A Guide To Equations And Inequalities - Mindset Learn

MINDSET LEARN GRADE 10 MATHEMATICSA Guide to Equations and InequalitiesTeaching ApproachThe videos in this series cover the revision of linear equations, equations with fractions andunknowns in the denominator, quadratic equations, literal equations, simultaneous equationsand word problems. They also cover inequalities.In the first video on revision of linear equations we remind pupils how to identify linearequations and work on examples that require basic simplification techniques and fractions. Itis important to remind your learners how to check their solutions by substituting their answerback into the original equation. Emphasise the importance of substituting into the originalequation. Learners must be careful with their signs when taking terms from one side of theequation to the other. Remind them that when you divide by a negative the signs, of all termswill change. Also try the games suggested in the resources sections to remind learners thatMaths can be fun!When dealing with fractional equations, stress the importance of restrictions and make sureto include examples in your lesson where a solution cannot be accepted because it isexcluded by the restriction. It may be necessary to revise factorising before the lesson onfactorising denominators.Make sure pupils know all the different methods to solve simultaneous linear equations;graphical, substitution and elimination. These methods can be used to solve words problemstoo.Our first video in linear inequalities shows solutions represented in set builder notation andinterval notation but please use interval notation in your examples and tests as this is themethod required by CAPS.We go over quite a few word problems just to give learners an idea of how to approachdifferent types of questions as this a section they often struggle with. However there is notonly one way to deal with all word problems and learners may still not be able to solve theones in a test etc. Stress to them the importance of practising as many examples as possibleto get better at this section.MINDSET LEARN TEACHING RESOURCES PUBLISHED 20131

MINDSET LEARN GRADE 10 MATHEMATICSVideo SummariesSome videos have a ‘PAUSE’ moment, at which point the teacher or learner can choose topause the video and try to answer the question posed or calculate the answer to the problemunder discussion. Once the video starts again, the answer to the question or the rightanswer to the calculation is given.Mindset suggests a number of ways to use the video lessons. These include: Watch or show a lesson as an introduction to a lesson Watch of show a lesson after a lesson, as a summary or as a way of adding in someinteresting real-life applications or practical aspects Design a worksheet or set of questions about one video lesson. Then ask learners towatch a video related to the lesson and to complete the worksheet or questions, either ingroups or individually Worksheets and questions based on video lessons can be used as short assessments orexercises Ask learners to watch a particular video lesson for homework (in the school library or onthe website, depending on how the material is available) as preparation for the next dayslesson; if desired, learners can be given specific questions to answer in preparation forthe next day’s lessonLinear Equations1. Revising Linear EquationsLearners are shown how to identify a linear equation and how to solve simple linearequations. We also look at solving simple fractional equations and fractions withunknowns in the denominator.2. Solving Fractional EquationsWe solve fractional equations where the denominator of the fraction has to be factorised,we also show learners how to work out restrictions and to check their solutions.3. Literal EquationsLearners are introduced to equations with variables on both sides of the equality sign. Welook at basic linear literal equations and an example involving quadratic literal equations.Quadratic Equations1. Quadratic EquationsStandard form of a quadratic expression is introduced and simple quadratic equationssolved.2. More Challenging Quadratic EquationsA lot of the focus here is on factorising difficult trinomials in order to solve quadraticequations.MINDSET LEARN TEACHING RESOURCES PUBLISHED 20132

MINDSET LEARN GRADE 10 MATHEMATICSSimultaneous Equations1. Introduction to Simultaneous EquationsWe identify and define simultaneous equations, find an ordered pair that is a solution to asystem of linear equations in two unknowns.2. Solving Simultaneous Equations GraphicallySolutions to a system of simultaneous equations are read off from a graph.3. Solving Simultaneous Equations using SubstitutionLinear equations in two variables are solved simultaneously using the substitutionmethod.4. Solving Simultaneous Equations by Elimination IThe difference between the substitution method and elimination method is addressed inthis video. We look at examples that can be solved using either the elimination method orsubstitution method.5. Solving Simultaneous Equations by Elimination IIHere we show learners when it is advantageous to use the elimination method.Linear Inequalities1. Linear Inequalities on a Number LineA number line is used to represent a linear inequality you must use interval notation torepresent a linear inequality.2. Solving Linear InequalitiesSolve simple linear inequalities that involve multiplying or dividing by a negative number.3. More Linear InequalitiesSolve linear inequalities that have denominators.Word Problems1. Dimension and Speed Word ProblemsHere we look at a money problem and another basic problem where simultaneousequations need to be used.2. Simultaneous Equations Word ProblemsSolve word problems that involve digits using simultaneous linear equations.3. A Digit ProblemThis video deals with the commonly tested dimension and speed word problems.MINDSET LEARN TEACHING RESOURCES PUBLISHED 20133

MINDSET LEARN GRADE 10 MATHEMATICSResource MaterialResource materials are a list of links available to teachers and learners to enhance their experience ofthe subject matter. They are not necessarily CAPS aligned and need to be used with discretion.Linear Equations1 Revising Linear Equations2 Solving Fractional /02/nasty quations.html3 Literal es-05.cnxmlplusThis site has a fun and interactivegame for solving linear equations.Worksheet with fractionalequations that you can print outand use in the classroom.Help save the Zogs: Fun gamethat learners can only succeed atif their linear equations are up toscratch (can also be used whenteaching linear functions).This website has a calculator thatcan be used to solve fractionalequations it also has maths testsand worksheets.Videos/worksheets/games onsolving all types of equations fromgrades 0 to 12Many examples of literalequations are shown andexplained.Textbook that explains literalequations and the rest of grade10 maths.Quadratic Equations1 Quadratic Equations2 More Challenging modules/solvquad6.htmIf you have an equation of the2form "ax bx c 0", this sitecan solve the equation and hasworksheets.This site shows how quadraticequations should be approached.Simultaneous Equations1 Introduction toSimultaneous Equations2 Solving SimultaneousEquations Graphically3 Solving SimultaneousMINDSET LEARN TEACHING RESOURCES PUBLISHED 20diagrams/2 http://www.purplemath.com/modules/systlin4.htmSite explains simultaneousequations basics.Graphical solution ofsimultaneous equationsexplained.This site allows you to solve twoequations with two unknowns byputting your question into itssolver.Step by step approach to thesubstitution method is discussed.4

MINDSET LEARN GRADE 10 MATHEMATICSEquations usingSubstitution4 Solving Simultaneousequations by Elimination I &IIhttp://www.youtube.com/watch?v XM7Q4Oj5OTchttp://www.youtube.com/watch?v 3ceN1InfyDU&feature relatedhttp://www.youtube.com/watch?v 3ceN1InfyDU&feature relatedhttp://www.webmath.com/solver2.htmlA video on solving simultaneousequations by elimination.More video examples on solvingsimultaneous equations byelimination.More video examples on solvingsimultaneous equations byelimination.This site allows will solve twoequations with two unknowns byputting your question into itssolver.Linear Inequalities1 Linear Inequalities on aNumber Line2 Solving Linear Inequalities3 More linear blem.aspx?p kids.com/inequalities.htmlStep by step approach to linearinequalities.Interval notation ://www.purplemath.com/modules/quadprob2.htmGrade 9 revisionproblems videos:Linear inequality calculator.Maths worksheets includinginequalities worksheets:Word Problems1 Dimension and Speed WordProblems2 SimultaneousWord ProblemsEquations3 A Digit ProblemMINDSET LEARN TEACHING RESOURCES PUBLISHED 2013ofwordWord problem solving strategies.Examples on digit problems.Examples on speed/dist/time inkilometres.Dimension and other quadraticword problems.5

MINDSET LEARN GRADE 10 MATHEMATICSTaskQuestion 1Solve:1.1 ()()()1.2Question 2Solve for q:Question 3Liz and Thandi collect the toys from boxes of breakfast cereal. Liz has 10 toys more thanThandi has. Altogether they have 54 toys. Calculate how many toys each girl has.Question 4Solve for x and y:Question 5Solve for x:Question 6Convert 131toif:HINT: Change the subject of the formulaQuestion 7Solve:7.17.2 (7.3)Question 8Solve for x and y:Question 9Solve and write your answer in interval notation:9.1()()9.29.3MINDSET LEARN TEACHING RESOURCES PUBLISHED 20136

MINDSET LEARN GRADE 10 MATHEMATICSQuestion 10Michelle is paid R55 for everyday she works during the holiday and she must pay her fatherR66 for every day she doesn’t work. At the end of 30 days she has R77. For how many daysdid she work?Question 11The diagonal of a rectangle is 25 cm more than its width. The length of the rectangle is 17cm more than its width. What are the dimensions of the rectangle?Question 12A man runs to the shop and back in 15 minutes. His speed on the way to the shop is 5 km/hand his speed on the way back is4 km/h. Find the distance to the shop.HINT: work in km/hMINDSET LEARN TEACHING RESOURCES PUBLISHED 20137

MINDSET LEARN GRADE 10 MATHEMATICSTask AnswersQuestion 11.1 ()()()1.2()(())()Question 2(()(()()()()()())())Question 3Let the number of toys Thandi has xAltogether they have 77 toys therefore:Then Liz has: x 10x x 10 542x 44x 22So Thandi has 22 toys and Liz has 32 toys.Question 4y 10-2x . (1) (2)Substitute (1) into (2): x 2(10-2x) 8x 20-4x 8-3x -12and y 10-2(4) 2Solution (4,2)4a)MINDSET LEARN TEACHING RESOURCES PUBLISHED 20138

MINDSET LEARN GRADE 10 MATHEMATICSQuestion 5()Question 6() Question 77.1()()x 7 or x -7(7.2())) ( w-1 1 or w-1 -1w 2or w 0()()Question 8As all the coefficients are different you should use the elimination method to solve these equations. .1 .2( )( )( )( )Eqn (1) –(2)(() (1)) (2)32MINDSET LEARN TEACHING RESOURCES PUBLISHED 20139

MINDSET LEARN GRADE 10 MATHEMATICSsubstitute back into equation 1 and solve for x.()Answer (41;-19)Question 99.1()())9.2(())9.3 -5 2x -3 7-5 3 2x 7 3-2 2x 10-1 x 5(Question 10Let the number of days worked x Then the number of days not worked 30-x (This question couldalso be answered using simultaneous equations)Total pay 55x-66(30-x)77 55x-1980 66x77 1980 121x2057 121xx 17She worked 17 days.MINDSET LEARN TEACHING RESOURCES PUBLISHED 201310

MINDSET LEARN GRADE 10 MATHEMATICSQuestion 11Let the width x then the diagonal x 25 and the length x 17In a rectangle interior angles equal 90 therefore we have a right angled triangle and using)()Pythagoras: (()()The width 28cmdiagonal 53cmand length 45cmQuestion 12It is important to work in km/h so change fifteen minutes to ¼ hour.Let the time taken to run to the shop x then the time taken to run back will be ¼ -xFill in information in the table.SpeedDistanceTime5xxTo shop54(1/4 –x)¼ -xBack from shop4D S TThe distances to the shop and back from the shop are equal.()hr.The distance to the shop 5(1/9) 5/9km or 0.56kmMINDSET LEARN TEACHING RESOURCES PUBLISHED 201311