Cameroon CAP Vocational Trades cheat sheet

Ohm's law: U = R × I; power P = U × I = R × I²; for three-phase loads P = √3 × U × I × cos φ.

Mechanical advantage of a lever: MA = load arm ÷ effort arm; of a pulley block: MA = number of supporting rope strands.

Cutting speed Vc (m/min) = π × D(mm) × N(rpm) ÷ 1000; feed rate Vf = fz × z × N for milling.

Concrete mix by volume, common site ratios: 1:2:4 (C20-class) and 1:1.5:3 (C25-class); water/cement ratio controls strength.

Solder and braze differ by temperature: soft soldering below 450 °C, brazing above 450 °C but below the parent metal melting point.

Series circuit: current common, voltages add; parallel circuit: voltage common, currents add; R_parallel = (R1×R2)/(R1+R2) for two resistors.

Thermal expansion ΔL = α × L × ΔT; a 1 m steel bar (α ≈ 12×10⁻⁶/°C) grows about 0.6 mm over 50 °C.

Thread notation M12×1.75 means metric coarse: nominal diameter 12 mm, pitch 1.75 mm; tapping drill = 12 − 1.75 = 10.25 mm.

Filing sequence: select cut (bastard for stock removal, smooth for finish), cross-file then draw-file, check flatness with straightedge before final pass.

Hacksaw blade: 18–24 TPI for thick sections, 32 TPI for thin tube; minimum three teeth engaged in the cut to avoid tooth stripping.

Drilling order: centre punch, pilot drill, then full size; use cutting fluid on steel, none on cast iron (dry).

Tapping: start tap must be square to the hole (use a tapping block); advance half-turn, back quarter-turn to break chips; use tapping paste.

Brazing/soldering joint preparation: clean to bright metal, apply flux, heat the joint not the filler, capillary draw fills the gap.

Concrete placing: compact in 300–500 mm layers with a poker vibrator, keep formwork tight; cure wet for at least 7 days.

Masonry bond: running bond offsets half a brick per course; 10 mm joints typical; plumb and level checked every course.

Electrical termination: strip insulation to conductor length, no nicked strands, torque terminal to spec, tug-test, then insulate and label.

Welding basics: correct electrode angle 70–80° to the work, arc length roughly equal to electrode diameter, slag removed between passes.

Micrometer reading = barrel reading (mm) + thimble reading × 0.01 mm; check zero before use and use the ratchet stop.

Vernier caliper: main scale + (coinciding vernier line × 0.02 mm) for a 50-division vernier; close jaws to check zero.

Torque wrench must be stored at its lowest setting; recalibrate periodically - never use it to loosen fasteners.

Grinding wheel: maximum peripheral speed marked on the wheel; ring-test a wheel before mounting; never exceed the marked rpm.

Abrasive wheel guard must cover the wheel except the working arc; tool rest gap ≤ 3 mm on a bench grinder.

Steel designation: e.g. S235 means minimum yield 235 MPa; E24/E30 refer to structural steel grades in older notation.

Lubrication rule: grease for slow, high-load bearings; oil for high-speed, low-load; follow the manufacturer's interval.

Insulation resistance test at 500 V DC; a healthy LV installation typically reads ≥ 1 MΩ to earth.

Pneumatic/hydraulic maintenance: drain moisture traps, check filter elements, verify pressure at the gauge against the set value.

Hierarchy of control: eliminate, substitute, engineering controls, administrative controls, then PPE as last resort.

PPE by task: safety glasses for chipping/grinding, face shield for cutting, gloves off near rotating machinery, hearing protection above 85 dB(A).

Lockout/tagout: isolate, lock, tag, dissipate stored energy, verify zero energy before work.

Electrical first aid: do not touch the casualty until supply is isolated; then assess breathing and call emergency services.

Fire classes: A solids (water), B liquids (foam/CO₂), C gases (dry powder), D metals (special powder); never water on live electrical equipment.

COSHH-type logic: obtain the safety data sheet, note flash point and exposure limits, ventilate, and store chemicals in labelled containers.

Waste segregation: metal swarf, used oil, batteries and electronic waste go to separate collection points; never to drains or open burning.

Manual handling: keep load close, back straight, lift with legs, avoid twisting; two-person lift above roughly 25 kg where practicable.

Incident reporting: record near-misses as well as injuries; investigate root cause, not just the immediate act.

First-angle projection: the view placed on the far side of the object; third-angle: view on the near side. Check the symbol on the title block.

Scale 1:50 means drawing dimension 1 mm represents 50 mm real; 2:1 means the drawing is twice real size.

Line types: continuous thick = visible outline; dashed = hidden; chain thin = centre line; continuous thin = dimension and projection lines.

Dimensioning rules: dimensions in mm without units unless stated, no repeated dimensions, no dimensions on hidden lines where avoidable.

Tolerance 25 ±0.2 gives limits 24.8 and 25.2, total tolerance 0.4 mm; H7/h6 is a clearance fit, H7/p6 an interference fit.

Surface roughness Ra in micrometres: 3.2 general machining, 1.6 fine, 0.8 precision grinding.

Area and volume: circle area πr²; cylinder volume πr²h; triangle area ½ × base × height.

Pythagoras and trig: c² = a² + b²; sin = opposite/hypotenuse, tan = opposite/adjacent; useful for setting out right angles (3-4-5 rule).

Percentage and ratio: material cost uplift = base × (1 + %/100); mix ratio 1:3 totals 4 parts, so one part = total ÷ 4.

Job instruction briefing: state the task, the standard, the safety points and the deadline, then confirm understanding by asking the worker to repeat back.

Written handover note contains: date/time, machine or site, work done, outstanding work, defects found, name and signature.

Work order/Job card fields: client, description, parts and labour, authorisation signature, completion sign-off.

Conflict handling sequence: listen without interrupting, restate the other view, agree the facts, agree the action and the review date.

Confidentiality: client data, drawings and prices are not shared outside the business without authorisation.

Punctuality and absence: notify the supervisor before the shift starts, state the reason and expected return, follow the firm's procedure.

Customer complaint response: acknowledge, record details, investigate, propose remedy within a stated time, follow up.

Team roles: a competent person is designated for safety; apprentices work under supervision and must ask when unsure.

Cost price = direct materials + direct labour + direct expenses; add overhead absorption to get total cost.

Selling price = total cost ÷ (1 − desired margin); marking up by 30% on cost is not the same as a 30% margin.

Break-even quantity = fixed costs ÷ (unit price − unit variable cost).

Gross profit = sales − cost of goods sold; net profit = gross profit − operating expenses.

Cash flow differs from profit: a profitable job can still fail if the client pays late; track receivables weekly.

Depreciation straight line = (cost − residual value) ÷ useful life years.

VAT-style tax: price excluding tax × (1 + rate) = price including tax; the collected tax is not business income.

Quotation must state scope, exclusions, validity period, payment terms and delivery date to be enforceable.

Business registration in Cameroon: sole trader (entreprise individuelle) or company (SARL, SA) registered with the CFCE and holding a taxpayer number (NIU).

French/English technical writing: use the passive or impersonal register for reports; define abbreviations at first use.

Common false friends: French 'actually' = currently, 'eventually' = possibly; English 'librairie' = bookshop, not library.

Percentage change = (new − old) ÷ old × 100; a 20% rise followed by a 20% fall leaves 96% of the original.

Rule of three: if a parts cost 4 500 FCFA, then b parts cost b × 4 500 ÷ a FCFA.

Units: 1 m = 100 cm = 1000 mm; 1 m² = 10 000 cm²; 1 L = 1 dm³ = 1000 cm³; 1 kg = 1000 g.

Basic electricity science: conventional current flows from + to −; conductors, semiconductors and insulators differ in free electrons.

Civics: rights are paired with duties; tax payment and respect for public property are civic obligations.

Statistics basics: mean = sum ÷ count; median = middle value when ordered; the mode is the most frequent value.

Reading a graph: identify axes and units before quoting values; interpolate only between known points.

Gear ratio = driven teeth ÷ driving teeth; output speed = input speed × (driving ÷ driven).

Belt slip reduces transmitted power; a crossed belt reverses rotation direction.

Stress σ = F ÷ A (N/mm² = MPa); strain ε = ΔL ÷ L0; Young's modulus E = σ ÷ ε in the elastic range.

Hardness scales are not interchangeable directly: convert only with a validated table.

Heat treatment: hardening (heat and quench), tempering (reheat to reduce brittleness), annealing (soften, relieve stress).

AC single-phase: RMS voltage × RMS current × power factor = real power in watts.

Cable sizing depends on current-carrying capacity, voltage drop (limit typically 5%) and protective device rating.

Pressure in hydraulics: P = F ÷ A; doubling the piston area halves the pressure for the same force.

Marking out: datum face first, blue the surface, scribe once only, punch centres before drilling.

Chiselling and hacksawing: secure work in a vice at elbow height, cut on the forward stroke, apply light pressure on return.

Bending sheet metal: allow for bend radius; bend allowance ≈ (π/180) × angle × (radius + k × thickness).

Pipe threading: chamfer the end, use cutting oil, reverse every half turn, check with the matching ring gauge.

Plastering: two-coat application, scratch coat keyed, finish coat floated and trowelled; allow drying between coats.

Roof timber setting out uses the 3-4-5 method to square a corner before cutting rafters.

Electrical conduit bending: use the correct spring or bender, avoid kinks, keep minimum bend radius so cable can be pulled.

Assembly torque sequence: tighten in a cross or star pattern in stages to avoid distortion of flanges and gaskets.

Final inspection: compare against the drawing, check dimensions, finish and function, then complete the job card.

Hand tool safety: a mushroomed chisel head or loose hammer handle must be dressed or replaced, not used.

Files cut on the forward stroke; clean with a file card; never use without a handle.

Drill bit geometry: 118° point for general steel, 135° split point for hard material; lip clearance prevents rubbing.

Measuring tool care: wipe and oil after use, store calipers with jaws slightly open, keep in a case away from magnetic fields.

Machine guards and emergency stops are tested before each shift; report defects and tag out the machine.

Material selection: mild steel for weldability, stainless for corrosion, aluminium for low weight, brass for conductivity and machining.

Cement storage: keep dry, off the floor, use oldest first; lumps indicate hydration and reduced strength.

Compressor maintenance: drain the receiver daily, check the safety valve and belt tension, log the service.

Noise: 80 dB(A) is the lower action value, 85 dB(A) the upper; hearing protection is mandatory above the upper value.

Dust: silica from cutting concrete causes silicosis; use water suppression or extraction plus a suitable respirator.

Welding hazards: UV arc eye, fumes (use extraction), fire risk from sparks (clear 10 m of combustibles, have an extinguisher).

Working at height: use a scaffold with guardrails and toe boards; ladders at 75° with 1 m above the landing point.

Excavation: support sides beyond 1.2 m depth, keep spoil back from the edge, check for buried services before digging.

Electrical safety: RCD/earth leakage protection, inspect leads for damage, use 110 V or isolated supply on wet sites where required.

First aid kit contents: gloves, sterile dressings, burns gel, eye wash, triangular bandage; check expiry dates.

Environmental spill response: stop the source, contain with absorbent, dispose as hazardous waste, report the incident.

Isometric drawing uses 30° axes and full lengths along each axis; do not foreshorten unless stated.

Section views: hatch at 45°, spacing even, adjacent parts hatched in opposite directions.

Geometric tolerancing symbols: flatness, straightness, perpendicularity, concentricity; a datum is the reference feature.

Bolt circle: coordinates = centre + R × cos θ and centre + R × sin θ for each hole angle θ.

Taper and angle: taper = (D − d) ÷ L; included angle from half-angle using tan = opposite ÷ adjacent.

Volume of a frustum (cone) = (πh ÷ 3)(R² + Rr + r²).

Unit conversion for pressure: 1 bar = 100 kPa ≈ 1.02 kgf/cm²; 1 N/mm² = 1 MPa.

Reading a vernier height gauge and a dial indicator: zero the datum first, then read displacement from the dial.

Telephone and radio protocol: identify yourself and the site, state the purpose, confirm the message back.

Technical report structure: title, objective, method, results, conclusion, recommendations, signature and date.

Non-discrimination and harassment: any complaint is recorded and referred to the designated person; retaliation is itself an offence.

Site meeting record: decisions, responsible person and deadline for each action.

Instructions that are unsafe may be refused; report the refusal in writing through the chain of command.

Email etiquette at work: clear subject line, one topic, professional tone, no confidential data in the body if the address is external.

Apprenticeship conduct: arrive early, keep the work area clean, ask before using another worker's tools.

Diversity and teamwork: assign tasks by competence, share the plan, and give credit for completed work.

Labour cost = hourly rate × hours + social charges (% of gross wage).

Overhead absorption rate = total overhead ÷ total direct labour hours (or machine hours).

Stock valuation: FIFO and weighted average give different cost of sales; choose one method and apply it consistently.

Working capital = current assets − current liabilities; a positive figure supports day-to-day operation.

Invoice must show: business name and taxpayer number (NIU), client, date, description, quantity, unit price, tax, total, payment due date.

Credit control: agree terms in writing, invoice promptly, send a reminder at due date, escalate in defined stages.

Simple record keeping: cash book, sales and purchase records, stock sheet, payroll file - kept for the legally required period.

Risk management for a small workshop: insurance for fire and liability, written contracts, a deposit on large jobs.

Growth decisions: compare the cost of new equipment with the extra revenue it enables, using payback period = cost ÷ annual net gain.

Solving a linear equation: isolate the unknown by applying the same operation to both sides, then verify by substitution.

Proportional quantities: two quantities are proportional if their ratio is constant; graph is a straight line through the origin.

Area of a trapezium = ½(a + b) × h; circumference = 2πr; use π ≈ 3.14 unless told otherwise.

Scientific method: observation, hypothesis, experiment, analysis, conclusion; a control is needed for a valid comparison.

Matter and energy: states of matter depend on particle arrangement and energy; heat transfers by conduction, convection and radiation.

Health science: hand hygiene and clean water prevent most communicable disease; vaccination builds immunity.

Civics: the rule of law means the same rules apply to all; public services are funded by taxes.

Reading comprehension technique: identify the question word, locate the passage sentence, answer in your own words with the same meaning.

Time and money problems: convert to the same unit (minutes, or FCFA) before calculating; check the answer's order of magnitude.

Machine elements: a bearing's designation (e.g. 6205) encodes type, dimensions series and bore = last two digits × 5 mm.

Fastener strength classes: 8.8 means tensile 800 MPa and yield 0.8 × 800 = 640 MPa.

Weld symbols: fillet weld shown as a triangle on the reference line; the size is written to the left of the symbol.

Thermal efficiency of a heating appliance = useful heat output ÷ energy input × 100%.

Wood moisture content = (wet mass − dry mass) ÷ dry mass × 100%; timber for joinery is typically dried to 10–15%.

Concrete strength class C25/30: characteristic cylinder strength 25 MPa, cube strength 30 MPa at 28 days.

Electrical protection: a circuit breaker's curve (B, C, D) sets the instantaneous trip multiple of its rating.

Measurement uncertainty: the smallest division of an instrument limits its reading precision; record to that precision.

Setting a workpiece in a four-jaw chuck: adjust each jaw in turn while checking run-out with a dial indicator.

Lathe turning: set tool height to centre, select spindle speed from cutting speed, take roughing then finishing passes.

Milling: climb vs conventional milling - conventional is safer on older machines with backlash.

Wood joint execution: mark with a knife line, cut on the waste side, pare to the line, test fit before gluing.

Glue-up: apply even pressure, clean squeeze-out before it sets, allow the stated clamp time.

Painting preparation: sand, dust off, prime bare surfaces, apply thin coats, respect recoat times.

Tiling: set out from the centre to avoid narrow cut tiles at edges, use a notched trowel and spacers.

Pipe fitting: deburr and chamfer, apply jointing compound to the male thread only, tighten without over-straining the fitting.

Commissioning: test, record results, demonstrate to the client, and hand over manuals and certificates.

Vernier, micrometer and dial gauge each have a calibration interval; a sticker or log records the last date.

A bench grinder wheel is dressed with a star dresser to restore shape and cutting action.

Battery tools: store at partial charge in a dry place, use the correct charger voltage, dispose of cells as hazardous waste.

Steel rules and tapes are checked against a reference; a worn tape end gives systematic error.

Hydraulic oil is selected by viscosity grade and checked for contamination; water in oil turns it milky.

Fastener corrosion protection: galvanising, zinc plating, or stainless; do not mix dissimilar metals in wet conditions (galvanic corrosion).

Electrical test instruments: a multimeter's CAT rating must match the installation category being tested.

Spare parts management: keep a minimum stock list for critical items, log issues and reorder point.

Risk assessment: likelihood × severity gives a rating; control the highest ratings first and review after any change.

Hand-arm vibration: limit exposure time with vibrating tools; report tingling or numbness early.

Chemical labelling: hazard pictograms, signal word, hazard and precautionary statements; never decant into unlabelled bottles.

Eye protection: goggles for chemical splash, safety glasses for impact, welding helmet with the correct shade number for the current.

Emergency plan: escape routes kept clear, assembly point known, extinguishers serviced annually and staff trained.

Personal hygiene on site: wash hands before eating, no eating in the work area, change out of contaminated clothing.

Environmental law principle: the polluter pays; waste producers are responsible for disposal through approved channels.

Accident investigation: preserve the scene where possible, interview witnesses separately, record facts and not opinions.

Orthographic views follow the rule: front, top and side views align - the top view sits directly above or below the front view depending on the projection angle.

Hidden detail is shown dashed; centre lines extend slightly beyond the outline.

A dimension is never duplicated; the drawing must be complete with one dimension per feature.

Geometric construction: bisect an angle with arcs from the two sides; construct a perpendicular bisector with equal arcs from both ends.

Development of a cylinder: flat pattern length = π × D; of a cone: sector radius = slant height.

Coordinate tables and bolt-hole pitch: for n holes on a circle, angular pitch = 360° ÷ n.

Tolerance stack-up: total variation is the sum of the individual tolerances in a chain of dimensions.

Interpreting a scale drawing: measure with a rule and multiply by the scale factor; never scale a dimension that is already written.

Giving feedback: describe the observed behaviour and its effect, then agree the expected behaviour - avoid personal judgement.

Client relations: confirm the scope in writing, warn early of delays, and never promise a date that has not been checked.

Working with a translator or second language: use short sentences, confirm key figures in writing, avoid slang.

Record keeping of instructions: date and initial any verbal instruction that changes the job, and confirm it by message.

Professional ethics: no bribery, no falsifying test results, no unqualified signing off of work.

Workplace health and safety duty: workers must follow training, use PPE and report hazards; employers must provide a safe system of work.

Team briefing content: task, hazards, method, roles, time, and questions.

Dress and identity: wear the correct PPE and identification; represent the business courteously on client premises.

Mark-up on cost = (price − cost) ÷ cost × 100; margin on price = (price − cost) ÷ price × 100.

A 25% mark-up on cost equals a 20% margin on price - check which one the client or the boss means.

Job costing sheet: materials, labour hours × rate, subcontract, transport, overhead, contingency, then price.

Quotation vs estimate: a quotation is a firm offer; an estimate is indicative and can change.

Payment security: progress payments on long jobs, retention held until acceptance, written variation orders for extra work.

Tax and social obligations: register, declare turnover, pay social contributions for employees, keep receipts.

Simple stock control: reorder point = average daily use × lead time + safety stock.

Business plan sections: market, product/service, resources, costs, forecast, finance needed, repayment.

Fractions and decimals: convert to a common denominator before adding; multiply numerators and denominators directly.

Powers of ten: 10³ = 1000, 10⁻³ = 0.001; use them to convert between mm, m and km quickly.

Geometry: sum of angles in a triangle = 180°; in a quadrilateral = 360°; angles on a straight line = 180°.

Speed, distance, time: distance = speed × time; keep units consistent (km/h with hours).

Science: force is measured in newtons, mass in kilograms; weight = mass × g (g ≈ 9.81 m/s²).

Environment and civics: deforestation and waste burning damage soil and air; community rules protect shared resources.

Reading a table or invoice: check totals by re-adding lines and verifying tax separately.

Comprehension of instructions: identify the action verb and the condition before starting the task.

Three-phase motor: synchronous speed = 120 × frequency ÷ number of poles; slip = (Ns − N) ÷ Ns.

Star-delta starting reduces the phase voltage by √3 and the starting torque to one third.

Transformer ratio = primary turns ÷ secondary turns = primary voltage ÷ secondary voltage.

Ohm's law applied to a circuit with resistors in series and parallel gives the total resistance before finding current.

Screw thread efficiency is reduced by friction; a square thread is the most efficient, a V-thread the strongest for clamping.

Material tests: tensile test gives yield and ultimate strength; hardness test gives resistance to indentation; impact test gives toughness.

Corrosion prevention by sacrificial anode uses a more active metal (e.g. zinc) to protect steel.

Welding current selection depends on electrode diameter and material thickness; too low a current causes lack of fusion.

Reading a work instruction: identify the drawing revision, material, quantity and inspection points before starting.

First-off inspection: check the first part fully before running the batch.

Scrap and rework: tag the part, record the cause, and get authorisation before reworking.

Tool change discipline: stop the machine, isolate, change, check alignment, then restart.

Housekeeping at end of shift: clear swarf, return tools to their place, leave the bench clear.

Working to a tolerance: aim for the middle of the tolerance band, not the limit, to allow for tool wear.

Safe lifting of a heavy component: use the correct sling and rated shackle, never exceed the marked safe working load.

Recording results: write measured values as read, with units, and initial the record.

A torque wrench's accuracy is typically ±4%; it must be within its calibration date to be used for critical joints.

An air compressor's safety valve is tested by hand-lifting the lever periodically; never plug or adjust it.

A machine's preventive maintenance plan lists task, frequency and responsible person; breakdown maintenance is the fallback.

Cutting tools wear at the flank and crater; a worn tool raises cutting force and worsens surface finish.

Grease nipple types must match the grease gun coupler; clean the nipple before greasing to avoid injecting dirt.

Electrical cable colour convention: green/yellow is protective earth, blue is neutral, brown/black is line in typical LV installations.

Storage of gas cylinders: upright, secured, valve cap on, away from heat, oxygen and fuel gas separated.

Measuring instrument zero error: record the zero reading and subtract it from all subsequent readings.

Permit-to-work is required for hot work, confined spaces and live electrical work; the permit states the precautions and the validity time.

Confined space: test the atmosphere for oxygen, flammable gas and toxic gas before entry, and provide a standby person.

Hot work fire watch continues for at least 30 minutes after the work ends.

Electrical isolation is proved dead with a tester that has been proved on a known live source first.

Slips and trips: keep walkways clear, clean spills immediately, use cable ramps across walkways.

Dust and fume extraction filters are checked and replaced on schedule; a blocked filter increases exposure.

Noise control at source beats hearing protection: enclose the machine or move the noisy operation away from people.

Reporting environmental incidents: record the quantity, location and action taken, and notify the responsible authority where required.

A fit designation H7/g6: capital letter is the hole, lower-case is the shaft; H means the hole's lower deviation is zero.

A clearance fit allows relative movement; an interference fit transmits force without a key.

Limits and fits tables give deviations in micrometres; convert to mm by dividing by 1000.

Angular measurement: 1° = 60 minutes, 1 minute = 60 seconds; convert decimal degrees to degrees, minutes, seconds.

Area of an irregular shape by the trapezoidal rule: sum of parallel offsets × spacing.

Estimating material quantity: add a waste allowance (typically 5–10%) to the calculated net quantity.

Reading a drawing's title block gives the part name, material, scale, revision and the person who approved it.

Centre of gravity and balance: the centre of a uniform rectangle is at the intersection of its diagonals.

A verbal instruction that changes cost or scope is confirmed in writing the same day.

When you do not understand a technical instruction, repeat it in your own words and ask for confirmation.

Reporting a defect: state the location, the symptom, when it was noticed and what you did.

Client handover: explain the work done, the operating instructions, the warranty and the contact for problems.

Respect for confidentiality covers client lists, drawings and prices; it continues after leaving the employer.

Disciplinary process: a fair hearing, a chance to respond, a written decision and a right of appeal.

Timekeeping and planning: estimate the job duration, add a contingency, and tell the client early if it changes.

Cultural and language diversity on site: use clear, standard technical words and check understanding rather than assuming it.

Contribution per unit = selling price − variable cost; it pays fixed costs first, then becomes profit.

Margin of safety = (actual sales − break-even sales) ÷ actual sales × 100%.

Cash flow forecast lists receipts and payments by month; a negative closing balance means a funding need.

Interest on a loan: simple interest = principal × rate × time; compare the total cost of credit, not just the monthly payment.

A written contract states parties, scope, price, payment schedule, deadline, penalties and dispute resolution.

Supplier management: get at least two quotations for large purchases, check delivery and quality, keep records.

Customer records support repeat business and credit decisions; keep them accurate and lawful.

Profit is not cash: set aside money for tax, social charges and equipment replacement.

Equation of a straight line: y = mx + c, where m is the gradient and c the intercept.

Percentages of a quantity: 15% of 8 000 = 0.15 × 8 000 = 1 200.

Averages: the mean is affected by extreme values; the median is more robust for skewed data.

Scientific units: power in watts, energy in joules or kilowatt-hours (1 kWh = 3.6 MJ).

Health and safety science: electricity passing through the body causes burns and heart fibrillation; low voltage is not automatically safe.

Civics: the vote and consultation are ways citizens influence decisions; public property is held for collective use.

Reading and writing a short report: use the past tense for work done, the present for facts, and short paragraphs.

Estimation skill: round numbers to check a calculator result is sensible before trusting it.

Fluid flow: flow rate Q = area × velocity; a smaller pipe raises velocity and pressure loss.

Pump head is measured in metres of fluid; power = (ρ × g × Q × H) ÷ efficiency.

Refrigeration cycle: compressor, condenser, expansion device, evaporator; the refrigerant changes state in each.

Electrical earthing provides a low-impedance path so the protective device operates quickly.

A capacitor stores charge Q = C × V; in AC it causes current to lead voltage.

A diode conducts in forward bias above about 0.7 V (silicon); a rectifier converts AC to DC.

Wood: grain direction determines strength; a joint is strongest when glue surfaces are along the grain.

Metal forming: hot working reduces strength needed and refines grain; cold working increases strength but reduces ductility.

Setting out a right angle on site: 3-4-5 triangle or a diagonal check (equal diagonals mean a true rectangle).

Brickwork gauge: a course height plus joint; a gauge rod marked with course heights keeps the work level.

Concrete test cubes are taken, cured and crushed at 7 and 28 days to confirm the mix strength.

Reinforcement: correct cover to the bar, correct lap length, and no bar left exposed to the weather.

Electrical wiring: separate power and signal cables, avoid joints in conduit, and label every circuit at the board.

Plumbing leak test: fill and pressurise, hold for the specified time, check joints, then drain and refill.

Welding distortion control: balance the welding sequence, tack first, and allow the part to cool between passes.

Final finish check: look along the surface in raking light to see high spots and scratches.

A hacksaw frame's blade tension should be firm; a loose blade wanders and breaks.

A cold chisel's cutting angle depends on the material: about 60–70° for steel, sharper for softer metals.

A screwdriver must match the slot width and thickness; a worn tip slips and damages the fastener.

A spirit level is checked by reversing it on the same surface; the bubble must read the same both ways.

A multimeter's continuity function must be tested on a known good circuit before trusting a 'no continuity' result.

A welding set's earth clamp must be connected to clean bare metal close to the work.

Abrasive paper grit number: lower number is coarser; work through the grades rather than jumping.

A machine's rated duty cycle limits how long it can run at full load; exceeding it causes overheating.

A risk assessment is recorded and reviewed when the process, equipment or people change.

Safety signs: red circle with a bar means prohibition, blue circle means mandatory action, yellow triangle means warning.

Emergency stop buttons are red on a yellow background and must be reachable and unobstructed.

Fire extinguisher PASS: pull the pin, aim at the base, squeeze the handle, sweep side to side.

Electrical burns and shock: isolate, call for help, start CPR if trained and the casualty is not breathing.

Ladder safety: one person at a time, three points of contact, do not overreach, secure the top.

Chemical splash in the eye: irrigate with clean water for at least 15 minutes and seek medical help.

Waste hierarchy: prevent, reuse, recycle, recover, dispose - disposal is the last option.

A drawing's scale bar allows distances to be checked even if the printer changes the paper size.

Auxiliary views show a surface true size when it is inclined to the main planes.

A section is identified by a cutting-plane line with arrows showing the viewing direction and letters naming the section.

A thread is drawn with a thick line for the crest and a thin line for the root; the thread run-out is shown.

A weld length and pitch (e.g. 50–100) means 50 mm of weld in every 100 mm.

A dimension from a datum avoids tolerance accumulation compared with a chain of dimensions.

A geometric tolerance frame reads: symbol, tolerance value, datum letter, from left to right.

The area of a triangle from three sides uses Heron's formula: A = √(s(s−a)(s−b)(s−c)) with s the semi-perimeter.

A job handover to the next shift is spoken and written; the written note is the record if there is a dispute.

When a client complains, do not argue about blame at the first contact; record the facts and agree the next step.

A safety briefing is recorded with names, topic, date and the person who delivered it.

Use of mobile phones on site follows the site rule; they are a distraction near machinery.

A worker who is unsure of a task has a duty to stop and ask; a supervisor has a duty to answer.

Written communication to a public body uses a formal register, a clear subject and a reference number.

Respect at work includes language: insults and discriminatory remarks are misconduct, not banter.

Professional development: keep a record of training, certificates and expiry dates.

Fixed costs do not change with output (rent, insurance); variable costs change with each unit (materials, piece labour).

Total cost = fixed cost + variable cost per unit × quantity.

Average cost per unit falls as fixed costs are spread over more units until capacity is reached.

A price list should state whether tax is included and the validity date.

Debtor days = trade receivables ÷ sales × 365; a high figure means cash is tied up with clients.

Stock turnover = cost of sales ÷ average stock; a low turnover means slow-moving stock.

Purchase decisions: compare whole-life cost (purchase, running, maintenance, disposal), not just the ticket price.

Record of assets: keep invoices for equipment; they support depreciation, insurance claims and resale.

Solving a proportion: a/b = c/d gives a × d = b × c; use it for scale and mix problems.

Converting units of area and volume: a length factor of 10 gives an area factor of 100 and a volume factor of 1000.

A right triangle with sides 3, 4 and 5 has a right angle between the 3 and 4 sides.

Reading a chart: check the scale, the units and whether the axis starts at zero before drawing conclusions.

Science and the workplace: friction generates heat; lubrication reduces it and saves energy.

Civics and the environment: environmental protection is a shared duty of citizens, businesses and the state.

Writing a formal letter: sender, date, recipient, subject, body, closing and signature.

Checking work: re-read the question, verify units, and confirm the answer is in the requested form.

A lever's mechanical advantage is the ratio of load to effort; the principle of moments states that clockwise moments equal anticlockwise moments at equilibrium.

Stress concentration occurs at sharp changes of section; a fillet radius reduces it.

A bearing's life rating L10 is the life reached by 90% of a group of identical bearings under the same load.

An electric motor's rated output is mechanical power at the shaft; input power = output ÷ efficiency.

A fuse protects against overload and short circuit by melting; its rating must be below the cable's current capacity.

A transistor amplifies or switches; the base current controls the collector current in a bipolar transistor.

A composite material combines properties: reinforced concrete uses steel for tension and concrete for compression.

A material's density = mass ÷ volume; it determines weight and buoyancy calculations.

Filing a flat surface: use the full length of the file, keep the pressure even, and check with a straightedge in two directions.

Sawing to a line: cut on the waste side, start with a light stroke to establish the kerf, then use full strokes.

Drilling a large hole: drill a pilot hole first, then open to size; use a slower speed for large diameters.

Counterboring and countersinking: counterbore gives a flat seat for a socket head; countersink gives a conical seat for a flat head.

Threading a rod: chamfer the end, use the correct die, oil, and reverse to break chips.

Soft soldering a joint: clean, flux, heat the joint, apply solder to the joint not the iron, do not move until set.

Assembling a bolted joint: flat washer under the nut, correct grade, tighten in a cross pattern to the specified torque.

Testing a repair: operate the equipment through its full range and check for leaks, noise, heat and correct function.

A machine's nameplate gives voltage, current, power, speed and duty; check it before connecting.

A guard is interlocked so the machine cannot run with the guard open.

A belt drive is tensioned so it deflects a small amount under thumb pressure; too tight wears bearings.

A chain drive needs lubrication and correct slack; a worn chain is replaced as a set with the sprockets.

A bearing is fitted with the correct driver on the inner or outer ring, never by hammering the balls.

A seal is replaced if it leaks; the shaft surface must be clean and undamaged.

A filter is replaced at the stated interval or when the pressure drop indicates blockage.

A tool is inspected before use; a damaged tool is removed from service and reported.

A hazard is a source of harm; a risk is the chance and severity of harm from that hazard.

PPE is personal, inspected before use, and replaced when damaged; it does not replace engineering controls.

A fire needs fuel, oxygen and heat; removing any one stops the fire.

A CO₂ extinguisher is used on electrical and flammable liquid fires; it is not effective on deep-seated solid fires.

A spill is contained at the source with a spill kit; absorbent is disposed as hazardous waste.

A worker has the right to stop work if there is a serious and imminent danger.

An accident is recorded in the accident book; a serious accident is reported to the authority.

Noise and dust exposure is reduced by working wet, enclosing the process, and rotating staff away from the source.

A radius is dimensioned with an R, a diameter with a Ø, a square with a square symbol.

A chamfer is dimensioned by its length and angle, e.g. 2 × 45°.

A keyway and key are dimensioned by width and depth; the key is slightly shorter than the keyway.

A gear's module m = pitch diameter ÷ number of teeth; the outside diameter = m × (teeth + 2).

A taper of 1:10 means 1 mm change in diameter per 10 mm length.

A scale of 1:100 on a building plan means 1 cm on the plan represents 1 m on site.

A tolerance of ±0.05 on a 20 mm dimension gives limits 19.95 and 20.05.

A percentage error = (measured − true) ÷ true × 100%; a negative value means the measurement is low.

A supervisor's instruction is followed unless it is unsafe; an unsafe instruction is reported.

A written quotation is a formal communication and must be accurate and clear about exclusions.

A meeting is minuted with decisions and actions, not a transcript of the discussion.

A complaint is answered within the stated time, even if only to say when the answer will come.

A colleague's personal information is not shared without a work reason.

A message about a delay is sent as soon as the delay is known, with a revised date.

A professional introduces themselves, states their role and the purpose of the contact.

A worker who has made a mistake reports it early; hiding it makes the problem worse.

A business's fixed costs must be covered before any profit is made.

A cash sale improves cash flow; a credit sale creates a receivable and a risk of non-payment.

A deposit reduces the risk of a client cancelling after materials are bought.

A variation order is agreed in writing before extra work is done.

A simple profit and loss account lists sales, cost of sales, gross profit, expenses and net profit.

A balance sheet lists assets, liabilities and owner's equity at a date.

A tax invoice is a legal document; a proforma invoice is a request for payment before supply.

A business keeps separate personal and business money to see the true result.

A ratio is simplified by dividing both terms by their highest common factor.

A percentage is a fraction with denominator 100; 25% = ¼ = 0.25.

A mean is calculated by adding the values and dividing by the number of values.

A graph's gradient is the change in y divided by the change in x.

A force diagram shows the size and direction of each force; the resultant is found by adding them.

A material's state changes at fixed temperatures at a given pressure: melting, boiling, condensing, freezing.

A citizen's duties include respecting the law, paying taxes and protecting public property.

A short report uses headings, short sentences and a clear conclusion.

A series circuit's total resistance is the sum of the resistances; the current is the same everywhere.

A parallel circuit's total resistance is less than the smallest individual resistance.

A capacitor blocks DC and passes AC; its reactance falls as frequency rises.

An inductor opposes a change in current; its reactance rises with frequency.

A transformer works on AC only; it does not change frequency.

A three-phase system's line voltage is √3 times the phase voltage in star connection.

A screw's mechanical advantage is increased by a finer thread and a longer lever.

A material's toughness is its ability to absorb energy before fracture; hardness is resistance to indentation.

A centre punch mark is enlarged with a pilot drill before the full-size drill to keep the hole on position.

A hole is deburred after drilling to remove the sharp edge and protect the worker.

A tap is started square and turned with a tap wrench; a broken tap is removed with a tap extractor.

A die is started square on a chamfered rod and turned with a die stock.

A surface is finished by draw filing or with abrasive cloth, working along the length.

A joint is checked for square before it is fixed permanently.

A machine is cleaned and the swarf removed after use; swarf is disposed of safely.

A measurement is repeated and the average taken to reduce random error.

A tool's safe working load is marked on it; it is never exceeded.

A sling is inspected for cuts and wear before use; a damaged sling is destroyed.

A jack is used on a firm level base and is chocked; it is never used to support a load while working under it.

A ladder is inspected for cracks and missing feet before use.

A power tool's cable is checked for damage and the plug for a sound earth connection.

A battery is charged in a ventilated area away from sparks.

A machine's emergency stop is tested before the shift starts.

A maintenance log records what was done, by whom and when.

A risk assessment considers who might be harmed and how.

A control measure is checked to confirm it works.

A safety data sheet gives the hazards, first aid, storage and disposal of a chemical.

A flammable liquid is stored in a closed labelled container away from ignition sources.

A confined space is never entered without a permit and a standby person.

A working platform has guardrails, toe boards and a safe means of access.

A first aider is trained and the first aid box is checked regularly.

An environmental spill is reported and cleaned up with the correct absorbent.

A drawing is read from the title block outwards: part, material, scale, revision.

A hidden line is not dimensioned if the feature can be dimensioned on a visible view.

A centre line is used for axes of symmetry and bolt circles.

A dimension is placed outside the outline where possible and not crossed by other lines.

A tolerance is the permitted variation from the nominal dimension.

A fit is the relationship between the hole and shaft sizes.

A scale drawing is measured with a rule and multiplied by the scale factor.

A calculation is checked by estimating the answer first.

A job card is completed with the work done, parts used and time taken.

A client is told about a problem as soon as it is found, with options and costs.

A colleague is treated with respect regardless of their role.

A safety rule is followed even when no one is watching.

A message is confirmed when it is important.

A record is kept of training and certificates.

A complaint is recorded and answered.

A worker asks for help when a task is beyond their competence.

A break-even point is where total revenue equals total cost.

A mark-up is added to cost; a margin is a percentage of the selling price.

A cash flow forecast shows when money comes in and goes out.

A quotation states the scope, price, terms and validity.

A contract is agreed in writing for large jobs.

A record of sales and purchases supports tax and credit decisions.

A stock level is controlled with a reorder point.

A business plan sets out the market, resources, costs and finance.

A fraction is converted to a decimal by dividing the numerator by the denominator.

A percentage is converted to a decimal by dividing by 100.

A proportion is solved by cross-multiplication.

An equation is solved by doing the same operation to both sides.

An angle is measured in degrees; a right angle is 90°.

A force is a push or a pull measured in newtons.

A citizen has rights and duties under the law.

A report is written clearly with a conclusion.