UNIT 4



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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 |

|P1 Manipulate and simplify three algebraic expressions using the laws |Task 1 | | |

|of indices and two using the laws of logarithms | | | |

|P2 solve a linear equation by plotting a straight-line graph using |Task 2 | | |

|experimental data and use it to deduce the gradient, intercept and | | | |

|equation of the line | | | |

|P3 - Factorise by extraction and grouping of a common factor from |Task 3 | | |

|expressions with two, three and four terms respectively | | | |

|M1 -Solve a pair of simultaneous linear equations in two unknowns |Task 4 | | |

|M2 Solve one quadratic equation by factorisation and one by the |Task 5 | | |

|formula method. | | | |

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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 ONE – ALGEBRAIC METHODS |

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|Grading criteria |Achieved? |

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|P1 - Manipulate and simplify three algebraic expressions using the laws of indices and two using the laws of logarithms | |

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|P2 - Solve a linear equation by plotting a straight-line graph using experimental data and use it to deduce the gradient, | |

|intercept and equation of the line | |

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|P3 - Factorise by extraction and grouping of a common factor from expressions with two, three and four terms respectively | |

|M1 - Solve a pair of simultaneous linear equations in two unknowns | |

|M2 - Solve one quadratic equation by factorisation and one by the formula method. | |

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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 - LAWS OF INDICES AND LOGARITHMS

P1 - Manipulate and simplify three algebraic expressions using the laws of indices and two using the laws of logarithms

1. Simplify the following using the 3 rules of indices

(a) [pic][pic] (b) [pic]

(c) [pic] (d) [pic] x 5[pic]

[P1 PART]

2. Simplify the following using all 3 rules of logarithms:

(a) log81 + log3 – log27 (b) log252 -5log5 + log25

[P1 PART]

TASK 2 - LINEAR EQUATIONS AND STRAIGHT LINE GRAPHS

P2 - Solve a linear equation by plotting a straight-line graph using experimental data and use it to deduce the gradient, intercept and equation of the line

1. The readings of an ammeter were taken in an electrical circuit as the resistance changed and the table below was generated.

|Resistance R (Ω) |51.4 |53.8 |56.0 |58.0 |61.0 |64.0 |

|Current C (Amps) |7.0 |4.99 |3.96 |3.31 |2.70 |2.26 |

It is thought that R and I are related approximately by the law R =[pic] + b

a. Plot a straight line graph to verify that this is so and find the constants a and b.

b. Write down the equation of the line hence the law which relates R and I.

[P2]

TASK 3 - FACTORISATION AND QUADRATICS

P3 - Factorise by extraction and grouping of a common factor from expressions with two, three and four terms respectively

1. Factorise the following

12a2b + 4ab3 (b) –b2a –a2b – 24

(c) (2 + a)2 -2 – a (d) 15a2(a-b)2 – 25a(a – b)

[P3 part]

2. Factorise the following using ‘difference of two squares’ method:

64 –a2 (b) a2 – 4 b2

(c) (a - 3)2 – 49 (d) 5a2 – 20

[P3 part]

3. Factorise the following expressions

i) x2 + 8x + 7 (ii) y2 + 2y -15

(iii) ab2c – a2bc2 + 2abc2

[P3 part]

TASK 4 - SIMULTANOUS EQUATIONS

M1 - Solve a pair of simultaneous linear equations in two unknowns

1. Find the values of [pic]and [pic]in the following equations:

(a) 2[pic] + 3[pic] = 5

3[pic] - 4[pic] = 7

(b) 5[pic] + 2[pic]= 12

4[pic]- 3[pic] = 9

[M1]

TASK 5 QUADRATIC EQUATIONS USING FACTORISATION & FORMULA

M2 - Solve one quadratic equation by factorisation and one by the formula method.

2. Solve the following equations by factorisation

(a)[pic] + 2[pic] - 8 = 0 (b) [pic] - 4[pic] + 4 = 0

[M2 part]

3. Solve the following equations by using the quadratic formula

(a) 3[pic]-10[pic] + 5 = 0 (b) [pic] -8[pic] + 15 = 0

[M2 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 ONE - ALGEBRAIC METHODS

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

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