NBT key terms

A conclusion drawn from evidence and reasoning rather than stated outright. Readers combine clues in a text or data set with background knowledge to work out what is implied.

The central point a passage is built around, usually broad enough to cover all its supporting details. Separating it from examples and minor points is a common comprehension task.

A set of statements in which some, the reasons, are offered as support for another, the claim. The key question is always whether that support is adequate.

A statement offered as a reason in support of an argument's main claim. Premises may be stated openly or left unstated, and their truth affects how strong the argument is.

The claim an argument is trying to establish, meaning what the reasons are meant to support. It is not simply the final sentence of a passage.

An unstated belief an argument needs in order to work. If the assumption is false, the reasons no longer support the claim, so identifying it exposes weak reasoning.

A slanted treatment of a topic caused by the writer's interests, beliefs or word choices. It often shows through selective facts, loaded language or omitted viewpoints rather than outright falsehood.

The attitude a writer conveys towards the subject or the reader, such as critical, amused or urgent. It is inferred from word choice, sentence style and emphasis rather than stated directly.

Restating a passage's meaning in your own words while keeping the same level of detail. It differs from a summary, which shortens, and from a quotation, which copies.

A shortened restatement that keeps only the main points and essential support of a passage, expressed in your own words. A good summary adds no new information and no personal opinion.

A word or phrase, such as however or therefore, that signals how sentences and paragraphs connect. These links carry logical meaning, so misreading them distorts the argument.

The level of formality in language suited to a particular audience and situation, ranging from casual to academic. Shifts in register often signal changes in purpose or audience.

Expression that means something beyond its literal wording, such as metaphor, simile or hyperbole. Recognising it stops a reader from mistaking a comparison for a factual claim.

A statistical relationship in which two variables tend to move together. Correlation on its own does not show that one variable causes the other, since a third factor may drive both.

The subset of people or items actually measured in a study, drawn from the larger population of interest. Conclusions are only as trustworthy as the sample is representative.

The arithmetic average, found by adding all the values and dividing by how many there are. It is pulled strongly by extreme values, unlike the median.

The middle value when data are arranged in order, or the average of the two middle values when the count is even. It is far less distorted by outliers than the mean.

The size of an increase or decrease expressed as a fraction of the original value, multiplied by one hundred. Confusing it with percentage points is a very common error.

A comparison of two quantities by division, showing how many times one contains the other. Ratios can be scaled up or down without altering the relationship between the quantities.

A ratio that compares quantities measured in different units, such as kilometres per hour or rand per kilogram. Rates underpin many data-interpretation and calculation questions.

An equation stating that two ratios are equal, used to solve scaling problems. The word is also used more loosely to mean a share of a whole.

The general direction in which data move over time or across categories, ignoring short-term fluctuations. Describing a trend requires the overall pattern, not a single data point.

The relationship between distances on a graph, map or diagram and the real quantities they stand for. Misreading the scale, or a broken axis, leads to false conclusions.

Changing a measurement from one unit to another by multiplying by a conversion factor, for example metres to kilometres. Units must match before quantities can be compared or calculated.

A rule that assigns exactly one output value to each permitted input value. The phrase exactly one matters: a rule giving two outputs for one input is not a function.

The domain is the set of all input values a function accepts; the range is the set of all outputs it actually produces. Restrictions arise from division by zero and square roots of negatives.

The steepness of a line, calculated as the change in the vertical value divided by the change in the horizontal value between two points. Parallel lines share a gradient.

An equation in which the highest power of the variable is two, usually written as ax squared plus bx plus c equals zero, with a not zero. It has at most two real solutions.

The expression b squared minus 4ac taken from a quadratic equation. Its sign shows whether the equation has two, one or no real solutions.

Rules for combining powers, such as adding exponents when multiplying like bases and subtracting them when dividing. They extend naturally to zero and negative exponents.

An irrational root, such as the square root of two, that cannot be written as an exact fraction or terminating decimal. Surds are simplified by removing perfect-square factors.

A statement comparing two expressions with symbols such as less than, less than or equal to, or greater than. Multiplying or dividing by a negative number reverses the sign's direction.

Two or more equations that must be satisfied by the same set of variable values at the same time. Solutions are found by substitution or elimination and can be checked in every equation.

A list of numbers in which each term after the first is found by adding a fixed constant, called the common difference. The nth term equals a plus (n minus one) times d.

The sum of a sequence in which each term is a constant multiple, the common ratio, of the term before it. Such a series has a finite sum only when that ratio lies between minus one and one.

Interest calculated on both the original amount and the interest already accumulated, so the balance grows by a constant factor each period. It outgrows simple interest over time.

A ratio linking the sides of a right-angled triangle to one of its acute angles, namely sine, cosine or tangent. These ratios extend to any angle through the unit circle.

A number between zero and one expressing how likely an event is, found as favourable outcomes divided by total equally likely outcomes. For independent events the probabilities are multiplied.

A line that a curve approaches ever more closely as it extends, without normally reaching it. It marks a value that is excluded from the domain or range of the function.