Punjab PSEB Matric Mathematics key terms

The counting numbers starting from 1, that is 1, 2, 3, and so on. They do not include zero, fractions, or negative values.

All the counting numbers together with zero, that is 0, 1, 2, 3, and so on. No fractions or negative values appear in this set.

The set made of all whole numbers and their negatives, such as -3, -2, -1, 0, 1, 2, 3. Fractions and decimals are excluded from this set.

Any number that can be written as a fraction p/q, where p and q are integers and q is not zero. Decimals that terminate or repeat are examples.

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

An irrational root of a rational number written with a radical sign, such as the square root of 5. It cannot be simplified to a rational value.

The process of rewriting a fraction so that no radical appears in the denominator. Multiply numerator and denominator by a suitable surd or conjugate.

Two expressions that differ only in the sign between two terms, such as a plus root b and a minus root b. Their product removes the surd.

For positive integers a and b, there exist unique whole numbers q and r such that a equals bq plus r, where r is smaller than b.

The highest common factor is the largest number that divides each of the given numbers exactly, leaving no remainder. It is also called the greatest common divisor.

The lowest common multiple is the smallest number that is a multiple of each of the given numbers. For two numbers, HCF times LCM equals their product.

Writing a number as a product of prime numbers only, for example 60 equals 2 times 2 times 3 times 5. Each composite number has a unique such form.

Every composite number can be expressed as a product of primes in exactly one way, apart from the order of the factors. This justifies prime factorisation methods.

An algebraic expression in which variables have only whole-number exponents and no variable sits in a denominator. Examples include 3x squared plus 2x minus 7.

The highest power of the variable that appears in a polynomial with a non-zero coefficient. It fixes the maximum number of zeros the polynomial can have.

A value of the variable at which the polynomial evaluates to zero. Geometrically it is where the graph meets the x-axis.

The rule giving roots of ax squared plus bx plus c equals zero as minus b plus or minus the square root of b squared minus 4ac, all divided by 2a.

The quantity b squared minus 4ac taken from a quadratic equation. Its sign tells whether the roots are real and distinct, real and equal, or not real.

The classification of a quadratic equation's solutions as real and distinct, real and equal, or imaginary, decided by whether the discriminant is positive, zero, or negative.

A sequence in which each term after the first is obtained by adding a fixed number, called the common difference, to the term before it.

The constant amount added to each term of an arithmetic progression to get the next term. It may be positive, negative, or zero.

The general term of an arithmetic progression, written a plus n minus 1 times d, where a is the first term and d the common difference.

The total of the first n terms of an arithmetic progression, given by n over 2 times the sum of the first and last terms.

Triangles whose corresponding angles are equal and whose corresponding sides are in the same ratio. They share shape but not necessarily size.

Also called Thales' theorem: a line drawn parallel to one side of a triangle divides the other two sides in the same ratio.

In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. Its converse also holds true.

Triangles that are identical in both shape and size, so all corresponding sides and angles match. Standard tests include SSS, SAS, ASA, and RHS.

A ratio of two sides of a right-angled triangle linked to one acute angle, named sine, cosine, tangent, cosecant, secant, or cotangent.

An equation involving trigonometric ratios that holds for every angle where the expressions are defined, such as sine squared plus cosine squared equals one.

The angle measured upward from the horizontal line of sight to an object above the observer. It is used in height and distance problems.

The angle measured downward from the horizontal line of sight to an object below the observer. It equals the angle of elevation from the object.

The set of all points in a plane at a fixed distance from a fixed point called the centre. The fixed distance is the radius.

A straight line that touches the circle at exactly one point, called the point of contact. It is perpendicular to the radius at that point.

A line segment joining two points on a circle. The longest chord passes through the centre and is called a diameter.

The region enclosed by two radii and the arc between them. Its area equals the angle at the centre divided by 360, multiplied by pi r squared.

The region between a chord and the arc it cuts off. Its area is found by subtracting the triangle's area from the sector's area.

The space inside a cone or pyramid with its top cut off parallel to the base. It is computed from the radii of both circular ends and the height.

The total exposed area obtained by adding the curved and flat surfaces of joined solids, carefully excluding faces hidden where the solids meet.

The average of data arranged in classes, calculated by multiplying each class mark by its frequency, adding these products, and dividing by total frequency.

The middle value of ordered data grouped into classes, found using the cumulative frequency and the formula based on the median class.

The value that occurs most often, estimated for grouped data from the modal class using the frequencies before and after that class.

A number between 0 and 1 measuring how likely an event is, calculated as the number of favourable outcomes divided by the total equally likely outcomes.

The complete list of all possible outcomes of a random experiment. For a single die throw it contains the numbers 1 through 6.

The event that a given event does not happen. Its probability equals 1 minus the probability of the event itself.