5. Calculus

The Calculus topic has the largest number of suggested teaching hours of the five syllabus topics: 28 hours for SL (just one more hour than the Statistics & Probability topic at SL) and 55 hours for HL (4 hours more than the Geometry & Trigonometry topic at HL).

∼ quick link ∼
downloadable exercise sets, quizzes & tests for teaching units in Calculus

Changes compared to previous Maths HL-SL syllabusses:
∗ No definition of derivative from first principles in SL
∗ No volumes of revolution in SL
∗ The following ‘new’ content was in previous 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 & Test

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_HL_Test1_integral_calculus_v1 
First HL test on integral calculus; syllabus content covered: 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

Differential equations HL (TN) 28 February 2021

HL syllabus content: first order differential equations; numerical solution of \(\frac{{{\rm{d}}y}}{{{\rm{d}}x}} = f\left(...
more

Euler's method-applet & example 24 January 2021

Here is a question where Euler's method is used to approximate a point (\(y\)-coordinate) on the solution curve of a differential...
more

Differentiation basics 8 June 2020

The introductory content for differential calculus is not too different between SL and HL; however, SL students do not need...
more

Integration basics 30 April 2020

When first teaching integration, I think it is helpful to look back at differentiation and try to impress upon students...
more

Integration by parts (tutorial) 29 April 2020

In developing a technique for integrating functions it is important to remember the fact that differentiation and integration...
more

Integration by substitution (tutorial) 27 April 2020

Throughout this tutorial you will often see the Leibniz notation for derivatives and differentials, named after the German...
more

All materials on this website are for the exclusive use of teachers and students at subscribing schools for the period of their subscription. Any unauthorised copying or posting of materials on other websites is an infringement of our copyright and could result in your account being blocked and legal action being taken against you.