzes & tests for teaching units in Calculus
Changes compared to 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: 1st 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
Calculus - syllabus overview
Syllabus item numbers are in brackets.
SL - Calculus
SL core (AA & AI)
differentiation basics (5.1, 5.2, 5.3)
tangents & normals (5.4)
integration basics (5.5)
SL (AA)
differentiation rules & 2nd derivative (5.6, 5.7)
maxima, minima & optimization (5.8)
kinematics (5.9)
integration & areas (5.10, 5.11)
HL - Calculus
HL (AA)
further calculus (5.12)
evaluating limits (5.13)
implicit differentiation & related rates (5.14)
optimization (5.14)
further differentiation & integration (5.15, 5.16)
areas & volumes (5.17)
differential equations (5.18)
Maclaurin series (5.19)
Exercise Sets, Quizzes & Tests
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
Selected Pages
5. Calculus
Maclaurin series HL (TN) Free
HL syllabus content: Maclaurin series; use of simple substitution, products, integration and differentiation to obtain other...
5. Calculus
Differentiation basics Free
teaching materialsThe introductory content for differential calculus is similar for SL and HL students; however, SL students...
5. Calculus
Differential equations HL
HL syllabus content: first order differential equations; numerical solution of \(\frac{{{\rm{d}}y}}{{{\rm{d}}x}} = f\left(...
5. Calculus
Integration basics
go to teaching materials ↴It is certainly helpful for students to understand that the process of integration (i.e. finding...
5. Calculus
Integration by parts (tutorial)
In developing a technique for integrating functions it is important to remember the fact that differentiation and integration...
5. Calculus
Implicit differentiation & related rates HL
go to teaching materials ↴syllabus content: HL 5.14 - implicit differentiation; related ratesUp to this point, students...