MCAS Grade 10 Math key terms

A number that can be written as a fraction a/b, where a and b are integers and b is not zero. Its decimal form terminates or repeats a fixed block of digits.

A real number that cannot be written as a fraction of two integers. Its decimal expansion never ends and never settles into a repeating pattern, as with the square root of 2 or pi.

Rules for combining powers with the same base: add exponents when multiplying, subtract when dividing, and multiply when raising a power to a power. A negative exponent means take the reciprocal.

A compact way to write very large or very small numbers as a product of a number from 1 up to 10 and a power of ten, for example 4.7 times 10 to the sixth power.

An exponent written as a fraction. The denominator names a root and the numerator names a power, so 27 raised to the two-thirds power means cube-root 27 first, then square the result.

An expression containing a root symbol, such as the square root of 50. Simplifying usually means pulling out perfect-power factors so the expression is rewritten with the smallest possible number under the root.

An expression built from constants and whole-number powers of a variable, combined by addition, subtraction, and multiplication, with no variable in a denominator or under a radical.

Rewriting a sum or difference as a product of simpler expressions. Common strategies are removing a greatest common factor and splitting a trinomial into two binomial factors.

If the product of two or more factors equals zero, then at least one of those factors must equal zero. It is why setting each factor of a factored equation to zero finds every solution.

An equation that can be rearranged into the form a x squared plus b x plus c equals zero, with a not equal to zero. Its real solutions are the x-intercepts of the related parabola.

A formula giving the solutions of any quadratic equation in standard form: x equals negative b plus or minus the square root of b squared minus four a c, all divided by two a.

The value b squared minus four a c taken from a quadratic equation. It is the number under the square root in the quadratic formula, and its sign shows whether there are two, one, or no real solutions.

A rewriting method that turns a quadratic expression into a perfect square plus a constant, which produces vertex form and can solve equations that do not factor neatly.

Two or more equations that must all be true for the same values of the variables. Solutions can be found by graphing, substitution, or elimination, and may be none, one, or many.

A rule that assigns to each allowed input exactly one output. On a graph, a relation is a function only if no vertical line crosses it more than once.

The complete set of input values for which a function is defined. In a real-world model the domain is often limited by what makes sense, such as time being nonnegative.

The set of all output values a function actually produces as its input runs through the domain. On a graph, it is the collection of y-values the curve covers.

How much a quantity changes per one unit of change in another quantity, computed as change in output divided by change in input. For a linear function it is constant and equals the slope.

A function whose graph is a straight line, writable in the form f of x equals m x plus b. Its output changes by the same amount for every one-unit increase in input.

A function of the form f of x equals a times b to the x power, where the base b is positive and not equal to 1. Each one-unit increase in x multiplies the output by b.

Change by a constant percent or factor each period, modeled with a growth factor of 1 plus r or a decay factor of 1 minus r. Doubling and halving situations follow this pattern.

A function that can be written as f of x equals a x squared plus b x plus c with a not equal to zero. Its graph is a parabola that opens upward when a is positive.

The turning point of a parabola, either its minimum or its maximum. For a quadratic written in standard form, the x-coordinate of the vertex equals negative b divided by two a.

A transformation that keeps every distance and angle measure the same: a translation, rotation, or reflection. Applying rigid motions to a figure produces a congruent figure.

Two figures are congruent when a sequence of rigid motions carries one exactly onto the other, so all corresponding sides and angles are equal in measure.

Two figures are similar when a sequence of rigid motions and dilations maps one onto the other. Corresponding angles match and all side lengths share a single scale factor.

A transformation that enlarges or shrinks a figure by a scale factor from a fixed center point. Angle measures stay the same and every side length is multiplied by that factor.

In any right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: a squared plus b squared equals c squared, where c is the hypotenuse.

A ratio comparing two sides of a right triangle. Sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, and tangent is opposite over adjacent.

An angle whose vertex sits on a circle and whose sides are chords. Its measure is exactly half the measure of the central angle that cuts off the same arc.

The distance between two points equals the square root of the sum of the squared horizontal and vertical differences between them, a direct use of the Pythagorean theorem on the coordinate plane.

The sum of all data values divided by how many values there are. It uses every value, so outliers can pull it noticeably away from the center of the data.

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

A measure of how far data values typically sit from their mean. A larger value means a wider spread; in a normal distribution about 68% of values lie within one standard deviation.

The spread of the middle half of a data set, found by subtracting the first quartile from the third quartile. Extreme values do not affect it.

A straight line used to model the trend in a scatter plot, positioned to keep the residuals small. It supports predictions and shows whether the association rises or falls.

A number from negative one to one that measures how closely data follow a straight line and whether the pattern rises or falls. A value near zero means little linear association.

A table that counts individuals according to two categorical variables, with joint counts in the body and totals in the margins. It can be used to estimate conditional probabilities.

The probability that one event happens given that another event is known to have happened. It is computed by dividing the joint count by the total for the known condition.

A plus-or-minus amount attached to a sample estimate that describes how far the estimate could plausibly differ from the true population value. Larger random samples usually shrink it.