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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 - 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.
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.
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 Bill Foster and Christian Perfect, School of Mathematics & Statistics at Newcastle University.
Complex arithmeticThis leaflet explains how complex numbers can added, subtracted, multiplied and divided. (Engineering Maths First Aid Kit 7.2)
Complex Numbers Arithmetic - Numbas6 questions on complex numbers, multiplication, inverse, division and modulus and finding the distance between complex numbers.
Numbas resources have been made available under a Creative Commons licence by the School of Mathematics & Statistics at Newcastle University.
Complex Roots of Polynomials - Numbas2 questions finding roots of real polynomials.
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.
Composition of functionsWe can build up complicated functions from simple functions by using the
process of composition, where the output of one function becomes the input of another. It is also sometimes necessary to carry out the reverse process, decomposing a complicated function into two or more simple functions. This unit explains how. (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.
Composition of functionsWe can build up complicated functions from simple functions by using the
process of composition, where the output of one function becomes the input of another. It is also sometimes necessary to carry out the reverse process, decomposing a complicated function into two or more simple functions. This unit explains how. (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.
Conic sectionsIn this unit we study the conic sections. These are the curves obtained when a
cone is cut by a plane. We find the equations of one of these curves, the
parabola, by using an alternative description in terms of points whose
distances from a fixed point and a fixed line are equal. We also find the
equation of a tangent to a parabola using techniques from calculus, and we use this to prove the reflective property of the parabola. (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.
Conic sectionsIn this unit we study the conic sections. These are the curves obtained when a
cone is cut by a plane. We find the equations of one of these curves, the
parabola, by using an alternative description in terms of points whose
distances from a fixed point and a fixed line are equal. We also find the
equation of a tangent to a parabola using techniques from calculus, and we use this to prove the reflective property of the parabola. (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.
Coventry University's Mathematics Support Centre's WebsiteThe Mathematics Support Centre at Coventry University (originally known as the BP Maths Centre) was established in 1991. The Centre aims to provide early identification of problems and on-going support for individual students. This is achieved through use of diagnostic testing, the provision of a wide range of resources and the availability of one-to-one assistance on drop-in basis. The Centre�?�¢??s website was launched in September 2000 to:
- extend the support provision to students who did not find it easy to visit the Centre (e.g. part-time students).
- provide access to a range of resources at times when the Centre is closed.
- deliver new support activities such as online practice tests and email questions.
Cramer's ruleCramer's rule can be used to solve simultaneous equations using determinants.
This leaflet states and illustrates the rule. (Engineering Maths First Aid Kit 5.2)
DecimalsIn this unit we shall look at the meaning of decimals, and how they are related
to fractions. We shall then look at rounding to given numbers of decimal places or significant figures. Finally we shall take a brief look at irrational numbers. (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.
DecimalsIn this unit we shall look at the meaning of decimals, and how they are related
to fractions. We shall then look at rounding to given numbers of decimal places or significant figures. Finally we shall take a brief look at irrational numbers. (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.
Degrees and radiansThis leaflet explains how angles can be measured both in degrees and in radians.
It explains how to convert from degrees to radians and vice-versa. (Engineering Maths First Aid Kit 4.1)
DeterminantsThis leaflet explains what is meant by a determinant and shows how it can be
evaluated. (Engineering Maths First Aid Kit 5.1)
Developing a statistical advisory service through effective partnershipsStatistical Advisory Services are an innovative and valued approach to providing statistical advice centrally to final year undergraduate and postgraduate students. This paper reflects on the experiences of a new UK university in developing such a service through a HE STEM Practice Transfer Adopters partnership project. The Projectâ??s adopted strategies to partner with other university stakeholders are evaluated. In particular, partnerships with faculty- based staff and running staff development training courses are identified as effective development strategies.
Peter Samuels and Maggie Gibson (2013) Developing a statistical advisory service through effective
partnerships, HEA STEM, http://wwwnew1.
heacademy.ac.uk/assets/Documents/disciplines/stem/conf-proceedings-
2013/MSOR/full%20papers/msor_062.pdf
Developing the Interface between Engineering and Mathematics at Edinburgh UniversityA few years ago the department of mathematics at Edinburgh looked at the problem of interfacing between mathematics and engineering courses and came up with a system to enable greater student understanding. The implementation of this system and how it is helping students is reviewed in this case study.
Diagnostic Testing within Institutions - Manchester Metropolitan UniversityTwo weeks are spent doing revision prior to three diagnostic tests. These are designed to assess studentsâ?? strengths and weaknesses after they have spent some time working in a mathematical context. The tests are all paper-based multi-choice questions (MCQs). They are hand-marked, but owing to the small number of students there is little time delay between assessment and distribution of the results.
Diagnostic Testing within Institutions - University of BristolAll students are tested via two computer-based tests each consisting of 10 multi-choice questions (MCQs). These tests are set from a large bank of questions using the â??TALâ?? (Teach And Learn) computer system developed at the University of Bristol. The topics covered include arithmetic, algebra, geometry, functions, calculus, and probability. A â??leave unansweredâ?? option is provided and negative marking used to discourage guessing. The tests are accessed through a Web interface, so in principle could be accessed from anywhere. It has been run with large-scale simultaneous access and, although a little slow, is relatively robust.
Differentiating sin(x) and cos(x) from first principlesIn this unit we show how to differentiate the sine and cosine functions
from first principles. (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.
Differentiating sin(x) and cos(x) from first principlesIn this unit we show how to differentiate the sine and cosine functions
from first principles. (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.
Differentiation by taking logsIn this unit we look at how we can use logarithms to simplify certain functions before we differentiate them. (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.
Differentiation by taking logsIn this unit we look at how we can use logarithms to simplify certain functions before we differentiate them. (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.
