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1. The document defines important terms related to circles such as radius, diameter, chord, arc, sector, and segment. It also provides the relationship between degrees and radians. 2. Formulas are presented for calculating the length of an arc, perimeter of a segment, area of a triangle formed by the radius and a chord, area of a sector, and area of a segment. 3. Instructions are given on how to convert between degrees and radians using a calculator and how to find sine, cosine, and tangent values for angles measured in radians.

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Radians And Arc Length

1. Radian measure relates the angle measure to the arc length intercepted by the angle on a circle of radius r. If the arc length is equal to r, the angle measure is 1 radian.
2. To use formulas for arc length and area of a sector, the angle measure must be in radians. The document provides conversions between degrees and radians and examples of using the arc length and area formulas.
3. The key ideas are that radian measure relates the angle to arc length on a circle, and formulas require the angle be in radians rather than degrees. Examples show converting between degrees and radians and using the formulas.

AS LEVEL CIRCULAR MEASURE GEOMETRY EXPLAINED

The document defines a radian as the angle subtended by an arc of a circle equal in length to the radius. It states that π radians equals 180 degrees, so 1 radian equals about 57.29 degrees. Formulas are provided for finding the circumference of an arc and area of a sector using radians. Examples are given to practice converting between radians and degrees and using the formulas. Special angle values are listed in a table. Past exam questions are worked through, applying concepts of radians, sectors, arcs, and right triangles in semi-circles.

Add Math(F4) Circular Measure 8.3

This document discusses calculating the area of a sector of a circle. It provides the formula for finding the area of a sector, which is (θ/360)πr^2, where θ is the central angle in radians and r is the radius. It includes examples of using the formula to find the area, radius, or central angle given two of the three values. It also provides a worksheet with areas and radii of sectors to calculate the missing central angles.

Areas of Circles and Sectors

The document discusses calculating the areas of circles, sectors, and segments of circles. It defines a circle as having the area of πr^2, a sector as a fractional part of the total circle area defined by an arc and its radii, and a segment as the portion of a sector minus the area of the triangle formed by the arc and its radii. It provides examples of calculating the areas of full circles, sectors of varying central angles, and segments.

Trigonometric identities

This document discusses trigonometric functions and identities. It provides definitions of trig functions like sine, cosine, tangent, and cotangent. It then lists 8 fundamental trigonometric identities and the reciprocal, quotient, and Pythagorean relations between trig functions. It gives conditions and rules for transforming trig identities and examples of proving identities like secθ cotθ = cscθ and 2cos2θ - 1 = cos2θ−sin2θ. The document assigns proving additional identities like secѲ/cscѲ = tanѲ as homework.

bearings.ppt

The document discusses bearings and how to calculate them. A bearing is defined as an angle measured clockwise from true north. Examples are given of calculating the bearing between two points using trigonometry. Related concepts like calculating the reverse bearing by adding or subtracting 180 degrees are also covered. Several multi-step word problems are worked through demonstrating how to find distances and bearings between points when given travel directions or legs.

Geometry circle properties

This document discusses various angle and length properties of circles and polygons. It defines key circle terms like radius, diameter, chord, and tangent. It then outlines five angle properties of circles: 1) the angle at the center is twice the angle at the circumference, 2) a right angle is formed when a radius bisects a semicircle, 3) angles in the same segment are equal, 4) angles in a cyclic quadrilateral add to 180 degrees, and 5) alternate segments theorem relating angles outside and inside a circle. It also discusses finding the sum of internal angles and the measure of one internal angle for regular polygons.

surface area and volume

The document provides information on surface area and volume formulas and calculations for basic 3D shapes including prisms, cubes, cylinders, cones, and spheres. It defines key terms like surface area and volume and provides example calculations and formulas for finding the surface area and volume of cubes, rectangular prisms, cylinders, cones, and spheres. Diagrams and examples are included to illustrate the different shapes and how to set up the surface area and volume calculations.

Radians And Arc Length

1. Radian measure relates the angle measure to the arc length intercepted by the angle on a circle of radius r. If the arc length is equal to r, the angle measure is 1 radian.
2. To use formulas for arc length and area of a sector, the angle measure must be in radians. The document provides conversions between degrees and radians and examples of using the arc length and area formulas.
3. The key ideas are that radian measure relates the angle to arc length on a circle, and formulas require the angle be in radians rather than degrees. Examples show converting between degrees and radians and using the formulas.

AS LEVEL CIRCULAR MEASURE GEOMETRY EXPLAINED

The document defines a radian as the angle subtended by an arc of a circle equal in length to the radius. It states that π radians equals 180 degrees, so 1 radian equals about 57.29 degrees. Formulas are provided for finding the circumference of an arc and area of a sector using radians. Examples are given to practice converting between radians and degrees and using the formulas. Special angle values are listed in a table. Past exam questions are worked through, applying concepts of radians, sectors, arcs, and right triangles in semi-circles.

Add Math(F4) Circular Measure 8.3

This document discusses calculating the area of a sector of a circle. It provides the formula for finding the area of a sector, which is (θ/360)πr^2, where θ is the central angle in radians and r is the radius. It includes examples of using the formula to find the area, radius, or central angle given two of the three values. It also provides a worksheet with areas and radii of sectors to calculate the missing central angles.

Areas of Circles and Sectors

The document discusses calculating the areas of circles, sectors, and segments of circles. It defines a circle as having the area of πr^2, a sector as a fractional part of the total circle area defined by an arc and its radii, and a segment as the portion of a sector minus the area of the triangle formed by the arc and its radii. It provides examples of calculating the areas of full circles, sectors of varying central angles, and segments.

Trigonometric identities

This document discusses trigonometric functions and identities. It provides definitions of trig functions like sine, cosine, tangent, and cotangent. It then lists 8 fundamental trigonometric identities and the reciprocal, quotient, and Pythagorean relations between trig functions. It gives conditions and rules for transforming trig identities and examples of proving identities like secθ cotθ = cscθ and 2cos2θ - 1 = cos2θ−sin2θ. The document assigns proving additional identities like secѲ/cscѲ = tanѲ as homework.

bearings.ppt

The document discusses bearings and how to calculate them. A bearing is defined as an angle measured clockwise from true north. Examples are given of calculating the bearing between two points using trigonometry. Related concepts like calculating the reverse bearing by adding or subtracting 180 degrees are also covered. Several multi-step word problems are worked through demonstrating how to find distances and bearings between points when given travel directions or legs.

Geometry circle properties

This document discusses various angle and length properties of circles and polygons. It defines key circle terms like radius, diameter, chord, and tangent. It then outlines five angle properties of circles: 1) the angle at the center is twice the angle at the circumference, 2) a right angle is formed when a radius bisects a semicircle, 3) angles in the same segment are equal, 4) angles in a cyclic quadrilateral add to 180 degrees, and 5) alternate segments theorem relating angles outside and inside a circle. It also discusses finding the sum of internal angles and the measure of one internal angle for regular polygons.

surface area and volume

The document provides information on surface area and volume formulas and calculations for basic 3D shapes including prisms, cubes, cylinders, cones, and spheres. It defines key terms like surface area and volume and provides example calculations and formulas for finding the surface area and volume of cubes, rectangular prisms, cylinders, cones, and spheres. Diagrams and examples are included to illustrate the different shapes and how to set up the surface area and volume calculations.

sine and cosine rule

- The Sine Rule and Cosine Rule can be used to find unknown sides and angles in triangles that are not right-angled.
- The Sine Rule states that the ratio of the sine of an angle to its opposite side is equal to the ratio of any other angle-side pair. It is generally easier to use than the Cosine Rule.
- The Cosine Rule relates all three sides of a triangle to one of its interior angles. It can be used to find a single unknown when three other parts of the triangle are known.

Scalar product of vectors

The dot product of two vectors a and b is a scalar value defined as |a||b|cosθ, where |a| and |b| are the lengths of the vectors and θ is the angle between them. The dot product will be 0 if the vectors are perpendicular, positive if the angle between them is less than 90 degrees, and negative if the angle is greater than 90 degrees. If one vector is a unit vector, the dot product equals the length of the other vector projected onto the direction of the unit vector.

Trigonometric Identities.

The document discusses three main groups of trigonometric identities: reciprocal relations which relate trig functions that are inverse of each other like tangent and cotangent; quotient relations which show relationships between ratios of trig functions like tangent being equal to the sine over the cosine; and the Pythagorean relation which is the fundamental relationship between sine and cosine where the square of one added to the square of the other is equal to 1. Examples are provided for each type of identity and an activity is included to practice using and filling in identity formulas.

Polygons

Chapter 3 Polygons
3.1 Definition
3.2 Terminology
3.3 Sum Of Interior Angles Of A Polygon
3.4 Sum Of Exterior Angles Of A Polygon
3.5 Diagonals in one vertex of any Polygon
3.6 Diagonals in any vertices of a Polygon
3.7 Quadrilaterals

Trigonometry presentation

Trigonometry is the study of triangles and their relationships. The document discusses how trigonometry is used in fields like architecture, astronomy, geology, and for measuring distances and heights. It provides examples of how trigonometry can be used to calculate the height of a building given the distance and angle of elevation to its top.

Trigonometric ratios

The document discusses trigonometric ratios and their properties. It defines the three basic trigonometric ratios - sine, cosine, and tangent - for any angle. It also discusses reciprocal ratios like cosecant, secant, and cotangent, which are the reciprocals of the basic ratios. The document provides examples of calculating trigonometric ratios for various angles and triangles. It also examines ratios of complementary and special angles like 0, 30, 45, 60, 90 degrees.

4.6 Exponential Growth and Decay

This document discusses exponential growth and decay functions. It provides examples of how to set up and solve exponential equations to model population growth, fish population decline, world poultry production increase, and bacterial growth. It also explains how to calculate half-life and doubling time for exponential decay and growth. Examples are worked through to find the half-life of tritium decaying at 5.471% per year and a radioactive substance decaying at 11% per minute, and to determine the amount of radioactive substance remaining after 6 years given its half-life is 3 years. The document concludes with assignments for students.

Law of sine and cosines

This document provides information on solving problems involving right triangles using trigonometry, including the Law of Sines and Law of Cosines. It includes examples of using trigonometry to solve problems involving angles of elevation/depression, finding areas and volumes, and determining distances. Tables of trigonometric function values are presented along with explanations of evaluating functions in different quadrants using reference angles. Proofs and examples are given for applying the Law of Sines and Law of Cosines to find missing sides and angles of triangles.

Trigonometric identities

This document provides an introduction to trigonometry. It discusses key topics like the Pythagorean theorem, coordinate plane, angles, degree and radian measurement, trigonometric functions, and trigonometric identities. The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. Trigonometric functions are used to calculate values by plugging in angles. Trigonometric identities are equalities that are always true, unlike equations which are only true for certain values.

Trigonometry

Trigonometry is a branch of mathematics that studies triangles and the relationships between the lengths of their sides and the angles between those sides. It defines trigonometric functions that describe these relationships and are applicable to cyclical phenomena like waves. Trigonometry has its origins in ancient Greek and Indian mathematics and was further developed by Islamic mathematicians. It is the foundation of surveying and has many applications in fields like astronomy, music, acoustics, and more.

Math's assignment ON circles

The document provides information about circles including definitions, properties, theorems and history. It defines a circle as a simple closed curve where all points are equidistant from the center. Key properties discussed are that a circle's circumference and radius are proportional, and its area is proportional to the square of the radius. Theorems covered relate to chords, tangents, secants and inscribed angles. The document also discusses squaring the circle problem and circles in history from ancient Greeks to modern mathematics.

Trigonometry ratios in right triangle

This document discusses right triangle trigonometry. It defines the six trigonometric functions as ratios of sides of a right triangle. The sides are the hypotenuse, adjacent side, and opposite side relative to an acute angle. It shows how to calculate trig functions for a given angle and how to find an unknown angle given two sides of a right triangle using inverse trig functions. Examples are provided to demonstrate solving for missing sides and angles of right triangles using trig ratios and the Pythagorean theorem.

Permutation and combination

- Permutation refers to arrangements that consider order, while combination refers to selections where order does not matter.
- The number of permutations of n distinct objects taken r at a time is nPr = n!/(n-r)!, while the number of combinations is nCr = n!/r!(n-r)!.
- Examples are given to illustrate permutations involving restricted arrangements and circular permutations. Restricted permutations consider cases where certain objects are always or never included.

Unit 4.1

This document discusses angles and their measurement. It explains that angles are measured in degrees, with a full circle being 360 degrees, or radians, where the radian measure is based on arc length. It provides examples of converting between degrees and radians. It also discusses measuring angular motion in revolutions per minute versus linear motion in miles per hour or feet per second. Circumference and arc length formulas are presented using both degree and radian measures.

Trigonometry

Trigonometry deals with triangles and the angles between sides. The main trigonometric ratios are defined using the sides of a right triangle: sine, cosine, and tangent. Trigonometric functions can convert between degrees and radians. Standard angle positions and trigonometric identities relate trig functions of summed and subtracted angles. The sine and cosine rules relate the sides and angles of any triangle, allowing for calculations of missing sides or angles given other information. Unit circle graphs further illustrate trigonometric functions.

Trigonometry Functions

This document provides an overview of trigonometric functions. It covers angles and their measurement in degrees and radians. It then discusses right triangle trigonometry, defining the six trigonometric functions and properties like fundamental identities. Special angle values are computed for 30, 45, and 60 degrees. Trig functions of general angles and the unit circle approach are introduced. Graphs of sine, cosine, tangent, cotangent, cosecant and secant functions are examined.

Sine and cosine rule

The document provides guidance on using trigonometric rules to solve problems involving sides and angles of triangles. It explains that the Sine Rule is used when there is a "matching pair" of a known side and its corresponding angle. The Cosine Rule is used when there is no right angle or matching pair. Examples are given of using both rules to calculate missing sides or angles of triangles.

Ratio, Rates And Proprotion

The document discusses ratios, rates, unit rates, proportions, and scale drawings. It provides examples of writing and solving proportions using cross products. It also gives examples of finding unit rates, using scales to relate actual sizes to scale models or drawings, and solving problems involving ratios, rates, proportions, and scales.

Permutations and combinations ppt

Priya Anand's 11th class mathematics document discusses permutations and combinations. It defines permutations as arrangements of objects from a group that consider order, and combinations as selections of objects from a group that do not consider order. The document outlines the key concepts, formulas, differences and examples of permutations and combinations. It explains that permutations are used when order matters, while combinations are used when order does not matter.

Trig substitution

1. The document describes techniques for integrating trigonometric functions using trigonometric substitution and identities involving sine, cosine, tangent, and secant.
2. Trigonometric substitution involves redefining the variable in terms of a trigonometric function, unlike traditional substitution which defines a new variable.
3. The techniques are demonstrated through examples such as finding antiderivatives of √9-x^2/x^2 and √x^2+4/x^2.

Chapter 8 circular measure

This document provides information about circular measure including radians, conversion between radians and degrees, length of arc, and area of sectors. It defines a radian as the angle subtended by an arc equal in length to the radius. Formulas are given for converting between radians and degrees, finding the length of an arc given the radian measure of its central angle, and finding the area of a sector given its radian measure and the radius. Several examples demonstrate applying these formulas to solve problems involving radians. Exercises provide additional practice problems for students to work through.

Year 6 – Circumference of Three-Quadrants (Worksheet)

Year 6 – Circumference of Three-Quadrants (Worksheet). More worksheets for FREE at:
http://www.tes.co.uk/teaching-resource/Year-6-Circumference-of-3-Quadrants-Worksheet-6398354/

sine and cosine rule

- The Sine Rule and Cosine Rule can be used to find unknown sides and angles in triangles that are not right-angled.
- The Sine Rule states that the ratio of the sine of an angle to its opposite side is equal to the ratio of any other angle-side pair. It is generally easier to use than the Cosine Rule.
- The Cosine Rule relates all three sides of a triangle to one of its interior angles. It can be used to find a single unknown when three other parts of the triangle are known.

Scalar product of vectors

The dot product of two vectors a and b is a scalar value defined as |a||b|cosθ, where |a| and |b| are the lengths of the vectors and θ is the angle between them. The dot product will be 0 if the vectors are perpendicular, positive if the angle between them is less than 90 degrees, and negative if the angle is greater than 90 degrees. If one vector is a unit vector, the dot product equals the length of the other vector projected onto the direction of the unit vector.

Trigonometric Identities.

The document discusses three main groups of trigonometric identities: reciprocal relations which relate trig functions that are inverse of each other like tangent and cotangent; quotient relations which show relationships between ratios of trig functions like tangent being equal to the sine over the cosine; and the Pythagorean relation which is the fundamental relationship between sine and cosine where the square of one added to the square of the other is equal to 1. Examples are provided for each type of identity and an activity is included to practice using and filling in identity formulas.

Polygons

Chapter 3 Polygons
3.1 Definition
3.2 Terminology
3.3 Sum Of Interior Angles Of A Polygon
3.4 Sum Of Exterior Angles Of A Polygon
3.5 Diagonals in one vertex of any Polygon
3.6 Diagonals in any vertices of a Polygon
3.7 Quadrilaterals

Trigonometry presentation

Trigonometry is the study of triangles and their relationships. The document discusses how trigonometry is used in fields like architecture, astronomy, geology, and for measuring distances and heights. It provides examples of how trigonometry can be used to calculate the height of a building given the distance and angle of elevation to its top.

Trigonometric ratios

The document discusses trigonometric ratios and their properties. It defines the three basic trigonometric ratios - sine, cosine, and tangent - for any angle. It also discusses reciprocal ratios like cosecant, secant, and cotangent, which are the reciprocals of the basic ratios. The document provides examples of calculating trigonometric ratios for various angles and triangles. It also examines ratios of complementary and special angles like 0, 30, 45, 60, 90 degrees.

4.6 Exponential Growth and Decay

This document discusses exponential growth and decay functions. It provides examples of how to set up and solve exponential equations to model population growth, fish population decline, world poultry production increase, and bacterial growth. It also explains how to calculate half-life and doubling time for exponential decay and growth. Examples are worked through to find the half-life of tritium decaying at 5.471% per year and a radioactive substance decaying at 11% per minute, and to determine the amount of radioactive substance remaining after 6 years given its half-life is 3 years. The document concludes with assignments for students.

Law of sine and cosines

This document provides information on solving problems involving right triangles using trigonometry, including the Law of Sines and Law of Cosines. It includes examples of using trigonometry to solve problems involving angles of elevation/depression, finding areas and volumes, and determining distances. Tables of trigonometric function values are presented along with explanations of evaluating functions in different quadrants using reference angles. Proofs and examples are given for applying the Law of Sines and Law of Cosines to find missing sides and angles of triangles.

Trigonometric identities

This document provides an introduction to trigonometry. It discusses key topics like the Pythagorean theorem, coordinate plane, angles, degree and radian measurement, trigonometric functions, and trigonometric identities. The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. Trigonometric functions are used to calculate values by plugging in angles. Trigonometric identities are equalities that are always true, unlike equations which are only true for certain values.

Trigonometry

Trigonometry is a branch of mathematics that studies triangles and the relationships between the lengths of their sides and the angles between those sides. It defines trigonometric functions that describe these relationships and are applicable to cyclical phenomena like waves. Trigonometry has its origins in ancient Greek and Indian mathematics and was further developed by Islamic mathematicians. It is the foundation of surveying and has many applications in fields like astronomy, music, acoustics, and more.

Math's assignment ON circles

The document provides information about circles including definitions, properties, theorems and history. It defines a circle as a simple closed curve where all points are equidistant from the center. Key properties discussed are that a circle's circumference and radius are proportional, and its area is proportional to the square of the radius. Theorems covered relate to chords, tangents, secants and inscribed angles. The document also discusses squaring the circle problem and circles in history from ancient Greeks to modern mathematics.

Trigonometry ratios in right triangle

This document discusses right triangle trigonometry. It defines the six trigonometric functions as ratios of sides of a right triangle. The sides are the hypotenuse, adjacent side, and opposite side relative to an acute angle. It shows how to calculate trig functions for a given angle and how to find an unknown angle given two sides of a right triangle using inverse trig functions. Examples are provided to demonstrate solving for missing sides and angles of right triangles using trig ratios and the Pythagorean theorem.

Permutation and combination

- Permutation refers to arrangements that consider order, while combination refers to selections where order does not matter.
- The number of permutations of n distinct objects taken r at a time is nPr = n!/(n-r)!, while the number of combinations is nCr = n!/r!(n-r)!.
- Examples are given to illustrate permutations involving restricted arrangements and circular permutations. Restricted permutations consider cases where certain objects are always or never included.

Unit 4.1

This document discusses angles and their measurement. It explains that angles are measured in degrees, with a full circle being 360 degrees, or radians, where the radian measure is based on arc length. It provides examples of converting between degrees and radians. It also discusses measuring angular motion in revolutions per minute versus linear motion in miles per hour or feet per second. Circumference and arc length formulas are presented using both degree and radian measures.

Trigonometry

Trigonometry deals with triangles and the angles between sides. The main trigonometric ratios are defined using the sides of a right triangle: sine, cosine, and tangent. Trigonometric functions can convert between degrees and radians. Standard angle positions and trigonometric identities relate trig functions of summed and subtracted angles. The sine and cosine rules relate the sides and angles of any triangle, allowing for calculations of missing sides or angles given other information. Unit circle graphs further illustrate trigonometric functions.

Trigonometry Functions

This document provides an overview of trigonometric functions. It covers angles and their measurement in degrees and radians. It then discusses right triangle trigonometry, defining the six trigonometric functions and properties like fundamental identities. Special angle values are computed for 30, 45, and 60 degrees. Trig functions of general angles and the unit circle approach are introduced. Graphs of sine, cosine, tangent, cotangent, cosecant and secant functions are examined.

Sine and cosine rule

The document provides guidance on using trigonometric rules to solve problems involving sides and angles of triangles. It explains that the Sine Rule is used when there is a "matching pair" of a known side and its corresponding angle. The Cosine Rule is used when there is no right angle or matching pair. Examples are given of using both rules to calculate missing sides or angles of triangles.

Ratio, Rates And Proprotion

The document discusses ratios, rates, unit rates, proportions, and scale drawings. It provides examples of writing and solving proportions using cross products. It also gives examples of finding unit rates, using scales to relate actual sizes to scale models or drawings, and solving problems involving ratios, rates, proportions, and scales.

Permutations and combinations ppt

Priya Anand's 11th class mathematics document discusses permutations and combinations. It defines permutations as arrangements of objects from a group that consider order, and combinations as selections of objects from a group that do not consider order. The document outlines the key concepts, formulas, differences and examples of permutations and combinations. It explains that permutations are used when order matters, while combinations are used when order does not matter.

Trig substitution

1. The document describes techniques for integrating trigonometric functions using trigonometric substitution and identities involving sine, cosine, tangent, and secant.
2. Trigonometric substitution involves redefining the variable in terms of a trigonometric function, unlike traditional substitution which defines a new variable.
3. The techniques are demonstrated through examples such as finding antiderivatives of √9-x^2/x^2 and √x^2+4/x^2.

sine and cosine rule

sine and cosine rule

Scalar product of vectors

Scalar product of vectors

Trigonometric Identities.

Trigonometric Identities.

Polygons

Polygons

Trigonometry presentation

Trigonometry presentation

Trigonometric ratios

Trigonometric ratios

4.6 Exponential Growth and Decay

4.6 Exponential Growth and Decay

Law of sine and cosines

Law of sine and cosines

Trigonometric identities

Trigonometric identities

Trigonometry

Trigonometry

Math's assignment ON circles

Math's assignment ON circles

Trigonometry ratios in right triangle

Trigonometry ratios in right triangle

Permutation and combination

Permutation and combination

Unit 4.1

Unit 4.1

Trigonometry

Trigonometry

Trigonometry Functions

Trigonometry Functions

Sine and cosine rule

Sine and cosine rule

Ratio, Rates And Proprotion

Ratio, Rates And Proprotion

Permutations and combinations ppt

Permutations and combinations ppt

Trig substitution

Trig substitution

Chapter 8 circular measure

This document provides information about circular measure including radians, conversion between radians and degrees, length of arc, and area of sectors. It defines a radian as the angle subtended by an arc equal in length to the radius. Formulas are given for converting between radians and degrees, finding the length of an arc given the radian measure of its central angle, and finding the area of a sector given its radian measure and the radius. Several examples demonstrate applying these formulas to solve problems involving radians. Exercises provide additional practice problems for students to work through.

Year 6 – Circumference of Three-Quadrants (Worksheet)

Year 6 – Circumference of Three-Quadrants (Worksheet). More worksheets for FREE at:
http://www.tes.co.uk/teaching-resource/Year-6-Circumference-of-3-Quadrants-Worksheet-6398354/

Year 6 – Circumference of Semicircles (Worksheet)

Year 6 – Circumference of Semicircles (Worksheet). More worksheet for FREE at:
http://www.tes.co.uk/teaching-resource/Year-6-Circumference-of-Semicircles-Worksheet-6398353/

Making a Pie Chart

How to make a pie chart in Excel. Simple instructions for beginners, some knowledge of excel needed.
Level - Easy. 2nd in a series on Pie Charts

PIE CHART

This document provides instructions on how to construct a pie chart. It explains that a pie chart represents data in circular sections, with the central angle of each section proportional to the percentage of the total value it represents. It provides an example of exam results data and shows how to calculate the central angle for each result and draw a pie chart representing this information.

Circle

The document defines and explains key terms related to circles:
1. A circle is a closed curve in which all points are equidistant from the center. It has properties like radius, diameter, circumference, chords, arcs, and segments.
2. Key terms are defined, like radius as the line from the center to the edge, diameter as a chord passing through the center, and circumference as the distance around the circle.
3. Examples are given of circles in daily life, music, and sports to illustrate the concept. Diagrams accompany the definitions of terms like chord, arc, semicircle, and segments.

Law of tangent

The document discusses the law of tangents, which sets up a ratio relationship between the sum and difference of two sides of a triangle and the tangents of half the sum and differences of the angles opposite the sides. An example problem demonstrates using the law of tangents to solve for a missing side of a triangle given two sides and one angle measure. The full working of the problem is shown, applying the tangent law formulas and then using the law of sines to find the final missing side measurement.

PERIMETERS AND AREAS OF PLANE FIGURES - MENSURATION

This document discusses calculating perimeters and areas of plane figures. It begins by reviewing formulas for finding perimeters and areas of shapes like rectangles, squares, triangles, and trapezoids. It then introduces Heron's formula for calculating the area of a triangle given its three side lengths. Several examples demonstrate using this formula and other techniques to find areas of composite figures made of rectangles, triangles, and trapezoids. The document aims to consolidate knowledge of area and perimeter calculations.

Circles

This document defines and explains key terms and concepts related to circles in geometry. It discusses what a circle is, the history of circles, and important circle terminology like diameter, radius, chord, arc, sector, and segment. It also covers theorems about relationships between chords, tangents, secants, and angles in circles. Key ideas are that a circle is a set of points equidistant from the center, and that circles have been an important mathematical concept throughout history.

Cbse 10th circles

The document summarizes key definitions and properties related to circles and tangents to circles:
- It defines circles, radii, diameters, chords, secants, and tangents. It also defines tangent circles and common tangents.
- It states theorems about tangents, including that a tangent line is perpendicular to the radius at the point of tangency, and a line perpendicular to the radius at a point on the circle is a tangent.
- It provides examples demonstrating identifying special segments and lines related to circles, identifying common tangents, and using properties of tangents to solve problems.

2 circular measure arc length

The document discusses calculating arc length and the area of a sector of a circle. It defines that the arc length s is equal to the radius r multiplied by the central angle θ in radians. The area of a sector is equal to (1/2) * r^2 * θ, where θ is in radians. It provides examples of calculating arc length when given r and θ, and the area of sectors when given r and the central angle measure.

Circles IX

Vaibhav Goel presented on circles and their properties. The presentation included definitions of key circle terms like radius, diameter, chord, and arc. It also proved several theorems: equal chords subtend equal angles at the center; a perpendicular from the center bisects a chord; there is one circle through three non-collinear points; equal chords are equidistant from the center; congruent arcs subtend equal angles; and the angle an arc subtends at the center is double that at any other point. The presentation concluded that angles in the same segment are equal and cyclic quadrilaterals have opposite angles summing to 180 degrees.

maths ppt on circles

A circle is defined as all points in a plane that are equidistant from a fixed center point. The center point is called the center of the circle, and the fixed distance from the center is called the radius. The longest chord that can be drawn through the center is the diameter. If two chords of a circle are equal in length, then their distances from the center are also equal, as proven using the Side-Side-Side congruence rule for triangles.

Chapter 8 circular measure

Chapter 8 circular measure

Year 6 – Circumference of Three-Quadrants (Worksheet)

Year 6 – Circumference of Three-Quadrants (Worksheet)

Year 6 – Circumference of Semicircles (Worksheet)

Year 6 – Circumference of Semicircles (Worksheet)

Making a Pie Chart

Making a Pie Chart

PIE CHART

PIE CHART

Circle

Circle

Law of tangent

Law of tangent

PERIMETERS AND AREAS OF PLANE FIGURES - MENSURATION

PERIMETERS AND AREAS OF PLANE FIGURES - MENSURATION

Circles

Circles

Cbse 10th circles

Cbse 10th circles

2 circular measure arc length

2 circular measure arc length

Circles IX

Circles IX

maths ppt on circles

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Teknik Peningkatan Prestasi

This document provides guidance for mathematics teachers to improve student performance in Additional Mathematics for the SPM 2009 exam. It identifies common weaknesses and mistakes by student category (very weak to excellent). Suggestions are given to rectify issues for different topics in Paper 1 and Paper 2, such as functions, quadratic equations, vectors, and integration. For weaker students, the focus is on getting partial marks. For stronger students, emphasis is placed on careless mistakes. Teachers are advised to provide targeted practice addressing specific weaknesses.

Skills In Add Maths

This document provides examples of solving equations, expanding and factorizing expressions, solving simultaneous equations, working with indices and logarithms. It includes over 100 problems across these topics for students to practice. The problems range in complexity from basic single-step equations to multi-part logarithmic expressions and systems of simultaneous equations.

Add10kelantan

1. This document appears to be an answer key or marking scheme for a mathematics exam with 25 questions. It provides the answers, workings, or mark schemes for each question on the exam.
2. For each question, it lists the number of marks awarded for the full or partial answers. The total marks are tallied at the end.
3. The document contains detailed mathematical solutions and workings for the questions, evaluating answers for correctness according to set schemes.

Soalan ptk tambahan

1. Dokumen tersebut membincangkan perancangan dan pelaksanaan pengajaran pembelajaran di dalam bilik darjah.
2. Beberapa aspek utama yang dibincangkan termasuk objektif pengajaran, penggunaan sumber dan teknik pengajaran, serta kemahiran guru.
3. Dokumen ini memberikan panduan kepada guru dalam merancang dan melaksanakan proses pengajaran dan pembelajaran yang berkesan.

Attachments 2012 04_1

Attachments 2012 04_1

Janjang aritmetik

Janjang aritmetik

Teknik Peningkatan Prestasi

Teknik Peningkatan Prestasi

Skills In Add Maths

Skills In Add Maths

Add10kelantan

Add10kelantan

Add10sabah

Add10sabah

Add10terengganu

Add10terengganu

Add10perak

Add10perak

Add10ns

Add10ns

Add10johor

Add10johor

Strategi pengajaran pembelajaran

Strategi pengajaran pembelajaran

Soalan ptk tambahan

Soalan ptk tambahan

Refleksi

Refleksi

Perancangan pengajaran pembelajaran

Perancangan pengajaran pembelajaran

Penilaian

Penilaian

Pengurusan bilik darjah

Pengurusan bilik darjah

Pengurusan murid

Pengurusan murid

Penguasaan mata pelajaran

Penguasaan mata pelajaran

Penggunaan sumber dalam p & p

Penggunaan sumber dalam p & p

Pemulihan dan pengayaan

Pemulihan dan pengayaan

C1 Rubenstein AP HuG xxxxxxxxxxxxxx.pptx

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Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1

Jemison, MacLaughlin, and Majumder "Broadening Pathways for Editors and Authors"

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- 1. All in One CIRCULAR IMPORTANT TERMS 1. Definition : 1 IMPORTANT FORMULAE r r radian θ IN RADIAN 1 jejari Minor 2. Important relationship segment r A o O diameter 180 = π radian major π r chord 1 o = 180 radian C O θ segment 0 180 r tangent 1 radian = B π Minor arc 3. To change the unit . 2. ( s AB ) = r 0 Example : Convert 30 to radian:- 1. Length of arc AB Major arc 0 π Minor sector 30 = 30 x 180 radian O Major sector OR using calculator casio fx 570 ms) 30 shift DRG 1 = 3. Perimeter of segment ABC i) Change to radian mode ii) = sAB + chord AB = r + 2 r sin H r BASIC FORMULA θ 4. To find the sin , cos or tan for the A 4. Area of triangle OAB = r 2 r angle in O sin Radian using calculator θ Example : Find sin 1.5 radian 5. Area of sector OAB = r 2 Method 1 : If in radian mode . sin θ = O/H SAB = 6. Area of segment ABC cos θ = A / H A = sin 1.5 = = r 2( - sin ) Method 2: If in degree mode Sin 1.5 shift DRG 2 =