Secondary 4 Mathematics-Cultural, Social and Technical Option Ministerial Examination - Québec flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Order of operations

Evaluate brackets first, then exponents, then multiplication and division left to right, then addition and subtraction left to right. A fraction bar groups its numerator and denominator.

Direct proportionality

Two quantities are directly proportional when their ratio is constant, so y = kx. The graph is a straight line through the origin, and doubling x doubles y.

Slope of a line

Slope m equals the change in y divided by the change in x between two points: m = (y2 − y1)/(x2 − x1). It measures steepness and direction.

Quadratic formula

For ax² + bx + c = 0 with a ≠ 0, the roots are x = (−b ± √(b² − 4ac))/(2a). The discriminant b² − 4ac tells how many real roots exist.

Function

A relation in which every value of the independent variable corresponds to exactly one value of the dependent variable. One x cannot produce two different y-values.

Area of a trapezoid

The area equals half the sum of the two parallel bases multiplied by the height: A = (b1 + b2)h/2, where h is the perpendicular distance between the bases.

Pythagorean relation

In a right triangle the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c². It applies only to right triangles.

Cosine law

In any triangle, a² = b² + c² − 2bc·cos A. Use it when you know two sides and the included angle, or all three sides.

Similar figures ratio

If two similar figures have a side ratio k, their areas are in ratio k² and their volumes in ratio k³. Corresponding angles remain equal.

Volume of a cone

The volume of a cone or pyramid equals one third of the base area multiplied by the height: V = (base area × height)/3. A cylinder uses the full product.

Sine law

In any triangle, the ratio of a side to the sine of its opposite angle is constant: a/sin A = b/sin B = c/sin C. Use it with a matched side-angle pair.

Median of a distribution

Arrange the data in increasing order. If the number of values is odd, the median is the middle value; if even, it is the mean of the two middle values.

Interquartile range

The interquartile range equals the third quartile minus the first quartile, IQR = Q3 − Q1. It measures the spread of the middle half of the data.

Weighted mean

The weighted mean equals the sum of each value multiplied by its weight, divided by the total of the weights. It is used when groups have different sizes.

Box-and-whisker plot

A diagram showing minimum, first quartile, median, third quartile and maximum. The box covers the middle half of the data and each whisker reaches an extreme value.

Random sample

A sample in which every member of the population has an equal chance of being selected. It reduces bias and supports generalization to the whole population.

Mean

The mean is the sum of all data values divided by the number of values. It is sensitive to extreme values, which can pull it away from the centre.

Complement rule

The probability that an event does not occur equals one minus the probability that it occurs: P(not A) = 1 − P(A).

Mutually exclusive events

Two events that cannot occur at the same time. Their combined probability is the sum of their individual probabilities, since the intersection is empty.

Odds in favour

The ratio of the probability that an event occurs to the probability that it does not: P(A) : P(not A). Odds a:b correspond to probability a/(a + b).

Expected value

The sum of each possible outcome multiplied by its probability. It represents the average result over many repetitions, not the result of a single trial.

Independent events

Events whose probabilities are unaffected by one another. The probability that both occur is the product of their individual probabilities.

Without replacement

A draw in which the selected item is not returned before the next draw. The total number of outcomes and the favourable count both decrease.

Modelling cycle

Understand the situation, identify variables, build a model, apply it, validate it against the context, then communicate the result and its limits.

Choosing a model from data

Constant differences between consecutive values suggest a linear model; constant ratios suggest exponential growth or decay; constant second differences suggest a quadratic model.

Validating a result

Check units, order of magnitude, sign and constraints, and test the model on data not used to build it. A result that violates the context is rejected.

Break-even point

The level of sales at which total revenue equals total cost, so profit is zero. Above it the enterprise earns a profit; below it, a loss.

Simple interest

Interest computed only on the original principal: I = P·i·t, where i is the annual rate as a decimal and t is the time in years.

Compound interest

Interest computed on principal plus accumulated interest: C = P(1 + i)^n, where i is the rate per period and n the number of periods.

Periodic interest rate

When a nominal annual rate is compounded m times per year, the periodic rate is the annual rate divided by m and the number of periods is years × m.

Unit price

The price of one unit of measure, found by dividing total price by quantity. Comparing unit prices identifies the better value among package sizes.

Successive discounts

Discounts applied one after another multiply rather than add. A 20% discount followed by 10% leaves 0.8 × 0.9 = 0.72 of the original price.