Linear Inequalities โ GCSE Maths
Introduction
- Inequalities are similar to equations. Equations do have specific values that satisfies the equation on the hand Inequalities have feasible region( set of the values satisfying the inequality ) .
- Example of Inequality-
- Using Inequalities, we can solve real-life problems where the maximum or minimum quantity of something is calculated under multiple constraints.
- They are basically used to represent those problems which are restricted by some constraint or conditions. That is why they are used in various fields like Business, Engineering and Economics etc.
Inequality is an expression in which variables and constants are present and one expression is lesser than the other.
- The Solution to these Inequalities exist in form of intervals (set of integers that lies between two numbers) –
Example: (-12,1] The number is greater than -12 and lesser than 1.ย 
Linear Inequalities
- The Inequalities in which the maximum power raised to a variable is one.
Example:
2x + 9 < 15
Steps to Solve Linear Inequality:ย
- Step#1: Find value of the variable using addition, Subtraction, Multiplication or division on both sides of inequality so that the variable will get isolated.
(Whenever we change sign on both the sides the symbol is reversed from greater than to lesser than and vice versa)
- Step#2: Express the solution in form of interval or using number line.
x = (-โ,3)
Solved Example
Solved ExampleProblem: Solve the following linear inequalities –
(1) 3y – 8 > 18ย ย ย ย ย ย (2) 5 + 6y < 17
Solution:
(1) 3y – 8 > 18ย ย
Step#1:ย
- Adding 8 on both sides-
- Dividing both sides by 3-
Step#2: Representing the solution in form of interval- y = (6, โ)
(2) 5 + 6y < 17
Step#1:ย
- Subtracting 5 on both sides-
- Dividing both sides by 6-
Step#2: Representing the solution in form of interval-ย y = (-โ, 2)ย 
Solved Example:
Problem:ย Write the Inequalities that these number lines represents:
Solution:ย
Answer : (-2,2), Inequality = -2 < x < 2
2.
Answer : (-4,1), Inequality = -4 โค x โค 1
3.
Answer : (6,โ), Inequality = x > 6
4.
Answer : (3,7), Inequality = 3 โค x < 7
5.
Answer : (6,10), Inequality = 6 โค x โค 7
ย
Solved Example:
Problem: Solve the Inequality and represent the answer in interval form as well as on the number line.
Step#1:
- Subtract 125 on both the sides-
- Divide by -5 on both the sides-
(The symbols were changed that is why Inequality symbol is reversed from โ>โ to โ<โ)
- Interval : (-โ,5)
- Number Line :
Solved Example:
Problem: Draw the number lines to show these Inequalities –
(1) x > 12
(2) 5 < x โค 7
(3) 3 < x < 5
(4) 10 โค x โค 13
(5) 15 โค x
Solution:
- x > 12
2.ย 5 < x โค 7
4.ย 10 โค x โค 13
5. 15 โค x
Table of Content
Quadratic Simultaneous Equations โ GCSE Maths
Introduction
- Two or more equations that share variables and have set of values for variables that satisfy both the equations are called Simultaneous Equations.
- If the maximum power raised to the variable in Simultaneous equations is one then these are called Linear Simultaneous Equations.
- Similarly If the power raised to the variables is two they are called Quadratic Simultaneous Equations.
Step by Step Solving Quadratic Simultaneous Equations
Example:ย 
Putting y = 2x -1 in 2nd equation –
For x = -3 from 1st Equation-
Solved Example:
Problem:ย 
Step#1: Substitute the value of one variable from linear equation(to eliminate one variable)-
From 1st Equation-
Put x = -2 in 1st Equation โ
Step#3:Final Answer-
Solved Example:
Problem:ย 
Step#1: Substitute the value of one variable from linear equation(to eliminate one variable)-
From 1st Equation,
Put in 2nd Equation,
Divide by 2 on both sides and doing factorisation-
Put y = 4 in 1st Equation โ
Solved Example:
Problem:ย 
Step#1: Substitute the value of one variable from linear equation(to eliminate one variable)-
From 1st Equation-
Step#2: Substitute the values obtained back into the original equation and find possible values of another variable-
Put x = -3 in 1st Equation โ
Solved Example:
Problem:ย 
Step#1: Substitute the value of one variable from linear equation(to eliminate one variable)-
From 1st Equation,
Put x = 1 in 2ndย Equation โ
Solved Example:
Problem:ย 
Step#1: Substitute the value of one variable from linear equation(to eliminate one variable)-
From 1st Equation,
Put x = 1 in 2ndย Equation โ
Box Plots โ GCSE Maths
Introduction
- Box plot is an important concept used in Statistics to represent quantities related to a given dataset graphically and helps us to provide conclusions about that dataset.
- Box plots include graphical representation of these five quantities – Median, Maximum Value, Smallest value, First quartile and the Third Quartile.
Box Plots
- Basically Box Plots are graphical representation of the following quantities which describe a datasetโs important features โ
- Example-
- Total values are 15 the increasing order of these will be –
- Median – When the elements of the dataset are sorted( in increasing or decreasing order) then the middle element is called the Median.
- Median will be the middle element that is 4, we can also use the following formula to find median –
- Greatest value – The maximum value among of datasetโs elements.
- In the given example the greatest value is 9.
- Smallest value – The smallest value among the elements.
- In the given example the smallest value is 0.
- Quartile(1st Quartile) – Basically it is first 25% part of the data. The formula to find 1st quartile is –ย
- Quartile(3rd Quartile) – Basically it is first 75% part of the data. The formula to find 3rd quartile is –
In the given example-ย 
Examples including even and odd number of elements:
Problem: Draw the box plot for the following dataset –
Examples including even and odd number of elements:
Problem: Following is a dataset given that is the time taken by 11 students to complete an essay –
(b) Find out the upper and lower Quartiles
(c) Draw the box plot for the dataset
Solution:
(a) Median for the dataset is-ย 
Examples including even and odd number of elements:
Problem: Here is the data collected from a company of the experience of their 10 employees –
To draw the box plot for the given dataset containing an even number of elements first we find Median, Quartiles and Minimum and Maximum value –
- Final Answer-ย
Table of Content
Interior and Exterior Angles in Polygons - GCSE Maths
Introduction
- The Word Polygon is made up of two words –
- A closed shape made of line segments .
- To make a Polygon, minimum three line segments are required which end up making a Triangle.
- Basic Polygons are Triangle, Square and Rectangle.
- Polygons have vertices, angles and sides.
- An Angle is basically the distance between two rays starting at the same point.
- Polygons have two types of angles, they are – Interior and Exterior angles.
- Polygons are 2-Dimensional shapes and we can use them to make 3-Dimensional objects.
Importance of polygons:
- Polygons play a vital role in understanding geometric concepts like shapes, angles, area and perimeter.
- Polygons are present in our daily life, in buildings, houses, and the design of objects.
- Students learn about angle and length measurements, which are used to solve real-world problems and make maths meaningful.
Types of Polygons
Polygons are classifies into two types –
- Regular Polygons
- Irregular Polygons
Regular Polygons:
- Polygons with equal sides and equal angles.
Irregular Polygons:
- Polygons with unequal sides and unequal angles.
ย
Some Important polygons are as follows-
Interior Angles in Polygons
- The Angles present inside the polygon are known as Interior Angles.
- The polygon with the minimum number of sides is a Triangle and the sum of the interior angles of a Triangle is 180 degree.
- Consider other Polygons divided into triangles –
- We can conclude that every polygon can be divided into triangles, with the number of triangles formed being two fewer than the number of sides of the polygon.
- Since each triangle has interior angles that add up to 180ยฐ, the sum of the interior angles of a polygon is given by: –
Where n = Number of sides of the Polygon
Example: The Pentagon has 5 sides so –
- If we want to find the interior angle of a regular polygon, the formula is-
ย
Solved Example:
Problem: Find the missing interior angles in the following Polygon.
The Polygon shown in the diagram is a Hexagon.ย
In which –ย 
Solved Example:
Problem: Work out the size of the angle for the following value of n (Number of sides of Regular Polygon).
Solution:ย
Using formula-ย 
Put (n = 5)
A Polygon with 5 sides is called a Pentagon.
Divide the sum of angles by number of sides :
Exterior Angles in Polygons
- When we extend any side of a Polygon, then the resulting angle made is called an Exterior Angle.
- When the exterior angles are combined together they form a circle which represents a complete angle of 360 degrees.
- The angles shown below are Exterior angles.
- In the following diagram a Regular Pentagon is shown.
- We know exterior angles summed up together gives us 360 degrees.
- Hence, the relationship between an exterior angle and the sides of the regular polygon, pentagon is-
Solved Example:
Problem: Find the number of sides of the polygon shown in the image given below:ย 
Step#1: Find the angle of a regular pentagon-
The angle of a regular pentagon will be โ
The two angles together make:ย 
As interior and exterior angles are supplementary โ
Solved Example:
Problem: Find out the value of exterior angle x and interior angle y of polygon.
Step#1: Finding the Exterior Angle-
The polygon is an Octagon, and we can find the exterior angle by the formula –
As the Interior and Exterior angles are supplementary, thus-
Solved Example:
Problem: Find the values of the unknown angles.
Step#1: Find the Exterior Angle-
The interior angle of a rectangle is 90ยฐ, hence the exterior angle will be-
In triangle A and B,ย 
In triangle B,
Solved Example:
Problem: Find the value of the unknown angle.
In the diagram, interior angle is 85ยฐ and x is unknown.
As they are supplementary-
Simultaneous Equations - GCSE Maths
Introduction
- Two or more equations are solved together at the same time.
- A solution of these equation is the value of variables which satisfy both of the equations.
Examples:
Types of Simultaneous Equations
- Simultaneous equations can be linear (where variables are raised to the power 1) or non linear (exponent more than 1)
- Solution of Simultaneous equation: values of variables that satisfy both the equations.
- Simultaneous equations are used in various fields like mathematics, physics, computer science and economics.
Methods to Solve Simultaneous Equations
There are two methods to solve Simultaneous Equations-
- Elimination method: In this method, we eliminate one of the variables by adding or subtracting the equations, which results in a simpler equation with only one variable.
- Substitution method : In this method one variable is expressed in terms of the other variable and then its value is substituted in other equation, which results in a simpler equation with one variable.
Steps to Solve Simultaneous Equations by Elimination Method
Elimination method
Let us solve the following simultaneous equations step by step using the elimination method:
Step#1: Identify the variable that can be eliminated :
We can see that if we multiply the 2nd equation with 2 then the coefficient of x in both the equations will become equal and then it can be eliminated by subtraction :
2x + 3y = 5 …(1)
1x – 1y = 0 …(2)
Step#2: Add or subtract the equations to get a combined equation with only one variable:
Here, one variable (x) will get eliminated if we subtract equation 2 from 1:
The combined equation is:
Step#3: Use the known variableโs value to find the other variableโs value :
Pick one of the simultaneous equations and put the value of y in it –
So, the solution of these simultaneous equations is:
Steps to Solve Simultaneous Equations by Substitution Method
Substitution method:
Let us solve the pair of Simultaneous equations by using Substitution method :ย ย ย ย ย
Step#1: Find one variableโs value in the form of the other variable:
Example:
From 1st Equation:
Taking LCM
Step#3: Use the known value of one variable to find the value of the other-
Pick one of the original Equations:
From 1st Equation, put x=3,
x=3 andย y=3
Solved Example:
Problem: Solve the following pair of Simultaneous equations by using the Elimination method.
Solution:
Step#1: Identify the variable that can be eliminated:ย
Multiply equation 2nd by 3 so that the coefficients of x in both the equations become equal.
The resulting equations are:
Step#2: Subtract the 2nd equation from the 1st:
Step#3: Use the known value of one variable to find the value of the other variable –
Pick one of the original Equations and put y = 0 –
Solved Example:
Problem: Solve the following pair of Simultaneous equations by using the Substitution method.
Solution:
Step#1: Find one variableโs value in the form of the other variable:
From 1st Equation-
From 1st Equation:
Solved Example:
Problem: Solve the following pair of Simultaneous equations by using the Elimination method.
Solution:
Step#1: Identify the variable that can be eliminated :
Here, if we multiply the 1st equation with 3 and 2nd equation with 4 then the coefficient of x in both the equations will become equal –
and the 1st equation becomes –
Step#2: Subtract the 2nd equation from 1st.
The combined equation is-
Step#3:Use the known variableโs value to find other –
From equation (1), Put y = 1 –
Hence the solution of these simultaneous equations areย x = 1 and y = -1
Let us check whether the values satisfy the 2nd equation or not :
From 2nd equation,put x = 1 and y = -1 ย –
Hence, the solution is correct.
Compound Measures โ GCSE Maths
Introduction
- When we calculate a quantity using other quantities then it is called a Compound Measure which represents the relationship between these quantities and the units used.
- The Compound Measures are denoted as Ratio or Rate such as โperโ unit (km/h, m/s etc.)
- These Measures are widely used in Business, Engineering and Science and solving real-life problems.
Examples:
- Speed
- Density
- Pressure
Easy Way to Solve Problems
- We can make it easy to solve the problems related to Compound Measures by learning the Triangle method.
- Consider following three Compound Measures –
How to use the Triangle Method
- Let us see the use of the Triangle to find one quantity if the other two are known.
To find Speed:
- Hide Speed in the Triangle, then using Distance and Time as the quantities remaining, formula for calculating Speed will be-ย
To find Distance:
- Hide Distance in the Triangle, then using Speed and Time as the quantities remaining, formula for calculating Distance isย
- Hide Time in the Triangle, then using Speed and Distance as the quantities remaining formula for calculating Time is –
Solved Example
Problem: If a distance of 50m is travelled in 10 seconds then what is the speed of the vehicle?
Solution:
ย ย ย ย ย Step #1: Write the Formula
Step #2: Substitute the known values in the formula
Step #3: Solve
Solved Example
Problem: If mass of a liquid is 1kg and the volume is 200cm3, then find out its Density.
Step #1: Write the Formula
Step #2: Substitute the known values in the formula
Step #3: Solve
Solved Example
Problem:ย Suppose a block of 100cm2 area is lying on the table and Peter starts lifting it with force of 10N. Then find out the Pressure applied in the process?
Solution:
Step #1: Write the Formula
Step #2: Substitute the known values in the formula
Step #3: Solveย
ย
Solved Example
Problem: If Olivia runs at a speed of 20km/h, then how far will she run in 5 hours?
Solution:
Step #1: Write the Formula
Step #2: Substitute the known values in the formula
Step #3: Solveย
ย
Solved Example : Reasoning Problems
1. A rock weighs 18g and its volume is found to be 24cm3,then find out the density of the rock?
Solution:
The mass and and volume of the rock are given as – Mass = 18g, Volume = 24cm3
Step #1: Write the Formula
Solved Example : Reasoning Problem
2. Suppose a train travels with the speed of 100km/h and the distance between two stations (A to B) is 400 meters and third station(from B to C) is 500 meters then find out the total time taken by the train to travel the distance from first to third station(A to C)?
Solution:
First we need to convert the units of speed which are in km/h into m/sec by multiplying it with 5/18.
Total distance from A to C is –
distance from A to B + distance from B to C
800 + 1400 = 2200 meters
Step #1: Write the Formula
Step #2: Substitute the known values in the formula and solve
Solved Example : Reasoning Problem
Problem: Calculate the pressure exerted by the block shown in diagram ?
Solution:
The force applied by block is 475N and area –
Step #1: Write the Formula for Area, substitute known values and solve
Step #1: Write the Formula For Pressure, substitute known values and solve
Acids โ GCSE Chemistry
Introduction
What are Acids and Base?
ACIDS
- An Acid is a substance that releases H+ ions in water. Acids usually have sour taste and can turn blue litmus paper into red.
Examples:
Base
- A base is a substance that releases OHโป (hydroxide) ions in water. Bases usually have a bitter taste, feel soapy, and turn red litmus paper blue.
Examples:
Uses of Acids
- The carbonic acid gives fizz to soda drinks.
- Acetic acid(vinegar) is used for pickling.
- HCl is used for concrete cleaning and for pool PH adjustment.
- Acids are also used in batteries and metal works.
Uses of Bases
- The soap and detergent products contain Sodium hydroxide(base).
- Ammonia is common household cleaner and fertilizer raw material.
- Calcium Hydroxide(slaked lime) is used to soften water, to deal with acidic soil and is used in cement.
What is pH Scale and How it is measured?
- pH Scale is a numerical scale that is used to measure how acidic or basic a substance is. This scaleโs value ranged from 0 to 14-
Fact: Bee stings are acidic and has pH between 5 and 5.5
Formula to find the pH of any solution
- The pH of any substance is a measure of how much acidic or a basic that substance is. The formula to measure pH is –
Where, [H+] is the concentration of Hydrogen ions in (Moles per Liter or M)
Steps to calculate PH
- Find the H+ concentration, for strong acids like HCl (Hydrochloric acid). The concentration of acid equals the concentration of H+ ions.
- For weak acids and bases you may need to use an equilibrium expression or the Ka (Acid Dissociation constant).
Example:
Calculating PH Values
- HCl (Hydrochloric Acid) is a strong acid(dissolves completely)
- This reaction is responsible for the acidic nature of Hydrochloric Acid
The concentration of Hydrogen ions is same as the concentration of Hydrochloric acid.
- If [HCl] = 0.001M
Concept of Dilute and Concentrated Solution
Dilute or Concentrated โ Acidic or Basic
- The terms Dilute and Concentrated describe the amount of solute dissolved in a given quantity of solvent, not the chemical strength or nature of the solute.
- In brief: A Small amount of solute in a large amount of solvent.
- Concentrated Solution: A Large amount of solute in a smaller amount of solvent. These terms tell us how much solute is present, but not how weak or strong the solute is in terms of chemical behaviour.
Examples to Clarify
- Dilute Acid: Small amount of Hydrochloric acid in large amount of water. Still an acid but weak and not dangerous.
- Concentrated Acid: A large amount of HCl in little amount of water. Still an acid but stronger and much corrosive.
- Dilute Base: A small amount of Sodium Hydroxide(NaOH) in water. Still a base but mild.
Examples of Acid and Base Reaction
- The reaction between Acid and base is called Neutralisation reaction. Often when an acid and base react salt and water is formed.
Examples
- Hydrogen Bromide reacts with Potassium Hydroxide to form water and Potassium Bromide. Potassium Bromide is formed from the K+ ions from the base(KOH) and OH– ions from the acid HBr.
- Hydrochloric acid reacts with Ammonia to form Ammonium Chloride(salt). Ammonium Chloride is made up of NH4+ cations from the base NH3 and Cl– anions from the acid HCl.
Some Uses of Acid Base Reactions
- Let us discuss some specific types of Acid Base reaction in which type of base used changes and acid remains the same –
1. Acid and Metal Hydroxide:
- When an Acid reacts with metal hydroxide, a salt and water are formed. These are a type of double displacement reactions.
Examples
- Hydrochloric acid reacts with Sodium Hydroxide to form Water and Sodium Chloride.
- Here, Hydrochloric Acid reacts with Aluminium Hydroxide to from Water and Aluminium Chloride.
Properties
- It is an Exothermic reaction.
- The reaction do not produce any gas.
- Both soluble and insoluble metal hydroxides can react with acids.
2. Acid and Metal oxide:
- When an Acid reacts with metal oxide, a salt and water are formed.
Examples
- Reaction of Hydrogen Bromide and Magnisium oxide gives us Water and Magnisium Bromide.
- Hydrochloric Acid reacts with Aluminium Oxide and forms Water and Aluminium Chloride.
Properties
- It is an Exothermic reaction.
- The reaction do not produce any gas.
3. Acid and Metal Carbonates:
- When an Acid reacts with metal carbonate, Carbon Dioxide and Water are formed.
Examples
- Nitric Acid reacts with Sodium Carbonate and forms Nitrate, Carbon dioxide and water.
- Sulfuric acid reacts with Sodium carbonate to form Nitrate, Carbon dioxide and water.
Properties
- The reaction is mildly Exothermic.
- In the reaction of acid and carbonates the CO2 gas is produced. The gas can be tested by passing it through limewater which turns milky/cloudy if there is CO2.
Formation of Water from its ions
- We know that Water(a compound) consists of two elements, Hydrogen and Oxygen (constituents).
Activation Energy:
- The energy required to reach at the stage of breaking bonds within Hydrogen and Oxygen Molecules.
Bond Breaking:
- The energy required to break the bonds present in reactants.
Energy Release:
- Energy is released in the form of Water and Light, and that is why Hydrogen is used as fuel in rocket
Frequently Asked Questions
Solution:
Acids donate H+ ions on the other hand bases donate OH– ions when dissolved in a solution.
Solution:
It is the reaction of Acid and Base and is called neutralisation reaction as the ions from acid and base combine and form water.
Solution:
Maintaining the PH level is crucial for proper functioning of many systems in our everyday life including human body.
Solution:
pH = – log+10[H+]
Solution:
The concept of dilute and concentrated solution tells us how much strong an acidic or basic solution is.
Radioactivity Dangers and Medicines โ GCSE Physics
Introduction
- Radioactivity means a process in which unstable atom nuclei spontaneously emit energy in order to gain stability.
- Radiations are primarily of three types – Alpha(ฮฑ) Radiations, Beta(ฮฒ) Radiations and Gamma(ฮณ) Radiations.
- There are many medicinal applications of Radioactivity. Also, the small amount of radiation is safe, but higher exposure to radiation can damage cells and DNA, causing cancer and serious health issues.
Let us study the applications of radiation in medical treatments, and also know about the dangers of radiation
Uses of Radiation
1. Food Irradiation
- In our environment, some foods naturally contain radioactive substances. We know that food contains a special type of bacteria that cause it to decompose eventually. But some of those bacteria can cause food poisoning.
- To prevent food poisoning, the food is irradiated using gamma rays. Here, the microorganisms are killed.
Steps
- Food is typically packaged before irradiation.
- Packaged food is moved through an irradiation chamber.
- The food is exposed to a controlled dose of ionising radiation.
- Radiation disrupts the DNA of microorganisms, preventing them from reproducing.
- Irradiation does not heat the food or leave behind any chemical residue.
2. Radioactivity Detecting
- Radioactive substances are used as tracers. For example, the underground pipe leakage detection by the Geiger-Muller Tube.
Steps
- Sensitive detectors like the Geiger-Muller tube are used to scan the area surrounding the underground pipe.
- The radioactive tracer is introduced into the pipe. The tracer flows through the pipe, and where there is leakage, the tracer-containing fluid will escape.
- The detectors measure the radiation levels. Higher level of readings indicate the presence of radioactive tracers, hence pointing to the pipe leakage location.
3. Smoke Alarms
- Radioactive substances are used as smoke alarms.
Steps
- The Smoke Alarm contains an electrical circuit, which has two electrically charged plates with an air gap between them. A source is connected to the plate, which releases Americium-241.
- This Radioactive substance will ionise the air molecules, now they are attracted to oppositely charged plates of the circuit, allowing a small amount of current to flow that is measured by the detector.
- The Smoke alarm will not sound as long as the current is flowing. But when the smoke gets into the gap between the plates, the ions will slow down, decreasing the amount of current measured by the detector. Now, at this point of current dropping, the alarm will start ringing.
4. Checking Thickness
- Paper is made by squeezing wood pulp between two rollers. These rollers must apply same force on wood pulp to squeeze it into the same sized paper.
Steps
- The detector counts the rate at which beta particles get through the paper on one side.
- When the paper is too thin, the count rate detected is higher. Then, a computer senses this rise in count rate and sends a signal to decrease the pressure applied by rollers to maintain the thickness of paper. Similarly, when the paper is thick, the opposite happens.
Dangers of Radiation
- A large amount of radiation can cause tissue damage like reddened skin and other effects that cannot be seen.
- A small amount of radiation over a long period of time can damage DNA inside a cell, a process known as mutation. Some mutations can cause the cell to malfunction and may cause cancer.
- Not all mutations are harmful, the cell can repair the damage itself if the radiation dose is small.
- In hospitals, radioactivity is used for various purposes. The medical staff working with radiation have limited their exposure in several ways, including increasing their distance from the source and minimising the time they spend in radiation. Staffโs exposure to radiation is closely measured using Dosimeter badges.
- Nuclear Accidents allow the radioactive materials to escape into the environment. Accidents like this are harmful as they can cause people to get irradiated or contaminated.
- Food and water can also get contaminated means that it can enter the food chain. Contamination with radioactive materials of long half-lives poses a greater hazard as the effect will last longer.
Radioactivity in Medicine
- Radioactivity materials are used to diagnose medical issues without having to cut a patientโs body.
- Radioactivity can be used to diagnose cancer using tracers in the body. It can also be used to treat cancer.
Radioactivity tracer detecting medical issue in body, STEPS –
- A radioactive tracer that emits Gamma Rays is introduced into the patientโs body. The tracer is generally injected into the bloodstream. One or more Gamma cameras detect the location of the tracer.
- The tracer finds the location of internal bleeding. The cameras detect the highest gamma radiation, which is where the bleeding occurs.
- Gamma cameras are used to detect tumours, and then the tracer is made using radioactive Glucose molecule.
Frequently Asked Questions
Solution:
When there is spontaneous emission of energy from the unstable nucleus of an atom to become stable, the process is called Radioactivity.
Solution:
Radioactivity is measured using Dosimeter badges.
Solution:
In diagnosis through radioactivity, doctors can find health issues without having to cut the patientโs body. A radioactive substance is introduced into a humanโs body, and its radiation is detected/measured through cameras.
Solution:
- Distance: Maintaining a shorter distance from the source.
- Time: The time spent in radiation exposure should be decreased.
- Shielding: Use materials which can block radiation like lead.
Solution:
X-Rays, CT Scans, etc. and other techniques that involve imaging techniques are a source of radiation exposure.
Astronomy โ GCSE Physics
Introduction to Astronomy
- The Astronomy is branch of Science that deals with the study of Astronomical objects like Stars, Planets and Asteroids etc.
- We can also say that the study of the objects that are beyond Earthโs atmosphere and are present in far away galaxies is known as Astronomy.
- It uses the concepts of Mathematics, Physics and Chemistry in order to explain the origin and the overall evolution of Universe.
What is a Protostar?
ย
- Protostar is a dense core which is very hot and is surrounded by dust and gas.
- Protostar is the early development phase of a star formation.
- The Protostar looks like a Star but its core is not that hot for nuclear fusion to take place.
- As the core of Protostar contracts its temperature rises leading to nuclear fusion and it becomes a main sequence star.
- when protostar rotates it generates a magnetic field.
What is a Star? And Life Cycle of a Star
A glowing ball of hot gas with a high amount of mass is called a Star.
- The most familiar star to us is Sun which give us light and warmth .
Their are many galaxies in the Universe. Our galaxy is Milky way that contains billions of stars just like other galaxies.
Though there are billions of stars in our Galaxy, a few thousands of them are visible to the naked eye from Earth.
Stars shine because there is process that keeps on going on their surface that process is Nuclear Fusion.
Stars seems to twinkle from Earthโs surface because the atmosphere contain many flying dust particles and due to the temperature conditions.
- Life Cycle of a star isย process which spans billions of years. The process contains gravitational collapse and nuclear fusion. The process happens in following stages –
Steller Nebulae(Birth): In the beginning there is a large cloud of dust particles and gas which we call as Nebulae. They are measured in light years(Astronomical distance unit). These Nebulae regions collapse due to gravitational forces which forms Protostars.ย ย ย Example: Orion Nebulae
Protostar(Early Development): Protostar is a dense, hot core surrounded by dust and gas. Protostar is the early development phase of a star formation. When the core contracts due to gravitational forces then temperature rises and the process of nuclear fusion can start and then protostar becomes main sequence star.
Main Sequence(Stable Phase): When the environment of protostar is hot and exceeds a range of temperature, then nuclear fusion starts. The hydrogen gets converted into Helium and high energy is released and protostar becomes main sequence, the longest phase of star formation which lasts for billions of years. Here it shines brightly, our sun is currently in this phase.
Red Giant/Super Giant: Huge and massive stars used their fuel fastly, when the fuel is used star starts collapsing within itself.Stars having fuel for further fusion forms Red giant(lesser massive and red coloured) or Super giant(massive and blue coloured).
White Dwarf(medium or low mass stars): When the fuel is exhausted, including Helium, Red Giant becomes unstable and the outer layers move into space, forming planetary nebulae and then the core left behind is called white dwarf which is very dense. The mass of a typical white dwarf is half of the mass of Sun. The White Dwarf cools down over years and becomes Black Dwarf.
Neutron Star/Black Hole: A Neutron Star is the result (remnant) of a big explosion(Supernova) of a massive star. A neutron star has a mass greater than the Sun, which is compressed into a sphere. A Neutron Star is composed of Neutrons (subatomic particles with no electrical charge).
A Black hole is a highly massive object in space with a powerful gravitational pull that even light can not escape it. Thereโs a boundary around Black Hole(event horizon) which warps spacetime. Anything that crosses that boundary can never come back from Black Hole.
What is Solar System?
- Solar System is a moving system bounded by gravitational forces consisting of sun and planets with their asteroids, comets and dwarf planets in space.
Solar System is magnificent and well moving system.
A large and hot ball is in the center of this system , Sun and its gravitation is so strong that it keeps other planets revolving around it.
The path or the journey that a planet takes around the Sun is called an Orbit.
The Orbit of each planet in the Solar System is elliptical means shaped like an egg.
Each planet of the Solar System do not travel at the same speed around the Sun. The farther is the planet from the sun the more time it takes to complete one orbit (slower speed).
- Mercury is closest planet to Sun and fastest to complete its orbit. It takes 88 Earth days to complete one orbit around the Sun.
Next planet is Venus, the hottest planet in the Solar System takes 224 Earth days to complete the orbit.
Then comes our Earth, planet where life exists takes 365 days to complete one orbit around the Sun.
Mars the 4th planet from sun takes 686 Earth days to complete an Orbit around the Sun.
Jupiter, the biggest planet in the Solar System takes 4332 earth days to complete an orbit.
Saturn, 6th from Sun having glorious ring system takes 10,756 Earth days to complete an orbit.
Uranus, takes 30,687 Earth days and Neptune takes 60,190 Earth days to complete an orbit around the Sun.
What are Dwarf Planets and Asteroid like celestial bodies in Space?
- Our solar system also contains other planets called Dwarf planets, including Pluto, Makemake, Eris, Haumea, and Ceres. They are called Dwarf planets because they are spherical due to their gravitation but are not massive enough to be considered as planets. And just like planets they also revolve around the Sun in their orbits.
Solar System not only contains planets but asteroids, meteoroids, meteors and comets etc. which orbits the sun and contributes to solar systemโs complexities. They are-
Comet
Asteroid
Meteoroid
Meteor
Meteorites
- Comets: Comets are big balls of dust, rock and metal. It is surrounded by an icy shell. When comets go too close to something hot like Sun its ice sublimates and hot wind of Sun blows the sublimated ice backwards creating a tail of the Comet.those comet which orbits longer than 200 years are Long Period Comets and Those comet which orbits shorter than 200 years are Short ย Period Comets. Comets orbit the sun in highly elliptical path.
- Asteroid: Asteroids are just rock, dust and metal. Most Asteroids are formed between the Mars and Jupiter, the region is called as Asteroid Belt. They are dangerous for Earth. They are the reason that caused dinosaurs to go, when an asteroid hit our Earth 65 million years ago.
- Meteoroids: They are rocky floating space remains in Solar System. They are smaller than Asteroids. Some of them come from Asteroid belt whereas some come from the Moon.
- Meteors: We know them as shooting stars. They are just meteoroids that hit the surface of Earth. They are as the size of pebbles. When Meteors hit the surface of Earth they slowly burn and that cause a big flash of light in the sky.
- Meteorites: Meteorites are just Meteoroids that successfully hit the ย Earthโs surface surviving through its atmosphere. They are dangerous asย due to their small size they cannot be detected. Even when their size is is ย small they travel with high velocity that is why they are dangerous.
Geostationary Satellites
- Geostationary Satellite is placed at an altitude of approximate 36,000 km above the Earthโs surface and just over the equator, the Geostationary satellite moves with Earth (West to East) in an orbit around it. It takes 24 hours to complete one orbit just like Earth take the same amount of time to rotate about its axis once.
- Geostationary satellite is named so because it seems to be stationary when seen from the Earthโs surface while it is moving.
- Applications of Geostationary satellite includes –
ย ย ย ย ย ย Weather Forecasting
ย ย ย ย ย ย Television, Telephoneย and Radio Broadcasting
ย ย ย ย ย ย Military satellites
ย ย ย ย ย ย Navigation systems, Google Maps etc.
Frequently Asked Questions
Sun( A star in its Main sequence phase, massive and very hot).
They are made from rock and floats in our Solar system, they are of very small size and travel with high velocity. Unlike Meteoroids they may reach the syrface of Earth and hit it causing danger.
The key difference between them is that Comets are surrounded by an icy shell but Asteroids are not.
Shooting Stars is actual are the Meteors falling at the Earthโs
surface but they burn during this journey, hence are not dangerous.
The Asteroid belt is present in between Mars and Jupiter as most of the Asteroids are formed in this region.
Mercury.
Because the Sun is not massive enough to end up as black hole, the Sun needs to be 20 times more massive to become a black hole.
The celestial bodies present in our Universe that are spherical due to their gravity and orbits the Sun are called Dwarf Planets.
A Satellite that is placed over the equator at a distance of 36,000 km from Earth. The satellite moves with Earth in same direction and thus seems to be stationary. There are many applications of these satellites like weather forecasting and google maps etc.
Radioactivity โ GCSE Physics
What is Radioactivity?
- An Atom is the basic unit of matter. Atom contains Electrons(negatively charged), Protons(positively charged) and Neutrons(neutral) in such a way that the protons and neutrons are present in nucleus and electrons revolve around them in orbitals.
The nucleus is present in center that contributes for mass of an Atom. The nucleus is positively charged due to the presence of Protons.
- When the nucleus of an Atom is Unstable then it releases some of its energy in the form of radiation from nucleus and becomes stable. This process of decay of an Atom is called Radioactivity.
What are Background Radiations?
- The Explosion of low level ionising radiations from the radioactive substances present naturally in our environment and from space.
Sources: The rocks containing small amount of Uranium produces Radioactive gas. The main source is Radon gas. This gas can enter into houses. Most of the high energy rays coming from sun are stopped in the upper atmosphere but some of them reach the surface of Earth and are known as Cosmic rays.
- Variation of Background radiation in different parts of the UK :
- The amount of radioactive gas produced by rocks depends on the rock type.
- Some foods naturally contain radioactive substances.
- In hospitals, X-rays and Gamma-rays are used, which causes background radiation is caused.
- High energy particles coming from the sun when could not be stopped by the atmosphere they reach at the surface of Earth causing background radiations and are called as Cosmic Rays.
How Radioactivity is measured? And Types of Radiation
- Types of Radiation:
There are four kind of Radiations –
1) Alpha Radiationย ย ย ย
2) Beta Radiation
3) Gamma Radiation
4) Neutron Radiation
(1) Alpha Radiation (ฮฑ) – When the nucleus shoots out an Alpha particle (two neutrons and two protons), we know that the helium atom also contains two protons and two neutrons in its nucleus. Thus, the radiation where Helium atom(without any electron) is emitted is called Alpha Radiation.
(2) Beta Radiation(ฮฒ) –It generally occurs when a neutron in an atomic nucleus turns into proton and electron. The proton remains in the nucleus but the electron escapes the atom.
3) Gamma Radiation (ฮณ) – When an extremely high-energy photon(a small packet of light energy) escapes the nucleus which we call Gamma-ray. It is similar to emission of ordinary light from atom but the gamma ray can damage our surroundings. Gamma-rays involves high energy, The x-rays are similar to gamma-rays but are less energetic.
(4) Neutron Radiation (n) – Here a neutron escapes the nucleus of an atom. This is the most dangerous type of radiation.
# Brief Description about different types of Radiations –
# How can we stop Radiations?
- Alpha radiations consists of heavy and slowly moving particles with a lot of electrical charge, thus they can be easily stopped using a single sheet of paper.
- Beta radiations consist of light and fast moving particles with electrical charge. This means that they can be stopped by thin plates of material.
- Gamma radiations consists of fast moving particles with no electrical charge, they are harder to stop. We use dense material like Lead to stop Gamma-ray.
- Neutron radiations consist heavy particles with no electrical charge. They can travel long distance. We need something that contains large amount of Hydrogen in it.
Applications of Radioactive Substances
Radioactive Substances are dangerous, but they also have many advantages, which is why we can apply them in our real life to resolve some problems, like –
Food naturally contains bacteria that eventually cause them to decompose. Some of them can result in food poisoning, but using gamma-rays we can irradiate them to make it safer to eat.
- They can be used as Tracers. For example, following its path using the GM Tube to detect whether there is leakage from underground pipe. Higher level of radiations are observed at places of leakage.
- Cancer diagnosis by tracers in the body.
- Checking paper thickness.
Frequently Asked Questions
Solution:
- Alpha decay, Beta decay, Gamma decay are primary types of radioactive decay
Solution:
Medical imaging, leakage detection and irradiating food to prevent food poisoning.
Solution:
- No, the ionizing radiation is not always harmful but the higher doses are. Low doses are present naturally in our environment which we call Background radiations.
Solution:
- The main resource is Radon gas from rocks and cosmic rays(sun rays that could not be stopped by Atmosphere).Also the rays used in Hospitals.
Solution:
- Background radiation can enter in a house in multiple ways From the building material, soil and water, cosmic rays, rocks and through cracks etc.