5 1 classifying triangles
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There are 7 types of triangles classified by their sides and angles: equilateral triangles have 3 congruent sides; isosceles triangles have 2 congruent sides; scalene triangles have no congruent sides; equiangular triangles have 3 congruent angles; acute triangles have 3 acute angles; obtuse triangles have 1 obtuse angle; and right triangles have 1 right angle. The lesson teaches how to classify triangles based on these properties of their sides and angles.
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This document contains formulas for calculating the areas, volumes, and surface areas of various 2D and 3D shapes. It includes formulas for calculating the area of triangles, parallelograms, trapezoids, circles, rhombi/kites, and regular polygons. For 3D shapes it includes formulas for calculating the volume, surface area, and lateral area of rectangular prisms, other prisms, cylinders, pyramids, and cones. It also contains the Pythagorean theorem and formulas for calculating trigonometric ratios, circumferences, and the altitude of a triangle.
Maths Top 50 Formulas
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive function. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
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12 3 volume of prisms, cylinders, pyramids & cones
This document discusses formulas for calculating the volumes of various geometric shapes. It provides the formulas for finding the volumes of cylinders, cones, and prisms. For cylinders, the volume formula is given as V = πr^2h. For cones, the volume formula is V = 1/3πr^2h. An example calculation is shown for each. Formulas are also provided for finding the volumes of prisms using the formula V = Bh, where B is the area of the base and h is the height.
12 2 surface area of solids
The document discusses how to calculate the surface area of different 3D shapes like rectangular prisms, cylinders, triangular prisms, cones, and pyramids. It provides the formulas for surface area of each shape and works through examples of using the formulas to find the surface area when given dimensions of the shape.
1.1 writing algebraic expressions lesson
The document discusses writing algebraic expressions from word phrases and vice versa. It provides examples of key word phrases for the basic operations of addition, subtraction, multiplication, and division. It also gives examples of translating phrases like "3 more than x" or "the product of 3 and a number t" into algebraic expressions like "x + 3" or "3t". The objective is to be able to write an algebraic expression for a word phrase or a word phrase for an expression.
9 3 multiplying polynomials by monomials lesson
This document discusses multiplying polynomials by monomials using algebra tiles. It provides examples of multiplying different polynomials by monomials, such as 3(x + 4) = 3x + 12, x(x + 3) = x^2 + 3x, and -3x(2x + 1) = -6x^2 - 3x. It also models other examples like 2(x + 5) = 2x + 10, 4(3x + 1) = 12x + 4, and -5(-x - 2) = 5x + 10 to demonstrate how to multiply polynomials by monomials.
6 1 relations lesson
A relation maps numbers from its domain to numbers in its range through a series of operations. A relation can be represented as a set of ordered pairs. The domain is the set of first elements in each ordered pair, representing the inputs. The range is the set of second elements, representing the outputs. A relation can be thought of as a machine that takes numbers as inputs and produces other numbers as outputs through some operation.
5 6 probability and odds lesson
This document defines key probability terms like outcomes, events, randomness, and equally likely outcomes. It explains how to calculate probability as a ratio of favorable outcomes to total possible outcomes. Examples are provided like finding the probability of rolling an even number on a standard six-sided die. The complement of an event is also defined as the opposite outcome. Finally, odds are defined as the ratio of favorable outcomes to unfavorable outcomes or vice versa.
5 3 percent proportion
The document discusses percent proportions, which compare part of a quantity to the whole quantity or base using a percent. It provides examples of setting up and solving percent proportion word problems by writing the proportion, cross multiplying, and solving for the unknown value. Examples include finding what percent of $15 is $9, what number is 30% of 150, and what number is 12 equal to 80% of. The document demonstrates that the percent proportion formula is: part/base = percent/100 and can be used to find unknown parts, bases, or percents.
4 1 multiplying rational numbers examples
1) The document discusses multiplying rational numbers. It provides two rules for determining the sign of the product: if the numbers have the same sign, the product is positive, and if they have different signs, the product is negative.
2) Examples are provided of multiplying rational expressions by writing them as fractions and cancelling terms if possible.
3) The document emphasizes that when there is an odd number of negative signs in the factors being multiplied, the product will be negative, and if there is an even number of negative signs, the product will be positive.
4 1 multiplying rational numbers examples
1) The document discusses multiplying rational numbers. It provides two rules for determining the sign of the product: if the numbers have the same sign, the product is positive, and if they have different signs, the product is negative.
2) Examples are provided of multiplying rational expressions by writing them as fractions and cancelling terms if possible.
3) The document emphasizes that when there is an odd number of negative signs in the factors being multiplied, the product will be negative, and if there is an even number of negative signs, the product will be positive.
3 2 adding and subtracting rational numbers lesson
This document provides a lesson on adding and subtracting rational numbers. It begins with a warm up problem and example of adding decimals. It then teaches how to add and subtract rational numbers with like denominators by adding or subtracting the numerators and keeping the denominator. Several examples are provided using number lines and evaluating expressions. The document ends with a two part lesson quiz to assess understanding.
2.1 graphing integers on a number line lesson
- A number line is a line with evenly spaced marks that represent numbers like integers, fractions, and other quantities.
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- Movement right on the number line represents increasing or positive numbers, while movement left represents decreasing or negative numbers.
2.1 graphing integers on a number line lesson
- A number line is a line with evenly spaced marks that represent numbers like integers, fractions, and other quantities.
- Numbers can be graphed on a number line by placing a point at the mark corresponding to the number.
- Movement right on the number line represents increasing/positive numbers, while movement left represents decreasing/negative numbers.
1.2 order of operations lesson
The document discusses the order of operations, known as PEMDAS or P.E.M.D.A.S. It states that PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction and is the proper order to follow when evaluating mathematical expressions. Following PEMDAS is important to get the correct solution and avoid mistakes. Examples are provided to demonstrate how to use PEMDAS to simplify expressions step-by-step.
1.1 writing expressions and equations lesson
This document provides an introduction to expressions and equations in algebra. It defines expressions as statements that do not contain an equals sign, such as 2x - 4, while equations are statements that do contain an equals sign, such as 4n + 7 = 11. The lesson explains that students will practice writing verbal expressions and equations from algebraic forms, and vice versa. It provides examples and emphasizes using words like "more than", "less than", and "times" rather than symbols like "+" and "-".
13 4 tangent ratio lesson
This document discusses using tangent ratios to determine side lengths in right triangles. It defines tangent ratios as the ratio of the length of the opposite leg to the length of the adjacent leg. Tangent ratios can be used to find the measure of distances that are difficult to measure directly. The tangent inverse function, denoted Tan-1, can be used to find a missing angle measure when two sides of a triangle are known. Examples demonstrate setting up and solving tangent ratios and using the tangent inverse to find missing angle measures.
14 5 segment measures lesson
1) The document discusses finding measures of angles formed by chords, secants, and tangents of circles. It provides theorems for calculating angle measures based on intercepted arc lengths.
2) Formulas are presented for calculating lengths of segments associated with circles, including secants, chords, and tangents.
3) Examples demonstrate using the theorems and formulas to find missing angle measures and segment lengths in various circle geometry problems involving combinations of secants, chords and tangents.
14 4 secant-tangent angles
Secant-tangent angles are formed when a secant line intersects a tangent line either on or outside of a circle. If the vertex is outside the circle, the degree measure is half the difference between the intercepted arcs. If the vertex is on the circle, the degree measure is half the intercepted arc. When two tangent lines form an angle, the degree measure is also half the difference between the intercepted arcs.
14 3 secant angles lesson
This document discusses secants, tangents, and the angles they form in relation to circles. It states that a secant line intersects a circle at two points, and if two secants intersect inside a circle, the measure of the angle formed is half the sum of the intercepted arcs. The document provides examples of finding measures of interior and exterior angles formed by secants and tangents, as well as measures of intercepted arcs. Students are expected to apply the concepts to solve problems involving angles and arcs formed by secants and tangents intersecting inside, outside, and on the circumference of circles.
14 2 tangents to a circle lesson
This document defines key terms related to circles such as radius, diameter, chord, secant, and tangent. It provides examples of identifying different types of line segments in relation to a circle. Theorems are stated about tangent lines being perpendicular to radii and tangent segments from a common external point being congruent. Examples are worked through applying these theorems, such as finding if a segment is tangent to a circle using the Pythagorean theorem and solving for the radius of a circle given side lengths.
14 1 inscribed angles and intercepted arcs
This document discusses inscribed angles and relationships in circles. It defines an inscribed angle as an angle whose vertex is on the circle. The measure of an inscribed angle is equal to half the measure of its intercepted arc. Examples are provided to demonstrate finding the measure of inscribed angles given arc measures, and vice versa. The document also states that if two inscribed angles intercept the same arc, they are congruent. It provides examples of solving for variables using the relationship between inscribed angles and their intercepted arcs.
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12 3 volume of prisms, cylinders, pyramids & cones
12 3 volume of prisms, cylinders, pyramids & cones
3 2 adding and subtracting rational numbers lesson
3 2 adding and subtracting rational numbers lesson
5 1 classifying triangles
- 1. Lesson 5.1 Classifying Triangles Today, you will learn to… * classify triangles by their sides and angles * find measures in triangles
- 2. A B C ∆ ABC
- 3. Equilateral Triangle 3 congruent sides
- 4. Isosceles Triangle 2 congruent sides
- 5. Scalene Triangle no congruent sides
- 6. Equiangular Triangle 3 congruent angles
- 7. Acute Triangle 3 acute angles 60° 70° 50°
- 8. Obtuse Triangle 1 obtuse angle 95° 25°60°
- 9. Right Triangle 1 right angle 60° 30°
- 10. We classify triangles by their sides and angles. SIDES ANGLES Equilateral Isosceles Scalene Equiangular Acute Obtuse Right