NVO Grade 10 Mathematics key terms

A letter or symbol that stands for an unknown or changing number in an expression or equation. Its value can differ from one situation to another.

The number multiplied by a variable in a term. In 7x the coefficient is 7; in -3xy it is -3.

A combination of numbers, variables, and operations without an equals sign. It can be simplified or evaluated but not solved.

A statement that two expressions have equal value, joined by an equals sign. Solving it means finding values of the variable that make the statement true.

An equation in which every variable appears to the first power only, so its graph is a straight line. Example: 4x - 9 = 15.

A measure of how steep a line is, calculated as the change in y divided by the change in x between two points. Also called rate of change.

The point where a graph crosses the vertical axis, occurring where x equals zero. In y = mx + b it is the value b.

A rule that assigns exactly one output value to each input value. Different inputs may share an output, but one input cannot give two outputs.

The complete set of input values for which a function is defined. For example, a function with a denominator cannot use inputs that make it zero.

The set of all output values a function actually produces from its domain. It is read from the vertical axis of a graph.

A function whose highest power of the variable is two, written generally as y = ax² + bx + c. Its graph is a parabola.

The U-shaped curve that is the graph of a quadratic function. It opens upward when the leading coefficient is positive and downward when negative.

The highest or lowest point of a parabola, where the curve changes direction. It marks the maximum or minimum value of the quadratic function.

The vertical line through a parabola's vertex that divides the curve into two mirror-image halves. Its equation is x = -b/(2a).

Two or more equations considered together, whose solution is the set of values satisfying all of them at once. Graphically it is where the lines intersect.

An algebraic method for solving systems by replacing one variable with an equivalent expression from another equation, producing a single equation in one variable.

A method for solving systems in which equations are added or subtracted, sometimes after multiplying, so that one variable cancels out.

A small raised number showing how many times a base is used as a factor. In 5³ the exponent 3 means 5 × 5 × 5.

In a power, the number or expression being repeatedly multiplied. In 2⁶ the base is 2 and it is used as a factor six times.

A number that, when multiplied by itself, gives the original number. The square root of 49 is 7 because 7 × 7 = 49.

Any number that can be written as a fraction of two integers with a nonzero denominator. Its decimal form terminates or repeats.

A real number that cannot be written as a fraction of two integers. Its decimal form never ends and never repeats, as with pi or the square root of 2.

A whole number that may be positive, negative, or zero, with no fractional or decimal part. Examples include -4, 0, and 12.

The distance of a number from zero on the number line, always nonnegative. The absolute value of both 6 and -6 is 6.

A way of writing very large or very small numbers as a number between 1 and 10 multiplied by a power of 10, such as 3.2 × 10⁵.

The relationship stating that in a right triangle the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c².

The longest side of a right triangle, located opposite the right angle. It is the side labeled c in the Pythagorean relationship.

A triangle containing exactly one angle of 90 degrees. Its sides satisfy the Pythagorean relationship and its acute angles are complementary.

Shapes with the same angles whose corresponding side lengths are proportional. Their sizes differ but their shape is identical.

Figures that have exactly the same size and shape, so corresponding sides and angles are equal. One can be moved onto the other without resizing.

The ratio comparing a length in an image to the matching length in the original figure. It describes how much a figure is enlarged or reduced.

A change in a figure's position, size, or orientation on a coordinate plane, such as a translation, reflection, rotation, or dilation.

The amount of three-dimensional space a solid occupies, measured in cubic units. Formulas differ by shape, for example a prism uses area of base times height.

The total area of all outer faces or curved surfaces of a three-dimensional solid, measured in square units.

A solid with two parallel circular bases joined by a curved surface. Its volume equals pi times the radius squared times the height.

The arithmetic average of a data set, found by adding all values and dividing by how many there are. It is affected strongly by extreme values.

The middle value of a data set arranged in order. With an even count, it is the mean of the two middle values.

A value that divides ordered data into four groups of roughly equal size. The first and third quartiles mark the edges of the interquartile range.

The difference between the third quartile and the first quartile of a data set. It measures the spread of the middle half of the data.

A measure of how far data values typically lie from the mean. A larger value indicates data spread more widely around the average.

A data value that is unusually far from the rest of the set. It can strongly affect the mean but has little effect on the median.

A number from 0 to 1 describing how likely an event is, often computed as favorable outcomes divided by total equally likely outcomes.

The set of all possible outcomes of a probability experiment. For one roll of a fair die it contains the six numbers 1 through 6.

Events whose outcomes do not influence each other. The probability of both occurring equals the product of their separate probabilities.

How much one quantity changes relative to another, often written as change in output divided by change in input. For a line it equals the slope.

A relationship in which two quantities have a constant ratio, so doubling one doubles the other. Its graph is a straight line through the origin.

A straight line on which every point corresponds to a real number, with zero at a chosen point and equal spacing for units.