Numerical Methods (AQA A-Level Further Maths): Quizzes

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Numerical Integration
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10 questions from this quiz

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When is numerical integration essential?

Functions impossible to integrate or data

In the mid-ordinate rule, where is the height of each rectangle measured?

At the centre of the strip's width

What is the mid-ordinate rule formula for area from aa to bb with nn strips?

A=ban(y1+y2++yn)A = \frac{b-a}{n}(y_1 + y_2 + \cdots + y_n)

What is a critical requirement for using Simpson's rule?

An even number of strips

What is the coefficient pattern in Simpson's rule?

1-4-2-4-2-4-2-...-4-2-4-1

What result does Simpson's rule give for quadratic functions?

The exact answer

What is the formula for relative error?

approxexactexact\frac{\text{approx} - \text{exact}}{\text{exact}}

Which method is more accurate?

Simpson's rule

For y=10xx2y = 10x - x^2 from x=0x=0 to x=10x=10 with 10 rectangles, what is the strip width?

1

Which function cannot be integrated using standard analytical methods?

y=ex2y = e^{x^2}

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