Grade 9 Mathematics - Common Quarterly Examination 2025

Vocabulary flashcards covering core concepts from the Class 9 Mathematics Common Quarterly Examination, including Set Theory, Real Numbers, Polynomials, and Geometry.

Non-Empty Subsets of a Set

The total number of non-empty subsets of a set with $n$ elements is given by $2^n - 1$. For set $A = \{x, y, z\}$, the number of non-empty subsets is $2^3 - 1 = 7$.

Intersection of Disjoint Sets

If $B - A = B$, the sets $A$ and $B$ have no common elements, which means their intersection $A \cap B = \phi$ (the empty set).

Irrational Number

A real number that cannot be expressed as a ratio of two integers $\frac{p}{q}$ where $q \neq 0$. An example is $\pi$.

Exterior Angle Theorem

A geometric rule stating that the exterior angle of a triangle is equal to the sum of its two interior opposite angles.

Roster Form

A representation of a set where all elements are explicitly listed inside curly braces and separated by commas, with repeated elements written only once.

Power Set

The collection or set of all subsets of a given set $A$, denoted as $P(A)$. The number of elements in $P(A)$ is $2^n$, where $n$ is the number of elements in $A$.

Symmetric Difference of Two Sets

The set of elements that belong to either set $P$ or set $Q$, but not to both, defined as $P \Delta Q = (P - Q) \cup (Q - P)$.

Zeros of a Polynomial

The value(s) of $x$ for which a polynomial expression evaluates to $0$. For instance, the zero of $2x + 5$ is $x = -\frac{5}{2}$.

Remainder Theorem

A theorem stating that if a polynomial $P(x)$ is divided by a linear factor $(x - a)$, the remainder of the division is $P(a)$.

Synthetic Division

A shortcut method for dividing a polynomial by a linear factor of the form $(x - a)$ using only the numerical coefficients of the terms.

Scientific Notation

A standardized way of writing numbers as the product of a number $a$ (where $1 \le |a| < 10$) and a power of $10$, expressed in the form $a \times 10^n$.

Centroid of a Triangle

The point of concurrence where the three medians of a triangle intersect.

Orthocentre of a Triangle

The point of concurrence where the three altitudes of a triangle intersect.

Circumcentre of a Triangle

The point of concurrence of the perpendicular bisectors of the three sides of a triangle.

Incentre of a Triangle

The point of concurrence of the three internal angle bisectors of a triangle.