NSE Math 10 key terms

Any number that can be written as a fraction of two integers, with a nonzero denominator. Its decimal form either ends or repeats a fixed block of digits forever.

A real number that cannot be written as a fraction of two integers. Its decimal expansion never ends and never settles into a repeating block, as with pi or the square root of two.

Any point on the number line, including every rational and irrational value. Real numbers can be compared, ordered, and combined with the usual arithmetic operations.

A whole number with no fractional part, such as negative four, zero, or seven. Integers are closed under addition, subtraction, and multiplication but not always under division.

The distance of a number from zero on the number line, always zero or positive. It removes any negative sign, so the absolute value of negative six is six.

A small raised number showing how many copies of a base are multiplied together. In three to the fourth power, four is the exponent and means multiply four threes.

A value that produces a given nonnegative number when multiplied by itself. The principal square root is the nonnegative one, written with the radical symbol.

A compact way to write very large or very small numbers as a number between one and ten multiplied by a power of ten. It makes the scale of a quantity easy to compare.

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

A mathematical phrase built from numbers, variables, and operations but containing no equality or inequality sign. It can be simplified or evaluated but not solved.

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

A letter or symbol standing in for an unknown or changing quantity. It lets a single rule describe many cases at once.

An equation in which every variable appears to the first power and no variables are multiplied together. Its graph is a straight line and it usually has exactly one solution.

Two or more equations that must all hold true at the same time. A solution is an ordered set of values satisfying every equation in the system simultaneously.

An equation whose highest power of the variable is two, usually written with a squared term. It may have two, one, or no real solutions.

Rewriting an expression as a product of simpler pieces. For quadratics, it often turns an equation into factors whose zeros are easy to read off.

If a product of factors equals zero, then at least one factor must equal zero. This rule converts a factored equation into simpler separate equations.

A statement comparing two expressions with less than, greater than, or their or-equal versions. Its solution is a range of values rather than a single number.

The complete collection of values that make an equation or inequality true. For an inequality it is often shown as an interval or shaded region on a number line.

A rule assigning exactly one output to each allowed input. The set of allowed inputs is the domain and the resulting outputs form the range.

The set of all input values for which a function is defined. Values causing division by zero or a negative under an even root are excluded.

The set of all output values a function actually produces. It depends on both the rule and the domain being used.

A measure of how steeply a line rises or falls, computed as vertical change divided by horizontal change between two points. Parallel lines share the same slope.

The point where a graph crosses the vertical axis, occurring where the input equals zero. In a linear model it often represents a starting value.

A function in which the variable sits in the exponent, producing repeated multiplication by a fixed factor. It grows or decays at a constant percentage rate.

How much an output changes for each unit change in the input, often an average over an interval. For a straight line it equals the slope everywhere.

A shift, stretch, compression, or reflection that moves or reshapes a graph. Each change to the rule produces a predictable change to the picture.

The highest or lowest point on a parabola, where the graph turns around. For a quadratic it marks the maximum or minimum output value.

The relationship between figures with identical size and shape, related by rigid motions alone. Corresponding sides and angles of congruent figures are equal.

The relationship between figures with the same shape but possibly different sizes. Corresponding angles are equal and corresponding side lengths share a constant ratio.

The constant multiplier relating corresponding lengths in similar figures. Its square gives the ratio of areas and its cube gives the ratio of volumes.

In a right triangle, the square of the hypotenuse equals the sum of the squares of the two legs. It links side lengths and underlies the distance formula.

A triangle containing one ninety-degree angle, whose longest side is opposite that angle. Its side lengths satisfy the Pythagorean relationship.

A ratio of two side lengths in a right triangle tied to one acute angle, such as sine, cosine, or tangent. It lets an unknown side or angle be found.

A rule giving the straight-line distance between two coordinate points, derived from the Pythagorean theorem. It squares coordinate differences, adds them, and takes the square root.

The arithmetic average of a data set, found by adding all values and dividing by how many there are. It is pulled toward unusually large or small values.

The middle value of a data set arranged in order, or the average of the two middle values when the count is even. It resists distortion by extreme values.

The spread of the middle half of a data set, equal to the third quartile minus the first quartile. It ignores the most extreme quarter at each end.

A typical distance of data values from their mean, computed from squared deviations. A larger value signals more spread around the average.

A symmetric bell-shaped curve describing many real measurements, centered at the mean. Roughly sixty-eight percent of values lie within one standard deviation of the mean.

A number from zero to one expressing how likely an event is. It can come from counting equally likely outcomes or from observed relative frequency.

The complete list or set of all possible outcomes of a random experiment. Every event is a subset of this collection.

The chance an event occurs given that another event is already known to have happened. It restricts attention to a smaller part of the sample space.

A connection in which one quantity is a constant multiple of another, graphed as a line through the origin. Doubling one quantity doubles the other.

A rate expressed per single unit of the second quantity, such as cost per item or distance per hour. It is found by dividing one quantity by the other.

A real-world situation represented by a straight-line relationship with a constant rate of change. It predicts outcomes by starting value plus rate times input.

A real-world situation represented by repeated multiplication by a constant factor, used for growth or decay. Percent change per period is the key feature.