Inverse and division of complex numbers.  Four parts.

Solving a system of three linear equations in 3 unknowns using Gaussian Elimination (or Gauss-Jordan algorithm) in 5 stages. Solutions are all integers. Introductory question where the numbers come out quite nice with not much dividing. Set-up is meant for formative assessment. Adapated from a question copied from Newcastle.

Solving a system of three linear equations in 3 unknowns using Gaussian Elimination (or Gauss-Jordan algorithm) in 5 stages. Solutions are all integers. Introductory question where the numbers come out quite nice with not much dividing. Set-up is meant for formative assessment. Adapated from a question copied from Newcastle.

This is a set of questions designed to help you practice adding, subtracting, multiplying and dividing fractions.

All of these can be done without a calculator.

Dividing Cubic expressions to find the quotient

Dividing Cubic expressions to find the quotient

Face, Place and actual value, adding, subtracting, multiplying, dividing and rounding decimals.

Given potential audience, the percentage that view, and the percentage of these that click, calculate the CPA by dividing potential audience by clickers. 

All numbers randomised.

Dividing powers of x - set out as a fraction

Exam Question

This question provides practice at adding, subtracting, dividing and multiplying complex numbers in rectangular form.

Practice with adding, subtracting and dividing basic algebraic fractions

Practice with adding, subtracting and dividing basic algebraic fractions

Solving a system of three linear equations in 3 unknowns using Gaussian Elimination (or Gauss-Jordan algorithm) in 5 stages. Solutions are all integers. Introductory question where the numbers come out quite nice with not much dividing. Set-up is meant for formative assessment. Adapated from a question copied from Newcastle.

Practice dividing polynomials using the long division method.

Dividing a cubic polynomial by a linear polynomial. Find quotient and remainder.

Divide $ f(x)=x ^ 4 + ax ^ 3 + bx^2 + cx+d$ by $g(x)=x^2+p $ so that:
$\displaystyle \frac{f(x)}{g(x)}=q(x)+\frac{r(x)}{g(x)}$

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.

Three equilateral triangles are divided equally into 3, 4 and 5 parts respectively. Calculate the distance between two marked points.

Based on a puzzle by Catriona Shearer, shared on Twitter.

Practice with adding, subtracting and dividing basic algebraic fractions

Practice with adding, subtracting and dividing basic algebraic fractions

Dividing a cubic polynomial by a linear polynomial. Find quotient and remainder.

In the Gaussian integer ring $\mathbb{Z}[i]$ , find the remainder $r=r_1+r_2i$, where $a \gt 0,\;b \gt 0$ , on dividing $a+bi$ by $c+di$ .

In the ring $\mathbb{Z}[\sqrt{2}]$ , find the remainder $r=r_1+r_2\sqrt{2}$, where $a \gt 0,\;b \gt 0$ , on dividing $a+b\sqrt{2}$ by $c+d\sqrt{2}$ .

In the  ring $\mathbb{Z}[\sqrt{-2}]$ , find the remainder $r=r_1+r_2\sqrt{-2}$, where $a \gt 0,\;b \gt 0$ , on dividing $a+b\sqrt{-2}$ by $c+d\sqrt{-2}$ .

Questions on adding, subtracting, multiplying and dividing numbers in standard form.

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

Several problems involving dividing fractions, with increasingly difficult examples, including mixed numbers and complex fractions. 

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