Photomath: Photomath is a popular AIpowered math solver app that can solve mathematical problems simply by taking a picture of the problem. The app also provides stepbystep solutions and offers graphing and scientific calculator functions.
Wolfram Alpha: Wolfram Alpha is an AIbased computational knowledge engine that can answer complex mathematical questions and solve equations. The platform offers a wide range of mathematical tools, including calculus, algebra, geometry, and statistics.
MyScript Calculator: MyScript Calculator is an AIpowered handwriting recognition app that can convert handwritten mathematical equations into digital text and solve them in realtime. The app supports a range of mathematical operations, including fractions, roots, and trigonometry.
Khan Academy: Khan Academy is an online learning platform that uses AI algorithms to personalize learning experiences for math students. The platform offers a range of video tutorials, exercises, and quizzes to help students improve their math skills.
GeoGebra: GeoGebra is an AIpowered math software that allows students to create, analyze, and solve mathematical problems in various fields, including geometry, algebra, and calculus. The platform offers a range of tools, including interactive graphs, geometry tools, and spreadsheets.
Cymath: Cymath is an AIpowered math solver app that can solve algebra, calculus, and graphing problems. The platform provides stepbystep solutions and also offers a feature to scan handwritten math problems and solve them.
Microsoft Math Solver: Microsoft Math Solver is an AIpowered math solver app that can solve a wide range of math problems, including algebra, calculus, and statistics. The platform provides stepbystep solutions and also offers graphing and scientific calculator functions.
Mathpix: Mathpix is an AIpowered math solver app that can recognize and solve handwritten or typed math problems. The app can convert images of equations into LaTeX, a markup language used for mathematical equations, making it easy to input equations into other software or documents.
Calculus Made Easy: Calculus Made Easy is an AIpowered math app that provides explanations and examples for calculus problems. The platform offers interactive graphs and animations to help students visualize complex concepts.
Brainscape: Brainscape is an AIpowered flashcard app that can help students memorize math formulas and concepts. The app uses spaced repetition algorithms to optimize learning and retention, and offers a wide range of math topics to study.
These AI tools can help math students with everything from solving complex equations to memorizing formulas and concepts. As always, it’s important to choose the right tool for your needs and to use them as a supplement to your own learning and problemsolving skills.
]]>In simple terms, an algorithm is a stepbystep set of instructions for solving a problem or achieving a goal. In the context of computer science, an algorithm is a set of instructions that a computer can follow to perform a task. These instructions are based on mathematical concepts, such as logic, probability, and optimization.
One of the most powerful applications of algorithms is in the field of artificial intelligence (AI). AI algorithms can analyze large amounts of data to find patterns and make predictions. This has led to breakthroughs in areas such as image and speech recognition, natural language processing, and autonomous vehicles.
For example, Google’s search algorithm uses complex mathematical models to analyze billions of web pages and return the most relevant results for a given search query. Similarly, Facebook’s newsfeed algorithm uses machine learning to show users the most relevant posts based on their interests and behavior.
But algorithms are not limited to the digital realm. They are also used in industries such as healthcare and finance to make more accurate and informed decisions. For instance, doctors can use algorithms to analyze medical images and identify potential health problems, while financial analysts can use algorithms to analyze market trends and make investment decisions.
However, with great power comes great responsibility. Algorithms can have unintended consequences, such as perpetuating bias and discrimination. For instance, facial recognition algorithms have been shown to be less accurate in identifying people with darker skin tones, leading to concerns about racial bias. Similarly, hiring algorithms have been criticized for perpetuating gender and racial biases.
To address these issues, mathematicians and computer scientists are developing new algorithms that are more transparent, accountable, and fair. This includes using techniques such as explainable AI, which allows users to understand how algorithms make decisions, and bias mitigation, which aims to remove bias from algorithms.
In conclusion, algorithms are a powerful tool that is changing the world in countless ways. From improving healthcare to making financial decisions, algorithms are transforming industries and making our lives easier and more efficient. However, it is important to use algorithms responsibly and ethically, and to continue developing new algorithms that are transparent, accountable, and fair.
It is recommended that you read each question carefully before attempting to answer it, and show all working where necessary. Remember, the key to success in math is practice and perseverance, so don’t be discouraged if you encounter difficult questions. Use your problemsolving skills and apply the concepts and formulas you have learned to arrive at the correct answer.
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Mathematics plays a crucial role in insurance, as it provides the foundation for calculating risks, determining premiums, and estimating losses. Here are some examples of Application of Mathematics in Insurance:
Actuarial science: Actuarial science is a branch of mathematics that deals with assessing risks and financial outcomes in uncertain situations. Actuaries use statistical models to determine the likelihood of future events and calculate the expected cost of claims for a particular insurance policy.
Calculus: Calculus is used to model changes over time, which is essential for insurance companies when determining future liabilities. For example, it can be used to estimate the growth rate of a policyholder’s investments or the expected value of a life insurance policy.
Probability and statistics: Insurance companies use probability and statistics to assess the likelihood of a particular event occurring, such as a car accident, theft, or natural disaster. This helps them to determine the appropriate premium to charge for a particular policy.
Linear algebra: Linear algebra is used in insurance to model large data sets, such as claims history or policyholder information. It helps insurers to identify trends and patterns, which can be used to improve risk assessment and pricing.
Optimization: Optimization techniques are used in insurance to find the best policy mix that maximizes the company’s profits while minimizing risk exposure. This can involve complex mathematical modeling, such as linear programming or game theory.
In addition to the examples mentioned above, here are some other ways that mathematics is used in insurance:
Data analysis: Insurance companies collect vast amounts of data about their policyholders, including their age, gender, occupation, and driving history. By using mathematical techniques such as clustering, regression analysis, and data visualization, insurers can gain insights into the behavior and characteristics of their customers. This information can be used to improve risk assessment and pricing, as well as to develop more targeted marketing campaigns.
Financial modeling: Insurance companies must manage their financial assets and liabilities carefully to ensure that they remain solvent and able to pay claims. Mathematical modeling techniques such as assetliability management (ALM) and cash flow analysis are used to forecast future income and expenses, as well as to determine the optimal investment strategy for the company’s portfolio.
Fraud detection: Insurance fraud is a significant problem, costing companies billions of dollars each year. Mathematical techniques such as anomaly detection, network analysis, and machine learning are used to identify patterns of fraud and to develop algorithms that can detect suspicious claims.
Risk management: Insurance companies use mathematical models to assess and manage their exposure to risk. This involves analyzing the likelihood and potential impact of various events, such as natural disasters, economic downturns, and changes in regulation. By quantifying these risks and developing strategies to mitigate them, insurers can ensure that they remain financially stable and able to meet their obligations to policyholders.
Pricing and underwriting: The use of mathematical models is particularly important in the pricing and underwriting of insurance policies. By analyzing historical data, insurers can determine the probability of different events occurring and calculate the expected cost of claims. This information is used to set premiums and deductibles that reflect the level of risk associated with a particular policy. Actuaries and other mathematical experts play a critical role in this process, using advanced statistical techniques to develop pricing models that are accurate and equitable.
In conclusion, mathematics is essential to the insurance industry, providing the tools and techniques necessary to assess risk, manage financial assets and liabilities, detect fraud, and develop pricing models that are fair and accurate. The use of mathematical models and techniques helps insurance companies to make informed decisions based on data and statistics, ensuring that they are financially stable and able to meet the needs of their policyholders. As the insurance industry continues to evolve, mathematical expertise will remain a key asset for insurers, enabling them to adapt to new challenges and opportunities in an increasingly complex and competitive marketplace.
Medieval India was a period of great mathematical activity, with numerous mathematicians making important contributions to the field. From the 5th to the 15th century, Indian mathematicians made significant contributions to the development of mathematics and its applications in astronomy, engineering, and commerce.
These mathematicians, along with many others, helped to lay the foundations of modern mathematics in India and made important contributions to the development of the field. Their legacy continues to be celebrated and studied today.
One of the earliest and most prominent mathematicians of medieval India was Aryabhata, who lived in the 5th century. He made significant contributions to the fields of mathematics and astronomy, including the development of a numerical system for expressing very large numbers and the calculation of the value of π to four decimal places. His mathematical text, the “Aryabhatiya,” was a comprehensive work that covered a wide range of mathematical topics, including arithmetic, algebra, and trigonometry.
Another important mathematician of medieval India was Bhaskara II, who lived in the 12th century. He made significant contributions to the field of mathematics, including the development of several mathematical techniques and the creation of a comprehensive mathematical text called the “Bijaganita.” This text covered a wide range of mathematical topics, including arithmetic, algebra, trigonometry, and geometry, and it was widely used for centuries to come.
The 14th century saw the rise of the Kerala School of Astronomy and Mathematics, which was founded by Madhava of Sangamagrama. Madhava made important contributions to the field of mathematics, including the discovery of infinite series and the development of several mathematical techniques. He was also the first to use the Taylor series to represent functions, a technique that is widely used today.
Another notable mathematician of the Kerala School was Nilakantha Somayaji, who lived in the 15th century. He was a prolific mathematician and astronomer, and he made important contributions to the field of mathematics, including the development of several mathematical techniques and the creation of a comprehensive mathematical text called the “Tantrasangraha.” This text covered a wide range of mathematical topics, including algebra, trigonometry, and geometry, and it was widely used for centuries to come.
The medieval period also saw the development of several mathematical techniques and algorithms that were used for practical purposes, such as in commerce and engineering. For example, Indian mathematicians developed methods for solving linear and quadratic equations, as well as algorithms for performing various mathematical operations, such as multiplication and division. They also made important contributions to the field of astronomy, including the calculation of the positions of celestial bodies and the creation of astronomical tables.
In conclusion, medieval India was a period of significant mathematical activity, with numerous mathematicians making important contributions to the field. From the 5th to the 15th century, Indian mathematicians made significant contributions to the development of mathematics and its applications in astronomy, engineering, and commerce. Their legacy continues to be celebrated and studied today, and their contributions have had a lasting impact on the field of mathematics and its applications.
One of the most important uses of mathematics in the gaming industry is in game design. Game designers use mathematical concepts such as probability, set theory, and algorithms to design game rules and mechanics. For example, a game designer might use probability to determine the odds of a certain event occurring in a game, such as a character landing a critical hit. Set theory is used to define the relationships between game elements, such as the relationship between characters and weapons in an RPG. Algorithms are used to create game mechanics such as character movements, random events, and score calculation.
Artificial intelligence (AI) is another area where mathematics is heavily used in the gaming industry. Math is used to program the behavior of nonplayer characters (NPCs) in a game, allowing them to make decisions and respond to player actions in a realistic way. This requires the use of mathematical concepts such as decision theory, game theory, and machine learning. For example, game designers might use decision theory to determine the best course of action for an NPC in a given situation, while game theory is used to analyze the relationships between NPCs and the player. Machine learning algorithms can be used to train NPCs to improve their behavior over time.
3D graphics are another important aspect of modern gaming, and mathematics plays a key role in their creation. Math is used to create and render 3D graphics, including character animations and environmental effects. This requires the use of mathematical concepts such as linear algebra, calculus, and computer graphics.
For example, linear algebra is used to manipulate the position and orientation of objects in 3D space, while calculus is used to create smooth animations and transitions. Computer graphics algorithms are used to render the final images that are displayed on the screen.
Some examples include:
Physics simulation is another important use of mathematics in the gaming industry. Math is used to simulate realistic physics in games, such as object collisions, realistic movements, and environmental effects. This requires the use of mathematical concepts such as classical mechanics, fluid dynamics, and particle systems. For example, classical mechanics is used to simulate the movements of rigid bodies, while fluid dynamics is used to simulate the behavior of liquids and gases. Particle systems are used to create special effects such as fire, smoke, and explosions.
In addition to the above, mathematics is also used in various other aspects of the gaming industry, such as in the development of algorithms for various aspects of gaming, such as pathfinding and resource management. Pathfinding algorithms are used to determine the best path for characters to follow in a game, while resource management algorithms are used to manage the distribution of resources, such as weapons and ammunition.
In conclusion, mathematics plays a crucial role in the gaming industry, as it is used in a variety of ways to develop and enhance the gaming experience. From designing game rules and mechanics, to programming artificial intelligence and simulating realistic physics, mathematics is integrated into every aspect of game development. With the continual advancement of technology, it is likely that the role of mathematics in the gaming industry will continue to grow and evolve, as game designers strive to create even more engaging and immersive gaming experiences for players.
In this post we have explained how to secure your required marks in Mathematics. This post is targeted for the students who had a bad records in the class 12 terminal exams. This article will help you to score a good marks beyond your skills based on the previous years patterns. This article “How to Secure Your Target Marks in Class 12” is for all boards valid in India.
This post is applicable if you belong to any of the listed boards:
How to secure your Target Marks
Secure Passing Marks 
· Go through the questions given in this ebook.
· Try to attempt 60% of the questions. · What to skip? 1. Inverse Trigonometry 2. Approximation 3. Limit Sum Method 4. Second Exercise of LPP 5. Miscellaneous Exercises · Focus On 1. Probability: Baye’s Theorem & Probability Distribution. 2. 3 Dimensional Geometry Plane 3. Elementary Operation of Matrix to find inverse of the matrix. 4. Continuity · How to write the paper? – Do the questions that you are sure about.

Secure Above 60 Marks  · Go through the questions given in this ebook.
· What to skip? 1. Inverse Trigonometry 2. Approximation 3. Limit Sum Method 4. Second Exercise of LPP 5. Miscellaneous Exercises except 3D & Differentiability. · Focus On 1. Conceptual Questions of Vectors 2. Probability: Baye’s Theorem, Law of total probability & Probability Distribution. 3. 3 Dimensional Geometry of Lines and Planes 4. Elementary Operation of Matrix to find inverse of the matrix. · How to write the paper? – Do 1 Marks questions first. – Do the 6 marks questions that you are sure about.

Secure 90 Above  · Do everything from NCERT.
· Never skip any topic from PYQs · How to write the paper? – Do the paper serially and neatly.

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To pass board exams with better grades, students must use the right study materials. Studying the Class 12 Assam Board Recipe Book while practicing the Assam Board Class 12 Mathematics Questionnaire – 2022 can be the right choice of learning materials.
[Get All The Previous Year Papers – Here]
That’s why we have provided free Assamese Hs 2nd Year Math Problem Paper 2022 with solutions here.
Every year, AHSEC evaluates 2nd year HS students by passing their board exams. With his help, the committee decides which students will be considered to have passed or failed in the academic year. You can preview the solutions of the last year paper. Hope you like our post on “Class 12 Mathematics 2022 Paper Solutions (Assam Board – HS 2nd Year).”
class12assamboard2022solutionsFormulation of linear programming is the representation of a problem situation in a mathematical form. It involves welldefined decision variables, with an objective function and set of constraints.
Objective function:
The objective of the problem is identified and converted into a suitable objective function. The objective function represents the aim or goal of the system (i.e., decision variables) which has to be determined from the problem. Generally, the objective in most cases will be either to maximize resources or profits or, to minimize the cost or time.
Constraints:
When the availability of resources is in surplus, there will be no problem in making decisions. But in real life, organizations normally have scarce resources within which the job has to be performed in the most effective way. Therefore, problem situations are within confined limits in which the optimal solution to the problem must be found.
Nonnegativity constraint
Negative values of physical quantities are impossible, like producing a negative number of chairs, tables, etc., so it is necessary to include the element of nonnegativity as a constraint.
All the characteristics explored above give the following Linear Programming (LP).
A value of (x,y) is in the feasible region if it satisfies all the constraints and signs restrictions. This type of linear programming can be solved by two methods:
1) Graphical method
2) Simplex algorithm method
Step 1: Convert the inequality constraint as equations and find the coordinates of the line.
Step 2: Plot the lines on the graph. (Note: if the constraint is a type, then the solution zone lies away from the center. If the constraint is s type, then the solution zone is towards the center.)
Step 3: Obtain the feasible zone.
Step 4: Find the coordinates of the objectives function (profit line) and plot it on the graph representing it with a dotted line.
Step 5: Locate the solution point. (Note: If the given problem is maximization, Zmax then locates the solution point at the far most point of the feasible zone from the origin, and if minimization, Zmin then locates the solution at the shortest point of the solution zone from the origin).
Step 6: Solution type
i). If the solution point is a single point on the line, take the corresponding values of x and y.
ii). If the solution point lies at the intersection of two equations, then solve for x and y using the two equations.
iii). If the solution appears as a small line, then a multiple solution exists.
iv). If the solution has no confined boundary, the solution is said to be an unbound solution.
Question 1.
Two designers P and Q, earn ₹ 600 and ₹ 800 per day respectively. A can design 12 banners and 8 pairs of posters while B can design 20 banners and 8 pairs of posters per day. To find how many days should each of them work and if it is desired to produce at least 120 banners and 64 posters at a minimum labor cost, formulate this as an LPP.
Question 2.
A company produces two types of mobiles, A and B, that require silicon and plastic. Each unit of type A requires 3 g of silicon and 1 g of plastic while that of type B requires 1 g of silicon and 2 g of plastic. The company can use at the most 9 g of silicon and 8 g of plastic. If each unit of type A brings a profit of ₹ 40 and that of type B ₹ 50, find the number of units of each type that the company should produce to maximize profit. Formulate the above LPP and solve it graphically and also find the maximum profit.
Question 3.
A man wants to invest an amount of ₹5000. His broker recommends investing in two types of stocks A’ and ‘B’ yielding 30% and 27% return respectively on the invested amount. He decides to invest at least ₹ 2000 in stock A’ and at least ₹ 1000 in stock ‘B’. He also wants to invest at least as much in stock A’ as in stock ‘B’. Solve this linear programming problem graphically to maximise his returns.
Question 4.
Find graphically, the maximum value of Z = 2x + 5y,
subject to constraints given below
2x+ 4y ≤ 8;
3x + y ≤ 6;
x + y ≤ A;
x ≥ 0, y ≥ 0.
Question 5.
One kind of pizza requires 800 g of flour and 100 g of fat, and another kind of cake requires 400 g of flour and 200 g of fat. Find the maximum number of pizzas which can be made from 20 kg of flour and 4 kg of fat, assuming that there is no shortage of the other ingredients used in making the cakes. Make it an LPP and solve it graphically.
AHSEC Class 12 Mathematics Previous Question Paper 2016  Click Here 
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Science is one subject that typically goes through a progressions occasionally. The progressions in the substance are made as per the development of the subject and for the most part to meet the arising needs of society. The ongoing AHSEC Board Class 12 Maths prospectus has been planned according to the Public Educational program Structure 2005 and as per the rules referenced in Spotlight Gathering on Educating of Arithmetic 2005. This has been essentially finished to meet the arising needs of all classes of understudies. The points that are picked are additionally considered to be exceptionally helpful, in actuality, circumstances and more prominent accentuation has been kept on the utilization of different ideas.
Title  Marks 
Relations and Functions (Chapters – 2)  10 
Algebra (Chapters – 2)  13 
Calculus (Chapters – 5)  44 
Vectors Algebra and ThreeDimensional Geometry  17 
Linear Programming  06 
Probability  10 
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