PLIEGO PARTICULAR DE ESPECIFICACIONES
COMPUTO Y CERTIFICACION :
Learning hours: 60
NQF level 4: BTEC Higher National – H1
Description of unit
This unit provides the learner with the fundamental mathematical knowledge and analytical techniques needed to successfully complete the core and specialist optional units in this qualification. This unit has been designed to enable learners to use fundamental mathematical processes in the solution of Construction, Civil Engineering or Building Services Engineering problems.
It is also intended as a base for further study of analytical methods and engineering mathematics needed for those engaged in the Civil Engineering and Building Services Engineering disciplines.
Summary of learning outcomes
To achieve this unit a learner must:
1 Apply analytical methods to the management and production of construction, civil engineering or building services installation processes and operations
2 Apply analytical methods to surveying, testing and control problems in the construction, civil engineering or building services engineering process 3 Analyse and solve problems using statistics and probability
4 Apply analytical methods to analyse structural, building or building services engineering systems and provide appropriate solutions.
Content
The content comprises all the mathematics needed to achieve the outcomes. The various topic areas should be addressed as and when they are needed to analyse problems in the discipline the learner is following. There is therefore no requirement for the content to be covered in its entirety and the content can be taken as a guide. For example, it is not necessary for
construction learners to use calculus to satisfy assessment requirements but those studying civil engineering and building services engineering units should do so to ensure they meet the wider needs of their programme.
1 Analytical methods to the management and production
Algebra: linear, simultaneous and quadratic equations, laws of indices and logarithms, common and Naperian logarithms, indicial equations, direct and inverse proportion, inequalities, functional notation and manipulation of algebraic problems
Graphical representation: functions, points of intersection between two graphs, graph sketching (straight line, polynomial, exponential and logarithmic), fit lines to experimental data using least squares method
Space, time and motion: plot space/time and velocity/time diagrams, determine displacement, velocity and acceleration. Laws of motion, momentum, impulse and projectiles
Matrices: multiplication, transposition and inversion, applications
2 Analytical methods to surveying, testing and control problems
Trigonometry: basic trigonometric ratios and their inverses, trigonometric ratios for the four quadrants, solution of triangles, calculation of areas and volumes of solids
Determine co-ordinates: in 2-D and 3-D geometry Other functions: trapezoidal and Simpson’s rule
3 Statistics and probability
Tabular and graphical form: data collection methods, histograms, bar charts, line diagrams, cumulative frequency diagrams, scatter plots
Central tendency and dispersion: introduction to the concept of central tendency and variance measurement, mean, median, mode, standard deviation, variance and interquartile range, application to construction, civil engineering, and building services engineering
4 Analytical methods to analyse structural, building, or building services engineering systems
Trigonometric methods: to solve problems such as static forces, relative motion, frameworks, metrology, friction torque, electrical and mechanical energy problems Calculus: to differentiate and integrate simple equations and demonstrate applications of calculus (refer to Delivery guidance on delivering calculus to construction disciplines)
Outcomes and assessment criteria
Outcomes Assessment criteria for pass
To achieve each outcome a learner must demonstrate the ability to:
1 Apply analytical methods to the management and production of construction, civil engineering or building services installation processes and operations
· determine manpower, materials and equipment requirements on a day to day basis, and/or
· produce appropriate long term plans and cost analyses to meet particular situations, and/or
· compare and contrast the effectiveness and
efficiency of solutions to construction situations in terms of use of manpower, equipment, and materials 2 Apply analytical methods to
surveying, testing and control problems in the construction, civil engineering or building services engineering process
· apply mathematical and trigonometrical functions to surveying problems and evaluate results, and/or
· represent construction/engineering data in tabular and graphical form and analyse the results, and/or
· use sinusoidal functions and radian measures to solve construction/engineering problems, and/or
· use trigonometric and hyperbolic identities to solve trigonometric equations and to simplify complex trigonometric expressions
3 Analyse and model
construction situations using statistics and probability
· apply statistical techniques to issues of quality and safety, and/or
· apply probability techniques to issues of reliability and quality in the construction/engineering process 4 Apply analytical methods to
analyse structural, building, or building services
engineering systems and supply appropriate design solutions
· use trigonometric functions to solve problems such as static forces, relative motion, frameworks,
metrology, friction torque, electrical and mechanical energy problems, and/or
· use the principals of calculus to solve problems appropriate to construction, civil engineering and building services engineering
Guidance
Delivery
This unit may be delivered as a stand-alone unit, or partially integrated into other appropriate units. Centres should contextualise the analytical methods in the content and design a teaching process applicable to their programme. For those parts that are to be delivered in a completely integrated way, care must be taken to provide tracking of evidence of outcomes.
The aim of this unit is to provide the minimum mathematical knowledge, skills and
understanding to successfully complete a BTEC Higher National programme of study. Some disciplines require further study of mathematics to underpin particular areas of civil
engineering and building services engineering and this unit provides the learning that supports this progression.
Assessment
It is recommended that evidence for learning outcomes is achieved through well-planned course work and/or assignments designed to apply the analytical methods to the modelling and
solution of realistic problems. Assessment may be either formative or summative and either may feature as part of the process. Although assessments must be focused on the individual achievement of each learner, group work activities may contribute to the assessment.
Integrative assignments and project work will help to link this unit with other related units.
Where available, evidence from the workplace may also be incorporated to enhance the learning outcomes, provided that this evidence is appropriate and can be authenticated as the learner’s own work. The volume of evidence required for each assessment should take into account the overall number of assessments being contemplated within this unit and the design of the overall teaching programme.
In designing the assessment instruments, opportunities may also be included to generate evidence to meet the CIC Common Learning Outcomes and higher level skills appropriate to the outcomes of this unit, see Annex D and Annex F.
Links
This unit is intended to underpin and link with those units, which are analytical in nature. Entry requirements are at the discretion of the centre. However, it is strongly advised that where learners cannot provide evidence of previous mathematical study sufficient to successfully follow this unit, additional balancing studies should be incorporated in the learner’s individual learning plan.
The content of this unit has been designed and mapped against the 1998 CISC Occupational Standards and current NVQs at level 4. The mapping links indicate that the achievement of the learning outcomes of this unit will contribute skills, knowledge and understanding towards the evidence requirements of the following NVQs:
· Architectural Technology
· Building Control
· Spatial Data Management.
See Annex D for summary of mapping information.
Resources
The use of mathematical software packages is strongly recommended, wherever appropriate, to help learners understand and model scientific and engineering problems.
Support materials Textbooks
· Greer, A and Taylor, — Mathematics for Technicians — (Stanley Thomas, 1994)
· Stroud, K — Engineering Mathematics 4th Edition — (Macmillan, 1995)