Introduction to Calculus
Build intuition for differentiation and integration with guided problem sets and real-world rate-of-change applications.
8
sections
12
challenges
50 min
to complete
Introduction to Calculus is an interactive mathematics lab pitched at Level 3 — A-Level / BTEC (Level 3 on the UK framework). It is one worked example of what EngagedLab produces when a lecturer uploads their own mathematics teaching material: the platform classifies the content, structures it into a multi-section lab, and generates the retrieval-practice and challenge activities shown below.
Across 8 sections and 12 challenges (about 50 min of learner time), the lab moves beyond passive reading. Learners work through a applied problem and other domain tasks that ask them to apply, not just recall — reasoning that is tagged against Bloom’s taxonomy so the cognitive demand is visible. Each objective and quiz question is discipline-accurate and written to UK academic conventions.
The lab sets 3 explicit learning objectives — listed in full below — and every quiz question and challenge is aligned to them, so the assessment matches the intended outcome rather than drifting into trivia. The finished lab passes EngagedLab’s 32 quality gates and exports as an offline-capable SCORM 1.2/2004 or LTI 1.3 Advantage package, so progress and scores flow back to your VLE gradebook through AGS grade passback and cmi.suspend_data state persistence.
Learning objectives
Differentiate polynomial functions using the power rule.
Interpret the derivative as a gradient and a rate of change.
Integrate polynomials and apply the constant of integration.
Try a sample quiz
Pick an answer to see instant feedback — exactly as a learner would in the generated lab.
Q1. What is the derivative of f(x) = 3x² + 5x − 7?
Q2. What is ∫ (2x) dx?
Sample challenge
A ball’s height is h(t) = 20t − 5t² metres. Find its velocity function, then determine the time at which the ball is momentarily at rest.
Hint 1
Velocity is the rate of change of height — which operation gives you that?
Hint 2
Differentiate: v(t) = 20 − 10t. The ball is at rest when v(t) = 0, so 20 − 10t = 0 giving t = 2 seconds.
What every EngagedLab lab includes
Learning objectives
Outcome-aligned goals mapped to the qualification level.
Guided practice
Graduated hints that nudge, then scaffold — never hand over the answer.
Domain challenges
Subject-specific reasoning tasks, not generic multiple choice.
Knowledge-check quizzes
Spaced retrieval questions with instant feedback.
Case study
A multi-section scenario with stakeholder perspectives.
Reflection prompts
Metacognitive prompts that consolidate learning.
Curated reading list
4–6 further readings sorted by difficulty.