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Formula Sheets
for Exams
Disclaimer: This document includes the Formula Sheets provided with the Level and Certification examinations administered by the Nova
Scotia Apprenticeship Agency.
Please be advised that this document is accurate as of December 2019 but is subject to change.
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TABLE OF CONTENTS Blaster (1st Class, 2nd Class, 3rd Class): Provincial Certification 3
Boilermaker: Entry Level, Level 1, 2, Red Seal 5
Carpenter: Red Seal 8
Construction Electrician: Level 1, 2, 3, 4, Red Seal 9
Gasfitter (Class A and Class B): Red Seal 12
Industrial Electrician: Level 1, 2, 3, 4 14
Industrial Mechanic (Millwright): Level 1, Red Seal 16
Instrumentation and Control Technician: Level 1, 2, 3 18
Insulator (Heat & Frost): Red Seal 20
Ironworker (Generalist, Reinforcing, Structural/Ornamental): Red Seal 21
Landscape-Horticulturist: Red Seal 22
Lather (Interior Systems Mechanic): Red Seal 23
Machinist: Red Seal 24
Mobile Crane Operator: Red Seal 25
Powerline Technician: Red Seal 26
Sheet Metal Worker: Level 1, 2, 3, 4, Red Seal 27
Tool and Die Maker: Red Seal 33
Tower Crane Operator: Red Seal 34
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BLASTER (1st Class, 2nd Class, 3rd Class) PROVINCIAL CERTIFICATION
Numbers of series = Total number of detonators ÷ Number of detonators per series Resistance of circuit = Resistance of one series ÷ Number of series Resistance of connecting wire = Length of connecting wire x 2 x Resistance of wire (ohms) Resistance of detonator circuit = Number of detonators x Resistance of detonators (ohms) Resistance of firing wire = Length of connecting wire x 2 x Resistance of wire (ohms) Resistance of one series = Number of detonators x Resistance of detonators Total resistance of blasting circuit = Resistance of detonator circuit + Resistance of connecting wire + Resistance of firing line Ds (Scaled distance) = D (Distance)
W (Weight) V (Voltage) = I (Current) x R (Resistance) W (Weight) = D (Distance) 2
Ds (Scaled distance) Trench blasting
Metric Imperial
B = Burden (m) = 0.6 m per 25 mm of borehole diameter
B = Burden (ft.) = 2 ft. per in. of borehole diameter
S = Spacing (m) = B
S = Spacing (ft.) = B
J = Subgrade drilling (m) = 0.5-0.66 x B
J = Subgrade drilling (ft.) = 0.5-0.66 x B
T = Collar length (m) = S or B
Collar length (ft.) = S or B
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Quarry blasting
Metric Imperial
L = Bench height (m) L = Bench height (ft.)
B = Burden (m) = (25 to 35 x De) ÷ 1000
B = Burden (ft.) = (25 to 35 x De) ÷ 12
S = Spacing (m) = B x 1.0 to 1.8
S = Spacing (ft.) = B x 1.0 to 1.8
J = Subgrade drilling (m) = B x 0 to 0.5 J = Subgrade drilling (ft.) = B x 0 to 0.5
T = Collar length (m) = B x 0.7
T = Collar length (ft.) = B x 0.7
C = Length of explosives column (m) = J + L – T
C = Length of explosives column (ft.) = J + L - T
Loading Density (kg/m) = 0.0007854 x De2 x Explosive density
Loading Density (lb./ft.) = 0.3405 x De2 x Explosive density
Number of units in explosives column = C x 1000 ÷ Length of explosive unit
Number of units in explosives column = C x 12 ÷ Length of explosive unit
Weight of explosives per borehole (kg/hole) = Length of explosives column x Loading density
Weight of explosives per borehole (lb./hole) = Length of explosives column x Loading density
Volume of material per borehole (m3) = B x S x L
Volume of material per borehole (cu. yd.) = B x S x L ÷ 27
Powder factor (kg/m3) = Weight of explosives per borehole ÷ Volume of material per borehole
Powder factor (lb./cu. yd.) = Weight of explosives per borehole ÷ Volume of material per borehole
Powder factor (kg/tonne) = Weight of explosives per borehole ÷ Volume of material per borehole x Weight of materials
Powder factor (lb./ton) = Weight of explosives per borehole ÷ Volume of material per borehole x Weight of materials
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BOILERMAKER ENTRY LEVEL, LEVEL 1, 2
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BOILERMAKER RED SEAL
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CARPENTER RED SEAL
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CONSTRUCTION ELECTRICIAN LEVEL 1, 2, 3, 4
1. kVA = (V x A) / 1000
2. RPM = 120F / P
3. VS / VP = NS / NP
4. NS / NP = IP / IS
5. P = I2 R
6. I = E/R
7. P = E x I
8. PF = kw / kVA
9. True 3Φ Power = EL x IL x PF x 1.732
10. P (Watts) = hp x 746
11. EP x NS = ES x NP
12. PF = W/VA
13. V = VL / 1.73
14. 𝑉𝐴 = √𝑃2 + (𝑉𝐴𝑅𝐿 − 𝑉𝐴𝑅𝐶)2
15. Wye EP = EL /1.732
16. (Series Inductors) LT = L1 + L2 + L3
17. (Parallel Inductors) 1 / LT = 1 / L1 + 1/L2 + 1 / L3
18. (Parallel Capacitors) CT = C1 + C2 + C3
19. (Series Capacitors) 1 / CT = 1 / C1 + 1/C2 + 1 / C3
20. XL = 2πfl
21. XC = 1 / 2πfC
22. C2 = A2 + B2
23. 𝑍 = √𝑅2 + (𝑋𝐿 − 𝑋𝐶)2
24. Fault Current = Secondary current/ Impedance
25. 1 W = 3.41 BTU / H
26. N = 120F/P
27. Power (HP) = (Torque (lb.in.) x speed)/63,025
28. Motor Efficiency % = (Power out / Power in) x 100
29. TK = TC + 273.15
30. % Slip = (Stator speed – Rotor speed / Stator speed) x 100
31. % Voltage regulation (Transformers or Alternators) = ([Voltage no-load – Voltage full-load] /
Voltage full-load) x 100
32. 3Φ Amps = VA / (Volts x 1.732)
33. Motor Torque (N.m) = (W x 9.549) / Speed
34. 1 ft.lb. = 1.356 N.m
35. Torque (ft.lb.) = (HP x 5252) / Speed
36. 3Φ Apparent Power (VA) = EL x IL x 1.732
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37. TF = TC x 9/5 + 32
38. 1 gallon = .0036047 in.3
39. R factor = RSI x 5.68
40. R = KL/CM
41. RT = R1 + R2 + R3 (series)
42. Effective Value = Peak Value x 0.707
43. Angle Theta = cos-1 PF
44. IT = √IR 2 + (IXL − IXC)2 (parallel)
45. Tau (T) = RC
46. Tau (T) = L / R
47. Tau (T) = 63.2%
48. 1 – Φ half – wave rectifier: maximum value x 0.318
49. 1 – full – wave rectifier: maximum value x 0.637
50. 3 – half – wave rectifier: maximum value x 0.827
51. 3 – full – wave rectifier: maximum value x 0.955
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CONSTRUCTION ELECTRICIAN RED SEAL
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GASFITTER CLASS A RED SEAL
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GASFITTER CLASS B RED SEAL
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INDUSTRIAL ELECTRICIAN LEVEL 1, 2, 3, 4
1. kVA = (V x A) / 1000
2. RPM = 120F / P
3. VS / VP = NS / NP
4. NS / NP = IP / IS
5. P = I2 R
6. I = E/R
7. P = E x I
8. PF = kw / kVA
9. True 3Φ Power = EL x IL x PF x 1.732
10. P (Watts) = hp x 746
11. EP x NS = ES x NP
12. PF = W/VA
13. V = VL / 1.73
14. 𝑉𝐴 = √𝑃2 + (𝑉𝐴𝑅𝐿 − 𝑉𝐴𝑅𝐶)2
15. Wye EP = EL /1.732
16. (Series Inductors) LT = L1 + L2 + L3
17. (Parallel Inductors) 1 / LT = 1 / L1 + 1/L2 + 1 / L3
18. (Parallel Capacitors) CT = C1 + C2 + C3
19. (Series Capacitors) 1 / CT = 1 / C1 + 1/C2 + 1 / C3
20. XL = 2πfl
21. XC = 1 / 2πfC
22. C2 = A2 + B2
23. 𝑍 = √𝑅2 + (𝑋𝐿 − 𝑋𝐶)2
24. Fault Current = Secondary current/ Impedance
25. 1 W = 3.41 BTU / H
26. N = 120F/P
27. Power (HP) = (Torque (lb.in.) x speed)/63,025
28. Motor Efficiency % = (Power out / Power in) x 100
29. TK = TC + 273.15
30. % Slip = (Stator speed – Rotor speed / Stator speed) x 100
31. % Voltage regulation (Transformers or Alternators) = ([Voltage no-load – Voltage full-load] /
Voltage full-load) x 100
32. 3Φ Amps = VA / (Volts x 1.732)
33. Motor Torque (N.m) = (W x 9.549) / Speed
34. 1 ft.lb. = 1.356 N.m
35. Torque (ft.lb.) = (HP x 5252) / Speed
36. 3Φ Apparent Power (VA) = EL x IL x 1.732
37. TF = TC x 9/5 + 32
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38. 1 gallon = .0036047 in.3
39. R factor = RSI x 5.68
40. R = KL/CM
41. RT = R1 + R2 + R3 (series)
42. Effective Value = Peak Value x 0.707
43. Angle Theta = cos-1 PF
44. IT = √IR 2 + (IXL − IXC)2 (parallel)
45. Tau (T) = RC
46. Tau (T) = L / R
47. Tau (T) = 63.2%
48. 1 – Φ half – wave rectifier: maximum value x 0.318
49. 1 – full – wave rectifier: maximum value x 0.637
50. 3 – half – wave rectifier: maximum value x 0.827
51. 3 – full – wave rectifier: maximum value x 0.955
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INDUSTRIAL MECHANIC (MILLWRIGHT) LEVEL 1
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INDUSTRIAL MECHANIC (MILLWRIGHT) RED SEAL
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INSTRUMENTATION AND CONTROL TECHNICIAN LEVEL 1, 2, 3
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INSULATOR (HEAT & FROST) RED SEAL
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IRONWORKER (GENERALIST, REINFORCING, STRUCTURAL/ORNAMENTAL) RED SEAL
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LANDSCAPE-HORTICULTURIST RED SEAL
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LATHER (INTERIOR SYSTEMS MECHANIC) RED SEAL
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MACHINIST RED SEAL
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MOBILE CRANE OPERATOR RED SEAL
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POWERLINE TECHNICIAN RED SEAL
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SHEET METAL WORKER LEVEL 1, 2, 3, 4
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CONVERSIONS
1) 1 𝑓𝑡3 = 1728 𝑖𝑛3
2) 1 𝑓𝑡2 = 144 𝑖𝑛2
3) 1 𝑓𝑡 = 12 𝑖𝑛
4) 1 𝑓𝑡3 = 6.22 𝑖𝑚𝑝. 𝑔𝑎𝑙.
5) 1 𝑓𝑡3 = 7.48 𝑈𝑆 𝑔𝑎𝑙.
6) 1 𝑖𝑚𝑝. 𝑔𝑎𝑙. = 277.4 𝑖𝑛3
7) 1 𝑈𝑆 𝑔𝑎𝑙. = 231 𝑖𝑛3
8) 1 𝑖𝑛 = 25.4 𝑚𝑚
9) 1 𝑓𝑡 = 30.48 𝑐𝑚
10) 1 𝑚𝑒𝑡𝑒𝑟 = 39.37 𝑖𝑛
11) 1 𝑚 = 1000 𝑚𝑚 𝒐𝒓 100 𝑐𝑚
12) 1 𝑐𝑚 = 10 𝑚𝑚
13) 1 𝐾𝑚 = 1000 𝑚
14) 1 𝐾𝑔 = 2.2 𝑙𝑏𝑠
15) 1 𝑚3 = 1000 000 𝑐𝑚3
16) 1 𝑚2 = 10 000 𝑐𝑚2
17) 1 𝑖𝑚𝑝. 𝑔𝑎𝑙. 𝑜𝑓 𝑊𝑎𝑡𝑒𝑟 = 10.05 𝑙𝑏𝑠.
18) 1 𝑈𝑆 𝑔𝑎𝑙. 𝑜𝑓 𝑊𝑎𝑡𝑒𝑟 = 8.35 𝑙𝑏𝑠.
19) 1 𝑓𝑡3 𝑜𝑓 𝑊𝑎𝑡𝑒𝑟 = 62.5 𝑙𝑏𝑠
20) 1 𝑙𝑏. 𝑜𝑓 𝐴𝑖𝑟 = 13.33 𝑓𝑡3
21) 𝑆𝑝𝑒𝑐𝑖𝑓𝑖𝑐 𝐻𝑒𝑎𝑡 𝑜𝑓 𝐴𝑖𝑟 = 0.24 𝐵𝑡𝑢
22) 1 𝑓𝑡2 𝑜𝑓 10 𝑔𝑎𝑢𝑔𝑒 𝑀𝑖𝑙𝑑 𝑆𝑡𝑒𝑒𝑙 = 5 𝑙𝑏𝑠.
23) 𝐶𝑎𝑙𝑜𝑟𝑖𝑓𝑖𝑐 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑁𝑎𝑡𝑢𝑟𝑎𝑙 𝐺𝑎𝑠 = 1000 𝐵𝑡𝑢/ℎ𝑟
24) 𝐶𝑎𝑙𝑜𝑟𝑖𝑓𝑖𝑐 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑃𝑟𝑜𝑝𝑎𝑛𝑒 𝐺𝑎𝑠 = 2500 𝐵𝑡𝑢/ℎ𝑟
25) 1 psi = 6.895 kPa
26) 1 psi = 27.7 “ wc
27) 1 Btu ( Does the following ):
• Raises 1 lb. of water by 1°F
• Raises 1 ft³ of air by 55°F
• Raises 55 ft³ of air by 1°F
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SHEET METAL WORKER RED SEAL
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TOOL AND DIE MAKER RED SEAL
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TOWER CRANE OPERATOR RED SEAL