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1.11.2 Integrating standard functions

1.11.2 Integrating standard functions

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Question 111
a.

A metal worker is crafting a sculpture where the upper profile is defined by the curve with equation

y=15x2−12x y = \frac{1}{5}x^2 - \frac{12}{\sqrt{x}} y=51​x2−x​12​

at the point Q(4,−2.8)Q(4, -2.8)Q(4,−2.8).

Find the equation of the tangent to this profile at point QQQ.

Give your answer in the form ax+by+c=0ax + by + c = 0ax+by+c=0, where aaa, bbb and ccc are integers.

[4]
b.

The lower profile of the sculpture, given by the curve with equation y=f(x)y = f(x)y=f(x), also passes through the point Q(4,−2.8)Q(4, -2.8)Q(4,−2.8). Given that

f′(x)=15x2−12x f'(x) = \frac{1}{5}x^2 - \frac{12}{\sqrt{x}} f′(x)=51​x2−x​12​

find the expression for f(x)f(x)f(x), giving the coefficients in simplest form.

[5]
Markscheme

1.11.2 Integrating standard functions Questions

  1. A Level
  2. /Maths
  3. /1.11.2 Integrating standard functions

139 exam-style questions on AQA A Level Maths 1.11.2 Integrating standard functions. Each one has a worked solution and a mark scheme showing where the marks go.

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