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Best SAT Classes in Kathmandu, Nepal

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Best SAT Classes in Kathmandu, Nepal

Also, Visit: SAT Date in Nepal | The New Digital SAT | SAT Quant Instructor | SAT Verbal Instructor | SAT Free Resources | SAT Calculator Policy

MKS instructors

Verbal Instructor

Mr. Bijay Shivakotee
Nepal’s Most experienced and score-oriented instructor is himself an American college graduate. He has been a full-time GRE | GMAT | SAT | Language proficiency test instructor since 2000.

Quantitative Instructor

Mr. Manoj K. Singh
Highly experienced and score-oriented Instructor. To address students’ needs and make Tests easy, he developed  Learning Management System (LMS), which managed students’ overall study. 

SAT Preparation Class in Nepal

Excellent

Based on 689 reviews

Suman Rai

2023-11-01

Provides good learning platform. Satisfied

Prashant Kuikel

2023-10-31

"I had a fantastic experience with MKS Institution. Their online LMS portal made learning incredibly convenient, and the access to unlimited study materials was a game-changer. The instructors were knowledgeable, and the quality of education was top-notch. I wholeheartedly recommend it to anyone looking for quality education."

Divyanshu Gupta

2023-10-31

Best institution in ktm valley

Upendra Mahatara

2023-10-17

In MKSprep, classes are taught by the expert and the environment is quite and suitable for the students to focus on assignment and the many alumni have scored 1300+ so if you're looking for SAT class I highly recommend MKSprep for your better future.

deepa pariyar

2023-10-12

Best for sat

kundan

2023-10-08

Nice place for SAT

Best Live Online SAT Class in Nepal for 2023

When it comes to finding the best live online SAT class in Nepal, MKSprep Institute stands out as a top choice. Renowned for its exceptional track record in test preparation, MKSprep offers a comprehensive and tailored learning experience for students aiming to excel in the SAT. Their live online classes combine the expertise of highly qualified instructors with a dynamic virtual classroom environment, ensuring that students receive personalized attention and engage in interactive discussions. The institute’s well-structured curriculum covers all sections of the SAT, including Mathematics, Evidence-Based Reading and Writing, and the optional Essay. MKSprep’s commitment to student success is reflected in its strategic approach to teaching, which incorporates actual SAT practice questions, full-length mock tests, and detailed performance analysis. By choosing MKSprep for their live online SAT class, students in Nepal are making a proactive investment in their academic future, equipping themselves with the skills and knowledge needed to conquer the SAT and achieve their desired scores confidently.

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SAT Class in Pokhara, Nepal

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The best and most effective SAT class in Pokhara

MKSprep is the Best live online class provider in Nepal. We have the best team instructor in town. Hundreds of students from Pokhara itself. 

Master the SAT with MKSprep: Comprehensive SAT Classes in Pokhara for Every Learner

Are you an aspiring student planning to take the SAT and searching for the perfect preparation course? Look no further than MKSprep, offering top-notch SAT classes in Pokhara to help you excel in your college admissions journey. We understand the diverse learning needs of our students, which is why we provide physical, online, and hybrid class options to suit your preferences and requirements.

Our state-of-the-art Learning Management System (LMS) is the cornerstone of our SAT courses, equipping you with a wealth of resources to enhance your SAT preparation. Our LMS includes the following:

1. 10 full-length tests that mirror the real SAT experience, enabling you to practice under authentic conditions and gauge your progress effectively.
2. 200+ section-wise tests tailored to help you focus on specific areas, boost your confidence, and improve your overall SAT score.
3. Interactive PowerPoint presentations on each topic, designed to facilitate better comprehension and retention of crucial concepts.
4. In-depth concept explanations for each topic, ensuring a thorough understanding of the subject matter and laying a solid foundation for your SAT preparation.
5. PDF practice questions on each topic, allowing you to practice and consolidate your learning at your own pace.
6. A hard-copy book to complement your online learning, offering you the convenience of studying offline and making annotations as needed.

At MKSprep, the right instructor can significantly impact your SAT preparation. That’s why we’ve carefully selected the best instructors in the field, renowned for their extensive experience and proven success in guiding students to SAT excellence.

Take your chance to unlock your potential and achieve your desired SAT score with our comprehensive MKSprep courses. Enroll today and get ready to ace the SAT!

SAT (College Board) Official Site

MKS SAT Preparation specialty

Physical & Online Class

We have online & Physical classes. You can take either one or both.

Class Recording

We record every class. You can access the class recordings from home.

Unlimited Class

You can access the class until you get desired score.

Best Instructors in Nepal

Our most experienced instructors have the best track record for the best score in Nepal.

Learning Management System Portal

Our LMS portal helps you to manage your whole study plan with tons of study material.

LMS Portal feature

Time-bound Test

Interactive Slide Show

Post Class Plan

Video Lectures

MKS instructors

Verbal Instructor

Mr. Bijay Shivakotee
Nepal’s Most experienced and score-oriented instructor is himself an American college graduate. He has been a full-time GRE | GMAT | SAT | Language proficiency test instructor since 2000.

Quantitative Instructor

Mr. Manoj K. Singh
Highly experienced and score-oriented Instructor. To address students’ needs and make Tests easy, he developed  Learning Management System (LMS), which managed students’ overall study. 

As part of the college admissions process, colleges and universities in the United States use the SAT (Scholastic Assessment Test). Developed and administered by the College Board, the SAT is designed to assess a student’s readiness for college-level work by measuring their critical reading, writing, and mathematical skills. High school juniors and seniors primarily take the test, although younger students can also participate.
Structure:
The SAT is divided into two main sections: Evidence-Based Reading and Writing and Math. There is also an optional Essay section. The test is scored on a scale of 400 to 1600, with each of the two main sections worth 200 to 800 points.

Preparation:
Students can prepare for the SAT by reviewing the content covered in the test, taking practice tests, and developing test-taking strategies. The College Board offers free resources through its website and partnership with Khan Academy, such as sample questions and full-length practice tests. Many students also choose to enroll in SAT prep courses, hire tutors, or use self-paced study guides.

Excellent

Based on 689 reviews

Suman Rai

2023-11-01

Provides good learning platform. Satisfied

Prashant Kuikel

2023-10-31

"I had a fantastic experience with MKS Institution. Their online LMS portal made learning incredibly convenient, and the access to unlimited study materials was a game-changer. The instructors were knowledgeable, and the quality of education was top-notch. I wholeheartedly recommend it to anyone looking for quality education."

Divyanshu Gupta

2023-10-31

Best institution in ktm valley

Upendra Mahatara

2023-10-17

In MKSprep, classes are taught by the expert and the environment is quite and suitable for the students to focus on assignment and the many alumni have scored 1300+ so if you're looking for SAT class I highly recommend MKSprep for your better future.

deepa pariyar

2023-10-12

Best for sat

kundan

2023-10-08

Nice place for SAT

Importance of the SAT:

The SAT is one of the most widely used standardized tests for college admissions in the United States, along with the ACT. College admissions officers use SAT scores with other factors, such as high school GPA, extracurricular activities, recommendation letters, and personal essays, to evaluate an applicant’s potential for success in college. However, some colleges and universities have adopted test-optional or test-flexible policies, allowing applicants to decide whether or not to submit their SAT scores as part of their application.

Why SAT Test?

The SAT (Scholastic Assessment Test) is an essential aspect of the college admissions process in the United States because it serves several purposes:

1. Standardized assessment: The SAT provides a standardized measure of a student’s academic abilities, allowing colleges and universities to compare applicants on a consistent scale. High schools nationwide have varying levels of academic rigor, grading systems, and course offerings. The SAT helps level the playing field by offering a single, objective assessment of a student’s readiness for college-level work.
2. Predicting college success: Research has shown that SAT scores can effectively predict a student’s success in college, particularly when combined with a high school GPA. The test measures critical thinking, problem-solving, and analytical skills essential for higher education success.
3. Identifying strengths and weaknesses: The SAT is designed to assess a student’s reading, writing, and mathematics skills. By evaluating their performance on the test, students can identify their strengths and weaknesses, helping them make informed decisions about their college major and career path.
4. Access to scholarships and financial aid: Many scholarships and financial aid programs use SAT scores as part of their eligibility criteria. By taking the SAT, students can access valuable financial resources to help offset the cost of college tuition and other expenses.
5. College readiness: Preparing for and taking the SAT can help students develop important study habits and test-taking strategies that will serve them well in college. The process of studying for the SAT encourages students to review and reinforce their knowledge of core academic subjects, helping them feel more prepared for the challenges of higher education.

While the SAT remains an important factor in college admissions, it’s essential to remember that it’s just one component of a student’s overall application. Colleges and universities also consider factors such as high school GPA, extracurricular activities, recommendation letters, and personal essays when evaluating applicants. Additionally, some institutions have adopted test-optional or test-flexible policies, allowing students to choose whether or not to submit their SAT scores as part of their application.

SAT 3-D Geometry

Understanding Solid Geometry – A Foundation (Part 1)

Welcome to our course on SAT preparation, with a particular focus on the intriguing topic of Solid Geometry. We’re glad to have you here at MKSprep, located in Putalisadak, Kathmandu, Nepal. Our goal is to provide you with comprehensive guidance to grasp this complex area with relative ease. This is the first of our eight-part series on Solid Geometry.

In this first part, we aim to lay a solid foundation that will facilitate your understanding of solid geometry’s complex principles and theories. Solid Geometry is a vital aspect of the mathematics section of the SAT. It focuses on the properties and relations of points, lines, surfaces, solids, and higher-dimensional analogs. This knowledge will be crucial for your SATs and integral to various fields like physics, engineering, computer graphics, and more.

The fundamentals of solid geometry can seem daunting initially, but we promise that once you’ve understood the basics, the complex problems become more straightforward. We will commence with the most basic forms – cuboids and cubes, examining their properties and how to calculate aspects like volume, surface area, and diagonal lengths.

Understanding these simple solid shapes is crucial before proceeding to more complex ones in our subsequent lessons. We will provide exercises after each session, offering you the opportunity to practice what you have learned. Remember, like every other aspect of mathematics, the key to mastering solid geometry lies in understanding the concepts and practicing regularly.

We hope you are as excited as we are about this journey we’re embarking on together. Buckle up, grab your notebook, and get ready to delve into the fascinating world of Solid Geometry!

Stay tuned for the next part, where we’ll explore the intriguing world of prisms and pyramids!

Exploring Prisms and Pyramids – The Building Blocks (Part 2)

Welcome back to the second installment of our eight-part series on Solid Geometry for SAT preparation. We’re excited to venture deeper into the realm of three-dimensional shapes. Building upon the fundamental understanding of cuboids and cubes from the first session, we’re now ready to explore the captivating world of prisms and pyramids.

In this lesson, we’ll familiarize ourselves with prisms and pyramids, their definitions and properties, and discuss volume and surface area calculations.

A prism is a three-dimensional geometric figure with two parallel, congruent bases connected by parallelogram faces. Depending on the shape of the base, prisms can be classified into various types – rectangular prisms, triangular prisms, and more. Let’s look at the basic formulas associated with prisms:

1. The volume of a Prism (V): It’s calculated as the product of the base area (B) and the height (h) of the prism. Thus, the formula becomes V = B * h.
2. Surface Area of a Prism (A): This is calculated as the sum of twice the base area (B) and the product of the base perimeter (P) and height (h). Hence, the formula is A = 2B + Ph.

A pyramid is a polyhedron whose base is a polygon, and whose lateral faces are triangles converging to a single point called the apex. The base can take multiple shapes, leading to variations like square pyramids, triangular pyramids, etc. The key formulas associated with pyramids are:

1. The volume of a Pyramid (V): The volume is equal to one-third of the product of the base area (B) and the height (h). Thus, V = 1/3 * B * h.
2. Surface Area of a Pyramid (A): It is calculated as the sum of the base area (B) and half the product of the base perimeter (P) and the slant height (l). The formula is A = B + 1/2 * P * l.

We will delve into each of these shapes, working through examples to illustrate these formulas and their applications. By incorporating diagrams, step-by-step problem-solving, and tips to remember these formulas, we aim to ensure that these concepts are cemented in your memory.

By the end of this part, you’ll have a robust understanding of prisms and pyramids and be well-equipped to handle related SAT questions confidently. To reinforce your newly acquired knowledge, we will conclude with a set of exercises that mimic real SAT problems.

In the third part of our series, we’ll journey into the exciting world of cylinders and cones. Keep practicing, stay curious, and remember – every step forward, no matter how small, gets you closer to mastering solid geometry.

Diving into Cylinders and Cones – Expanding Perspectives (Part 3)

Greetings and welcome to Part 3 of our detailed exploration into Solid Geometry as part of our SAT preparation series. Having understood prisms and pyramids in Part 2, we’re now primed to dive deeper and expand our understanding to include cylinders and cones, integral components of the solid geometry domain.

In this lesson, we’ll immerse ourselves in understanding the nuances of cylinders and cones. We’ll cover their definitions, and intrinsic properties and delve into the world of calculations, including volume and surface area.

A cylinder is a solid geometrical figure with straight parallel sides and a circular or oval cross-section. It is like a prism but with circular bases. The essential formulas related to cylinders are:

1. The volume of a Cylinder (V): The volume is computed as the product of the base area (which is a circle in this case, πr²) and the height (h) of the cylinder. Thus, V = πr²h.
2. Surface Area of a Cylinder (A): This is calculated as the sum of the areas of the two bases and the lateral surface area. Hence, the formula is A = 2πrh + 2πr².

A cone is a three-dimensional geometric shape that tapers smoothly from a flat base to a point called the apex or vertex. Here are the key formulas associated with cones:

1. The volume of a Cone (V): The volume is equal to one-third of the product of the base area (again, a circle here, so πr²) and the height (h). Thus, V = 1/3πr²h.
2. Surface Area of a Cone (A): It’s calculated as the sum of the base area and the lateral area (which is a sector of a circle). Hence, the formula is A = πr(r + l), where l is the slant height of the cone.

Through the course of this session, we’ll take a detailed look at these shapes, working on example problems to apply these formulas and providing strategies to remember them effectively. We will break down the logic behind these formulas and use visuals to aid comprehension.

By the end of this session, you will have a solid understanding of cylinders and cones and be well-prepared to solve related SAT questions confidently. We will wrap up with a set of practice problems to reinforce the concepts covered and prepare you for real-world SAT problems.

Looking forward to our next session, where we will unveil the intriguing world of spheres. Remember, like any mathematical topic, the key to mastering solid geometry lies in continual practice and concept reinforcement. Keep practicing, stay inquisitive, and see yourself ace solid geometry!

The Sphere – Geometry’s Smooth Operator (Part 4)

Welcome back to the fourth installment of our eight-part series on Solid Geometry, designed to prepare you for the SAT examination. Having mastered the realms of prisms, pyramids, cylinders, and cones, we now move on to explore the most symmetric of all solid geometric figures: the sphere.

In this session, we will cover the fundamental properties of spheres, and their definitions and take a deep dive into volume and surface area calculations.

A sphere is a set of points in space that are all equidistant from a fixed point called the center. It is one of the most symmetrical shapes in three-dimensional space. The crucial formulas associated with spheres are:

1. The volume of a Sphere (V): The volume of a sphere is calculated as four-thirds of the product of pi (π) and the cube of the radius (r). The formula thus becomes V = 4/3πr³.
2. Surface Area of a Sphere (A): The surface area of a sphere is four times the product of pi (π) and the square of the radius (r). Hence, the formula is A = 4πr².

In this session, we will break down these formulas, explain why they work, and how to use them effectively to solve problems. Using diagrams and step-by-step problem-solving, we aim to make the concept of spheres as approachable as possible. Remember, a sphere’s symmetry can make it one of the easier solids to work with once you understand the basics.

By the end of this part, you’ll have a comprehensive understanding of spheres and be well-equipped to answer related SAT questions confidently. To fortify your understanding, we will conclude the session with a series of exercises that simulate actual SAT problems.

Stay tuned for the next session, where we will dive into the fascinating world of composite solids. Keep practicing, and remember, with every problem you solve, you are one step closer to mastering solid geometry. Your journey towards acing the SAT continues, and we are with you at every step of the way!

Composite Solids – When Shapes Combine (Part 5)

Welcome to the fifth part of our comprehensive eight-part series on Solid Geometry for SAT preparation. Having individually explored prisms, pyramids, cylinders, cones, and spheres, we’re now ready to tackle a slightly more complex but equally intriguing aspect of Solid Geometry – composite solids.

Composite solids, or composite figures, are shapes that comprise two or more different basic solids. These can be a combination of any of the solids we’ve learned so far. Calculations involving composite solids may seem intimidating initially, but they can be easily dissected and understood with the right approach.

In this session, we’ll familiarize ourselves with the composite solids process. There aren’t specific formulas for composite solids as they are combinations of basic solids. We’ll use our knowledge of individual solid figures to find composite figures’ volume and surface area.

Here’s the general approach:

1. The volume of Composite Solids: The volume of a composite solid is found by adding or subtracting the volumes of its component shapes. If a composite solid can be divided into simpler parts, find the volume of each part and then add (if the parts are combined) or subtract (if a part is removed) these volumes.
2. Surface Area of Composite Solids: The surface area of a composite solid is calculated by adding or subtracting the surface areas of its component shapes. However, note that when shapes are combined, some surfaces may no longer be exposed, and thus their areas are not included in the total surface area.

This session will involve breaking down composite solids into simpler shapes, identifying their component parts, and using our knowledge of the individual shapes to compute the desired quantities. We’ll walk through this process with the help of several example problems, providing a step-by-step approach to handling such questions.

By the end of this session, you’ll have developed a solid strategy for handling composite solids and be well-prepared to tackle related SAT questions confidently. As always, we’ll conclude with a series of exercises to consolidate the concepts learned and give you hands-on practice.

In the next session, we’ll vent into the exciting cross-sections world. Keep practicing and stay motivated! With every new concept learned, you are getting closer to becoming a master of solid geometry. Remember, we’re with you every step of the way on your journey towards acing the SAT!

Cross-Sections – A Different View of Solids (Part 6)

Welcome to the sixth installment of our in-depth eight-part series on Solid Geometry. So far, we have ventured into the fascinating world of prisms, pyramids, cylinders, cones, spheres, and even composite solids. Now, we’re ready to explore yet another intriguing dimension of solid geometry – cross-sections.

Cross-sections provide a different perspective on solids by allowing us to examine what the interior of solid looks like when cut in a specific manner. This concept doesn’t involve new formulas but a different approach to visualizing and understanding solid shapes.

In this session, we will delve into:

1. Understanding Cross-Sections: Cross-sections are the shapes we get when cutting straight through an object. The shape of a cross-section depends on the type of cut, or “slice,” made into the solid.
2. Identifying Cross-Sections: Recognizing the shape resulting from a given slice requires you to visualize the cut mentally. We’ll go through various examples to practice this.
3. Volume and Surface Area with Cross-Sections: Cross cross-sections can sometimes help determine a solid’s volume or surface area. We’ll discuss when and how this method can be useful.

We’ll explore various types of cross-sections across different solids and learn how to identify the shape resulting from a cross-section. We’ll look at it all from horizontal and vertical slices to oblique and diagonal ones. This session will be filled with diagrams and visual aids to make the concept of cross-sections as intuitive as possible.

By the end of this session, you’ll have a robust understanding of cross-sections in solid geometry, preparing you to confidently solve related SAT questions. As always, we’ll conclude with practice problems to reinforce the concepts learned and give you a taste of real SAT problems.

In our next session, we’ll explore the fascinating world of 3D coordinates and how they are used in solid geometry. Keep practicing and stay curious. Remember, every new concept brings you one step closer to becoming a pro at solid geometry and acing the SATs. We’re here to support you throughout this journey, so let’s keep going!

3D Coordinates – Plotting in Space (Part 7)

Welcome back to our enlightening journey through Solid Geometry. This is the seventh part of our eight-part series aimed at preparing you for the SAT examination. Having mastered concepts ranging from basic solids to composite figures and cross-sections, we’re now ready to venture into an exciting realm that brings an added dimension to our understanding – the world of 3D coordinates.

3D coordinates are an extension of the two-dimensional coordinate system that we’re familiar with, introducing a third dimension, usually denoted by ‘z.’ This allows us to plot points in three-dimensional space, offering a more robust representation of the world around us.

In this session, we will focus on:

1. Understanding 3D Coordinates: An ordered triple (x, y, z) denotes a point in three-dimensional space. We’ll delve into understanding these coordinates and how they help us represent points in 3D space.
2. Distance between Two Points in 3D Space: The distance d between two points (x₁, y₁, z₁) and (x₂, y₂, z₂) is given by the formula d = sqrt((x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²).
3. Midpoint of a Line Segment in 3D Space: The midpoint M between two points (x₁, y₁, z₁) and (x₂, y₂, z₂) is given by M = ((x₁+x₂)/2 , (y₁+y₂)/2 , (z₁+z₂)/2).

We’ll explore these concepts in-depth and demonstrate them with plenty of examples. With the help of visual aids, we’ll plot points in 3D space, calculate distances, and find midpoints. We’ll also discuss practical applications of these concepts to solidify your understanding.

By the end of this part, you’ll have a firm understanding of 3D coordinates and their applications, preparing you to handle related SAT questions confidently. As usual, we’ll wrap up the session with practice exercises to consolidate your learning and provide you with a real taste of SAT problems.

Looking forward to our next and final session, we’ll be delving into transformations and symmetry in solid geometry. Keep practicing and stay motivated! Every new concept learned brings you closer to your goal of mastering solid geometry and acing the SAT. As always, we’re here to assist you at every step of your journey.

Transformations and Symmetry – Shaping the Perspective (Part 8)

Welcome to the final part of our comprehensive eight-part series on Solid Geometry for SAT preparation. We have journeyed through the realms of prisms, pyramids, cylinders, cones, spheres, composite solids, cross-sections, and 3D coordinates. In this final session, we will discover the fascinating world of transformations and symmetry in solid geometry.

Transformations refer to operations that change the position, size, or shape of a figure, while symmetry refers to the balance or correspondence in the position of parts on opposite sides of a line or plane or around a center or axis.

In this session, we’ll focus on:

1. Understanding Transformations: We’ll delve into different types of transformations, including translations (slides), rotations (turns), reflections (flips), and dilation (resizing). There are no specific formulas for these, as they are more conceptual in nature.
2. Recognizing Symmetry: We’ll discuss the three types of symmetry – reflective (mirror) symmetry, rotational symmetry, and point symmetry. We’ll learn how to recognize these different types of symmetry in various solid figures.

By exploring transformations, we’ll discover how a figure can be moved, resized, or turned while still maintaining its original shape. On the other hand, symmetry will allow us to see the inherent balance in different figures.

This session will involve a lot of visual examples to help you grasp these concepts. We’ll also solve a variety of problems that require the application of transformations and symmetry.

By the end of this session, you’ll have a solid understanding of transformations and symmetry in solid geometry, equipping you to handle related SAT questions confidently. We’ll conclude with practice problems that give you the opportunity to apply these concepts, further reinforcing your learning.

Having completed this series on Solid Geometry, you are now well-prepared for this portion of the SAT. Remember that continual practice is the key to fully grasping and retaining these concepts. Keep honing your skills, stay confident, and you’re sure to excel in your test. We’re delighted to have been part of your journey and wish you the best of luck!

Let’s explore the properties, formulas, and key features of a cube and a cuboid.

Cube A cube is a three-dimensional geometric shape that is a special kind of prism. It’s a box shape, and all its sides are square. It is also a type of cuboid. As such, it has some special properties:

1. Faces: A cube has six faces, all of which are equal-sized squares. This means that all sides of a cube are of the same length, which we typically denote as ‘a’.
2. Edges: A cube has twelve edges, and because all faces of a cube are squares, all edges are of the same length.
3. Vertices: A cube has eight vertices or corners.

Key formulas related to cubes include:

1. The volume of a Cube (V): The volume of a cube is found by cubing the length of one of its sides, V = a³.
2. Surface Area of a Cube (A): The surface area of a cube is six times the area of one of its faces. Since each face is a square of side length ‘a’, the surface area is A = 6a².
3. Space Diagonal of a Cube (d): The space diagonal of a cube, the line segment joining opposite corners of the cube, can be found using the formula d = √3 * a.

Cuboid A cuboid, also known as a rectangular prism, is another common three-dimensional geometric shape. Unlike a cube, not all faces of a cuboid are squares. A cuboid has rectangular faces and may or may not have all edges of the same length.

1. Faces: A cuboid has six faces, and all of them are rectangles.
2. Edges: A cuboid has twelve edges.
3. Vertices: A cuboid has eight vertices or corners.

Key formulas related to cuboids include:

1. The volume of a Cuboid (V): The volume of a cuboid is found by multiplying the length (l), width (w), and height (h) of the cuboid, V = lwh.
2. Surface Area of a Cuboid (A): The surface area of a cuboid is the sum of the areas of its six rectangular faces, A = 2lw + 2wh + 2hl.
3. Space Diagonal of a Cuboid (d): The space diagonal of a cuboid, the line segment joining opposite corners of the cuboid, can be found using the formula d = √(l² + w² + h²).

Remember, while these formulas provide a quick way to find the properties of cubes and cuboids, understanding the principles behind these shapes is crucial for solving more complex geometry problems.

Let’s delve into cones and cylinders’ properties, formulas, and key features.

Cone A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (usually circular) to a point called the apex or vertex. Here are some of its properties:

1. Base: A cone has one base, which is typically a circle.
2. Apex: The apex or vertex of a cone is the point opposite the base. All lines drawn from the apex to the base form the curved surface of the cone.
3. Height (h): The height of a cone is the perpendicular distance from the base to the apex.
4. Radius (r): The radius of a cone is the radius of the base circle.

Key formulas related to cones include:

1. The volume of a Cone (V): The volume of a cone is one-third the product of the area of the base (which is πr² for a circle) and the height, V = 1/3πr²h.
2. Surface Area of a Cone (A): The surface area of a cone is the sum of the base area (πr²) and the lateral area (which is πr times the slant height, l). Thus, A = πr(r + l).
3. Slant Height of a Cone (l): The slant height is the distance from any point on the circle to the apex. The Pythagorean theorem can be found if the height and radius are known: l = √(r² + h²).

Cylinder A cylinder is another common three-dimensional geometric shape. A typical cylinder has two identical circular bases and one curved side. Here are some of its properties:

1. Bases: A cylinder has two bases that are parallel and congruent circles.
2. Height (h): The height of a cylinder is the perpendicular distance between the two bases.
3. Radius (r): The radius of a cylinder is the radius of the base circle.

Key formulas related to cylinders include:

1. Volume of a Cylinder (V): The volume of a cylinder is the product of the base area (which is πr² for a circle) and the height, V = πr²h.
2. Surface Area of a Cylinder (A): The surface area of a cylinder is the sum of the areas of the two bases (2πr²) and the lateral area (which is 2πrh). Thus, A = 2πr(r + h).

Remember, while these formulas provide a quick way to find the properties of cones and cylinders, understanding the principles behind these shapes is crucial for solving more complex geometry problems.

Let’s examine spheres and hemispheres’ properties, formulas, and key features.

Sphere A sphere is a perfectly symmetrical, three-dimensional geometric shape, and all points on the surface of a sphere are equidistant from its center. Here are some of its properties:

1. Center: The center of a sphere is the point inside the sphere that is equidistant from all points on the sphere’s surface.
2. Radius (r): The radius of a sphere is the distance from the center to any point on the sphere’s surface.

Key formulas related to spheres include:

1. The volume of a Sphere (V): The volume of a sphere is determined by the formula V = 4/3πr³.
2. Surface Area of a Sphere (A): The surface area of a sphere is given by the formula A = 4πr².

Hemisphere A hemisphere is essentially half of a sphere. It is formed by cutting a sphere along a plane that passes through its center, yielding two identical halves. Here are some of its properties:

1. Radius (r): The radius of a hemisphere is the same as that of the original sphere, the distance from the center to any point on the surface.
2. Base: The base of a hemisphere is a circle formed by the cutting plane.

Key formulas related to hemispheres include:

1. Volume of a Hemisphere (V): Since a hemisphere is half a sphere, its volume is half the volume of a sphere. The formula for the volume of a hemisphere is V = 2/3πr³.
2. Surface Area of a Hemisphere (A): The surface area of a hemisphere includes the area of the circular base (πr²) plus half the surface area of the sphere (2πr²). So, A = 3πr².

Remember, these formulas provide a quick way to calculate the properties of spheres and hemispheres, but understanding the principles behind these shapes is vital for solving more complex geometry problems.

Pyramid

A pyramid is a three-dimensional geometric shape with a polygon as its base and triangular faces converging to a single point known as the apex. The shape of its base largely determines the shape and properties of a pyramid. Here, let’s consider three main types of pyramids: triangular, square, and pentagonal.

1. Triangular Pyramid (Tetrahedron) A triangular pyramid, also known as a tetrahedron, has a triangle for its base and three additional triangular faces.

Key features include:

• Faces: 4 faces (all triangles)
• Edges: 6 edges
• Vertices: 4 vertices

Key formulas related to a tetrahedron include:

• Volume (V): The volume is given by V = (Base Area * Height) / 3.
• Surface Area (A): The surface area is the sum of the areas of the base and the lateral faces.

2. Square Pyramid A square pyramid has a square for its base and four additional triangular faces.

Key features include:

• Faces: 5 faces (1 square, 4 triangles)
• Edges: 8 edges
• Vertices: 5 vertices

Key formulas related to a square pyramid include:

• Volume (V): The volume is given by V = (Base Area * Height) / 3.
• Surface Area (A): The surface area is the sum of the areas of the base and the lateral faces. The area of the lateral faces (the four triangles) is equal to the perimeter of the base times the slant height divided by 2.

3. Pentagonal Pyramid A pentagonal pyramid has a pentagon for its base and five additional triangular faces.

Key features include:

• Faces: 6 faces (1 pentagon, 5 triangles)
• Edges: 10 edges
• Vertices: 6 vertices

Key formulas related to a pentagonal pyramid include:

• Volume (V): The volume is given by V = (Base Area * Height) / 3.
• Surface Area (A): The surface area is the sum of the areas of the base and the lateral faces. The area of the lateral faces (the five triangles) is equal to the perimeter of the base times the slant height divided by 2.

It’s important to note that these formulas hold true for all pyramids — not just those with triangular, square, or pentagonal bases. The shape of the base determines the number of triangular faces, edges, and vertices the pyramid will have, but the calculations for volume and surface area remain consistent. Understanding these principles is key to being able to solve a variety of geometric problems involving pyramids.

Prism

A prism is a three-dimensional geometric figure that has identical parallel bases and rectangular faces connecting the bases. The shape of the base gives the prism its name. Let’s explore the properties and formulas for triangular, rectangular, and pentagonal prisms.

1. Triangular Prism A triangular prism has two triangular bases and three rectangular faces.

Key features include:

• Faces: 5 faces (2 triangles, 3 rectangles)
• Edges: 9 edges
• Vertices: 6 vertices

Key formulas related to a triangular prism include:

• Volume (V): The volume is given by V = Base Area * Height. The base area for a triangle is 1/2 * base * height.
• Surface Area (A): The surface area is the sum of the areas of the base and the lateral faces. The lateral area of a triangular prism is the perimeter of the base times the height of the prism.

2. Rectangular Prism (Cuboid) A rectangular prism, also known as a cuboid, has two rectangular bases and four rectangular faces.

Key features include:

• Faces: 6 faces (all rectangles)
• Edges: 12 edges
• Vertices: 8 vertices

Key formulas related to a rectangular prism include:

• Volume (V): The volume is given by V = Length * Width * Height.
• Surface Area (A): The surface area is given by A = 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height.

3. Pentagonal Prism A pentagonal prism has two pentagonal bases and five rectangular faces.

Key features include:

• Faces: 7 faces (2 pentagons, 5 rectangles)
• Edges: 15 edges
• Vertices: 10 vertices

Key formulas related to a pentagonal prism include:

• Volume (V): The volume is given by V = Base Area * Height. The base area for a regular pentagon is 1/2 * perimeter * apothem.
• Surface Area (A): The surface area is the sum of the areas of the base and the lateral faces. The lateral area of a pentagonal prism is the perimeter of the base times the height of the prism.

It’s important to note that these formulas hold true for all prisms, regardless of the shape of the base. The shape of the base will determine the number of faces, edges, and vertices the prism will have, but the calculations for volume and surface area remain consistent. Understanding these principles is key to being able to solve a variety of geometric problems involving prisms.

SAT Circles

Part 1: Understanding the Basics of Circles

Hello from MKSprep, the trusted SAT preparation center in Putalisadak, Kathmandu, Nepal. We are now ready to take a circular journey in our SAT math series! This first part of our in-depth exploration into Circles will set the foundation for understanding this key geometric shape.

Introduction to Circles

In mathematics, a circle is a shape consisting of all points in a plane at a given distance from a certain point, known as the circle’s center. The radius is the distance between any point on the circle and its center.

Diameter, Circumference, and Area

Here are some fundamental concepts related to circles:

• Diameter: The longest line can be drawn in a circle, passing through the center. The diameter is twice the radius of the circle.
• Circumference: The circumference is the boundary or the distance around the circle. For any circle, the circumference is more than three times the diameter. This relationship is expressed by the formula C = πd or C = 2πr.
• Area: The area of a circle is the number of square units that can fit inside it. It is calculated as A = πr².

Understanding these basic concepts is crucial for solving circle-related problems in the SAT math section.

Stay tuned for the next part, where we delve into the world of arcs and sectors. At MKSprep, we are committed to making your SAT preparation as smooth as possible!

Part 2: Arcs and Sectors in Circles

Welcome back to the SAT preparation series by MKSprep, your trusted SAT preparation center located in Putalisadak, Kathmandu, Nepal. In this second part on Circles, we dive deeper into two integral components – Arcs and Sectors.

Arcs in Circles

An arc in a circle is a portion of the circumference. The length of an arc is proportional to the degree measure of its central angle. In other words, if you have a 60° angle at the center of the circle, the length of the arc will be 1/6 of the total circumference. This relationship is expressed as Arc length = (θ/360°) × 2πr, where θ is the degree measure of the central angle.

Sectors in Circles

A sector of a circle is the region enclosed by two radii and their intercepted arc. It resembles a slice of pie. Similar to arcs, the area of a sector is proportional to the degree measure of its central angle. Therefore, if a circle is divided into a sector by a 60° angle, the area of the sector will be 1/6 of the total area of the circle. This relationship is expressed as Sector area = (θ/360°) × πr², where θ is the degree measure of the central angle.

Understanding these concepts will help you efficiently tackle SAT math questions related to arcs and sectors.

Stay tuned for our next lesson, where we will explore the properties of chords in circles. At MKSprep, we are committed to equipping you with the knowledge and skills needed for SAT success!

Part 3: Chords in Circles

Greetings once more from MKSprep, your preferred SAT preparation center located in Putalisadak, Kathmandu, Nepal. Continuing with our deep dive into Circles, in this third part, we will discuss an essential concept: Chords.

What is a Chord?

In the context of a circle, a chord is a straight-line segment that connects two points on the circle’s circumference. The longest possible chord of a circle runs through the circle’s center and is known as the diameter.

Properties of Chords

Here are some key properties of chords:

• Equal Chords: In the same circle or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.
• Perpendicular to the Chord: A radius or diameter that is perpendicular to a chord bisects the chord (divides it into two equal parts) and the arc it subtends (the arc that it cuts off).
• Chords Equidistant from the Center: In the same circle or congruent circles, two chords are equidistant from the center if and only if they are congruent.

Comprehending these properties is crucial for solving SAT math questions that involve chords in circles.

In our next installment, we will examine the concept of tangents to a circle. At MKSprep, we are dedicated to ensuring your SAT preparation is thorough and fruitful!

Part 4: Tangents to Circles

Welcome back to our SAT preparation series provided by MKSprep, your leading SAT preparation center in Putalisadak, Kathmandu, Nepal. In this fourth part of our deep dive into Circles, we’re going to explore the fascinating world of tangents.

What is a Tangent?

A tangent to a circle is a straight line that touches the circle at exactly one point, known as the point of tangency. An important property to remember is that a radius drawn to the point of tangency is always perpendicular to the tangent line.

Properties of Tangents

Here are some significant properties of tangents to remember:

• Tangent Segments from a Point: From a point outside a circle, the two tangent segments to the circle are congruent. This means they have the same length.
• Angles between Tangents and Radii: The angle between the radius of a circle and a tangent line drawn to that circle from the endpoint of the radius is always a right angle (90 degrees).
• Angles formed by Tangents: The angle formed by two tangents, two secants, or a secant and a tangent drawn from a point outside the circle is half the difference of the measures of the intercepted arcs.

Understanding these properties will significantly assist you in successfully navigating SAT math questions involving tangents to circles.

Join us for the next lesson, where we’ll delve into the intriguing topic of inscribed angles in circles. At MKSprep, we’re committed to providing you with the most effective SAT preparation possible!

Part 5: Inscribed Angles in Circles

Hello again from MKSprep, your SAT preparation center situated in the heart of Putalisadak, Kathmandu, Nepal. As we continue our exploration of Circles, this fifth part introduces a key concept: Inscribed Angles.

What is an Inscribed Angle?

An inscribed angle is formed by two chords in a circle with a common endpoint. This common endpoint forms the vertex of the inscribed angle. The other two endpoints define what is known as an intercepted arc on the circle’s circumference.

Properties of Inscribed Angles

Here are the essential properties of inscribed angles:

• Measure of an Inscribed Angle: The measure of an inscribed angle is half the measure of its intercepted arc.
• Inscribed Angles on the Same Arc: All inscribed angles that intercept the same arc are equal.
• Inscribed Angle and a Diameter: An inscribed angle that intercepts a semicircle (where the arc is a diameter) is always a right angle (90 degrees).

Grasping these properties will greatly assist you in solving SAT math problems involving inscribed angles in circles.

Stay tuned for our next section, where we will dive into the topic of sector and arc length in circles. At MKSprep, we are here to ensure that your SAT preparation journey is comprehensive and rewarding!

Part 6: Sectors and Arc Lengths in Circles

Welcome once again to our SAT preparation series offered by MKSprep, your trustworthy SAT preparation center in Putalisadak, Kathmandu, Nepal. We’re discussing sectors and arc lengths in this sixth part of our circle exploration.

What are Sectors and Arc Lengths?

A sector of a circle is a section of the circle enclosed by two radii and their intercepted arc. The length of an arc is simply the distance along the path of the circle from one point to another.

How to Find Sectors and Arc Lengths?

Here’s how you calculate these two key components:

• Sector Area: To find the area of a sector, you need to know the measure of the central angle that subtends it. The formula for the sector area is (central angle/360) * π * r², where r is the radius of the circle.
• Arc Length: The arc length is found using a similar formula as the sector area. The formula is (central angle/360) * 2πr, again where r is the radius of the circle.

Understanding these principles will be incredibly beneficial in tackling SAT math questions concerning sectors and arc lengths in circles.

Join us in the next segment, where we’ll investigate the compelling topic of chords in circles. MKSprep is dedicated to providing you with the highest standard of SAT preparation!

Part 7: Chords in Circles

Welcome back to MKSprep, your dedicated SAT preparation center in Putalisadak, Kathmandu, Nepal. In this seventh part of our circle series, we are focusing on the concept of chords.

What are Chords?

A chord is a straight-line segment that connects two points on the circumference of a circle. The longest possible chord in a circle is its diameter.

Significant Properties of Chords:

Let’s explore some of the important properties of chords:

• Equal Chords: Equal chords of a circle subtend equal angles at the circle’s center. Conversely, if the angles subtended by two chords at the center of the circle are equal, the chords are also equal.
• Perpendicular from the Center: If a perpendicular is drawn from the center of the circle to a chord, it bisects the chord. That means it divides the chord into two equal parts.
• Chords Equidistant from Center: Chords that are equidistant from the center of the circle are equal in length.

Knowing these chord properties can greatly assist you in answering SAT math questions related to chords in circles.

Join us in our final installment of this series, where we’ll be dealing with tangents and their properties. MKSprep is committed to making your SAT preparation journey as comprehensive as possible!

Part 8: Tangents to Circles

Congratulations on reaching the final part of our SAT preparation series on circles offered by MKSprep, your reliable SAT preparation center in Putalisadak, Kathmandu, Nepal. In this concluding segment, we’re studying the concept of tangents to circles.

What is a Tangent?

A tangent is a line that touches a circle at exactly one point, known as the point of tangency. No matter where the tangent line touches the circle, it is always perpendicular to the radius drawn to the point of tangency.

Key Properties of Tangents:

Below are some significant properties of tangents:

• Tangent Segment: A tangent segment is a line segment whose endpoints are the point of tangency and a point on the tangent line.
• Tangent Segments from an External Point: Those segments are congruent if two tangent segments are drawn to a circle from an external point.

Understanding these properties will be immensely helpful in answering SAT math questions related to tangents to circles.

With the conclusion of this part, we’ve covered all the fundamental elements of circles that you’ll encounter in the SAT. Thank you for choosing MKSprep as your companion in your SAT preparation journey!