Unit 8 Mathematics for Construction Assignment Brief
| Qualification | Pearson BTEC Higher Nationals Construction |
| Unit Number | 8 |
| Unit Title | Mathematics for Construction |
| Unit code | K/618/8087 |
| Unit level | 4 |
| Credit value | 15 |
Introduction
The aim of this unit is to develop students’ knowledge and understanding of the mathematical principles and theories that underpin many aspects of construction technology, structures and materials. Students will be introduced to mathematical methods and statistical techniques so that they can analyse and solve problems in a construction engineering context.
Topics included in this unit are: trigonometry and algebraic mathematical techniques; matrices; statistical techniques; differential and integral calculus; binomial and normal distribution; dimensional analysis; arithmetic progressions; vector analysis.
On successful completion of this unit, students will be able to employ mathematical methods in a variety of contextualised examples; use analytical and computational methods to evaluate and solve engineering construction problems; interpret data using statistical techniques and apply calculus techniques. Students will gain crucial employability skills such as critical thinking, problem solving, analysis, reasoning and data interpretation.
Learning Outcomes
By the end of this unit, students will be able to:
LO1 Use analytical and computational methods to solve construction-related problems
LO2 Investigate applications of statistical techniques to interpret, organise and present data by using appropriate computer software packages
LO3 Illustrate the wide-ranging uses of calculus within different construction disciplines by solving problems of differential and integral calculus
LO4 Use mathematical methods to solve vector analysis, arithmetic progression and dimensional analysis problems.
Essential Content
LO1 Use analytical and computational methods to solve construction-related problems
Analytical methods
Trigonometry
Irregular areas and volumes
Sine rule
Cosine rule
Area of triangles applications
Trigonometry
Coordinate systems
Basic trigonometric ratios and their inverses
Trigonometric ratios for the four quadrants
Solution of triangles
Areas and volumes of regular solids
Algebra
Linear
Simultaneous and quadratic equations (graphical or algebraic solving)
Matrices
Multiplication
Transposition
Inversion (up to 2 × 2)
Application to construction problems
Analysis and design issues
Processes and operations
Resource issues e.g., labour, finance
Project planning
Levelling, contouring
Triangulation, traversing, cut and fill, setting out
LO2 Investigate applications of statistical techniques to interpret, organise and present data by using appropriate computer software packages
Statistical methods
Presentation of data (histograms, frequency graphs, cumulative frequency graphs)
Central tendency and dispersion
Dispersion (standard deviation, variance, interquartile range)
Distribution theory: normal distribution
Measures of dispersion (range, variance, standard deviation, quartiles, deciles and percentiles)
Grouped and ungrouped data
Probability theory, binomial and normal distribution
Applications
Presentation of data
Estimation
Prediction
Quality control
LO3 Illustrate the wide-ranging uses of calculus within different construction disciplines by solving problems of differential and integral calculus
Differential calculus
Basic differentiation techniques applied to algebraic, trigonometric and logarithmic functions
Products and quotients
Function of a function
Second order derivatives
The location of stationary values
Integral calculus
Indefinite and definite integration techniques applied to algebraic, trigonometric and exponential functions
Practical construction problems
Solution of problems involving maxima and minima
Growth and decay
Centroids
Moments of inertia
Areas under curves and volumes of revolution
Use in electrical theory, structural mechanics, fluid mechanics as appropriate
LO4 Use mathematical methods to solve vector analysis, arithmetic progression and dimensional analysis problems
Trigonometrical techniques
Vector analysis (e.g., static forces, relative motion, frameworks)
Arithmetic progressions
Dimensional analysis
Learning Outcomes and Assessment Criteria
| Pass | Merit | Distinction |
| LO1 Use analytical and computational methods to solve construction-related problems |
D1 Evaluate analytical and statistical findings from construction problems completed and justify the techniques adopted to solve such problems. |
|
| P1 Solve construction problems using trigonometry techniques.
P2 Solve construction problems using algebraic techniques. |
M1 Apply the use of matrices to solve problems. | |
| LO2 Investigate applications of statistical techniques to interpret, organise and present data by using appropriate computer software packages | ||
| P3 Apply statistical methods, including the calculation of the mean and standard deviation, to produce accurate and appropriate solutions to construction engineering problems.
P4 Calculate probabilities within both binomially distributed and normally distributed random variables. |
M2 Interpret the results of a statistical hypothesis test conducted from a given scenario. | |
| LO3 Illustrate the wide-ranging uses of calculus within different construction disciplines by solving problems of differential and integral calculus |
D2 Analyse differential calculus techniques in the determination of maxima and minima in constructionrelated problems. |
|
| P5 Use differential calculus techniques to solve functions which incorporate: axn, sine ax, cosine ax, loge x, eax and methods including function of a function.
P6 Use integral calculus techniques to determine indefinite and definite integrals of functions involving axn, sine ax, cosine ax, 1/x and eax. |
M3 Apply the rules of integral calculus to determine solutions for complex constructionrelated problems. | |
| LO4 Use mathematical methods to solve vector analysis, arithmetic progression and dimensional analysis problems |
D3 Evaluate the effectiveness and relevance, to the solving of complex construction problems, of the mathematical technique of vector analysis. |
|
| P7 Apply dimensional analysis to solve problems.
P8 Generalise answers from a contextualised arithmetic progression problems. |
M4 Solve construction problems using vector analysis. | |
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