Pearson
BTEC Level 3 National
in
Engineering
Unit 1: Engineering Principles
Sample
Assessment
Materials (SAMs)
For use with:
• Extended Certificate, Foundation Diploma, Diploma and Extended
Diploma in Engineering
• Diploma and Extended Diploma in Electrical and Electronic Engineering
• Diploma and Extended Diploma in Mechanical Engineering
• Diploma and Extended Diploma in Computer Engineering
• Diploma and Extended Diploma in Manufacturing Engineering
• Diploma and Extended Diploma in Aeronautical Engineering
First teaching from September 2016 Issue 2
,Edexcel, BTEC and LCCI qualifications
Edexcel, BTEC and LCCI qualifications are awarded by Pearson, the UK’s largest awarding body
offering academic and vocational qualifications that are globally recognised and benchmarked.
For further information, please visit our qualifications website at qualifications.pearson.com.
Alternatively, you can get in touch with us using the details on our contact us page at
qualifications.pearson.com/contactus
About Pearson
Pearson is the world's leading learning company, with 35,000 employees in more than 70 countries
working to help people of all ages to make measurable progress in their lives through learning.
We put the learner at the centre of everything we do, because wherever learning flourishes, so do
people. Find out more about how we can help you and your learners at qualifications.pearson.com
References to third-party material made in this specification are made in good faith. We do not endorse,
approve or accept responsibility for the content of materials, which may be subject to change, or any opinions
expressed therein. (Material may include textbooks, journals, magazines and other publications and websites.)
All the material in this publication is copyright
© Pearson Education Limited 2018
, Pearson BTEC Level 3
Engineering
Sample assessment material for first teaching Paper Reference
September 2016 XXXXX/XX
Information Booklet of Formulae and
Constants Insert
You do not need any other materials.
Instructions
• You will need the information in this booklet to answer most questions.
• Read the information carefully.
• You must not write you answers in this booklet.
• your answers given in the question paper will be marked.
Only
Turn over
*S50749A*
S50749A
©2015 Pearson Education Ltd.
1/1/1/1/1/1
Pearson BTEC Level 3 Nationals in Engineering – Unit 1 – Sample Assessment Materials 1
Issue 2 – February 2018 © Pearson Education Limited 2018
,Formulae and Constants
Maths
Rules of Indices
am x an = a (m+n)
am ÷ an = a(m-n)
(am)n = amn
Rules of Logarithms
log AB = log A + logB
A
log = logA – logB
B
logAx = xlogA
Trigonometric rules
b C
a
A B
c
Sine rule
a b c sinA sinB sinC
= or =
sinA sinB sinC a b c
Cosine rule
a2 = b2+c2 – 2bc cos A
2 Pearson BTEC Level 3 Nationals in Engineering – Unit 1 – Sample Assessment Materials
2 S50749A
Issue 2 – February 2018 © Pearson Education Limited 2018
, Volume and area of regular shapes
s
θ
r
length of an arc of a circle s = rθ (where θ is expressed in radians)
area of a sector of a circle A = ½ r2θ (where θ is expressed in radians)
r
h
volume of a cylinder v = π r2 h
total surface area of a cylinder TSA = 2 π rh + 2 π r2
r
volume of sphere v = 4/3 π r3
surface area of a sphere SA = 4 π r2
Pearson BTEC Level 3 Nationals in Engineering – Unit 1 – Sample Assessment Materials 3
S50749A 3
Issue 2 – February 2018 © Pearson Education Limited 2018
Turn over
, l h
r
volume of a cone v = 1⁄3 π r2 h
curved surface area of cone CSA = π r l
Quadratic Formula
To solve ax2 + bx + c = 0 , a ≠ 0
x = –b± √(b –4ac)
2
2a
Physical constants
Acceleration due to gravity g = 9.81m/s2
Permittivity of free space ε0 = 8.85×10−12 F/m
Permeability of free space µ0 = 4π×10−7 H/m
4 Pearson BTEC Level 3 Nationals in Engineering – Unit 1 – Sample Assessment Materials
4 S50749A
Issue 2 – February 2018 © Pearson Education Limited 2018
, Equations of linear motion with uniform acceleration
v = final velocity, u = initial velocity, a = acceleration, t = time and s = distance
v = u + at
s = ut + ½ at2
v2 = u2 + 2as
s = ½(u + v)t
Stress and strain
Direct stress σ = F/A
Direct strain ε = ΔL/L
Shear stress τ = F/A
Shear strain γ = a/b
Young’s Modulus (modulus of elasticity) E = σ/ε
Modulus of rigidity G =τ/γ
Work, Power, Energy and Forces
Force F = ma
Components of forces Fx = Fcosθ, Fy = Fsinθ
where θ is measured from the horizontal
Mechanical work W = Fs
Mechanical power P = Fv, P = W/t
P
Mechanical Efficiency Efficiency (η) = Pinout
Force to overcome limiting friction F = µN
(where N is the normal force)
Gravitational potential energy PE = mgh
Kinetic energy KE = ½ mv2
Pearson BTEC Level 3 Nationals in Engineering – Unit 1 – Sample Assessment Materials 5
S50749A 5
Issue 2 – February 2018 © Pearson Education Limited 2018
Turn over
,Angular parameters
Centripetal acceleration a=ω²r or a= v²/r
Power P = Tω
Rotational Inertia I = k m r2
The inertial constant for a solid
cylinder (flywheel) k = ½ and for a thin
walled hollow cylinder k ≈ 1 (along the
axis of rotation).
Rotational Kinetic energy KE = ½ Iω2
Angular frequency ω =2πf
1
Frequency f=
time period
360 θ(radians)
Radians to degrees conversion θ(degrees) =
2π
where 2π radians = 360°
2 π θ(degrees)
Degrees to radians conversion θ(radians) =
360
Fluid Principles
Continuity of volumetric flow A1v1 = A2v2
Continuity of mass flow ρA1v1 = ρA2v2
Hydrostatic thrust on an immersed plane surface F = ρgAx
Density ρ = m/V
6 Pearson BTEC Level 3 Nationals in Engineering – Unit 1 – Sample Assessment Materials
6 S50749A
Issue 2 – February 2018 © Pearson Education Limited 2018
, Static and DC Electricity theory
q
Current/electron flow I=
t
Coulomb’s law (q1q2)
F=
(4πε0 r2)
pl
Resistance R=
A
Resistance: temperature coefficient ∆R
= α∆T
R0
V
Ohm’s Law DC circuits I=
R
Total for resistors in series R =R +R +R…
T 1 2 3
1 1 1 1 …
Total for resistors in parallel = + +
RT R1 R2 R3
V2
Power P = IV, P = I2 R, P =
R
P
Electrical Efficiency Efficiency (η) = Pout
in
Kirchoff’s Current Law I = I1 + I2 + I3…
Kirchoff’s Voltage Law V = V1 + V2 +V3… or ∑PD = ∑IR
Capacitance
Electric Field Strength F V for uniform electric fields
E= or E =
q d
Capacitance C = εA
d
Time constant τ = RC
Charge stored Q = CV
Energy stored in a Capacitor W = 1 CV2
2
1 1 1 1 …
Capacitors in series c = c +c +c
T 1 2 3
Capacitors in parallel C =C +C +C …
T 1 2 3
Voltage decay on Capacitor discharge vc = Ve (–t⁄τ)
Pearson BTEC Level 3 Nationals in Engineering – Unit 1 – Sample Assessment Materials 7
S50749A 7
Issue 2 – February 2018 © Pearson Education Limited 2018
Turn over
, Magnetism and Electromagnetism
ф
Magnetic Flux Density B=
A
Magnetomotive Force Fm = NI
NI
Magnetic Field Strength or Magnetising force H=
l
B
Permeability = μ0 μr
H
Reluctance S = Fm
ф
dф dl
Induced EMF E = Blv, E = –N = –L
dt dt
1 LI2
Energy stored in an inductor W=
2
ф
Inductance of a coil L= N
I
V1 N
Transformer equation = 1
V2 N2
Single Phase Alternating Current Theory
Time Period T= 1
f
1
Capacitive reactance Xc =
2πfC
Inductive reactance XL = 2πfL
V
Ohm’s Law AC circuits I= (when voltage and current are
Z
in phase)
peak voltage
Root mean square voltage r.m.s.voltage =
√2
Total impedance of an inductor in series Z = √ X 2+ R2
L
with a resistance
Total impedance of a capacitor in series Z = √ X 2+ R2
c
with a resistance
2
Waveform average value Average value = × maximum value
π
r.m.s.value
Form factor of a waveform Form factor =
average value
8 Pearson BTEC Level 3 Nationals in Engineering – Unit 1 – Sample Assessment Materials
8 S50749A
Issue 2 – February 2018 © Pearson Education Limited 2018
BTEC Level 3 National
in
Engineering
Unit 1: Engineering Principles
Sample
Assessment
Materials (SAMs)
For use with:
• Extended Certificate, Foundation Diploma, Diploma and Extended
Diploma in Engineering
• Diploma and Extended Diploma in Electrical and Electronic Engineering
• Diploma and Extended Diploma in Mechanical Engineering
• Diploma and Extended Diploma in Computer Engineering
• Diploma and Extended Diploma in Manufacturing Engineering
• Diploma and Extended Diploma in Aeronautical Engineering
First teaching from September 2016 Issue 2
,Edexcel, BTEC and LCCI qualifications
Edexcel, BTEC and LCCI qualifications are awarded by Pearson, the UK’s largest awarding body
offering academic and vocational qualifications that are globally recognised and benchmarked.
For further information, please visit our qualifications website at qualifications.pearson.com.
Alternatively, you can get in touch with us using the details on our contact us page at
qualifications.pearson.com/contactus
About Pearson
Pearson is the world's leading learning company, with 35,000 employees in more than 70 countries
working to help people of all ages to make measurable progress in their lives through learning.
We put the learner at the centre of everything we do, because wherever learning flourishes, so do
people. Find out more about how we can help you and your learners at qualifications.pearson.com
References to third-party material made in this specification are made in good faith. We do not endorse,
approve or accept responsibility for the content of materials, which may be subject to change, or any opinions
expressed therein. (Material may include textbooks, journals, magazines and other publications and websites.)
All the material in this publication is copyright
© Pearson Education Limited 2018
, Pearson BTEC Level 3
Engineering
Sample assessment material for first teaching Paper Reference
September 2016 XXXXX/XX
Information Booklet of Formulae and
Constants Insert
You do not need any other materials.
Instructions
• You will need the information in this booklet to answer most questions.
• Read the information carefully.
• You must not write you answers in this booklet.
• your answers given in the question paper will be marked.
Only
Turn over
*S50749A*
S50749A
©2015 Pearson Education Ltd.
1/1/1/1/1/1
Pearson BTEC Level 3 Nationals in Engineering – Unit 1 – Sample Assessment Materials 1
Issue 2 – February 2018 © Pearson Education Limited 2018
,Formulae and Constants
Maths
Rules of Indices
am x an = a (m+n)
am ÷ an = a(m-n)
(am)n = amn
Rules of Logarithms
log AB = log A + logB
A
log = logA – logB
B
logAx = xlogA
Trigonometric rules
b C
a
A B
c
Sine rule
a b c sinA sinB sinC
= or =
sinA sinB sinC a b c
Cosine rule
a2 = b2+c2 – 2bc cos A
2 Pearson BTEC Level 3 Nationals in Engineering – Unit 1 – Sample Assessment Materials
2 S50749A
Issue 2 – February 2018 © Pearson Education Limited 2018
, Volume and area of regular shapes
s
θ
r
length of an arc of a circle s = rθ (where θ is expressed in radians)
area of a sector of a circle A = ½ r2θ (where θ is expressed in radians)
r
h
volume of a cylinder v = π r2 h
total surface area of a cylinder TSA = 2 π rh + 2 π r2
r
volume of sphere v = 4/3 π r3
surface area of a sphere SA = 4 π r2
Pearson BTEC Level 3 Nationals in Engineering – Unit 1 – Sample Assessment Materials 3
S50749A 3
Issue 2 – February 2018 © Pearson Education Limited 2018
Turn over
, l h
r
volume of a cone v = 1⁄3 π r2 h
curved surface area of cone CSA = π r l
Quadratic Formula
To solve ax2 + bx + c = 0 , a ≠ 0
x = –b± √(b –4ac)
2
2a
Physical constants
Acceleration due to gravity g = 9.81m/s2
Permittivity of free space ε0 = 8.85×10−12 F/m
Permeability of free space µ0 = 4π×10−7 H/m
4 Pearson BTEC Level 3 Nationals in Engineering – Unit 1 – Sample Assessment Materials
4 S50749A
Issue 2 – February 2018 © Pearson Education Limited 2018
, Equations of linear motion with uniform acceleration
v = final velocity, u = initial velocity, a = acceleration, t = time and s = distance
v = u + at
s = ut + ½ at2
v2 = u2 + 2as
s = ½(u + v)t
Stress and strain
Direct stress σ = F/A
Direct strain ε = ΔL/L
Shear stress τ = F/A
Shear strain γ = a/b
Young’s Modulus (modulus of elasticity) E = σ/ε
Modulus of rigidity G =τ/γ
Work, Power, Energy and Forces
Force F = ma
Components of forces Fx = Fcosθ, Fy = Fsinθ
where θ is measured from the horizontal
Mechanical work W = Fs
Mechanical power P = Fv, P = W/t
P
Mechanical Efficiency Efficiency (η) = Pinout
Force to overcome limiting friction F = µN
(where N is the normal force)
Gravitational potential energy PE = mgh
Kinetic energy KE = ½ mv2
Pearson BTEC Level 3 Nationals in Engineering – Unit 1 – Sample Assessment Materials 5
S50749A 5
Issue 2 – February 2018 © Pearson Education Limited 2018
Turn over
,Angular parameters
Centripetal acceleration a=ω²r or a= v²/r
Power P = Tω
Rotational Inertia I = k m r2
The inertial constant for a solid
cylinder (flywheel) k = ½ and for a thin
walled hollow cylinder k ≈ 1 (along the
axis of rotation).
Rotational Kinetic energy KE = ½ Iω2
Angular frequency ω =2πf
1
Frequency f=
time period
360 θ(radians)
Radians to degrees conversion θ(degrees) =
2π
where 2π radians = 360°
2 π θ(degrees)
Degrees to radians conversion θ(radians) =
360
Fluid Principles
Continuity of volumetric flow A1v1 = A2v2
Continuity of mass flow ρA1v1 = ρA2v2
Hydrostatic thrust on an immersed plane surface F = ρgAx
Density ρ = m/V
6 Pearson BTEC Level 3 Nationals in Engineering – Unit 1 – Sample Assessment Materials
6 S50749A
Issue 2 – February 2018 © Pearson Education Limited 2018
, Static and DC Electricity theory
q
Current/electron flow I=
t
Coulomb’s law (q1q2)
F=
(4πε0 r2)
pl
Resistance R=
A
Resistance: temperature coefficient ∆R
= α∆T
R0
V
Ohm’s Law DC circuits I=
R
Total for resistors in series R =R +R +R…
T 1 2 3
1 1 1 1 …
Total for resistors in parallel = + +
RT R1 R2 R3
V2
Power P = IV, P = I2 R, P =
R
P
Electrical Efficiency Efficiency (η) = Pout
in
Kirchoff’s Current Law I = I1 + I2 + I3…
Kirchoff’s Voltage Law V = V1 + V2 +V3… or ∑PD = ∑IR
Capacitance
Electric Field Strength F V for uniform electric fields
E= or E =
q d
Capacitance C = εA
d
Time constant τ = RC
Charge stored Q = CV
Energy stored in a Capacitor W = 1 CV2
2
1 1 1 1 …
Capacitors in series c = c +c +c
T 1 2 3
Capacitors in parallel C =C +C +C …
T 1 2 3
Voltage decay on Capacitor discharge vc = Ve (–t⁄τ)
Pearson BTEC Level 3 Nationals in Engineering – Unit 1 – Sample Assessment Materials 7
S50749A 7
Issue 2 – February 2018 © Pearson Education Limited 2018
Turn over
, Magnetism and Electromagnetism
ф
Magnetic Flux Density B=
A
Magnetomotive Force Fm = NI
NI
Magnetic Field Strength or Magnetising force H=
l
B
Permeability = μ0 μr
H
Reluctance S = Fm
ф
dф dl
Induced EMF E = Blv, E = –N = –L
dt dt
1 LI2
Energy stored in an inductor W=
2
ф
Inductance of a coil L= N
I
V1 N
Transformer equation = 1
V2 N2
Single Phase Alternating Current Theory
Time Period T= 1
f
1
Capacitive reactance Xc =
2πfC
Inductive reactance XL = 2πfL
V
Ohm’s Law AC circuits I= (when voltage and current are
Z
in phase)
peak voltage
Root mean square voltage r.m.s.voltage =
√2
Total impedance of an inductor in series Z = √ X 2+ R2
L
with a resistance
Total impedance of a capacitor in series Z = √ X 2+ R2
c
with a resistance
2
Waveform average value Average value = × maximum value
π
r.m.s.value
Form factor of a waveform Form factor =
average value
8 Pearson BTEC Level 3 Nationals in Engineering – Unit 1 – Sample Assessment Materials
8 S50749A
Issue 2 – February 2018 © Pearson Education Limited 2018
