Calculus
Overview
The last topic estimated the gradient of a curve using a tangent drawn by eye, or two points squeezed close together. Calculus turns that estimate into an exact answer: a single formula, the derivative, that gives the gradient at any point on a curve instantly, with no drawing and no approximation.
You will use differentiation to locate the highest and lowest points on a curve, to find the equation of a tangent, and to move between displacement, velocity and acceleration in problems about moving objects.
Objectives
- Differentiate integer powers of x using dy/dx notation
- Determine gradients, rates of change, maxima, minima, stationary points and turning points
- Apply calculus to linear kinematics and other simple practical problems, including distance/time and speed/time graphs
- Understand the relationship between displacement or distance, velocity and speed, and acceleration
Lesson Note
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Lesson Evaluation
Congratulations on completing the lesson on Calculus. Now that youve explored the key concepts and ideas, its time to put your knowledge to the test. This section offers a variety of practice questions designed to reinforce your understanding and help you gauge your grasp of the material.
You will encounter a mix of question types, including multiple-choice questions, short answer questions, and essay questions. Each question is thoughtfully crafted to assess different aspects of your knowledge and critical thinking skills.
Use this evaluation section as an opportunity to reinforce your understanding of the topic and to identify any areas where you may need additional study. Don't be discouraged by any challenges you encounter; instead, view them as opportunities for growth and improvement.
- What is dy/dx when y = 5x^4? A) 5x^3 B) 20x^3 C) 20x^4 D) 4x^3 Answer: B
- Differentiate y = 3x^2 - 7x + 2. A) 6x - 7 B) 3x - 7 C) 6x + 2 D) 6x^2 - 7 Answer: A
- At a stationary point of a curve, dy/dx equals: A) 1 B) undefined C) 0 D) the y-value Answer: C
- The curve y = x^2 - 4x + 3 has a stationary point at: A) (2, -1) B) (4, 3) C) (-2, -1) D) (2, 1) Answer: A
- If displacement s = t^2 - 4t, the velocity ds/dt equals: A) t - 4 B) 2t - 4 C) 2t D) t^2 - 4 Answer: B
Available on the Green Bridge App
Download the Green Bridge CBT app on your phone or computer to access full lesson notes, practice questions, and more.
Available on the Green Bridge App
Download the Green Bridge CBT app on your phone or computer to access full lesson notes, practice questions, and more.
Recommended Books
Practice Mock Questions
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