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Previous year question hub

Calculus and Optimization - Data Science & Artificial Intelligence Previous Year Questions

Practice Calculus and Optimization - Data Science & Artificial Intelligence previous year questions organised from real papers, with year-wise coverage and clear topic navigation.

3Papers
3Years
12Questions
1Topics

Calculus and Optimization question pattern

Every graph below is calculated only from this selection.

Questions by year

Compare question counts across years.

Difficulty distribution

How the classified questions are distributed by difficulty.

Easy 6 50%
Medium 6 50%

Question type distribution

MCQ, numerical, multiple-select and other formats found in these papers.

MSQ 5 41.7%
Numerical Answer Type (NAT) 4 33.3%
MCQ 3 25%

Subject weightage

Top subjects by unique question coverage.

Data Science & Artificial Intelligence
12 Qs

Most asked topics

Top topics across the included previous year papers.

Calculus and Optimization
12 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Single-variable Differential Calculus
12 Qs

Paper coverage

Question coverage for the most populated papers. Every active PYP paper remains listed below.

Data Science and Artificial Intelligence (DA) 2026
1 Qs
Data Science & Artificial Intelligence (DA) 2025
6 Qs
Data Science & Artificial Intelligence (DA) 2024
5 Qs

Browse by subtopics

Open a focused page built from the same verified paper data.

Single-variable Differential Calculus

Explore previous-paper coverage, trends and focused practice for Single-variable Differential Calculus.

12 questions3 papers3 years

Included previous year papers

Newest papers appear first. Search these papers or sort by year and name.

Paper nameYearPDFAttempt
Data Science and Artificial Intelligence (DA) 20262026
1 questions in this view		2026
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download Official answer keyOriginal authority-issued PDF Official Download
Data Science & Artificial Intelligence (DA) 20252025
6 questions in this view		2025
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download Official answer keyOriginal authority-issued PDF Official Download
Data Science & Artificial Intelligence (DA) 20242024
5 questions in this view		2024
ExamElite PDFs
ExamElite solutions
Official documents
Official question paperOriginal authority-issued PDF Official Download Official answer keyOriginal authority-issued PDF Official Download

Sample previous year questions

A varied preview from the papers represented in this selection, with every available option.

1
2024 · Data Science & Artificial Intelligence · Calculus and Optimization · Single-variable Differential Calculus
Data Science & Artificial Intelligence (DA) 2024
For any twice differentiable function \( f: \mathbb{R} \to \mathbb{R} \), if at some \( x^* \in \mathbb{R} \), \( f'(x^*) = 0 \) and \( f''(x^*) > 0 \), then the function \( f \) necessarily has a ______ at \( x = x^* \).
Note: \( \mathbb{R} \) denotes the set of real numbers.
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2
2025 · Data Science & Artificial Intelligence · Calculus and Optimization · Single-variable Differential Calculus
Data Science & Artificial Intelligence (DA) 2025
Let \(f(x) = \frac{e^x - e^{-x}}{2}\), \(x \in \mathbb{R}\). Let \(f^{(k)}(a)\) denote the \(k^{th}\) derivative of \(f\) evaluated at \(a\). What is the value of \(f^{(10)}(0)\)? (Note: ! denotes factorial)
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3
2026 · Data Science & Artificial Intelligence · Calculus and Optimization · Single-variable Differential Calculus
Data Science and Artificial Intelligence (DA) 2026
Let \( f(x) = x^3 - 3x^2 + 2 \) be a function defined on \( (-1, 3] \).
Which of the following statements is/are correct?
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4
2024 · Data Science & Artificial Intelligence · Calculus and Optimization · Single-variable Differential Calculus
Data Science & Artificial Intelligence (DA) 2024
Let f: ℝ → ℝ be the function f(x) = 1 / (1 + e^{-x}).
The value of the derivative of f at x where f(x) = 0.4 is ______ (rounded off to two decimal places).
Note: ℝ denotes the set of real numbers.
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5
2025 · Data Science & Artificial Intelligence · Calculus and Optimization · Single-variable Differential Calculus
Data Science & Artificial Intelligence (DA) 2025
Consider two functions \(f : \mathbb{R} \to \mathbb{R}\) and \(g : \mathbb{R} \to (1, \infty)\). Both functions are differentiable at a point \(c\). Which of the following functions is/are ALWAYS differentiable at \(c\)? The symbol \(\cdot\) denotes product and the symbol \(\circ\) denotes composition of functions.
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6
2024 · Data Science & Artificial Intelligence · Calculus and Optimization · Single-variable Differential Calculus
Data Science & Artificial Intelligence (DA) 2024
Let \(f : \mathbb{R} \to \mathbb{R}\) be a function. Note: \(\mathbb{R}\) denotes the set of real numbers.
\(f(x) = \begin{cases} -x, & \text{if } x < -2 \\ ax^2 + bx + c, & \text{if } x \in [-2, 2] \\ x, & \text{if } x > 2 \end{cases}\)
Which ONE of the following choices gives the values of \(a, b, c\) that make the function \(f\) continuous and differentiable?
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