Further Parametric Equations (Edexcel A-Level Mathematics): Quizzes

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Change of Sign
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What does the change of sign method identify for f(x)=0f(x) = 0?

Where f(x)f(x) changes from + to - or - to +

For interval [a,b][a, b], what must f(a)f(a) and f(b)f(b) have?

Opposite signs

When does the change of sign method work well?

When the function is continuous

When does the change of sign method NOT work well?

When the root is repeated

Graphically, when does a function have a root?

When graph crosses the xx-axis

If f(1)=4f(1) = -4 and f(2)=6f(2) = 6 for continuous f(x)f(x), what can we conclude?

A root exists in [1,2][1, 2]

To prove x=1.864x = 1.864 correct to 3 d.p., which interval must contain the root?

[1.8635,1.8645][1.8635, 1.8645]

What two conditions together indicate a root in an interval?

Change of sign and continuity

Which methods can narrow the interval where a root lies?

Decimal search or interval bisection

What type of solution does the change of sign method provide?

Approximate solution

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