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# Unit 7 mathemetical calculations for science

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### Unit 7 mathemetical calculations for science

1. 1. Diploma in Applied Science(Forensic Science)UNIT 7 MATHEMATICAL CALCULATIONS FOR SCIENCE
2. 2. Diploma in Applied Science (Forensic Science)Unit 7 Mathematical calculations for scienceAims and purposeThis unit gives learners the skills to use mathematical tools essential for biology, chemistryand physics. The unit starts with algebraic techniques and moves on to the applications oftrigonometry and calculus.Unit introductionThis maths unit enables learners to build onknowledge gained from unit 6: UsingMathematical Tools for Science or GCSEmathematics to investigate furthermathematical tools used in all disciplines inscience. It is an essential unit for learnerswho wish to pursue science at BTEC HigherNational level, foundation degree or degreelevel. The unit is not to make mathematiciansbut to use maths for science. Learners willuse maths to solve a number of scientificproblems, including: • how simultaneous equations help solve problems in chemical bonding and in electricity • how trigonometry can be used in forensic science by using the technique of voice recognition • how the method of calculus enables scientists to learn about growth studies in microbiology.Learners will develop their knowledge and understanding of algebraic methods, includingindices, logarithmic and simultaneous linear equations and quadratics. These tools will enablelearners to solve many scientific problems, such as sound levels (decibels), light detection(lux levels), measurement of pH, bacterial growth and electrical power. Then learners will beintroduced to the radian, as another method of angle measurement, and graphicalrepresentation of trigonometric functions. These trigonometric functions allow ampleopportunity for learners to integrate computer simulations and practical activities. Practicalactivities could include pendulum motion, mechanics and circular motion, amongst manyothers. Finally, a brief introduction to the important tool of calculus. Learners will be exposedto both simple differentiation and integration and will end with using these concepts to solvereal scientific problems. Problems could include areas such as population growth, radioactivedecay, motion of a particle, energy stored in springs and enzyme activity. On completing thisunit, learners will have been exposed to essential mathematical concepts that will bridge thegap between Levels 3 and 4.
3. 3. Learning outcomesOn completion of this unit a learner should: 1. Be able to use algebraic manipulations to solve scientific problems 2. Be able to use trigonometric methods to solve scientific problems 3. Be able to use calculus to solve scientific problems.
4. 4. Diploma in Applied Science (Forensic Science)Task 1: Logarithms and algebraA trainee scientist on a trial period with a multinational companyP1 Carry out calculations involving logarithms and indicesP2 Carry out calculations using algebraic equationsM1 Solve science problems involving indicesM2 Solve science problems using quadratic equationsD1 Solve science problems involving logarithmsD2 Solve science problems using simultaneous equationsYou need to complete the following taskFor P1, learners need to show that they cansolve problems using all the laws oflogarithms and indices, as indicated in the Unitcontent section. For M1, learners need to solvea chemistry and a physics problem using indices.For D1, learners need to successfully solveone problem from biology, one from chemistryand one from physics using logarithms.For P2, learners need to solve correctly,factorise, use simultaneous and quadraticequations, as detailed in the Unit contentsection. For M2, learners must solve,correctly, a scientific problem using quadraticequations. To achieve D2 learners need tosuccessfully solve a chemistry and physicsproblem using simultaneous equations.Grading tipsDeadline:________________
5. 5. Task 2: Circular measure and trigonometryA trainee scientists on a trial period with the London Olympic CommitteeP3 Carry out calculations involving circular measureP4 Carry our calculations involving trigonometric methodsM3 Solve science problems using circular measureM4 Solve science problems using trigonometric methodsD3 Explain, using circular measure, a real-life application of mathematicsD4 Explain, using trigonometric methods, a real-life application of mathematicsYou need to complete the following task:For P3, learners are required to convertradians to degrees and vice versa and solvesimple circular problems. For M3, learnersmust solve a scientific problem using circularmeasure. The D3 criterion requires learners toexplain the working of a real life applicationusing circular measure. The explanation shouldbe rigorous with use of equations clearlyindicated.For P4, learners must solve trigonometricproblems and cover all aspects of the Unitcontent section. The M4 criterion can beachieved by the learner solving a scienceproblem using trigonometry. For D4, learnersneed to explain the working of a real lifeapplication using trigonometry. As in D3 thismust be rigorous and the trigonometricequations used should be relevant to theapplication and clearly explained.Grading tipsDeadline _________________
6. 6. Task 3: CalculusA trainee scientist is employed to monitor the motion of a fuel efficient aeroplane. Will look atrate of change of distance and velocity in order to evaluate suitability.P5 Carry out calculations using calculusM5 Solve science problems using differentiationD5 Solve science problems using integrationYou need to complete the following taskFor P5, learners must cover all aspects of theUnit content section and successfully performcalculations using calculus. To achieve M5,learners must, correctly, solve a scientificproblem using differentiation. For D5, thelearner must use integration to solve ascientific problem, which can be in any scientificdisciple set by the learner or teacher.Grading tipsDeadline _________________
7. 7. Outline of evidence requirementsAssessment Assessment Description Complete Assignment criteria Carry out calculations involving P1 7.1 logarithms and indices Carry out calculations using P2 7.1 algebraic equations Solve science problems involving M1 7.1 indices Solve science problems using M2 7.1 quadratic equations Solve science problems involving D1 7.1 logarithms Solve science problems using D2 7.1 simultaneous equations Carry out calculations involving P3 7.2 circular measure Carry our calculations involving P4 7.2 trigonometric methods Solve science problems using M3 7.2 circular measure Solve science problems using M4 7.2 trigonometric methods Explain, using circular measure, a D3 7.2 real-life application of mathematics Explain, using trigonometric D4 methods, a real-life application of 7.2 mathematics Carry out calculations using P5 7.3 calculus Solve science problems using M5 7.3 differentiation Solve science problems using D5 7.3 integration