plumiSurfaces and contours: OCR A‑Level Further Maths questions
OCR A-Level Further Maths past-paper questions on 10.1 Surfaces and contours, 2018–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.
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All 7 questions on Surfaces and contours, as a list
- June 2025, AS Additional Pure Mathematics, Q3 (13 marks): 3 3 The surface S has equation z x y y x + for all real values of x and y. 2 6 3 4 = - + (a) (i) State the equation of the section of S cut by the plane y = 1.
- June 2023, Additional Pure Mathematics, Q1 (4 marks): 1 The surface S is defined for all real x and y by the equation z x 2 xy . The intersection of = + S with the plane P gives a section of the surface. On the axe
- June 2023, AS Additional Pure Mathematics, Q8 (6 marks): A surface, C, is given by the equation z f ( , ) x y for all real values of x and y. You are given = that C has the following properties. • The surface is conti
- June 2022, AS Additional Pure Mathematics, Q5 (6 marks): A research student is using 3‑D graph‑plotting software to model a chain of volcanic islands in the Pacific Ocean. These islands appear above sea‑level at regul
- November 2021, Additional Pure Mathematics, Q10 (7 marks): B A z y O x D C A student wishes to model the saddle of a horse. They use a surface described by a function of the z x y with a saddle point at the origin O. Th
- November 2021, AS Additional Pure Mathematics, Q2 (4 marks): 2 The surface S is given by z x 4 xy for 6 x 6 and 2 y 2 . = + - - G G G G (a) (i) Write down the equation of any one section of S which is parallel to the x-z
- November 2020, Additional Pure Mathematics, Q5 (13 marks): A designer intends to manufacture a product using a 3-D printer. The product will take the form of a surface S which must meet a number of design specifications
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