Exponents, Surds, Polynomials, Mensuration, Science, and Reasoning Notes

A comprehensive collection of vocabulary flashcards covering mathematics (exponents, surds, polynomials, mensuration), physics (light and electricity), chemistry (matter and atoms), biology (human health and diseases), and reasoning.

Base

The non-zero rational number $a$ in the expression $a^n$ which is multiplied by itself $n$ times.

Exponent

The natural number $n$ in the expression $a^n$ that indicates how many times the base is used as a factor.

Exponential form

The notation $a^n$ used to represent the product of a non-zero rational number multiplied by itself $n$ times.

Surd

A number form that does not have a proper root as an answer, such as $\sqrt{2}$ or $\sqrt{20}$.

Rationalising Factor (RF)

A term used to multiply a surd to change it into a rational number, such as $\sqrt[4]{6}$ being the RF for $\sqrt[4]{216}$.

Identity

In algebra, an equality that remains true for all possible values of the variables involved.

Division Algorithm for Polynomials

The theorem stating that for polynomials $p(x)$ and $g(x)$, there exist $q(x)$ and $r(x)$ such that $p(x) = g(x) \times q(x) + r(x)$, where $r(x) = 0$ or the degree of $r(x)$ is less than the degree of $g(x)$. child.

Zero (or Root) of a Polynomial

A real number $\alpha$ such that when replaced into the polynomial $f(x)$, the result is $f(\alpha) = 0$.

Remainder Theorem

If a polynomial $p(x)$ of degree $\geq 1$ is divided by $(x - a)$, then the remainder is equal to $p(a)$.

Factor Theorem

A theorem stating that if $p(a) = 0$, then $(x - a)$ is a factor of the polynomial $p(x)$.

Plane Figures

Geometrical figures that have only two dimensions, such as triangles, quadrilaterals, rectangles, squares, and circles.

Trapezium

A quadrilateral that has at least one pair of parallel sides (bases).

Rhombus

A quadrilateral where all four sides have equal length and the area is calculated as $\frac{1}{2} \times d_1 \times d_2$.

Cuboid

A solid bounded by six rectangular plane regions with dimensions length ($\ell$), breadth ($b$), and height ($h$).

Right Circular Cylinder

A solid generated by the revolution of a rectangle about one of its sides.

Light

A form of electromagnetic energy that causes the sensation of vision.

Luminous sources

Objects that emit light by themselves, including natural sources like the Sun and stars and artificial sources like electric lamps.

Non-luminous sources

Objects that do not emit light themselves but become visible when light from luminous objects falls on them, such as the moon or a table.

Transparent object

Bodies that allow light to pass through them completely, such as glass, water, and air.

Translucent object

Bodies that transmit only a part of the light that falls on them, such as frosted glass or paraffin wax.

Opaque object

Bodies that do not allow any light to pass through them, leading to the formation of shadows.

Rectilinear propagation of light

The principle that light travels in straight lines at a velocity of $3 \times 10^8\,m/s$ in a vacuum or air.

Shadow

The area formed on the opposite side of a light source when an opaque object obstructs the path of light.

Reflection of light

The phenomenon where a beam of light falls on a surface and a part of it is sent back into the same medium.

Angle of incidence

The angle made by the incident ray with the normal at the point of incidence, denoted as $\angle i$.

Law of Reflection

The principle stating that the angle of incidence is equal to the angle of reflection ($\angle i = \angle r$).

Conductors

Substances through which electric charges can flow easily, such as Silver, Copper, and Aluminium.

Insulators

Materials through which there is no flow of electric current, such as Plastic, Rubber, and Wood.

Electrical cell

A device that converts chemical energy into electrical energy.

Electric circuit

The path of flow of electricity from one terminal of a cell back to the other terminal.

Matter

Anything that occupies space, has mass, and can be perceived by the senses.

Homogeneous mixture

A mixture that has a uniform composition throughout, such as salt dissolved in water.

Heterogeneous mixture

A mixture that does not have a uniform composition throughout, such as sand mixed in water.

Sublimation

The process where a substance changes directly from a solid state to a gaseous state upon heating, without becoming a liquid.

Loading

A method using a substance like alum $(KAl(SO_4)_2 \cdot 12H_2O)$ to speed up the sedimentation of fine particles in liquid.

Distillation

The process of separating components from a liquid mixture using selective boiling and condensation to recover pure solvent.

Atom

The smallest particle of an element that can take part in a chemical reaction, consisting of a nucleus and extra nuclear region.

Dalton’s Atomic Theory (1808)

The theory stating that matter consists of small indivisible particles called atoms that are unique to each element.

Atomic radius

Measured in nanometers ($nm$), it is half the distance between adjacent atoms of the same element in a molecule.

Symbol

A brief representation of the name of an element introduced by Berzelius, often using Latin, English, or scientist names.

Metalloids

Elements that show properties of both metals and non-metals, such as Silicon.

Health

Defined by the WHO in $1948$ as a state of complete physical, mental, and social well-being, and not merely the absence of disease.

Disease

A malfunctioning of the body or a part of it that interferes with normal structure or function, resulting in discomfort or 'dis-ease'.

Symptom

A change in body function felt by a patient but not observable by a doctor, such as a headache.

Sign

An observable characteristic of a disease that helps a doctor identify the condition, such as a rash or swelling.

Incubation period

The time duration between the entry of germs into the body and the appearance of the first symptom of a disease.

Pathogens

Disease-causing organisms including bacteria, viruses, fungi, protozoans, and worms.

Acute disease

A disease that occurs suddenly and lasts for a short time, such as the common cold or malaria.

Chronic disease

A disease that lasts for a long time and generally cannot be fully cured, such as tuberculosis or asthma.

Antibiotic

An organic compound, such as Penicillin discovered by Alexander Fleming, produced by a microorganism that kills or inhibits the growth of bacteria.

Immunization

The process of stimulating the body to produce antibodies by artificial means, such as vaccines, to prevent specific diseases.

Vaccine

A preparation of weakened or dead infectious agents injected or given orally to prevent subsequent infection, first developed for smallpox by Edward Jenner.