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Expanding & Removing BracketsIn this unit we see how to expand an expression containing brackets. By this we mean to rewrite the expression in an equivalent form without any brackets in. Fluency with this sort of algebraic manipulation is an essential skill which is vital for further study.
(Mathtutor Video Tutorial)
The video is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Combining algebraic fractions - Numbas13 questions on combining algebraic fractions. An area in which students often need practice.
Numbas resources have been made available under a Creative Commons licence by the School of Mathematics & Statistics at Newcastle University.
Polynomial division - Numbas2 questions. First question divides a cubic by a linear polynomial. The second divides a degree 4 polynomial by a degree 2 polynomial. Numbas resources have been made available under a Creative Commons licence by Bill Foster and Christian Perfect, School of Mathematics & Statistics at Newcastle University.
Economics Fact & Formulae - Large Print versionA large print version of the Economics Facts & Formulae Leaflet. This zip file contains separate pdf files for each of the 5 sides of the leaflet reformated to A4 so that they are more accessible for students with visual impairments.
Completing the square - maxima and minimaThis is a workbook which describes how to complete the square for a quadratic expression. It goes on to show how the technique can be used
to find maximum or minimum values of a quadratic expression.
Completing the Square - by InspectionIn this unit we consider how quadratic expressions can be written in an equivalent form using the technique known as completing the square. This technique has applications in a number of areas, but we will see an example of its use in solving a quadratic equation.
(Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Matrices Test 01 (DEWIS)Five questions on matrix arithmetic testing matrix addition, scalar multiplication, transpose of a matrix and matrix multiplication. DEWIS resources have been made available under a Creative Commons licence by Rhys Gwynllyw & Karen Henderson, University of the West of England, Bristol.
Economics Facts & Formulae - Print versionThis is a high resolution electronic copy of the Economics Facts & Formulae Leaflet. It is designed to be printed on A4 as a double-sided folded leaflet. Print quality is printer dependant. An onscreen version is available in mathcentre.
Completing the Square - by InspectionIn this unit we consider how quadratic expressions can be written in an equivalent form using the technique known as completing the square. This technique has applications in a number of areas, but we will see an example of its use in solving a quadratic equation.
(Mathtutor Video Tutorial)
The video is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Completing the square - NumbasTwo questions on completing the square. The first asks you to express $x^2+ax+b$ in the form $(x+c)^2+d$ for suitable numbers $c$ and $d$. The second asks you to complete the square on the quadratic of the form $ax^2+bx+c$ and then find its roots.
Numbas resources have been made available under a Creative Commons licence by the School of Mathematics & Statistics at Newcastle University.
Solving simple linear equations - Numbas2 equations, both linear (the second needs a small amount of algebra to reduce to a linear equation).
Numbas resources have been made available under a Creative Commons licence by the School of Mathematics & Statistics at Newcastle University.
Polynomial division - Numbas2 questions. First question divides a cubic by a linear polynomial. The second divides a degree 4 polynomial by a degree 2 polynomial.
Numbas resources have been made available under a Creative Commons licence by the School of Mathematics & Statistics at Newcastle University.
Complex roots of real polynomials - NumbasFinding roots of a cubic and the roots of a quartic by inspection. Numbas resources have been made available under a Creative Commons licence by Bill Foster and Christian Perfect, School of Mathematics & Statistics at Newcastle University.
Solving equations involving logarithms and exponentialsThis leaflet shows how simple equations involving logarithms or exponentials can be solved. (Engineering Maths First Aid Kit 3.8)
Factorising simple expressionsThis leaflet explains how to factorise simple expressions by looking for common factors. (Engineering Maths First Aid Kit 2.5)
Completing the Square - maxima & maximaCompleting the square is an algebraic technique which has several applications. These include the solution of quadratic equations. In this unit we use it to find the maximum or minimum values of quadratic functions.
(Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Completing the Square (to find MAX and MIN values) Part 1Completing the square is an algebraic technique which has several applications. These include the solution of quadratic equations. In this unit we use it to find the maximum or minimum values of quadratic functions.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Completing the Square (to find MAX and MIN values) Part 2Completing the square is an algebraic technique which has several applications. These include the solution of quadratic equations. In this unit we use it to find the maximum or minimum values of quadratic functions.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Completing the Square (to find MAX and MIN values) Part 3Completing the square is an algebraic technique which has several applications. These include the solution of quadratic equations. In this unit we use it to find the maximum or minimum values of quadratic functions.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Completing the Square (to find MAX and MIN values) Part 4Completing the square is an algebraic technique which has several applications. These include the solution of quadratic equations. In this unit we use it to find the maximum or minimum values of quadratic functions.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Completing the Square (to find MAX and MIN values) Part 5Completing the square is an algebraic technique which has several applications. These include the solution of quadratic equations. In this unit we use it to find the maximum or minimum values of quadratic functions.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Completing the Square (to find MAX and MIN values) Part 6Completing the square is an algebraic technique which has several applications. These include the solution of quadratic equations. In this unit we use it to find the maximum or minimum values of quadratic functions.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Mathematics for Computer Science Facts & Formulae - Onscreen versionAn electronic version of the Facts & Formulae leaflet for computer science designed to be viewed onscreen. A higher resolution print version is available in mathcentre.
Completing the Square - maxima & maximaCompleting the square is an algebraic technique which has several applications. These include the solution of quadratic equations. In this unit we use it to find the maximum or minimum values of quadratic functions.
(Mathtutor Video Tutorial)
The video is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Logarithms 1Logarithms appear in all sorts of calculations in engineering and science, business and economics. Before the days of calculators they were used to assist in the process of multiplication by replacing the operation of multiplication by addition. Similarly, they enabled the operation of division to be replaced by subtraction. They remain important in other ways, one of which is that they provide the underlying theory of the logarithm function. This has applications in many fields, for example, the decibel scale in acoustics.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Logarithms 10Logarithms appear in all sorts of calculations in engineering and science, business and economics. Before the days of calculators they were used to assist in the process of multiplication by replacing the operation of multiplication by addition. Similarly, they enabled the operation of division to be replaced by subtraction. They remain important in other ways, one of which is that they provide the underlying theory of the logarithm function. This has applications in many fields, for example, the decibel scale in acoustics.
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
