(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 8.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 157, 7] NotebookDataLength[ 49612, 1580] NotebookOptionsPosition[ 43961, 1407] NotebookOutlinePosition[ 44999, 1440] CellTagsIndexPosition[ 44920, 1435] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell["Linear Functions", "Title", CellChangeTimes->{{3.529087234500142*^9, 3.529087240381353*^9}}], Cell[CellGroupData[{ Cell["\<\ In this topic students will learn:\ \>", "Subsection", CellChangeTimes->{{3.5290902394982233`*^9, 3.5290902480158377`*^9}}], Cell["Rearranging and substitution of equations", "Subsubsection", CellChangeTimes->{{3.529090255129451*^9, 3.529090284785103*^9}, { 3.536442984702235*^9, 3.536442984999235*^9}}], Cell["Solving linear equations", "Subsubsection", CellChangeTimes->{{3.529090298123126*^9, 3.529090302818734*^9}, { 3.529090857494913*^9, 3.5290908595541167`*^9}}], Cell["Graphing linear equations", "Subsubsection", CellChangeTimes->{{3.529090345219609*^9, 3.5290903463116107`*^9}, { 3.5290908452800913`*^9, 3.5290908829385576`*^9}}], Cell["\<\ Finding the equation of a straight line\ \>", "Subsubsection", CellChangeTimes->{{3.5290909059797983`*^9, 3.529090945354267*^9}, { 3.536446429052497*^9, 3.536446441955787*^9}}], Cell["\<\ Solving simultaneous linear equations\ \>", "Subsubsection", CellChangeTimes->{{3.529091073836093*^9, 3.5290910847873125`*^9}}], Cell[CellGroupData[{ Cell["", "Subsubsection"], Cell[TextData[{ ButtonBox["\[FilledLeftTriangle]\[ThickSpace]\[ThickSpace]\[ThickSpace]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPagePrevious"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowPrevSlideText"]], "\[ThickSpace]\[ThickSpace]|\[ThickSpace]\[ThickSpace]", ButtonBox["\[ThickSpace]\[ThickSpace]\[ThickSpace]\[FilledRightTriangle]", BaseStyle->"SlidePreviousNextLink", Appearance->{Automatic, None}, ButtonFunction:>FrontEndExecute[{ FrontEndToken[ FrontEnd`ButtonNotebook[], "ScrollPageNext"]}], ButtonNote->FEPrivate`FrontEndResource[ "FEStrings", "SlideshowNextSlideText"]] }], "PreviousNext"] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Rearranging & Substitution", "Section", CellChangeTimes->{{3.52908771745339*^9, 3.5290877250350037`*^9}}], Cell["\<\ An important skill you need to have to succeed this year is algebraically \ rearranging equations to make a particular pronumeral the subject.\ \>", "Text", CellChangeTimes->{{3.5290877299178123`*^9, 3.529087754082255*^9}, { 3.529088142590937*^9, 3.529088153604556*^9}, {3.5290882156926656`*^9, 3.5290882247406816`*^9}, 3.5290882582963405`*^9}], Cell[TextData[{ "Rearrange the equation ", Cell[BoxData[ FormBox[ RowBox[{"s", "=", RowBox[{ RowBox[{"u", " ", "t"}], "+", RowBox[{ FractionBox["1", "2"], "a", " ", SuperscriptBox["t", "2"]}]}]}], TraditionalForm]]], " to make ", StyleBox["a", FontSlant->"Italic"], " the subject:" }], "Text", CellChangeTimes->{{3.529088464612303*^9, 3.529088500804366*^9}}], Cell[TextData[Cell[BoxData[ FormBox[GridBox[{ {GridBox[{ { RowBox[{"s", "=", RowBox[{ RowBox[{"u", " ", "t"}], "+", RowBox[{ FractionBox["1", "2"], "a", " ", SuperscriptBox["t", "2"]}]}]}]}, { RowBox[{ RowBox[{"s", "-", RowBox[{"u", " ", "t"}]}], "=", RowBox[{ FractionBox["1", "2"], "a", " ", SuperscriptBox["t", "2"]}]}]}, { RowBox[{ RowBox[{"2", RowBox[{"(", RowBox[{"s", "-", RowBox[{"u", " ", "t"}]}], ")"}]}], "=", RowBox[{"a", " ", SuperscriptBox["t", "2"]}]}]}, { RowBox[{ FractionBox[ RowBox[{"2", RowBox[{"(", RowBox[{"s", "-", RowBox[{"u", " ", "t"}]}], ")"}]}], SuperscriptBox["t", "2"]], "=", "a"}]}, { RowBox[{ RowBox[{ "put", " ", "the", " ", "subject", " ", "to", " ", "the", " ", RowBox[{"left", ":", " ", "a"}]}], "=", FractionBox[ RowBox[{"2", RowBox[{"(", RowBox[{"s", "-", RowBox[{"u", " ", "t"}]}], ")"}]}], SuperscriptBox["t", "2"]]}]} }, GridBoxAlignment->{"Columns" -> {{"="}}}]} }, GridBoxItemSize->{"Columns" -> {{ Scaled[0.96]}}}], TraditionalForm]]]], "Text", CellChangeTimes->{{3.529088262180747*^9, 3.5290883492445*^9}, { 3.529088406793001*^9, 3.52908845760789*^9}, {3.5290887197971544`*^9, 3.5290887265363665`*^9}, {3.52908879130768*^9, 3.5290887994976945`*^9}}], Cell[TextData[{ "In ", StyleBox["Mathematica", FontSlant->"Italic"], " we can rearrange equations with unknowns using the \[OpenCurlyQuote]Solve\ \[CloseCurlyQuote] function. 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More on this later.\ \>", "Text", CellChangeTimes->{{3.529089066351763*^9, 3.529089099361421*^9}}], Cell["\<\ Once we\[CloseCurlyQuote]ve rearranged an equation we can solve for the \ subject by substituting in known values for the other variables.\ \>", "Text", CellChangeTimes->{{3.5290891094390388`*^9, 3.5290891452255015`*^9}}], Cell[TextData[{ "e.g. Given ", Cell[BoxData[ FormBox[ RowBox[{"s", "=", RowBox[{ RowBox[{"u", " ", "t"}], "+", RowBox[{ FractionBox["1", "2"], "a", " ", SuperscriptBox["t", "2"]}]}]}], TraditionalForm]]], ", if ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"s", "=", "30"}], ",", " ", RowBox[{"u", "=", RowBox[{ RowBox[{"5", " ", "and", " ", "t"}], "=", "3"}]}]}], TraditionalForm]], FormatType->"TraditionalForm"], " what is the value of ", StyleBox["a", FontSlant->"Italic"], "." }], "Text", CellChangeTimes->{{3.5290891753647547`*^9, 3.5290892582165003`*^9}}], Cell[TextData[Cell[BoxData[ FormBox[GridBox[{ {GridBox[{ { RowBox[{ RowBox[{"from", " ", RowBox[{"above", ":", " ", "a"}]}], "=", FractionBox[ RowBox[{"2", RowBox[{"(", RowBox[{"s", "-", RowBox[{"u", " ", "t"}]}], ")"}]}], SuperscriptBox["t", "2"]]}]}, { RowBox[{"=", FractionBox[ RowBox[{"2", RowBox[{"(", RowBox[{"30", "-", RowBox[{"5", "\[Times]", "3"}]}], ")"}]}], SuperscriptBox["3", "2"]]}]}, { RowBox[{"=", FractionBox["30", "9"]}]}, { RowBox[{"=", FractionBox["10", "3"]}]} }, GridBoxAlignment->{"Columns" -> {{"="}}}]} }, GridBoxItemSize->{"Columns" -> {{ Scaled[0.96]}}}], TraditionalForm]], CellMargins->{{7, 4}, {4, 4}}]], "Text", CellChangeTimes->{{3.5290892727089252`*^9, 3.529089392080335*^9}, { 3.5290894753376813`*^9, 3.5290895192985587`*^9}, {3.5290896292943516`*^9, 3.529089635113162*^9}}], Cell[TextData[{ "Again, we can use the \[OpenCurlyQuote]Solve\[CloseCurlyQuote] function in ", StyleBox["Mathematica", FontSlant->"Italic"], ". 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In ", StyleBox["Mathematica", FontSlant->"Italic"], " this represents multiply: ", StyleBox["u ", FontSlant->"Italic"], "\[Times] ", StyleBox["t", FontSlant->"Italic"], ". 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This form isn\[CloseCurlyQuote]t particularly useful when it comes to \ trying to graph the equation." }], "Text", CellChangeTimes->{{3.5290925623083076`*^9, 3.5290925919171596`*^9}, { 3.5290927290374007`*^9, 3.529092732734607*^9}, {3.529092796445119*^9, 3.529092806050336*^9}, {3.529092978633439*^9, 3.5290929921430626`*^9}}], Cell[TextData[{ "The most common form of a linear equation is the gradient - intercept form: \ ", Cell[BoxData[ FormBox[ RowBox[{"y", "=", RowBox[{ RowBox[{"m", " ", "x"}], "+", "c"}]}], TraditionalForm]]] }], "Text", CellChangeTimes->{{3.529093025417921*^9, 3.5290930575695777`*^9}}], Cell[TextData[{ "Either way, you can graph a function in ", StyleBox["Mathematica", FontSlant->"Italic"], " using the command Plot. 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