QCE Engineering

QCAA Engineering formula sheet: what is and is not on it

Quick answer

The QCAA Engineering external exam every QCE Engineering student sits comes with the QCAA Engineering formula sheet, and your teacher must give you the QCAA Engineering formula sheet in the IA2 exam. The sheet is a two-page "Formula and data book" with Statics, Materials, Dynamics and Electrical circuits formulas, one constant (g=9.8 m s−2g = 9.8\ \text{m s}^{-2}), seven unit prefixes and a panel of circuit and logic gate symbols. It prints no definitions, no units and no worked examples, so you still have to know what each symbol means. Both papers run 120 minutes with 5 minutes perusal, with a non-programmable scientific calculator, a protractor and a ruler, and no notes.

This guide follows the Engineering 2025 v1.0 syllabus, which Year 11 students sit from 2025 and Year 12 students from 2026. The formulas below are from the QCAA Engineering 2025 formula and data book (cover dated June 2026, no version number printed). QCAA also publishes a v1.3 syllabus dated January 2026, and we hold only its Units 3 and 4 subject matter, so confirm the version your school is teaching. Subject reports to date describe cohorts assessed under the 2019 syllabus. The papers and marked questions are on the QCAA Engineering page.

Do you get a formula sheet in the Engineering exam?

Yes, in two assessments, and the syllabus names a different supplier for each.

AssessmentWho provides the formula sheetOther resources
IA2 (Unit 3 examination)Your teacherNon-programmable scientific calculator, protractor, ruler. No notes
External assessment (Unit 4)The QCAANon-programmable scientific calculator, protractor, ruler. No notes

Both give 120 minutes working time and 5 minutes perusal. The 2019 syllabus gave 10 minutes, so older advice about reading time describes the superseded course. Every external paper from 2020 to 2025 was sat under the 2019 rules.

The syllabus uses the same name, the QCAA Engineering formula sheet, for both papers. The sheet itself says nothing about when it is supplied or what calculator you may use, so those rules come from the syllabus alone.

IA1 and IA3 are engineered solution tasks of up to 10 A4 pages and up to 2000 words, and the conditions we hold do not mention the sheet for either. We have not read the assessment conditions for Units 1 and 2, which schools set themselves, so ask your teacher what you may bring there. The exam dates are on the QCE exam timetable.

What is on the QCAA Engineering formula sheet?

The tables below follow the sheet's own headings and the order of its entries. Symbols are printed bare on the sheet, as they are here. Modified from the Engineering 2025 formula and data book, © State of Queensland (QCAA) 2025, licensed under CC BY 4.0: the layout and typesetting are ours, and the formulas are as printed.

Statics

FormulaFormula
c2=a2+b2c^2 = a^2 + b^2FH=Fcos⁡θF_H = F\cos\theta
sin⁡θ=oppositehypotenuse\sin\theta = \dfrac{\text{opposite}}{\text{hypotenuse}}FV=Fsin⁡θF_V = F\sin\theta
cos⁡θ=adjacenthypotenuse\cos\theta = \dfrac{\text{adjacent}}{\text{hypotenuse}}FT=FH2+FV2F_T = \sqrt{F_H^2 + F_V^2}
tan⁡θ=oppositeadjacent\tan\theta = \dfrac{\text{opposite}}{\text{adjacent}}tan⁡θ=FVFH\tan\theta = \dfrac{F_V}{F_H}
M=FdM = FdMT=M1+M2+M3+…M_T = M_1 + M_2 + M_3 + \dots

Materials

FormulaFormula
density=massvolume\text{density} = \dfrac{\text{mass}}{\text{volume}}E=FLA ΔL=σεE = \dfrac{FL}{A\,\Delta L} = \dfrac{\sigma}{\varepsilon}
σ=FA\sigma = \dfrac{F}{A}fos=yield stressallowable working stress\text{fos} = \dfrac{\text{yield stress}}{\text{allowable working stress}}
ε=ΔLL\varepsilon = \dfrac{\Delta L}{L}UTS=maximum loadoriginal cross-sectional area\text{UTS} = \dfrac{\text{maximum load}}{\text{original cross-sectional area}}

The sheet does not name EE in words. The syllabus calls it the modulus of elasticity or Young's modulus, with units of pascals, and calls σ\sigma stress. "fos" is the factor of safety.

Dynamics

The Dynamics section holds the kinematics, work and energy formulas and also the machines, pulleys, screws, gears and friction formulas. They are in the order printed, four to a row where the sheet has four.

FormulaFormulaFormulaFormula
F=maF = maKE=12mv2KE = \tfrac{1}{2}mv^2PE=mghPE = mghvav=stv_{\text{av}} = \dfrac{s}{t}
v=u+atv = u + atv2=u2+2asv^2 = u^2 + 2ass=ut+12at2s = ut + \tfrac{1}{2}at^2a=v−uta = \dfrac{v - u}{t}
MA=FLFEMA = \dfrac{F_L}{F_E}VR=dEdLVR = \dfrac{d_E}{d_L}W=FsW = FsP=WtP = \dfrac{W}{t}

The next three rows are the sheet's velocity ratio, gear and efficiency rows. The sheet prints them two to a row; the pulley and gear lines are long, so they are listed one per row here, in the sheet's reading order.

Formula
VR for screws=circumferencepitchVR \text{ for screws} = \dfrac{\text{circumference}}{\text{pitch}}
VR=radius, diameter, circumference of driven pulleyradius, diameter, circumference of driver pulleyVR = \dfrac{\text{radius, diameter, circumference of driven pulley}}{\text{radius, diameter, circumference of driver pulley}}
VR=input speedoutput speedVR = \dfrac{\text{input speed}}{\text{output speed}}
GR or VR for gears=radius, diameter, circumference or no. teeth of driven gearradius, diameter, circumference or no. teeth of driver gearGR \text{ or } VR \text{ for gears} = \dfrac{\text{radius, diameter, circumference or no. teeth of driven gear}}{\text{radius, diameter, circumference or no. teeth of driver gear}}
η=MAVR×100%\eta = \dfrac{MA}{VR} \times 100\%
GR or VR for gears=angular movement of driver gear (effort)angular movement of driven gear (load)GR \text{ or } VR \text{ for gears} = \dfrac{\text{angular movement of driver gear (effort)}}{\text{angular movement of driven gear (load)}}

Friction closes the section, four to a row.

FormulaFormulaFormulaFormula
μs=tan⁡θ\mu_s = \tan\thetaFf=μFNF_f = \mu F_NFf=μsFNF_f = \mu_s F_NFf=μkFNF_f = \mu_k F_N

Electrical circuits

FormulaFormulaFormula
V=IRV = IRP=VIP = VIE=PtE = Pt
RT=R1+R2+R3+…R_T = R_1 + R_2 + R_3 + \dotsVT=V1+V2+V3+…V_T = V_1 + V_2 + V_3 + \dotsIT=I1+I2+I3+…I_T = I_1 + I_2 + I_3 + \dots
1RT=1R1+1R2+…\dfrac{1}{R_T} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \dotsη=PoutPin×100%\eta = \dfrac{P_{\text{out}}}{P_{\text{in}}} \times 100\%η=EoutEin×100%\eta = \dfrac{E_{\text{out}}}{E_{\text{in}}} \times 100\%

None of the sums is labelled series or parallel. The syllabus's Unit 4 circuit dot points list the resistance and voltage sums for basic series circuits and the reciprocal resistance sum for basic parallel circuits. They print the current sum under both headings, so check with your teacher how it applies to each arrangement. The η\eta lines are the only efficiency formulas for circuits, and they carry the ×100%\times 100\% that turns a ratio into a percentage.

Constant, prefixes and symbols

The sheet's only constant is acceleration due to gravity, g=9.8 m s−2g = 9.8\ \text{m s}^{-2}.

Ratio to basic unitPrefixAbbreviation
10310^{3}kilok
10610^{6}megaM
10910^{9}gigaG
101210^{12}teraT
10−110^{-1}decid
10−210^{-2}centic
10−310^{-3}millim

The sheet also draws seven electric circuit symbols with no captions: a voltmeter and ammeter (a V and an A in circles), a lamp, a resistor, a switch, a cell and a battery. The names are our reading of the drawings. It labels six logic gates, OR, AND, XOR, NOR, NAND and NOT. The NOT gate's output is labelled A‾\overline{A} and the other five gates' outputs are labelled Q.

What is not on the Engineering formula sheet?

This is the list to learn or practise, because the sheet will not help you with it. Everything here is absent from the printed sheet.

Missing from the sheetWhat to do
Definitions of any symbolLearn what each symbol stands for. The 2025 syllabus Unit 1 Topic 3 table (p. 15) gives the quantity, symbol and SI unit, for example stress (σ\sigma) in pascals and moment of force (MM) in newton metres
Units beside the formulasLearn the SI units from the same syllabus table
Worked examplesPractise on the marked papers in the question bank
Strength-to-weight ratio, weight heldweight of project\dfrac{\text{weight held}}{\text{weight of project}}The syllabus prints it in Unit 1 (p. 14), but it is not on the sheet
A rule for counting ropes in a pulley systemThe syllabus says the MA or VR of simple pulley systems is found by adding the ropes supporting the load. The sheet only gives MAMA and VRVR
Micro, nano and pico prefixesOnly seven prefixes are printed. Convert these by learning the powers of ten
Series and parallel labelsMatch each circuit sum to its arrangement yourself
Logic gate truth tablesThe gates are drawn and named. Learn what each one outputs
Calculator or supply rulesThese are in the syllabus assessment conditions, not on the sheet

Two symbols are used for more than one quantity, which is why definitions matter. In the syllabus's symbol table EE is energy and also Young's modulus, and VV is electric potential and also volume. The sheet uses EE for both in different rows: E=PtE = Pt is energy and E=FLA ΔLE = \dfrac{FL}{A\,\Delta L} is Young's modulus.

Which unit does each formula belong to?

The external assessment specification says questions may ask you to "calculate using formulas drawn from across Unit 4 subject matter", and IA2 assesses Unit 3. The sheet is one document for both, so use the syllabus to place a formula.

  • Unit 3 (IA2). Stress, strain, Young's modulus, factor of safety and ultimate tensile strength are Unit 3 Topic 3 content (p. 25). These are five of the six Materials entries on the sheet. Density is Unit 1.
  • Unit 4 (external assessment). Machines, mechanisms and control (pp. 27 to 29) prints most of the Dynamics section (MAMA and VRVR, belts and gears, work, power, energy, efficiency, motion and friction) and every Electrical circuits formula: the circuit totals, Ohm's law, power and energy, and electrical efficiency.
  • Units 1 and 2 (Year 11). Force components, moments, Pythagoras, trigonometry, density, average velocity, acceleration, MAMA and VRVR, and Ohm's law first appear here.

How do you use the formula sheet in an Engineering calculation?

QCAA's reports are specific about what costs marks, and none of it is a lookup failure.

  • List the knowns and unknowns first (2024). The report recommends making a note of the known and unknown information in a short response calculation question and comparing it to the formula book to choose the method.
  • Do not take short cuts (2024). The report says students risk losing marks if they reach an incorrect response using a different method from the one in the subject matter. Alternative methods earn full marks only when the answer is correct.
  • State the reasoning for each step (2025). The report asks for explicit statements that fully explain the working, for example MA=VRMA = VR when 100% efficient.
  • Convert efficiency correctly (2023). To find input power from efficiency, divide by the efficiency written as a decimal. The report names the wrong move: treating 80% efficiency as 100% plus the 20% lost, then multiplying by 1.2.

Because the sheet is provided, memorising its contents is not the goal. The skill the reports describe is choosing the right relationship from the data and showing the steps.

What should you do before the exam?

  1. Get the current QCAA Engineering formula sheet from your teacher or QCAA and check it against the tables above. The cover on our copy is dated June 2026 and prints no version number.
  2. Learn the quantity, symbol and unit table from the syllabus, then the items in the "not on the sheet" table: the prefixes, the pulley rope rule and the logic gate outputs.
  3. Practise the calculation questions on the Machines, mechanisms and control topic, which carried about two thirds of the mapped marks in the 2020 to 2024 external papers in our question bank. Work each one with only the sheet and a scientific calculator.
  4. Read the cognitive verb and the mark count in the question, then write the knowns and unknowns beside it before choosing a formula.

The question bank holds the marked external papers for 2020 to 2024, so you can see how the board marks working as well as answers. The topic split is in the most tested topics guide, and other subjects are on the QCE hub.

Frequently asked questions

Do you get a formula sheet in the QCAA Engineering exam?

Yes. The 2025 syllabus says the QCAA provides the QCAA Engineering formula sheet in the external assessment, and that the teacher must provide it in IA2. Both are 120 minutes working time with 5 minutes perusal, a non-programmable scientific calculator, a protractor and a ruler, and no notes.

What formulas are on the QCAA Engineering formula sheet?

The 2025 formula and data book prints Statics, Materials, Dynamics (including machines, pulleys, gears, screws and friction) and Electrical circuits formulas, one constant (g = 9.8 m s⁻²), seven unit prefixes, and electric circuit and logic gate symbols. This guide reproduces every formula as printed.

Is the Engineering formula sheet in IA1 or IA3?

Not on the conditions we hold. IA1 and IA3 are engineered solution tasks of up to 10 A4 pages and up to 2000 words, and the syllabus names the formula sheet only for the IA2 examination and the external assessment. Your teacher's task sheet decides anything further.

Can I use a graphics calculator in Engineering?

Not on the syllabus conditions. For both IA2 and the external assessment the 2025 syllabus lists a non-programmable scientific calculator, a protractor and a ruler. The formula sheet itself says nothing about calculators, so check your task conditions before the day.

What is not on the QCAA Engineering formula sheet?

It prints no definitions of its symbols, no units, no worked examples and no truth tables. It has no strength-to-weight ratio formula, no rule for counting ropes in a pulley system, and only seven unit prefixes (micro, nano and pico are missing). Its series and parallel circuit formulas are not labelled.

Why are the two gear formulas upside down from each other?

The sheet prints gear ratio or velocity ratio twice with opposite orientations. The radius, diameter, circumference or teeth form is driven gear over driver gear. The angular movement form is driver gear (effort) over driven gear (load). Both are printed as the syllabus has them, so choose the form that matches your data.

Are stress and strain calculations in the external exam?

Under the 2025 syllabus the stress and strain formulas are Unit 3 subject matter, which IA2 assesses. The external assessment relates to Unit 4 and draws its calculations from Unit 4 formulas, although the sheet prints all of them together. The 2023 subject report said calculating stress or strain was Unit 2 content, which described the superseded 2019 syllabus.

What did QCAA tell students to do with the formula book?

The 2024 report advises noting the known and unknown information in a short response calculation question and comparing it to the formula book to choose the method. It also warns that a different method only earns full marks if the answer is correct.

Sources

  • Engineering 2025 formula and data book, QCAA, June 2026, p. 1 of 2, p. 2 of 2. The formulas, constant, unit prefixes and standard symbols reproduced in this guide. The cover is dated June 2026 and prints no version number.
  • Engineering 2025 v1.0 General senior syllabus, QCAA, January 2024, pp. 14-21, 22-31, 33, 38, 42, 46-47. Symbol and unit table, formulas printed in the Units 1 to 4 subject matter, and the IA2 and external assessment conditions that name the QCAA Engineering formula sheet.
  • Engineering 2019 v1.1 General Senior Syllabus, QCAA, April 2018. Superseded version, cited only for the earlier assessment conditions (10 minutes perusal).
  • Engineering subject report, 2024 cohort, QCAA, January 2025. Advice to compare known and unknown information to the formula book, and the warning on alternative methods.
  • Engineering subject report, 2023 cohort, QCAA, February 2024. The efficiency and input power arithmetic trap, and the 2019 unit-boundary ruling on stress and strain.
  • Engineering subject report, 2025 cohort, QCAA, January 2026. Advice to state the reasoning behind each calculation step.
  • AusGrader question bank, QCE Engineering, AusGrader. Marked external assessment papers for 2020 to 2024, and the share of mapped marks by Unit 4 topic.

Syllabus and assessment material referenced in this guide is © State of Queensland (Queensland Curriculum and Assessment Authority), licensed under CC BY 4.0. See our QCAA licensing notice. AusGrader is an independent study tool and is not affiliated with, endorsed by, or operated by the QCAA.

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