Further Mathematics · OCR H245 · Option A · Topic 8.05

Surfaces and partial differentiation

3-D surfaces, sections and contours, partial differentiation, stationary points, tangent planes.

  • 5 sub-topics
  • Taught in Year 13
  • 39 practice questions
  • 5 animated lessons
Practice questions (39) Lessons Worksheets coming soon All OCR Further Mathematics topics

What the specification says

Every sub-topic OCR can examine in this topic, with its reference number from the official specification. The Y12 and Y13 tags show when each sub-topic is usually taught.

  1. 8.05a-b3-D surfacesY13
  2. 8.05cSections and contoursY13
  3. 8.05dPartial differentiationY13
  4. 8.05e-fStationary pointsY13
  5. 8.05gTangent planesY13

Try 2 questions

Easy and medium questions from this topic, each with a worked solutions and the mark for every step. All 39 questions in this topic, free, no account needed.

Surfaces and partial differentiation

Easy

A point on a surface · Year 12 · 1 mark

  1. The point (2,3,k)(2, 3, k) lies on the surface z=x2−2yz = x^2 - 2y. What is kk?
    (1)

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  1. Substitute the x- and y-coordinates into the equation of the surface.DD: −2-2

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Surfaces and partial differentiation

Medium

A mixed second derivative · Year 12 · 1 mark

  1. For z=x3y2z = x^3y^2, what is ∂2z∂x ∂y\dfrac{\partial^2 z}{\partial x\,\partial y}?
    (1)

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  1. Differentiate with respect to yy, then with respect to xx. The order does not matter here.BB: 6x2y6x^2y

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