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
Integration basics Free
go to teaching materials ↴It is very helpful for students to understand that the process of integration (i.e. finding...
5. Calculus
Differentiation basics
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 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...