305 results for "polynomial".

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• Question

Using a given list of four complex numbers, find by inspection the one that is a root of a given cubic real polynomial and hence find the other roots.

• Question

This question tests the student's knowledge of the remainder theorem and the ways in which it can be applied.

• Question

Use a given factor of a polynomial to find the full factorisation of the polynomial through long division.

• Exam (13 questions)

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

Missing: Application with bacteria, turning points, difficult chain rule

• Question

Factorising polynomials using the highest common factor.

Adapted from 'Factorisation' by Steve Kilgallon.

• Question

Differentiate

$\sqrt{a x^m+b})$

• Question

Let $P_n$ denote the vector space over the reals of polynomials $p(x)$ of degree $n$  with coefficients in the real numbers.

Let the linear map $\phi: P_4 \rightarrow P_4$ be defined by:

$\phi(p(x))=ap(x) + (bx + c)p'(x) + (x ^ 2 + dx + f)p''(x)$

Using the standard basis for range and domain find the matrix given by $\phi$.

• Question

Let $P_n$ denote the vector space over the reals of polynomials $p(x)$ of degree $n$  with coefficients in the real numbers. Let the linear map $\phi: P_4 \rightarrow P_4$ be defined by: $\phi(p(x))=p(a)+p(bx+c).$Using the standard basis for range and domain find the matrix given by $\phi$.

• Question

Factorising polynomials using the highest common factor.

Adapted from 'Factorisation' by Steve Kilgallon.

• Exam (12 questions)

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

Missing: Application with bacteria, turning points, difficult chain rule

• Question

Complete the square for a quadratic polynomial $q(x)$ by writing it in the form $a(x+b)^2+c$.  Find both roots of the equation $q(x)=0$.

• Exam (12 questions)

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

Missing: Application with bacteria, turning points, difficult chain rule

• Question

Find the first 3 terms in the MacLaurin series for $f(x)=(a+bx)^{1/n}$ i.e. up to and including terms in $x^2$.

• Question

Find the first 3 terms in the Taylor series at $x=c$ for $f(x)=(a+bx)^{1/n}$ i.e. up to and including terms in $x^2$.

• Question

Using a given list of four complex numbers, find by inspection the one that is a root of a given cubic real polynomial and hence find the other roots.

• Question

Multiple choice question. Given a randomised polynomial select the possibe ways of writing the domain of the function.

• Question

Multiple choice question. Given a randomised polynomial select the possibe ways of writing the domain of the function.

• Question

This uses an embedded Geogebra graph of a cubic polynomial with random coefficients set by NUMBAS.  Student has to decide what kind of map it represents and whether an inverse function exists.

• Exam (12 questions)

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

Missing: Application with bacteria, turning points, difficult chain rule

• Exam (13 questions)

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

rebelmaths

• Exam (12 questions)

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

rebelmaths

• Exam (9 questions)

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

rebelmaths

• Exam (13 questions)

Questions about complex arithmetic; argument and modulus of complex numbers; complex roots of polynomials; de Moivre's theorem.

• Exam (5 questions)

5 questions on definite integrals - integrate polynomials, trig functions and exponentials; find the area under a graph; find volumes of revolution.

• Exam (12 questions)

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

rebelmaths

• Exam (12 questions)

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

rebelmaths

• Question

Use a given factor of a polynomial to find the full factorisation of the polynomial through long division.

• Question

Given a factor of a cubic polynomial, factorise it fully by first dividing by the given factor, then factorising the remaining quadratic.

• Question

Apply the factor theorem to check which of a list of linear polynomials are factors of another polynomial.

• Question

This uses an embedded Geogebra graph of a cubic polynomial with random coefficients set by NUMBAS.  Student has to decide what kind of map it represents and whether an inverse function exists.