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Exam packet

Formula sheet + GD&T card

Two pages to print, bind, and tab. Bind them — loose sheets are not open-book material.

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Formula and conversion sheet

ALGEBRA & PERCENT percent change = (new − old) / old × 100 x = (c − b) / a from ax + b = c
GEOMETRY circle: C = πd = 2πr A = πr² cylinder volume = πr²h right triangle: a² + b² = c² sin = opp/hyp cos = adj/hyp tan = opp/adj sine bar: h = L sin θ
CONVERSIONS 1 in = 25.4 mm exactly 1 in = 25 400 µm 1 µin = 0.0254 µm 1 mm = 0.03937 in 1 ft = 12 in °F = 1.8°C + 32 °C = (°F − 32) / 1.8
STATISTICS x = Σx / n R = xmax − xmin s² = Σ(x − x)² / (n − 1) s = √s² z = (x − μ) / σ empirical: ±1s ≈ 68% ±2s ≈ 95% ±3s ≈ 99.7%
CAPABILITY & 10:1 Cp = (USL − LSL) / 6σ Cpk = min((USL − x)/3σ, (x − LSL)/3σ) gage resolution ≲ tolerance span / 10 cal standard ≲ gage resolution / 10
GD&T Bonus @ MMC = |actual size − MMC size| Allowed position = FCF tolerance + bonus (+ datum shift if a datum is also MMC) Position Ø error = 2 × √(Δx² + Δy²) Axis 0.003 off in X and 0.004 off in Y → radial 0.005, diameter error 0.010
METROLOGY RULES 10:1 — inspection discrimination ≈ 1/10 of the tolerance calibration standard ≈ 1/10 of the inspection equipment Reference temperature 20 °C / 68 °F Steel expansion ≈ 6.5 µin/in/°F (11.7 µm/m/°C) GR&R guideline: <10% good · 10–30% maybe · >30% not acceptable 0.0001 in ≈ 2.54 µm
Field card

GD&T symbols and setup notes

Symbol / nameTypeWhat you are checkingTypical setup thought
StraightnessFormElement or axis not bowedNo datum required
FlatnessFormSurface in a tight slabNo datum; surface plate + indicator or CMM (coordinate measuring machine) plane
CircularityFormEach cross-section is a circleNo datum
CylindricityFormWhole cylinder in a tight shellNo datum; more than circularity
Profile of a line / surfaceProfileOutline vs. true profileOften to datums; comparator, CMM, vision
PerpendicularityOrientation90° to a datumDatum simulated first
AngularityOrientationGiven angle to a datumSine bar or CMM
ParallelismOrientationEqual distance to a datumIndicator sweep
PositionLocationAxis or centerplane vs. true positionFull DRF (datum reference frame); bonus possible at MMC (maximum material condition)/LMC (least material condition)
Concentricity / symmetryLocationMedian points (rarely the right call today)Hard to inspect; many shops use position instead
Circular runoutRunoutEach circular element as part rotates on datum axisIndicate while rotating on datum
Total runoutRunoutEntire surface as part rotatesSweep the whole face or cylinder

Material condition modifiers

M in a circle = MMC. L = LMC. No modifier = RFS (regardless of feature size). A circled P is projected tolerance zone (studs, pins that mate in a hole above the surface). A circled F is free-state (non-rigid parts).

Rule of thumb for inspectors

If the frame references A B C, build A, then B, then C. If a size feature has MMC on the tolerance, measure size first — you cannot know the allowed position without it. Record actual size and actual deviation, not just pass/fail, when the characteristic is variable.