Workplace Mathematics 10

The data picks the graph: categories → bar, change over time → line, parts of a whole → circle, distribution of a numeric variable → histogram.

A histogram's bars touch because the data is continuous ranges; a bar graph's bars separate because categories are distinct.

Reading a graph starts at the axes: what is measured, in what units, at what scale — before any conclusion.

A truncated (non-zero) axis exaggerates differences — a 2% gap can look like double.

Uneven scale steps or missing labels stretch some changes and squash others.

SOH-CAH-TOA: label the sides FROM the angle you know or want — opposite and adjacent trade places with the angle.

Missing side: pick the ratio linking the known angle, the known side, and the wanted side. Missing angle: use the inverse (sin⁻¹, cos⁻¹, tan⁻¹).

Calculator in DEGREES — a radians-mode answer is garbage with no warning.

Draw first: put the right angle where the ground meets the vertical, mark what's measured and what's wanted.

Slope rules in the trades come as angles or ratios — a ramp's 1:12 maximum is an angle of about 4.8°.

Metric moves by tens: mm → cm → m → km is just shifting the decimal. Imperial doesn't: 12 inches to a foot, 3 feet to a yard, 5280 feet to a mile.

Volume = area of the base × height, for every prism and cylinder — one idea, many shapes.

Cross-system anchors: 1 inch = 2.54 cm exactly; 1 m ≈ 3.28 ft — set up the conversion as multiplication by a ratio that cancels units.

Surface area sums the faces: a cylinder is two circles plus a rolled-out rectangle (2πr² + 2πrh).

Pick the tool and unit that fit the job: millimetres for machining, centimetres for fabric, metres for rooms.

Mean shares the total equally; median is the middle of the sorted list; mode is the most frequent; range is spread, not centre.

Experimental probability = favourable outcomes ÷ total trials — a measured fraction, not a prediction.

Outliers drag the MEAN toward themselves but barely move the median — one huge salary shifts the average, not the middle.

More trials pull the experimental result toward the theoretical value; small samples swing wildly.

Choose by purpose: skewed data (salaries, house prices) reads truer through the median; the mode suits categories like shoe sizes.

Gross pay is the before-deductions total: rate × hours, salary ÷ pay periods, sales × rate, or pieces × price.

Overtime usually pays 1.5× after the threshold — split regular and overtime hours before multiplying.

Piecework and commission reward output, not time — great weeks and thin weeks both happen.

Net = gross − deductions: income tax, CPP, EI, plus any union dues or benefits.

Percentage deductions compute on GROSS — 5.95% CPP on an $880 gross is $52.36 regardless of other lines.