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Students seem to not realise that $\frac{a}{b}\times c=c\times\frac{a}{b}=\frac{a\times c}{b}=\frac{c\times a}{b}=a\times c \div b=a\div b\times c=c\div b \times a \ne c \div (b\times a)\ldots $ etc. This question is my attempt to help rectify this.

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Multiply two algebraic fractions (unfortunately their appearance doesn't really change) and cancel. 

Collecting like terms, expanding a bracket (distributive law), substitution of values, finding factors, simplifying algebraic fractions.

Solve a simple linear equation algebraically. The unknown appears on both sides of the equation.

Tags: algebra, equations (linear), equations (quadratic)

Last updated Sep 2019

A random selection of algebra questions without solutions.

In class test contributes about 30% of your assesment work. Make sure you write your REG number.

Topics:
Algebra, Calculus, Trigonometeric Equations, Complex numbers & Partial Derivatives

Students must complete the exam within 120 mins (standard time).

Questions have variables to produce randomised questions.

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Example of an explore mode question. Student is given a 3x3 matrix and is asked to find the characteristic polynomial and eigenvalues, and then eigenvectors for each eigenvalue. The part asking for eigenvectors can be repeated as often as the student wants, to be used for different eigenvalues.

Assessed: calculating characteristic polynomial and eigenvectors.

Feature: any correct eigenvalue will be recognised by the marking algorithm, even multiples of the obvious one(s) (which can be read off from the reduced row echelon form)

Randomisation: Not randomised, just using particular matrices. I am still working on how to randomise this for 3x3; a randomised 2x2 version exists. I have several different versions for 3x3 (not all published yet), so I could make a random choice between these in a test.

The implementation uses linear algebra functions such as "find reduced echelon form" or "find kernel of a reduced echelon form", from the extension "linalg2".

Extra practice on some basic algebra skills, including solving linear equations. You can try as many times as you like and also generate new versions of the questions for extra practice.

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Inputting ratios of algebraic expressions. (Translation to German)

Practice with adding, subtracting and dividing basic algebraic fractions

More work with dividing and multiplying algebraic fractions

Putting algebraic fractions into their simplest forms