Search - Numbas at mathcentre.ac.uk

37 results.

Graphing: quadratic
Ready to use
Question in Graphing and Polynomials by Ben Brawn

No description given
Graphing: nth degree polynomial
Ready to use
Question in Graphing and Polynomials by Ben Brawn

Understanding the general facts about polynomials of degree n.
Graphing: linear
Ready to use
Question in Graphing and Polynomials by Ben Brawn

No description given
Graphing: quartic
Ready to use
Question in Graphing and Polynomials by Ben Brawn

No description given
Graphing: cubic
Ready to use
Question in Graphing and Polynomials by Ben Brawn

No description given
Polynomials: Expand and Simplify 1a
Ready to use
Question in MASH Bath: Question Bank by Ben McGovern and 1 other

Finding linear combinations of two quadtratic expressions of the form $ax^2+bx+c$ .
Cubics: Solving a Cubic Equation
Ready to use
Question in MASH Bath: Question Bank by Ben McGovern and 1 other

Solving a cubic equation of the form $ax^3+bx^2+cx+d=0$ .
Algebraic division and partial fractions, practice question 3
Needs to be tested
Question in Nahid's workspace by Nahid Chowdhury and 2 others

Find the remainder when dividing two polynomials, by algebraic long division.
Roots of a cubic real polynomial
Has some problems
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 1 other

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.
Quotient rule
Draft
Question in Bill's workspace by Bill Foster

Other method. Find $p,\;q$ such that $\displaystyle \frac{ax+b}{cx+d}= p+ \frac{q}{cx+d}$ . Find the derivative of $\displaystyle \frac{ax+b}{cx+d}$ .
Dividing polynomials 3
Draft
Question in Bill's workspace by Bill Foster

Divide $f(x)=x ^ 4 + ax ^ 3 + bx^2 + cx+d$ by $g(x)=x^2+p$ so that:
$\displaystyle \frac{f(x)}{g(x)}=q(x)+\frac{r(x)}{g(x)}$
Dividing Polynomials
Draft
Question in Bill's workspace by Bill Foster

Dividing a cubic polynomial by a linear polynomial. Find quotient and remainder.
Dividing polynomials 2
Draft
Question in Bill's workspace by Bill Foster

Algebraic manipulation/simplification.

Simplify $\displaystyle \frac{ax^4+bx^2+c}{a_1x^4+b_1x^2+c_1}$ by cancelling a a common degree 2 factor.
Product rule
Draft
Question in Bill's workspace by Bill Foster

Differentiate $(ax+b)^m(cx+d)^n$ using the product rule. The answer will be of the form $(ax+b)^{m-1}(cx+d)^{n-1}g(x)$ for a polynomial $g(x)$ . Find $g(x)$ .
Product rule
Draft
Question in Bill's workspace by Bill Foster

Differentiate $f(x) = x^m(a x+b)^n$ .
Integrate algebraic fraction
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Find $\displaystyle \int\frac{ax^3+ax+b}{1+x^2}\;dx$ . Enter the constant of integration as $C$ .
Indefinite integral of polynomial fraction
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Find $\displaystyle \int \frac{nx^3+mx^2+px +m}{x^2+1} \;dx$
Integral of improper polynomial fraction
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Find $\displaystyle \int \frac{nx^3+mx^2+nx + p}{1+x^2}\;dx$ . Solution involves $\arctan$ .
Integral of improper polynomial fraction
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Find $\displaystyle \int\frac{ax^3+ax+b}{1+x^2}\;dx$ . Enter the constant of integration as $C$ .
Indefinite integral of improper polynomial fraction
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Find $\displaystyle\int \frac{ax^3-ax+b}{1-x^2}\;dx$ . Input constant of integration as $C$ .
Indefinite integral of improper polynomial fraction
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Find $\displaystyle \int \frac{nx^3+mx^2+nx + p}{1+x^2}\;dx$ . Solution involves $\arctan$ .
How to enter algebraic expressions - Getting Started
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Inputting algebraic expressions into Numbas.
Differentiation: Product rule
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Differentiate $f(x) = x^m(a x+b)^n$ .
Quotient rule - differentiate quotient of linear terms
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Other method. Find $p,\;q$ such that $\displaystyle \frac{ax+b}{cx+d}= p+ \frac{q}{cx+d}$ . Find the derivative of $\displaystyle \frac{ax+b}{cx+d}$ .
Divide Polynomials
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Dividing a cubic polynomial by a linear polynomial. Find quotient and remainder.
Find greatest common divisor of two polynomials over the rationals
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

$f(X)$ and $g(X)$ as polynomials over the rational numbers $\mathbb{Q}$ .

Find their greatest common divisor (GCD) and enter as a normalized polynomial.
Factorise polynomial into irreducible factors
Draft
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

$f(X)$ and $g(X)$ are polynomials over $\mathbb{Z}_n$ .

Find their greatest common divisor (GCD) and enter it as a monic polynomial.

Hence factorize $f(X)$ into irreducible factors.
Finding the missing value of a constant in a polynomial, using the Factor Theorem
Ready to use
Question in Transition to university by Elliott Fletcher

Given a factor of a cubic polynomial, factorise it fully by first dividing by the given factor, then factorising the remaining quadratic.
Finding the full factorisation of a polynomial, using the Factor Theorem and long division
Ready to use
Question in Transition to university by Elliott Fletcher and 1 other

Use a given factor of a polynomial to find the full factorisation of the polynomial through long division.
Dividing a polynomial with remainders, using algebraic division
Ready to use
Question in Transition to university by Elliott Fletcher and 1 other

Find the remainder when dividing two polynomials, by algebraic long division.

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