# 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 [ 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; 2^{nd} 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 **worked solutions** for Intro Differential Calculus Test above

Test1 SL - Differential Calculus [ 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.; 2^{nd} 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 [ 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; 2^{nd} 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** **** worked solutions** for **Test1_SL_integral_calculus** above

Test2_SL_integral_calculus_v1 [ 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 **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

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.