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picture1_Simple Equations Problems Pdf 176671 | Y9 Max Series Volume 2 Sample


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File: Simple Equations Problems Pdf 176671 | Y9 Max Series Volume 2 Sample
topic equations theory 03 constructing equations using equations to solve word problems example 1 word problems can be categorised into the sum of two consecutive numbers is 87 find the ...

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                 TOPIC            EQUATIONS                                                                                                 THEORY
            03 CONSTRUCTING EQUATIONS
              Using equations to solve word problems                                               Example 1
                  Word problems can be categorised into:                                           The sum of two consecutive numbers is 87. 
                                                                                                    Find the numbers.  
                    (i)      Number Problems                                                        Solution
                    (ii)     Measurement Problems                                                   Step 1: Underline the keywords that suggest mathematical 
                    (iii)    Money Problems                                                                 operations.
                    (iv)     Age Problems
                  To solve word problems:                                                          Step 2: Select a pronumeral to represent the unknown
                                                                                                            quantity.
                    Step 1: Underline the keywords that suggest 
                             mathematical operations.                                                       Let the two consecutive numbers be  x  and  x+1.  
                    Step 2: Select a pronumeral to represent the                                    Step 3: Translate the word problem into an equation.
                             unknown quantity.
                    Step 3: Translate the word problem into an equation.                                    The sum of two consecutive numbers = 87
                                                                                                                        xx++()18= 7
                    Step 4: Solve the equation.
                    Step 5: Check that the solution satisfies the given                             Step 4: Solve the equation.
                             problem.                                                                                   xx++()18= 7
                    Step 6: State your answer in words.                                                                     21x +=87
                                                                                                                                28x = 6
                  The table below shows keywords for addition and                                                               x = 43
                    subtraction.                                                                    Step 5: Check that the solution satisfies the given problem.
                        Word        Operation       Word       Operation                                              x = 43
                         Plus           +           Minus           -                                                 x+=1431+=44
                         Sum            +        Difference         -                                                 43+=44    87
                      More than         +         Less than         -                               Step 6: State your answer in words.
                      Increased         +        Decreased          -                                       The two consecutive numbers are 43 and 44.
                          by                         by
                         Gain           +           Loss            -                               Example 2
                  The table below shows keywords for multiplication                                The sum of two consecutive even numbers is 146. 
                    and division.                                                                   Find the numbers.  
                                                                                                    Solution
                        Word        Operation       Word       Operation                            Step 1: Underline the keywords that suggest mathematical 
                        Times           #           Ratio          '                                        operations.
                      Multiplied        #          Divided         '                                Step 2: Select a pronumeral to represent the unknown
                          by                         by                                                     quantity.
                      Product of        #        Quotient of       '                                        Let the two consecutive even numbers be  x and
                       Twice or         #2           Half          '2                                       x+2.  
                        double
                        Triple         #3         One-third        '3                               Step 3: Translate the word problem into an equation.
                                                                                                            The sum of two consecutive even numbers = 146
                  In measurement and money problems, don’t forget to                                                  xx++()2 =146
                    include units in your answer.
              Number problems                                                                      Step 4: Solve the equation.
                                                                                                                         22x +=146
                  In number problems, you are required to find an                                                           2x = 144
                    unknown number given its relationship with the other                                                      x = 72
                    number(s).                                                                      Step 5: Check that the solution satisfies the given problem.
                  Number problems could involve                                                            The smaller even number:  x = 72
                    (i)   Two numbers                                                                       The next consecutive even number:  x+=274.
                    (ii)  Two or three consecutive numbers                                          Step 6 : State your answer in words.
                    (iii) Two of three consecutive even or odd                                              The two consecutive numbers are 72 and 74.
                        numbers
                                        TM
            YEAR 9 MATHS MAX SERIES  VOL.2                                        22                                                     www.matrix.edu.au
                TOPIC            EQUATIONS                                                                                       QUESTION
             03 CONSTRUCTING EQUATIONS (MEASUREMENT PROBLEMS)
                                                                                                 LEVEL        NOTES TO STUDENTS
             11.   A water storage tank is two-thirds full.  After 500 litres of                  4
                   water is drained out, the tank is two-fifths full.                             3
                                                                                                  2
                   (a) Let the full capacity of the water storage tank be x litres.               1
                       Write an expression in x for the initial amount of water in 
                       the tank.
                   (b) Write an equation and solve it to find the capacity of the                            The amount of water in the tank before and 
                       water storage tank.                                                                   after draining will be a fraction of  x .
                    
             12.   A truck is loaded with 80 drums.  Each drum weighs either                      4          Totalweight =
                   45 kg or 30 kg.  The total mass of the 80 drums is 2970 kg.                    3          number of drumsw# eightofdrums
                                                                                                  2
                   (a) Let the number of drums weighing 45kg be x. Write                          1
                       an expression in x for the total mass of 45kg drums 
                       and for the total mass of 30 kg drums. 
                   (b) Form an equation and solve it to find the number of                                   The question only asks for the number of 
                       drums weighing 45 kg.                                                                       drums   .
                                                                                                             45kg       ()x
                                       TM
            YEAR 9 MATHS MAX SERIES  VOL.2                                     31                                                 www.matrix.edu.au
                 YEAR 9 MATHS MAX SERIES VOL.2
              CONTENTS
               EQUATIONS                     01     SOLVING LINEAR EQUATIONS                                                              P07
                                                    …  What is a linear eqatin
                                                    … What es it ean t sle a linear eqatin
                                                    … Pr ere ­r slin€ eqatins
                                                    … Eqatins ‚ith ne ƒrneral n ne sie
                                                    … Eqatins ‚ith ƒrnerals n „th sies
                                                    … Eqatins ‚ith „ra …ets
                                                    … Eqatins inlin€ ­ra tins
                                             02 REARRANGING EQUATIONS                                                                     P†‡
                                                    … Rearran€in€ ­rla
                                             03 CONSTRUCTING EQUATIONS                                                                    P22
                                                    … ˆsin€ eqatins t sle ‚r ƒr„les
                                                    … ‰„er ƒr„les
                                                    … Measreent ƒr„les
                                                    … MneŠ Pr„les
                                                    … A€e Pr„les
                                             04 INEQUALITIES                                                                              P‹Œ
                                                    … What is an ineqalitŠ 
                                                    … Žraƒhin€ ineqalities n the n„er line
                                                    … Slin€ linear ineqalities 
                                                    … Slin€ an €raƒhin€ ineqalities ­ the ­r ax##b  
                                                    … Slin€ an €raƒin€ ineqalities inlin€ ­ra tins
                                        TM
              YEAR 9 MATHS MAX SERIES  VOL.2                                                                                     www.matrix.edu.au
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...Topic equations theory constructing using to solve word problems example can be categorised into the sum of two consecutive numbers is find i number solution ii measurement step underline keywords that suggest mathematical iii money operations iv age select a pronumeral represent unknown quantity let x and translate problem an equation xx check satisfies given state your answer in words table below shows for addition subtraction operation plus minus difference more than less increased decreased are by gain loss multiplication even division times ratio multiplied divided product quotient twice or half double triple one third don t forget include units you required its relationship with other s could involve smaller next three odd tm year maths max series vol www matrix edu au question level notes students water storage tank thirds full after litres drained out fifths capacity write expression initial amount b it before draining will fraction truck loaded drums each drum weighs either to...

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