Unit 4: Mathematics for Engineering
Technicians
Unit code: A/600/0253
QCF Level 3: BTEC National
Credit value: 10
Guided learning hours: 60
Aim and purpose
This unit aims to give learners a strong foundation in mathematical skills. These skills will help them to
successfully complete many of the other units within the qualification.
Unit introduction
One of the main responsibilities of engineers is to solve problems quickly and effectively. This unit will enable
learners to solve mathematical, scientific and associated engineering problems at technician level. It will
also act as a basis for progression to study other units both within the qualification, such as Unit 28: Further
Mathematics for Technicians, and at BTEC Higher National level.
This unit enables learners to build on knowledge gained at GCSE or BTEC First Diploma level and use it in a
more practical context for their chosen discipline. Learning outcome 1 will develop learners’ knowledge and
understanding of algebraic methods, from a look at the use of indices in engineering to the use of the algebraic
formula for solving quadratic equations. Learning outcome 2 involves the introduction of the radian as another
method of angle measurement, the shape of the trigonometric ratios and the use of standard formulae
to solve surface areas and volumes of regular solids. Learning outcome 3 requires learners to be able to
represent statistical data in a variety of ways and calculate the mean, median and mode. Finally, learning
outcome 4 is intended as a basic introduction to the arithmetic of elementary calculus.
Learning outcomes
On completion of this unit a learner should:
1 Be able to use algebraic methods
2 Be able to use trigonometric methods and standard formula to determine areas
3 Be able to use statistical methods to display data
4 Be able to use elementary calculus techniques.
Edexcel BTEC Level 3 Nationals specification in Engineering
– Issue 1 – January 2010 © Edexcel Limited 2009
1
, Unit content
1 Be able to use algebraic methods
am
Indices and logarithms: laws of indices (am x an = am+n, n
= a m − n , (am)n = amn), laws of logarithms
a
A
(log A + log B = log AB, log A = n log A, log A – log B = log ) eg common logarithms
n
B
(base 10), natural logarithms (base e), exponential growth and decay
Linear equations and straight line graphs: linear equations eg y = mx + c; straight line graph (coordinates
on a pair of labelled Cartesian axes, positive or negative gradient, intercept, plot of a straight line);
experimental data eg Ohm’s law, pair of simultaneous linear equations in two unknowns
Factorisation and quadratics: multiply expressions in brackets by a number, symbol or by another
expression in a bracket; by extraction of a common factor eg ax + ay, a(x + 2) + b(x +2); by grouping eg
ax – ay + bx – by; quadratic expressions eg a2 + 2ab + b2; roots of an equation eg quadratic equations
with real roots by factorisation, and by the use of formula
2 Be able to use trigonometric methods and standard formula to determine areas and
volumes
Circular measure: radian; degree measure to radians and vice versa; angular rotations (multiples of π
radians); problems involving areas and angles measured in radians; length of arc of a circle (s = rθ ); area
of a sector (A = ½ r2θ)
Triangular measurement: functions (sine, cosine and tangent); sine/cosine wave over one complete cycle;
graph of tan A as A varies from 0° and 360° (tanA = sin A/cos A); values of the trigonometric ratios for
angles between 0° and 360°; periodic properties of the trigonometric functions; the sine and cosine rule;
practical problems eg calculation of the phasor sum of two alternating currents, resolution of forces for a
vector diagram
Mensuration: standard formulae to solve surface areas and volumes of regular solids eg volume of a
4
cylinder = π r2 h, total surface area of a cylinder = 2π rh + π r2, volume of sphere = π r 3,
3
1
surface area of a sphere = 4 πr2, volume of a cone = π r2 h, curved surface area of cone =
π r x slant height
3
3 Be able to use statistical methods to display data
Data handling: data represented by statistical diagrams eg bar charts, pie charts, frequency distributions,
class boundaries and class width, frequency table; variables (discrete and continuous); histogram
(continuous and discrete variants); cumulative frequency curves
Statistical measurement: arithmetic mean; median; mode; discrete and grouped data
Edexcel BTEC Level 3 Nationals specification in Engineering
2 – Issue 1 – January 2010 © Edexcel Limited 2009
Technicians
Unit code: A/600/0253
QCF Level 3: BTEC National
Credit value: 10
Guided learning hours: 60
Aim and purpose
This unit aims to give learners a strong foundation in mathematical skills. These skills will help them to
successfully complete many of the other units within the qualification.
Unit introduction
One of the main responsibilities of engineers is to solve problems quickly and effectively. This unit will enable
learners to solve mathematical, scientific and associated engineering problems at technician level. It will
also act as a basis for progression to study other units both within the qualification, such as Unit 28: Further
Mathematics for Technicians, and at BTEC Higher National level.
This unit enables learners to build on knowledge gained at GCSE or BTEC First Diploma level and use it in a
more practical context for their chosen discipline. Learning outcome 1 will develop learners’ knowledge and
understanding of algebraic methods, from a look at the use of indices in engineering to the use of the algebraic
formula for solving quadratic equations. Learning outcome 2 involves the introduction of the radian as another
method of angle measurement, the shape of the trigonometric ratios and the use of standard formulae
to solve surface areas and volumes of regular solids. Learning outcome 3 requires learners to be able to
represent statistical data in a variety of ways and calculate the mean, median and mode. Finally, learning
outcome 4 is intended as a basic introduction to the arithmetic of elementary calculus.
Learning outcomes
On completion of this unit a learner should:
1 Be able to use algebraic methods
2 Be able to use trigonometric methods and standard formula to determine areas
3 Be able to use statistical methods to display data
4 Be able to use elementary calculus techniques.
Edexcel BTEC Level 3 Nationals specification in Engineering
– Issue 1 – January 2010 © Edexcel Limited 2009
1
, Unit content
1 Be able to use algebraic methods
am
Indices and logarithms: laws of indices (am x an = am+n, n
= a m − n , (am)n = amn), laws of logarithms
a
A
(log A + log B = log AB, log A = n log A, log A – log B = log ) eg common logarithms
n
B
(base 10), natural logarithms (base e), exponential growth and decay
Linear equations and straight line graphs: linear equations eg y = mx + c; straight line graph (coordinates
on a pair of labelled Cartesian axes, positive or negative gradient, intercept, plot of a straight line);
experimental data eg Ohm’s law, pair of simultaneous linear equations in two unknowns
Factorisation and quadratics: multiply expressions in brackets by a number, symbol or by another
expression in a bracket; by extraction of a common factor eg ax + ay, a(x + 2) + b(x +2); by grouping eg
ax – ay + bx – by; quadratic expressions eg a2 + 2ab + b2; roots of an equation eg quadratic equations
with real roots by factorisation, and by the use of formula
2 Be able to use trigonometric methods and standard formula to determine areas and
volumes
Circular measure: radian; degree measure to radians and vice versa; angular rotations (multiples of π
radians); problems involving areas and angles measured in radians; length of arc of a circle (s = rθ ); area
of a sector (A = ½ r2θ)
Triangular measurement: functions (sine, cosine and tangent); sine/cosine wave over one complete cycle;
graph of tan A as A varies from 0° and 360° (tanA = sin A/cos A); values of the trigonometric ratios for
angles between 0° and 360°; periodic properties of the trigonometric functions; the sine and cosine rule;
practical problems eg calculation of the phasor sum of two alternating currents, resolution of forces for a
vector diagram
Mensuration: standard formulae to solve surface areas and volumes of regular solids eg volume of a
4
cylinder = π r2 h, total surface area of a cylinder = 2π rh + π r2, volume of sphere = π r 3,
3
1
surface area of a sphere = 4 πr2, volume of a cone = π r2 h, curved surface area of cone =
π r x slant height
3
3 Be able to use statistical methods to display data
Data handling: data represented by statistical diagrams eg bar charts, pie charts, frequency distributions,
class boundaries and class width, frequency table; variables (discrete and continuous); histogram
(continuous and discrete variants); cumulative frequency curves
Statistical measurement: arithmetic mean; median; mode; discrete and grouped data
Edexcel BTEC Level 3 Nationals specification in Engineering
2 – Issue 1 – January 2010 © Edexcel Limited 2009
