Y9 algebra 1 Linear Equations
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This document provides an overview of solving linear equations, including equations involving brackets, fractions, and changing the subject of a formula. It presents several example equations and step-by-step solutions showing how to isolate the variable. Students are reminded to check their answers by substituting them back into the original equation. The document also introduces solving equations with fractions using the lowest common denominator approach.
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https://tinyurl.com/y9muob6q
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https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u
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This document discusses four methods for solving quadratic equations: factorization, completing the square, using a formula, and using graphs. It provides an example of solving the equation 2x^2 - 10x + 12 + x^2 + 6x = -9 by factorizing into (x - 3)(x - 1) = 0, finding that the solutions are x = 3 or x = 1.2) Changing the Subject - Harder.pptx
2) Changing the Subject - Harder.pptxBalvinder4
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This document discusses rearranging formulae to make a variable the subject. It provides examples of rearranging equations to make x, r, , y, b, and d the subject. The techniques demonstrated include subtracting, dividing, multiplying, factorizing, and using square and cube roots. The document emphasizes collecting all terms with the intended subject on the same side before dividing or factorizing to isolate that variable.Equations Revision
Equations Revisionandrewhickson
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1) The document outlines objectives and methods for solving linear equations, including solving single equations, equations with fractions, and simultaneous equations.
2) Key methods discussed are transposing terms, multiplying/dividing both sides by the same amount to isolate the variable, and using substitution or elimination for simultaneous equations.
3) Examples are provided to illustrate solving single equations with various operations like addition, subtraction, multiplication and division as well as equations containing fractions or brackets.
G9_RADICAL_EQUATION_3rdQuarterPeriod.pptx
G9_RADICAL_EQUATION_3rdQuarterPeriod.pptxDaniloFrondaJr
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The document discusses how to solve radical equations by isolating the radical expression, removing the radical sign by raising both sides to the appropriate power, solving the resulting equation, and checking solutions. It provides examples of solving various radical equations step-by-step and checking solutions. Key steps include isolating radicals, squaring or cubing both sides to remove radicals, combining like terms, and factoring resulting equations. Students must check solutions in the original equation to identify any extraneous roots.More from estelav (20)
7) change of base
7) change of baseestelav
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This document discusses logarithmic equations and calculations. It provides instructions on how to rewrite logarithmic equations without using logarithms, solve simultaneous logarithmic equations, calculate logarithms to specific bases and numbers of significant figures, change logarithmic bases, and solve logarithmic equations. The document aims to teach students how to perform various operations with logarithms including rewriting, solving, calculating, and changing bases.5) logarithms graphs
5) logarithms graphsestelav
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This document provides an overview of exponential and logarithmic functions:
1) It explores properties of exponential functions with the forms y = ax, where a > 1 represents exponential growth and 0 < a < 1 represents exponential decay. Key aspects like asymptotes and y-intercepts of these graphs are discussed.
2) Tables are completed and graphs are drawn to represent exponential growth and decay functions.
3) The natural logarithm function ln(x) is introduced and its graph is sketched using a calculator. Common features that logarithmic graphs share with exponential graphs are described.
4) Examples of simplifying logarithmic expressions and solving logarithmic equations are presented.4) logarithms laws
4) logarithms lawsestelav
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This document discusses logarithmic laws and their proofs. It contains:
- Exercises to verify logarithmic laws like loga(xy) = loga(x) + loga(y) and nloga(x) = loga(x)n
- Proofs of these laws using the definition of logarithms and index form
- More exercises for students to solve involving simplifying logarithmic expressions using these laws
The goal is for students to understand and be able to apply the key logarithmic laws through worked examples and practice questions.2) exponential growth and decay
2) exponential growth and decayestelav
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This document discusses exponential functions and their properties. It explores exponential growth and decay through graphs of functions like y=2^x and y=0.5^x. It shows that as x increases, exponential growth functions approach infinity, while decay functions approach zero. The document also introduces the irrational number e as the most important base for modeling continuous growth and decay. It shows how the function A=Ce^rt models continuous compound interest as the compounding period approaches infinity.1) exponential equations
1) exponential equationsestelav
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This document discusses exponential functions and equations. It explores the properties of exponential functions by examining their graphs and understanding exponential growth and decay. It also covers how to solve problems leading to exponential equations by learning about bases, exponents, powers, and index rules. The document teaches how to evaluate, write in different bases, identify exponential equations, and solve exponential equations. It includes exercises to solve from the attached document on exponential equations and functions.6) simultaneous and problems
6) simultaneous and problemsestelav
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This document discusses finding the intersection points between a line and parabola by solving simultaneous equations, finding the value of k that makes a line tangent to a parabola, and finding the maximum area of a rectangle with a perimeter of 28 cm.5) quadratic equations
5) quadratic equationsestelav
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This document discusses solving quadratic equations by different methods such as factorisation, using the quadratic formula, and completing the square. It explains how to determine the number of solutions a quadratic equation has based on the sign of its discriminant, namely:
- If the discriminant is positive, there are two real roots
- If the discriminant is zero, there is one repeated root
- If the discriminant is negative, there are no real roots.
Examples are provided to illustrate calculating the discriminant and determining the number and type of roots.4) quadratic functions factorised form
4) quadratic functions factorised formestelav
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This document discusses quadratic functions and their properties. It explains how to express quadratics in different forms like factored, general, and vertex form. It provides examples of finding the zeros, line of symmetry, and vertex of various quadratic functions. Students are asked to work through examples of sketching graphs, factorizing expressions, solving equations, and rewriting functions in different forms to investigate the properties of quadratic functions and their relationships between algebraic and graphical representations.3) quadratic vertex form
3) quadratic vertex formestelav
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The document discusses quadratic functions and their graphs. It aims to explore the properties of quadratic functions and express them in different forms, including vertex form. It provides examples of writing quadratic functions in vertex form given the vertex, as well as writing the function in general form given its vertex. The key points are that the vertex form of a quadratic function y = a(x - h)2 + k shows the vertex is (h, k) and the line of symmetry is x = h. Converting between the vertex and general forms allows finding the maximum point of a quadratic function.2) quadratics gral form
2) quadratics gral formestelav
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This document discusses properties of quadratic functions and their graphs. It explores expressing quadratic functions in different forms, sketching graphs of basic quadratic functions, and investigating the effects of changing coefficients on the graph. The key aspects covered are the relationship between the coefficients and the graph properties like the vertex, line of symmetry, and y-intercept. Examples of matching functions to graphs and writing functions in standard form are provided.1) quadratic functions
1) quadratic functionsestelav
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The document discusses quadratic functions and their graphs. It explores expressing quadratic functions in different forms, and transforming quadratic functions and their graphs through translations, stretches, and other changes. Key aspects covered include the vertex and line of symmetry of parabolas, and how changing the coefficients affects the graph shape and position. Examples of specific quadratic functions are analyzed and graphed.Y9 algebra 1 simultaneous equations by substitution method
Y9 algebra 1 simultaneous equations by substitution methodestelav
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The document provides examples of solving simultaneous equations by substitution. It includes examples of setting up two equations representing relationships between variables, substituting one equation into the other to isolate a single variable, and solving for the value of that variable. It then uses the solved variable to find the value of the other variable.Y9 algebra 1 Change of Subject
Y9 algebra 1 Change of Subjectestelav
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By the end of the lesson, students should be able to change the subject of a formula. The document provides examples of changing the subject of formulas for perimeter of a circle, cost of a taxi, volume of a cone, and other formulas. Students are asked to make different variables the subject of provided formulas, such as making d, a, m, h, or x the subject.Y9 algebra 1 Inequalities
Y9 algebra 1 Inequalitiesestelav
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This document provides an overview of inequalities and how to solve them algebraically. It discusses representing inequalities on number lines, and the rules for adding, subtracting, multiplying, and dividing terms when solving inequalities, such as changing the sign of the inequality when multiplying or dividing by a negative number. Examples are provided of solving inequalities algebraically and representing the solutions on number lines.Y9 algebra 1 Collecting Terms & Expanding Brackets
Y9 algebra 1 Collecting Terms & Expanding Bracketsestelav
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The document outlines key concepts and skills to be learned in an algebra lesson, including:
- Simplifying algebraic expressions by collecting like terms
- Expanding brackets
- Multiplying algebraic expressions
It then provides examples of simplifying algebraic expressions, expanding brackets, finding perimeters and areas of shapes, evaluating expressions, and converting between temperatures in Fahrenheit and Celsius.Ib maths sl chain rule
Ib maths sl chain ruleestelav
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The document discusses applying the chain rule to find derivatives of composite functions. It provides examples of identifying composite functions and using the chain rule formula to take derivatives. It lists practice problems for students to find derivatives of various composite functions using the chain rule, including functions with exponents like (x3 + 1)8, as well as trigonometric functions like y = sin(4x).Ib maths sl product and quotient rules
Ib maths sl product and quotient rulesestelav
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- The document discusses product and quotient rules for finding derivatives of functions.
- The product rule states that the derivative of two functions multiplied together (f(x) = u(x)v(x)) is the first function multiplied by the derivative of the second plus the second function multiplied by the derivative of the first.
- The quotient rule is provided but not explained for finding the derivative of a function that is a quotient of two other functions.Ib maths sl derivatives of transcendental functions
Ib maths sl derivatives of transcendental functionsestelav
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The document discusses derivatives of trigonometric, exponential, and logarithmic functions. It provides formulas for the derivatives of sine, cosine, natural log, and exponential functions. Examples are given of finding derivatives and using them to find equations of tangent lines, areas under curves, and predicting derivative patterns from graphs.IB Maths SL Transformations of functions
IB Maths SL Transformations of functionsestelav
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This document discusses transformations of graphs including translations, stretches, and reflections. It defines vertical and horizontal translations as shifting the graph of a function up or down by adding a constant c, or shifting it left or right by changing the input by a constant b. Stretches are defined as vertically stretching by a scale factor a or horizontally by 1/a. Reflections are defined as reflecting the graph across the x or y-axis. Examples and exercises are provided to illustrate each type of transformation.Ib maths sl definite integrals
Ib maths sl definite integralsestelav
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The document provides information on definite integrals including:
- Definite integrals calculate the area under a curve between two bounds, or limits
- The definite integral of a function F(x) from a to b is equal to F(b) - F(a)
- The value of a definite integral can be positive, negative, or zero depending on the function
- Properties of definite integrals including additivity, scaling, and partitioning the interval
- Examples of using definite integrals to calculate areas under curves are providedY9 algebra 1 Linear Equations
- 1. Linear油Equations By油the油end油of油the油lesson油you油should油be油able油to油: Solve油equations油involving油brackets. Solve油equations油with油fractions油by油using油cross油 multiplication. Change油the油油subject油of油a油formula.
- 2. Solve油the油equation: 4油x油足油(油5油足油x油)油=油7 Remember !!! Check your answer by substituting it into the equation 4油x油足油油5油油油+油x油=油7 5油x油足油油5油油=油7 5油x油油油=油12 油油x油油油=油12/5
- 3. 6油a油足油5油足油(油4油a油足油7油)油=油0 Solve油the油equation: 6油a油油足油油5油油足油4油a油油+油7油=油0 2油a油油油油+油2油=油0 2油a油油油油=油足2 油a油油油油=油足1 Remember !!! Check your answer by substituting it into the equation
- 4. Solve油the油equation: 3x油+油2油(油x油+油1油)油=油3油x油+油12 3x油油+油2油x油+油2油=油3油x油+油12油 5油x油+油2油=油3油x油+油12油 5油x油足油3油x油+油2油=油油油12油 2油x油油=油油油12油足油2 2油x油油=油油油10 油x油油=油油5 Remember !!! Check your answer by substituting it into the equation
- 5. Solve油the油equation: 3油(油2油p油+油1油)油足油2油(油2油p油+油1油)油=油10 6油p油+油3油足油油4油p油足油油2油=油10 2油p油+油1油油油油油=油10 2油p油油油=油9 油p油油油=油4.5 Remember !!! Check your answer by substituting it into the equation
- 6. Solve油the油equation: 4油(油3x油足油1油)油足油3油(油3x油+油2油)油=油0 12油x油足油油4油油足油9油x油油足油油6油=油0 3油x油油足油油10油油=油0 3油x油油=油10 油x油油=油10/3 Remember !!! Check your answer by substituting it into the equation
- 8. Solve油the油equation: Remember !!! Check your answer by substituting it into the equation
- 10. Solve油the油equation: Remember !!! Check your answer by substituting it into the equation
- 11. Which method do you like best? Solve油the油equation:
- 16. Solve油the油equation: Remember !!! Check your answer by substituting it into the equation