Calculus Tests & Review

This page contains several unit tests on calculus - differential calculus and integral calculus for both SL and HL.  Most of the tests below have worked solutions (solution keys) available as a separate document. I've also added some review quizzes on the bottom of this page. I welcome feedback on any of these materials. Just submit a comment at the bottom of the page.


Calculus Tests

Test_SLHL_Intro_Diff_Calculus_v1 smiley    [4 questions with no GDC; 5 questions with GDC allowed ]
syllabus content on test: derivative of \({x^n}\), sin(x), cos(x) and ln(x); tangents and normals; finding maximum and minimum; 2nd derivative & points of inflexion; optimization problems. Appropriate for all HL students and able SL students (worked solutions below)

Test_SLHL_Intro_Diff_Calculus_v1_SOL_KEY smiley   worked solutions for Intro Differential Calculus Test above
 

Test1 SL - Differential Calculus smiley  [ 4 questions with no GDC, and 4 questions with GDC allowed ]
syllabus content on test: finding a derivative from first principles; derivative of \({x^n}\);  derivative interpreted as gradient function; chain rule for composite functions; stationary points, maximum & minimum points, testing for max. and min.; 2nd derivative & points of inflexion; finding equation of a tangent line (worked solutions below)

Test1 SL - Diff Calculus - Solution Key     worked solutions for Test1 SL - Differential Calculus above

Test2 SL - Differential Calculus smiley     [ 4 questions with no GDC, and 4 questions with GDC allowed ]
syllabus content on test: finding equations of tangents & normal; chain rule for composite functions; product & quotient rules; maximum & minimum points; testing for maximum & minimum; 2nd derivative & points of inflexion; optimization (worked solutions below)
Test2 SL - Diff Calculus - Solution Key      worked solutions for Test2_SL_Differential_Calculus above

Test1_HL_diff_calculus_v1      [ 5 questions with no GDC, and 3 questions with GDC allowed ]
syllabus content on test: basic differentiation rules – including power rule & chain rule; differentiating using limit definition of derivative (first principles); finding and justifying maxima and minima; first & second derivative tests; tangents & normal; introductory optimization (worked solutions below)
Test1_HL_diff_calculus_v1_SOL_KEY     worked solutions for Test1_HL_diff_calculus above

Test2_HL_diff_calculus_v1    [ 4 questions with no GDC, and 3 questions with GDC allowed ]
syllabus content on test: differentiation from 'first principles'; chain rule; product rule; quotient rule; tangent & normal lines; max. & min. pts; points of inflexion; optimization (worked solutions below)
Test2_HL_diff_calculus_v1_SOL_KEY      worked solutions for Test2_HL_diff_calculus above

Test3_HL_diff_calculus_v1      [ 4 questions with no GDC, and 4 questions with GDC allowed ]
syllabus content on test: chain rule; product rule; quotient rule; implicit differentiation; points of inflexion; related rates; optimization (worked solutions below)
Test3_HL_diff_calculus_v1_SOL_KEY      worked solutions for Test3_HL_diff_calculus above

Test4_HL_diff_calculus_v2   [ 5 questions with no GDC, and 3 questions with GDC allowed ]
syllabus content on test: chain rule; product rule; quotient rule; implicit differentiation; points of inflexion; related rates; optimization (worked solutions below); correction to Q.6 on v1

Test4_HL_diff_calculus_v2_SOL_KEY    worked solutions for Test4_HL_diff_calculus above
 

Test1_SL_integral_calculus_v1    [ 5 questions with no GDC, and 4 questions with GDC allowed ]
syllabus content on test: indefinite & definite integrals; anti-differentiation with a boundary  condition to determine constant of integration; definite integral & area under a curve; definite integral & area between two curves; volume of revolution about the x-axis; kinematic problems - displacement, velocity & acceleration; total distance travelled (worked solutions below)

Test1_SL_integral_calculus_v1_SOL_KEY smiley   worked solutions for Test1_SL_integral_calculus above

Test2_SL_integral_calculus_v1 smiley  [ 4 questions with no GDC, and 3 questions with GDC allowed ]
syllabus content on test: indefinite & definite integrals; 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; volume of revolution about the x-axis; kinematic problems - displacement, velocity & acceleration, total distance travelled; definite integrals using technology (worked solutions below)

Test2_SL_integral_calculus_v1_SOL_KEY smiley  worked solutions for Test1_SL_integral_calculus above

Test1_HL_integral_calculus_v1      [ 6 questions with no GDC, and 3 questions with GDC allowed ]
syllabus content on test: indefinite & definite integrals; integration by substitution; anti-differentiation with a boundary condition to determine the constant of integration; integration by parts; definite integral and area under a curve; definite integral and area between two curves (worked solutions below)
Test1_HL_integral_calculus_v1    worked solutions for Test1_HL_integral_calculus above

Review Quizzes

Quiz_SL_calculus_No_GDC_v1 smiley
Quiz reviewing SL calculus content.  5 questions. GDC not allowed on any of the questions. Answers included on 2nd page. Worked solutions coming soon.

Quiz_HL_calculus_No_GDC_v1
Quiz reviewing a few HL calculus items. 6 questions.  GDC not allowed on any of the questions. Worked solutions available below.

Quiz_HL_calculus_No_GDC_v1_SOL_KEY
Worked solutions for HL calculus review Quiz above.

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