The Bisection Method (VCE SSCE Mathematical Methods): Quizzes

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The Bisection Method
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What does the bisection method find?

Approximate solutions to f(x)=0f(x) = 0

What must be true about f(a1)f(a_1) and f(b1)f(b_1) for the bisection method to work?

They must have opposite signs

How is the midpoint m1m_1 calculated in the bisection method?

m1=a1+b12m_1 = \frac{a_1 + b_1}{2}

If f(a1)×f(m1)<0f(a_1) \times f(m_1) < 0, which interval should be chosen?

[a1,m1][a_1, m_1]

What happens to the error with each iteration of the bisection method?

The error approximately halves

For polynomials of what degree is there no general formula to find all solutions?

Degree 5 and higher

In the pseudocode example, what is the stopping condition for the while loop?

b−a>2×0.01b - a > 2 \times 0.01

For x3+3x+6=0x^3 + 3x + 6 = 0, what is the solution correct to two decimal places?

−1.29-1.29

What is pseudocode?

Informal algorithm writing, structured

Why does a sign change in f(x)f(x) indicate a root exists?

Function crosses x-axis where f(x)=0f(x)=0

Explore VCE SSCE Mathematical Methods Revision Notes by Topics

Solving Cubic Equations

Cubic Functions of a Particular Form

Graphs of Factorised Cubic Functions

Solving Cubic Inequalities

Families of Cubic Polynomial Functions

Applications of Polynomial Functions

The Bisection Method

Quadratic Functions

Determining the Rule for a Parabola

The Language of Polynomials

Division and Factorisation of Polynomials

The General Cubic Function

Polynomials of Higher Degree

Determining the Rule for the Graph of a Polynomial

Solution of Literal Equations and Systems of Equations

Show more

Determining the Rule for a Parabola

The Language of Polynomials

Division and Factorisation of Polynomials

The General Cubic Function

Polynomials of Higher Degree

Determining the Rule for the Graph of a Polynomial

Solution of Literal Equations and Systems of Equations

Explore VCE SSCE Mathematical Methods Model Answers by Topics

Solving Cubic Equations

Cubic Functions of a Particular Form

Graphs of Factorised Cubic Functions

Solving Cubic Inequalities

Families of Cubic Polynomial Functions

Applications of Polynomial Functions

The Bisection Method

Quadratic Functions

Determining the Rule for a Parabola

The Language of Polynomials

Division and Factorisation of Polynomials

The General Cubic Function

Polynomials of Higher Degree

Determining the Rule for the Graph of a Polynomial

Solution of Literal Equations and Systems of Equations

Show more

Determining the Rule for a Parabola

The Language of Polynomials

Division and Factorisation of Polynomials

The General Cubic Function

Polynomials of Higher Degree

Determining the Rule for the Graph of a Polynomial

Solution of Literal Equations and Systems of Equations

Explore VCE SSCE Mathematical Methods Flashcards by Topics

Solving Cubic Equations

Cubic Functions of a Particular Form

Graphs of Factorised Cubic Functions

Solving Cubic Inequalities

Families of Cubic Polynomial Functions

Applications of Polynomial Functions

The Bisection Method

Quadratic Functions

Determining the Rule for a Parabola

The Language of Polynomials

Division and Factorisation of Polynomials

The General Cubic Function

Polynomials of Higher Degree

Determining the Rule for the Graph of a Polynomial

Solution of Literal Equations and Systems of Equations

Show more

Determining the Rule for a Parabola

The Language of Polynomials

Division and Factorisation of Polynomials

The General Cubic Function

Polynomials of Higher Degree

Determining the Rule for the Graph of a Polynomial

Solution of Literal Equations and Systems of Equations

Explore VCE SSCE Mathematical Methods Exam Questions by Topics

Solving Cubic Equations

Cubic Functions of a Particular Form

Graphs of Factorised Cubic Functions

Solving Cubic Inequalities

Families of Cubic Polynomial Functions

Applications of Polynomial Functions

The Bisection Method

Quadratic Functions

Determining the Rule for a Parabola

The Language of Polynomials

Division and Factorisation of Polynomials

The General Cubic Function

Polynomials of Higher Degree

Determining the Rule for the Graph of a Polynomial

Solution of Literal Equations and Systems of Equations

Show more

Determining the Rule for a Parabola

The Language of Polynomials

Division and Factorisation of Polynomials

The General Cubic Function

Polynomials of Higher Degree

Determining the Rule for the Graph of a Polynomial

Solution of Literal Equations and Systems of Equations

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