TCC Technical Cadet Initial Test cheat sheet

Order of operations: brackets, then indices (powers and roots), then multiplication and division left to right, then addition and subtraction left to right.

Percentage change = ((new − old) ÷ old) × 100%; a reverse percentage recovers the original value as final ÷ (1 ± rate).

Pythagoras: c² = a² + b² in a right triangle; useful whole-number triples are 3-4-5, 5-12-13 and 8-15-17.

Areas: rectangle lw, triangle ½bh, circle πr², trapezium ½(a+b)h. Circumference of a circle = 2πr.

Volumes: rectangular prism lwh, cylinder πr²h, cone ⅓πr²h, sphere (4/3)πr³.

SI conversions: 1 km = 1000 m, 1 m = 1000 mm, 1 kg = 1000 g, 1 hour = 3600 s, 1 kW = 1000 W, 1 m³ = 1000 L.

Ratio sharing: add the ratio parts, divide the total by that sum, then multiply by each part.

Right-triangle trigonometry: sin = opposite ÷ hypotenuse, cos = adjacent ÷ hypotenuse, tan = opposite ÷ adjacent.

Rounding: inspect the first digit dropped; 5 or more rounds the last kept digit up, 4 or less leaves it unchanged.

Newton's second law: F = ma. Weight is W = mg, with g ≈ 9.8 m/s² at the Earth's surface.

Motion equations: v = u + at, s = ut + ½at², v² = u² + 2as; average speed = total distance ÷ total time.

Work done W = Fd only when the force acts along the displacement, measured in joules; power P = W ÷ t = Fv, measured in watts.

Energy: kinetic KE = ½mv², gravitational potential PE = mgh; total energy is conserved but some always degrades to heat.

Moments: M = F × perpendicular distance from the pivot; a body in equilibrium has equal clockwise and anticlockwise moments.

Pressure P = F ÷ A in pascals; hydrostatic pressure in a fluid column is p = ρgh.

Density ρ = m ÷ V; relative density compares a substance with water, which is 1000 kg/m³.

Efficiency = useful output energy ÷ total input energy × 100%; it can never exceed 100%.

Stress = force ÷ cross-sectional area, strain = change in length ÷ original length, and Young's modulus = stress ÷ strain.

Gear ratio = teeth on driven gear ÷ teeth on driving gear; output speed = input speed ÷ ratio, while torque increases by the same ratio.

Two meshed external gears always rotate in opposite directions; an idler gear reverses direction but does not change the overall ratio.

Mechanical advantage = load ÷ effort = effort arm ÷ load arm; velocity ratio = effort distance ÷ load distance.

First-class lever: fulcrum between effort and load (crowbar). Second-class: load in the middle (wheelbarrow). Third-class: effort in the middle (tweezers), mechanical advantage below 1.

Fixed pulley changes direction only, MA = 1; a single movable pulley has MA = 2; a block and tackle has MA equal to the number of rope sections supporting the load.

Inclined plane MA = length of slope ÷ height. Screw MA = circumference of the thread ÷ lead.

An open belt drive turns both pulleys the same way; a crossed belt reverses the driven pulley.

Right-hand threads tighten when turned clockwise; a left-hand thread is marked LH and tightens anticlockwise.

Rim speed of a rotating part = circumference × revolutions per second, so a larger diameter gives a higher surface speed at the same rpm.

Ohm's law: V = IR. Power relationships: P = VI = I²R = V²/R.

Series circuit: R total = R₁ + R₂ + …; the current is identical everywhere and the voltages add to the supply voltage.

Parallel circuit: 1/R total = 1/R₁ + 1/R₂ + …; the voltage is the same across each branch and the branch currents add.

Kirchhoff's laws: current into a node equals current out; the sum of voltage rises and drops around any closed loop is zero.

Capacitors: in parallel C total = C₁ + C₂, in series the reciprocals add; stored energy = ½CV².

AC values: RMS = peak ÷ √2; frequency f = 1 ÷ period T; Australian low-voltage mains is nominally 230 V RMS at 50 Hz.

Resistor colour digits: black 0, brown 1, red 2, orange 3, yellow 4, green 5, blue 6, violet 7, grey 8, white 9; gold = ±5%, silver = ±10%.

A silicon diode conducts with about 0.7 V forward drop and blocks in reverse; an LED emits light while conducting.

A voltmeter connects in parallel across a component, an ammeter in series with it; resistance and continuity are measured with the supply isolated.

A fact can be verified; an opinion expresses judgement. An inference is a conclusion drawn from stated evidence, not the evidence itself.

Cause-and-effect signposts: because, since, therefore, hence, consequently, as a result, so that.

Contrast signposts: however, although, whereas, despite, nevertheless, on the other hand.

Instructions use the imperative mood ('isolate the supply') with sequence markers such as first, next, then, finally.

Active voice: the subject performs the action. Passive voice: the subject receives it ('the pump was replaced').

Apostrophes mark possession (the operator's log, the workers' lockers) or contraction (it's = it is); 'its' is possessive and takes no apostrophe.

Subject-verb agreement: a singular subject takes a singular verb; collective nouns such as 'the team' take a singular verb in Australian usage.

SI symbols are case sensitive and never pluralised: A (ampere), K (kelvin), mm, kW - lower-case k means kilo, upper-case K means kelvin.

Commonly confused pairs: affect (verb) / effect (noun); their / there / they're; principal / principle.

PPE: safety glasses for all drilling, grinding and cutting; hearing protection where noise exceeds about 85 dB(A); gloves removed near rotating spindles.

Fire classes: A solids (water), B flammable liquids (foam, CO₂, dry powder), C gases, D metals, E electrical (CO₂ or dry powder, never water), F cooking oils.

Files cut on the forward stroke only; fit every file with a handle and never strike a file with a hammer.

Hacksaw: 14-18 teeth per inch for thick sections and soft metals, 24 or more for thin tube and hard material; blade teeth point forward.

HSS drill bits: use lower spindle speed and more cutting fluid for harder materials; clamp the workpiece and remove the chuck key before starting.

Mild steel is ductile and weldable but not hardenable; high-carbon steel can be hardened and tempered; cast iron is brittle but rigid.

Measuring tools: steel rule 0.5 mm, metric vernier calliper typically 0.02 mm, metric micrometer 0.01 mm; read the main scale before the vernier or thimble.

Spanners must match the nut size; never extend a spanner with a pipe, and pull rather than push where access allows.

Before maintenance, isolate and lock out every energy source and attach a tag; tag out and report damaged tools instead of using them.

Number series: test the differences first, then the ratios, then look for two interleaved sequences.

If all A are B and all B are C, then all A are C; if no A are B and all C are A, then no C are B.

A statement 'if A then B' is equivalent to its contrapositive 'if not B then not A'; its converse 'if B then A' is not equivalent.

Combined work rate = 1/a + 1/b, giving time = ab ÷ (a + b) when two workers finish the job alone in a and b hours.

Two overlapping sets: the number in either group = count A + count B − count in both; those in neither are added separately.

Speed, distance and time: distance = speed × time; time = distance ÷ speed; speed = distance ÷ time.

Ratios are solved by cross-multiplication: a/b = c/d gives ad = bc.

Fault finding: splitting the circuit or system in half repeatedly isolates the faulty section in the fewest tests.

Correlation does not establish causation; a valid deduction must follow necessarily from the premises given.

First-angle projection places each view on the far side of the object, so the top view sits below the front view; third-angle places it on the viewer's side, top view above.

Line types: continuous thick = visible outline; short dashes = hidden detail; long-dash-dot chain = centre line; thin continuous = dimension and leader lines.

Scale 1:50 means one drawing unit represents 50 real units; 1:2 is half size and 2:1 is double size.

Dimension lines run parallel to the measured edge with arrowheads at both ends and the value above the line; no dimension is repeated.

A full section shows the cut face hatched with thin lines at 45°; the cutting-plane line carries arrows showing the viewing direction.

Isometric axes are 120° apart, drawn with the vertical axis upright and the other two at 30° to the horizontal, all to the same scale.

Orthographic layout uses front, top and side views aligned so that features project across consistently.

Circuit symbols: resistor as a rectangle (or zigzag), capacitor as two parallel lines, diode as a triangle against a bar, earth as three shortening horizontal lines.

The title block carries the drawing number, title, scale, projection symbol, material and revision; tolerances state the permitted size variation.