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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

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

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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)

Putting algebraic fractions into their simplest forms

More work with dividing and multiplying algebraic fractions

Practice with adding, subtracting and dividing basic algebraic fractions

Straightforward solving linear equations question.

Adapted from 'Simultaneous equations by substitution 2 with parts' by Joshua Boddy.

Entering numbers and algebraic symbols  in Numbas. (German translation)

Inputting algebraic expressions into Numbas.

Evaluación de una expresión algebraica con dos variables

Express $\displaystyle \frac{a}{x + b} \pm  \frac{c}{x + d}$ as an algebraic single fraction over a common denominator. 

The relationship between the frequency of an allele A, $x$, at a genetic locus in a diploid population and the fitness of a population with this frequency of allele A, $w$, is described by the function $w=ax^2+x(b-x)+c(b-x)^2$ . The aims are (a) ti simplify the algebraic expression, (b) calculate the fitness of a population with a given allele A frequency, and (c) calculate the allele A frequency when the fitness of the population is given.

NC NA Non-calculator and Number and Algebra strand. This number assesses students' ability to add and subtract very simple fractions. Students need two add two fractions (possibly mixed numbers) involving quarters and/or halves, then subtract their answer from a whole number. The answer must be entered in simplest form and will always be less than one.

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.

Add two algebraic fractions with coprime denominators. Part of HELM Book 1.4.3.

HELM Book 1.4.3 Exercises: addition and subtraction of algebraic fractions

There are two parts: 

(3x)/4-x/5+x/3 and (3x/4)-(x/5+x/3).

The numbers are randomised to small, coprime, positive integers.

This is a fixed, unmarked, question:

Show that (x1)/((1/x3)-(1/x2))) = (x1x2x3)/(x2-x3)

Simplify (qx+a)/(rx+b) +/- (sx+c)/(rx+b)^2

x is a randomised variable. a,b,c,d,q,r are randomised integers.

Simplify (qx+a)/(rx+b) +/- (sx+c)/(tx+d)

x is a randomised variable. a,b,c,d,q,r,s,t are randomised integers. a,b,c,d run from -5 to 5, including 0. q,r,s,t run from -3 to 3, and can be 0 if the constant term is nonzero, but are mostly 1.

Simplify ax/b +/- cx/d, where x is a randomised variable, and a,b,c,d are randomised integers.

Add two algebraic fractions. Part of HELM Book 1.4.3.

6 Exercises from HELM Book 1.4 Part 2: Multiplication and Division of Algebraic Fractions.

Simplify an algebraic fraction where both numerator and denominator must first be factorised. Part of HELM Book 1.4