UNIT 4 MATHEMATICS FOR TECHNICIANS



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|LEARNER NAME |ASSESSOR NAME |

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| |F. NDORO |

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|DATE ISSUED |HAND IN DATE |SUBMITTED ON |

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|Criteria |Task |Achieved |Feedback |

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|P10 apply the basic rules of calculus arithmetic to solve three |Task 1 | | |

|different types of function by differentiation and two different types| | | |

|of function by integration. | | | |

|D1 apply graphical methods to the solution of two engineering problems| | | |

|involving exponential growth and decay, analysing the solutions using |Task 2 | | |

|calculus | | | |

|D2 apply the rules for definite integration to two engineering | | | |

|problems that involve summation. |Task 3 | | |

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|This brief has been verified as fit for purpose |

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|Internal Verifier |ANTHONY SPICER |

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|Signature |A J Spicer |Date |27/07/2012 |

|Assessor's comments |

|Qualification |Edexcel Lev 3 National Diploma in Engineering |Assessor name |F. NDORO |

|Unit number and title |Unit 4 – Mathematics for Engineering Technicians|Learner name | |

| |(A/600/0253) | | |

|Assignment title | |

| |ASSIGNMENT FOUR – CALCULUS TECHNIQUES |

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|Grading criteria |Achieved? |

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|P10 apply the basic rules of calculus arithmetic to solve three different types of function by differentiation and two different types of | |

|function by integration. | |

| | |

|D1 apply graphical methods to the solution of two engineering problems involving exponential growth and decay, analysing the solutions using | |

|calculus | |

|D2 apply the rules for definite integration to two engineering problems that involve summation. | |

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|Learner feedback |

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|Assessor feedback |

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|Action plan |

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|Assessor signature | |Date | |

|Learner signature | |Date | |

TASK 1 – Basic rules of integration and differentiation

P10 apply the basic rules of calculus arithmetic to solve three different types of function by differentiation and two different types of function by integration.

1. Find the derived function of the following functions:

(a) y = 8[pic] (b) y = [pic]

(c) y = 6[pic] -20[pic] + 5 (d) [pic]

(e) [pic]

: [P10 PART]

2. Express [pic]as a function of[pic], if:

(a) [pic] = 3[pic] + 4[pic] (b) [pic] = 4[pic] - 3[pic] + 6

(c) [pic] (d) [pic]

(e) [pic]

: [P10 PART]

TASK 2 – APPLICATIONS OF CALCULUS IN ENGINEERING SOLUTIONS

(DIFFERENTIATION)

D1 apply graphical methods to the solution of two engineering problems involving exponential growth and decay, analysing the solutions using calculus

1. For a certain material, Newton’s law of cooling can be represented by the decay equation [pic] where t is the time in seconds. And [pic] is the temperature at any given instant in time.

(a) Plot [pic] against t at 0.5sec intervals for [pic]

(b) From your graph, find the initial temperature and the temperature that the body approaches as time increases to infinity.

(c) Determine the slope at t = 3 seconds both from the graph and by differentiation and give your comment as you compare the results.

: [D1 part]

2. The voltage across a capacitor C when it is being discharged through a resistor R is related to time t by the equation [pic]where T is the time constant and T = CR.

(a) Plot a graph of voltage [pic] against time [pic]

(b) From your graph, find the voltage and rate of change of voltage after 0.2 seconds given that R= 12k[pic]and C = 22[pic]

(c) Check that your answers in (b) are correct by differentiation

: [D1 part]

TASK 3 – APPLICATIONS OF CALCULUS IN ENGINEERING SOLUTIONS

(INTEGRATION)

D2 apply the rules for definite integration to two engineering problems that involve summation.

1. The total charge passed on to a battery is represented by the area under a graph of current against time. The law of the graph is [pic].

Determine the charge after 7 seconds.

: [D2 part]

2. The velocity of a falling object is related to time by the law [pic]. The distance fallen is the area under the velocity – time graph.

Calculate the distance fallen 10 seconds after release.

: [D2 part]

Student declaration

I declare that all the work submitted for this assignment is my own work or, in the case of group work, the work of myself and the other members of the group in which I worked, and that no part of it has been copied from any source.

I understand that if any part of the work submitted for this assignment is found to be plagiarised, none of the work submitted will be allowed to count towards the assessment of the assignment

Signed …………………………………… Date ………………………………

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UNIT 4 – MATHEMATICS FOR ENGINEERING TECHNICIANS (A/600/0253)

ASSIGNMENT FOUR – CALCULUS TECHNIQUES

Health and safety legislation, regulations and safe working practices in fabrication

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