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Exam (elaborations)

Final Exam Calculus 1 with solution (Sample 2)

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This document contains a full Calculus I final exam sample, including all questions and complete worked solutions. It covers essential first-semester calculus topics such as differential equations, integrals, absolute value integrals, limits, implicit differentiation, continuity of piecewise functions, and derivative techniques. The exam consists of seven multi-part problems and is formatted like an authentic assessment, making it useful for study, revision, and exam preparation. The total number of pages is 16.

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Institution
Calculus 1
Course
Calculus 1

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CALCULUS I
FINAL EXAM

Sample 2




Student Name: ___________________________________________

Student ID Number: ______________________________________



Course Title: Calculus I

Duration of Exam: 2 Hours

Number of Exam Pages: 8 pages (including this cover sheet)

Exam Type: Closed book

Additional Materials Allowed: Calculator and Formula sheet




Total Mark: /100




1

,Q1. (5 marks)

Solve the initial value problem

𝑑2𝑦
= 2 − 6𝑥 ; 𝑦 ′ (0) = 4, 𝑦(0) = 1.
𝑑𝑥 2




2

, Q2. Evaluate the following integrals (6 marks)


4
∫ 𝑥 √1 − 𝑥 2 𝑑𝑥




sin(2𝑥 + 1)
∫ 𝑑𝑥
𝑐𝑜𝑠 2 (2𝑥 + 1)




4
∫ |𝑥|𝑑𝑥
−4




3
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Connected book

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Joel R. Hass, Christopher D. Heil, Maurice D. Weir Thomas\' Calculus
  • 2017
  • 9780134438986
  • Unknown

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Course
Calculus 1
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Uploaded on
November 15, 2025
Number of pages
16
Written in
2020/2021
Type
Exam (elaborations)
Contains
Questions & answers

Subjects

  • limits
  • derivatives
  • integrals
  • definite integrals
  • indefinite integrals
  • implicit differentiation
  • fundamental theorem of calculus
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