MATH 1120
Calculus I — Practice Question Bank
150+ Exam-Style Problems with Fully Worked Solutions
Independent Study Resource
Not affiliated with or endorsed by Yale University
Original Content — fully sellable
Edition 2026
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,Table of Contents
1. How to Use This Question Bank
2. Chapter 1: Functions and Precalculus Review — 12 problems
3. Chapter 2: Limits and Continuity — 12 problems
4. Chapter 3: The Derivative: Definition and Interpretation — 10 problems
5. Chapter 4: Differentiation Rules — 12 problems
6. Chapter 5: Derivatives of Trig, Exponential, and Logarithmic Functions — 12 problems
7. Chapter 6: Chain Rule and Implicit Differentiation — 12 problems
8. Chapter 7: Related Rates and Linear Approximation — 10 problems
9. Chapter 8: Curve Sketching and the Shape of Graphs — 10 problems
10. Chapter 9: Optimization Problems — 10 problems
11. Chapter 10: Antiderivatives and Indefinite Integrals — 10 problems
12. Chapter 11: The Definite Integral and Area — 10 problems
13. Chapter 12: The Fundamental Theorem of Calculus — 10 problems
14. Chapter 13: Introduction to Differential Equations — 8 problems
15. Final Mixed Practice Exam — 25 problems
16. Full Answer Key with Worked Solutions
17. Quick Formula Reference
Explore our developer-friendly HTML to PDF API Printed using PDFCrowd HTML to PDF
,How to Use This Question Bank
This question bank is designed to complement the MATH 1120 Complete Study Guide. Where the guide
teaches the concepts, this bank trains you to execute them under exam conditions.
Recommended workflow
1. Attempt each problem without looking at the solution. Set a timer: 3–5 minutes per
problem for computational items, 5–8 minutes for applied problems.
2. Check your work. Compare your method and final answer against the worked solution.
3. Identify the pattern. Every problem in this bank tests a specific technique. If you miss a problem,
ask: which technique did it test? Drill that technique.
4. Revisit missed problems after 48 hours. Spaced repetition is the most effective retention tool.
5. Use the final mixed exam last. It integrates everything under one time limit.
Difficulty Legend
[C] Computational — apply a rule directly.
[A] Applied — translate a real-world scenario into calculus.
[X] Conceptual — test your understanding of the underlying ideas.
[★] Challenge — exam-level difficulty, multi-step problems.
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, Chapter 1 — Functions and Precalculus Review
Problems
1.1 [C] Find the domain of f(x) = √(x − 5) / (x − 9).
1.2 [C] If f(x) = 2x² − 3 and g(x) = x + 4, find f(g(2)).
1.3 [C] Determine whether f(x) = x⁴ − 2x² is even, odd, or neither.
1.4 [C] Solve for x: log₂(x) + log₂(x − 2) = 3.
1.5 [C] Find the inverse of f(x) = (3x − 5) / 2.
1.6 [A] A rectangle has perimeter 24. Express its area A as a function of the width w.
1.7 [X] Explain why f(x) = x² does not pass the horizontal line test, and what this implies about its
inverse.
1.8 [C] Simplify: ln(e⁵ · e³).
1.9 [A] A population grows at 3% per year. Write a function P(t) for the population at time t years,
given P(0) = 5000.
1.10 [C] Find the domain and range of f(x) = e^(x−1).
1.11 [★] Solve: e^(2x) − 3e^x + 2 = 0.
1.12 [X] Given f(x) = sin(x) and g(x) = x², determine whether f(g(x)) = g(f(x)).
Worked Solutions
1.1 Need x − 5 ≥ 0 → x ≥ 5, and x − 9 ≠ 0 → x ≠ 9. Domain: [5, 9) ∪ (9, ∞).
1.2 g(2) = 6. f(6) = 2(36) − 3 = 69.
1.3 f(−x) = x⁴ − 2x² = f(x). Even.
1.4 x² − 2x − 8 = 0 → (x−4)(x+2) = 0. x = 4 (x = −2 invalid).
1.5 f⁻¹(x) = (2x + 5)/3.
1.6 2w + 2l = 24 → l = 12 − w. A = 12w − w².
1.7 f(x) = x² takes the same value for x and −x, so it is not one-to-one. No inverse exists on the full domain.
Explore our developer-friendly HTML to PDF API Printed using PDFCrowd HTML to PDF
Calculus I — Practice Question Bank
150+ Exam-Style Problems with Fully Worked Solutions
Independent Study Resource
Not affiliated with or endorsed by Yale University
Original Content — fully sellable
Edition 2026
Explore our developer-friendly HTML to PDF API Printed using PDFCrowd HTML to PDF
,Table of Contents
1. How to Use This Question Bank
2. Chapter 1: Functions and Precalculus Review — 12 problems
3. Chapter 2: Limits and Continuity — 12 problems
4. Chapter 3: The Derivative: Definition and Interpretation — 10 problems
5. Chapter 4: Differentiation Rules — 12 problems
6. Chapter 5: Derivatives of Trig, Exponential, and Logarithmic Functions — 12 problems
7. Chapter 6: Chain Rule and Implicit Differentiation — 12 problems
8. Chapter 7: Related Rates and Linear Approximation — 10 problems
9. Chapter 8: Curve Sketching and the Shape of Graphs — 10 problems
10. Chapter 9: Optimization Problems — 10 problems
11. Chapter 10: Antiderivatives and Indefinite Integrals — 10 problems
12. Chapter 11: The Definite Integral and Area — 10 problems
13. Chapter 12: The Fundamental Theorem of Calculus — 10 problems
14. Chapter 13: Introduction to Differential Equations — 8 problems
15. Final Mixed Practice Exam — 25 problems
16. Full Answer Key with Worked Solutions
17. Quick Formula Reference
Explore our developer-friendly HTML to PDF API Printed using PDFCrowd HTML to PDF
,How to Use This Question Bank
This question bank is designed to complement the MATH 1120 Complete Study Guide. Where the guide
teaches the concepts, this bank trains you to execute them under exam conditions.
Recommended workflow
1. Attempt each problem without looking at the solution. Set a timer: 3–5 minutes per
problem for computational items, 5–8 minutes for applied problems.
2. Check your work. Compare your method and final answer against the worked solution.
3. Identify the pattern. Every problem in this bank tests a specific technique. If you miss a problem,
ask: which technique did it test? Drill that technique.
4. Revisit missed problems after 48 hours. Spaced repetition is the most effective retention tool.
5. Use the final mixed exam last. It integrates everything under one time limit.
Difficulty Legend
[C] Computational — apply a rule directly.
[A] Applied — translate a real-world scenario into calculus.
[X] Conceptual — test your understanding of the underlying ideas.
[★] Challenge — exam-level difficulty, multi-step problems.
Explore our developer-friendly HTML to PDF API Printed using PDFCrowd HTML to PDF
, Chapter 1 — Functions and Precalculus Review
Problems
1.1 [C] Find the domain of f(x) = √(x − 5) / (x − 9).
1.2 [C] If f(x) = 2x² − 3 and g(x) = x + 4, find f(g(2)).
1.3 [C] Determine whether f(x) = x⁴ − 2x² is even, odd, or neither.
1.4 [C] Solve for x: log₂(x) + log₂(x − 2) = 3.
1.5 [C] Find the inverse of f(x) = (3x − 5) / 2.
1.6 [A] A rectangle has perimeter 24. Express its area A as a function of the width w.
1.7 [X] Explain why f(x) = x² does not pass the horizontal line test, and what this implies about its
inverse.
1.8 [C] Simplify: ln(e⁵ · e³).
1.9 [A] A population grows at 3% per year. Write a function P(t) for the population at time t years,
given P(0) = 5000.
1.10 [C] Find the domain and range of f(x) = e^(x−1).
1.11 [★] Solve: e^(2x) − 3e^x + 2 = 0.
1.12 [X] Given f(x) = sin(x) and g(x) = x², determine whether f(g(x)) = g(f(x)).
Worked Solutions
1.1 Need x − 5 ≥ 0 → x ≥ 5, and x − 9 ≠ 0 → x ≠ 9. Domain: [5, 9) ∪ (9, ∞).
1.2 g(2) = 6. f(6) = 2(36) − 3 = 69.
1.3 f(−x) = x⁴ − 2x² = f(x). Even.
1.4 x² − 2x − 8 = 0 → (x−4)(x+2) = 0. x = 4 (x = −2 invalid).
1.5 f⁻¹(x) = (2x + 5)/3.
1.6 2w + 2l = 24 → l = 12 − w. A = 12w − w².
1.7 f(x) = x² takes the same value for x and −x, so it is not one-to-one. No inverse exists on the full domain.
Explore our developer-friendly HTML to PDF API Printed using PDFCrowd HTML to PDF
