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1.7 Differentiation

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Question 27

A magnetic flux contour line CCC within a specialized superconducting alloy is modeled by the equation

y2+60x−x2y=k,y>0 y^2 + 60x - x^2 y = k, \quad y > 0 y2+60x−x2y=k,y>0

where kkk is a constant and xxx and yyy represent spatial coordinates measured in micrometers.

a.

Find dydx\dfrac{dy}{dx}dxdy​ in terms of xxx and yyy.

[4]
b.

The point P(p,10)P(p, 10)P(p,10), where ppp is a constant, lies on CCC. Given that PPP is the minimum turning point on CCC,

find

(i) the value of ppp

(ii) the value of kkk

[5]
Markscheme

1.7 Differentiation Questions

  1. A Level
  2. /Maths
  3. /1.7 Differentiation

425 exam-style questions on OCR A Level Maths 1.7 Differentiation, covering 1.7.1 Derivative as gradient of the tangent, 1.7.2 Gradient of the tangent at a point, 1.7.3 Sketching the gradient function, 1.7.4 Second derivatives, 1.7.5 Second derivative as rate of change of gradient, 1.7.6 Convex, concave and points of inflection (A-level only), 1.7.7 Differentiation from first principles for powers of x, 1.7.8 Differentiation from first principles for sin x and cos x (A-level only), 1.7.9 Differentiating x^n, 1.7.10 Differentiating e^(kx) and a^(kx) (A-level only), 1.7.11 Differentiating trigonometric functions (A-level only), 1.7.12 Derivative of ln x (A-level only), 1.7.13 Tangents and normals, 1.7.14 Stationary points, 1.7.15 Increasing and decreasing functions, 1.7.16 Points of inflection (A-level only), 1.7.17 Product and quotient rules (A-level only), 1.7.18 Chain rule (A-level only), 1.7.19 Parametric and implicit differentiation (A-level only), 1.7.20 Constructing differential equations (A-level only), and 1.7 Differentiation. Each one has a worked solution and a mark scheme showing where the marks go.

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