Essential Mathematics, Grade 12 (40S)

Strategies include guess-and-check, looking for a pattern, working backward, and eliminating possibilities.

A good reasoning strategy often transfers from one game to a similar one.

A strategy is only reliable once it is verified, not just tried once.

Verifying the strategy in the new context confirms it really transfers.

Buying builds ownership; leasing pays for use over a term.

Leasing to buy applies lease payments toward eventual purchase.

Operating costs include fuel, maintenance, repairs, and depreciation.

Insurance cost depends on how and by whom the vehicle is used.

The best choice depends on budget, how far you drive, and how long you keep it.

The mean is the balance point; the median is the middle; the mode is the most common value.

A percentile rank tells the percent of scores at or below a value.

An outlier pulls the mean the most and the median the least.

A percentile rank is not the same as a percent score.

A weighted mean gives some values more importance, like exams counting more than quizzes.

Precision is how finely an instrument measures; accuracy is how close it is to the true value.

A measurement can be precise but not accurate, or accurate but not precise.

Every measurement carries uncertainty; the finer the instrument, the smaller it is.

A tolerance sets the acceptable maximum and minimum for a measurement.

Career choice weighs job description, education, aptitude, values, and pay.

A resume presents your qualifications for a specific career.

The preparatory period has its own costs before earning begins.

A career's salary sets the lifestyle its budget can support.

A mortgage is a long-term loan repaid with interest over many years.

Buying a home has one-time costs beyond the price: closing costs, land transfer tax, and legal fees.

Home insurance protects against loss; its cost depends on coverage and the home.

Owning builds equity but carries maintenance; renting is simpler but builds none.

Property tax is charged yearly based on the assessed value of the home.

The sine law relates sides to the sines of opposite angles.

Isosceles and equilateral triangles have equal sides and angles.

The cosine law finds a side or angle when the sine law does not apply.

Quadrilaterals differ by their angles, side lengths, and diagonals.

A regular polygon has all sides and all angles equal.

Expenses include supplies, rent, wages, and equipment.

Business owners keep receipts to support their income tax claims.

A feasible business fits the community's demand and the owner's resources.

Some expenses are deductible for a business but not for an individual.

The break-even point is where total sales equal total costs.

A probability from data is the fraction of outcomes that are favourable.

Odds compare favourable to unfavourable outcomes.

Expected value weighs each outcome by its probability.

Insurance and warranties price risk using probability.