Math 101 Exam 120 Questions 2026 – Derivatives, Trigonometry, Limits UBC

This document contains approximately 120 exam-style questions with verified answers for Math 101 at UBC . It provides a comprehensive and structured review of core calculus concepts, including differentiation rules, trigonometric identities, limits, and fundamental theorems. The material is presented in a clear question-and-answer format, making it highly effective for exam preparation, concept reinforcement, and active recall. As shown on page 1, it begins with essential conditions for differentiability (continuity and equal left/right limits) and introduces key trigonometric definitions such as reciprocal identities (e.g., cscθ = 1/sinθ). In addition, the document provides extensive coverage of trigonometric identities and formulas (pages 2–3), including Pythagorean identities, angle sum and difference formulas, and double-angle identities. It also explains equivalent forms of expressions such as cos(2x) and sin²(x), helping students simplify and manipulate trigonometric functions effectively. Later sections (pages 4–6) focus on differentiation rules, including power, product, quotient, and chain rules, as well as derivatives of exponential, logarithmic, and trigonometric functions. It also introduces inverse trigonometric derivatives and the formal definition of a derivative using limits, reinforcing foundational calculus principles. The document further expands into key theorems and applications (pages 6–7), including Rolle’s Theorem and the Mean Value Theorem, along with geometric formulas such as volume and surface area of spheres and cylinders. It also includes applied concepts like elasticity of demand, linking calculus to real-world applications. This resource is ideal for students enrolled in Calculus I, Differential Calculus, and Introductory Mathematics courses. It is particularly beneficial for undergraduate students at UBC preparing for midterms, finals, or practice exams. It may also support learners seeking a strong foundation in derivatives, trigonometry, and mathematical reasoning. The content aligns closely with widely used textbooks such as Calculus: Early Transcendentals (Stewart), which covers limits, derivatives, trigonometric identities, and fundamental theorems of calculus. Keywords: calculus basics, Math 101 exam questions, derivatives rules calculus, trigonometric identities formulas, chain rule product rule quotient rule, exponential logarithmic derivatives, inverse trig derivatives, limits definition derivative, Rolle theorem mean value theorem, trigonometry double angle formulas, geometry formulas volume surface area, elasticity of demand calculus