UAE TLS Mathematics Test key terms

A number that can be written as a fraction with an integer numerator and a nonzero integer denominator; its decimal form either terminates or repeats.

A real number that cannot be expressed as a ratio of two integers; its decimal expansion never terminates and never repeats, as with the square root of two or pi.

The largest positive integer that divides two or more given integers without leaving a remainder; for example, the greatest common divisor of twelve and eighteen is six.

The agreed sequence for evaluating expressions: work through grouping symbols first, then exponents, then multiplication and division left to right, then addition and subtraction left to right.

The difference between a new value and an original value, divided by the original value and usually expressed as a percent; it quantifies increase or decrease relative to the starting amount.

A rule that assigns to each input value exactly one output value; the set of allowed inputs is the domain and the resulting outputs form the range.

A measure of how steep a line is, computed as the change in the vertical coordinate divided by the corresponding change in the horizontal coordinate between any two points on the line.

The domain of a function is the complete set of input values for which it is defined; the range is the complete set of output values it actually produces.

A function that reverses another function, so that if the first sends a to b, the inverse sends b back to a; it exists only when each output comes from exactly one input.

A function whose rule can be written with a squared term as its highest power, and whose graph is a parabola opening upward or downward from its vertex.

A pattern in which a quantity increases by a fixed multiplicative factor over each equal time interval, producing a curve that rises increasingly steeply as the exponent grows.

The exponent to which a fixed base must be raised to produce a given number; for instance, the logarithm base ten of one thousand is three.

In a right triangle, the square of the hypotenuse equals the sum of the squares of the two legs; this relationship lets you find an unknown side length.

Shapes with the same form but possibly different size, having corresponding angles equal and corresponding side lengths in a constant ratio; scale factors link their measurements.

A relationship between two figures that have exactly the same shape and size, so that one can be moved onto the other by translations, rotations, and reflections alone.

The total area of all faces or curved surfaces of a three-dimensional solid, measured in square units, such as the combined area of a cylinder's two bases and its lateral surface.

The amount of three-dimensional space enclosed by a solid, measured in cubic units and computed by formulas that differ by shape, such as length times width times height for a box.

A unit of angle measure defined by arc length on a circle: one radian is subtended by an arc equal in length to the radius, and a full turn is two pi radians.

A circle of radius one centered at the origin of a coordinate plane; the coordinates of a point on it give the cosine and sine of the angle from the positive x-axis.

A relationship stating that in any triangle each side divided by the sine of its opposite angle is constant; it is useful for solving triangles when two angles and a side are known.

Half the difference between the highest and lowest values reached by a periodic wave, indicating how far it swings from its middle level; for sine waves it equals the leading coefficient.

The middle value of a data set ordered from smallest to largest; when the number of values is even, it is the mean of the two middle values.

A measure of how spread out values are around their mean, equal to the square root of the average squared deviation from the mean.

The probability that an event occurs given that another event is known to have occurred, computed as the probability of both events divided by the probability of the known event.

A symmetric bell-shaped probability distribution described by its mean and standard deviation, in which most values cluster near the center and become rarer toward the extremes in a predictable pattern.

The difference between the third quartile and the first quartile of a data set, describing the spread of the middle half of the values and resisting distortion by outliers.

The value a function's output approaches as its input approaches a specified number or grows without bound; the function need not actually reach that value.

The instantaneous rate of change of a function with respect to its input, defined as the limit of average rates over shrinking intervals and interpreted geometrically as the slope of the tangent line.

The signed area between a curve and the horizontal axis over a stated interval, defined as a limit of sums of many thin rectangles and evaluated using antiderivatives.

A line that a curve approaches ever more closely as it extends outward or nears a restricted point, without necessarily ever touching it.

A single example that proves a general statement false, such as the value two disproving the claim that every prime number is odd.

Reasoning that moves from accepted premises to a guaranteed conclusion by applying logical rules, so that true premises always yield a true conclusion when the argument is valid.

Reasoning that generalizes from observed examples to a broader rule, which is probable rather than certain and can be overturned by a single contradictory case.

A technique that establishes a statement by assuming its opposite, deriving a logical impossibility from that assumption, and concluding that the original statement must therefore be true.

Ongoing checks of student understanding used during instruction to adjust teaching and give feedback, rather than to assign a grade at the end of a unit.

A stable but incorrect idea that students bring to a topic, often built from overgeneralizing a rule that worked in a narrower setting, which persists unless directly addressed.

Temporary support a teacher provides, such as worked steps, prompts, or models, that lets a learner complete a task beyond current reach and is gradually withdrawn as competence grows.

Presenting the same mathematical idea in several forms, including numeric tables, graphs, symbols, and verbal descriptions, so students connect meanings rather than memorize isolated procedures.