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introductory mathematics add to library
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‎samplequestions/stacklibrary/Introductory-Mathematics/.gitignore‎

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**/*_question_manifest.json
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**/*_manifest_update.tmp

‎samplequestions/stacklibrary/Introductory-Mathematics/Week-1---Quadratic-functions-and-their-graphs/1-0-1-(What-is-a-quadratic-equation-).xml‎

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<?xml version="1.0" encoding="UTF-8"?>
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<quiz>
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<question type="description">
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<name>
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<text>1.0.1 (What is a quadratic equation?)</text>
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</name>
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<questiontext format="html">
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<text><![CDATA[<h1>Quadratic Equations</h1>
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<p>One important concept in mathematics is that of square numbers. A square number is a product of a whole number with itself. For example \(4 = 2 \times 2\) and \(9 = 3 \times 3\) are square numbers, whilst \(10\) is not. This terminology derives from the fact the area of a square is its side length multiplied by itself. A <b>quadratic equation</b> is an equation which deals with a variable (usually denoted by \(x\)) which has been squared. Indeed the word 'quadratic' comes from the Latin word for square!</p>
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<p>The graph of a quadratic function forms a curve called a parabola. Parabolas arise in a number of places in the real world. Examples include the curve mapped when throwing a projectile, the curve produced by water flowing from a fountain and parabolic reflectors to focus light. Therefore if we wish to understand these phenomena, we need to understand quadratic equations. We will examine more applications of quadratics in a later section.</p>
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<p>Any quadratic equation can be written in the following form:
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\[
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ax^2 + bx + c = 0,
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\]
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where \(x\) is an unknown variable and \(a, b\) and \(c\) are constants. This form of a quadratic is called the <b>standard form</b>.
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Note that we can allow \(b\) and/or \(c\) to be equal to zero, however \(a\) must be nonzero. In other words we must have a squared term in order for the equation be be a quadratic.
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</p>
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<h3>Example</h3>
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<p>Which of the following are examples of a quadratic equation?
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</p><ol type="a">
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<li>\(x^2 + 2x -4 = 0\)</li>
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<li>\(4x - x^2 = 5\)</li>
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<li>\(9x + 4 = 0\)</li>
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</ol>
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<p></p>
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<h3>Solution</h3>
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<p></p><ol type="a">
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<li>\(x^2 + 2x -4 = 0\) is a quadratic equation. It is in standard form where \(a =1, b = 2, c= -4\).</li>
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<li>\(4x - x^2 = 5\) is also a quadratic equation but it is not in standard form. However we can re-write the equation in standard form as \(-x^2 +4x - 5 = 0.\) This is now in standard form with \(a = -1, b = 4\) and \(c = -5\).</li>
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<li>\(9x + 4 = 0\) is not a quadratic equation as is doesn't have a squared term. It is a linear equation.</li>
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</ol><p></p>]]></text>
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</questiontext>
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<generalfeedback format="html">
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<defaultgrade>0</defaultgrade>
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<penalty>0</penalty>
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</quiz>

‎samplequestions/stacklibrary/Introductory-Mathematics/Week-1---Quadratic-functions-and-their-graphs/1-0-10-(Expand-brackets-(AlgMap-7-7)).xml‎

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<?xml version="1.0" encoding="UTF-8"?>
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<quiz>
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<question type="stack">
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<name>
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<text>1.0.10 (Expand brackets (AlgMap-7.7))</text>
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</name>
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<questiontext format="html">
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<text><![CDATA[<p>Expand the following: <br> <br> \( \left( {@cf1*x+c@} \right) \left( {@cf2*x+d@} \right)\) = [[input:ans]] [[validation:ans]]</p>]]></text>
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</questiontext>
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<generalfeedback format="html">
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<text><![CDATA[<p>In this example:<br></p>
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<p>\[\begin{align} {@(cf1*x+c)*(cf2*x+d)@} &amp;= {@(cf1*cf2)*x^2@}+\left({@(c*cf2*x)@}\right)+\left({@(d*cf1*x)@}\right)+\left({@(c*d)@}\right) \\ &amp;= {@ta@}. \end{align} \]</p>]]></text>
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<text>2020070100</text>
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<text>a:rand(10)+1;
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b:rand(10)+1;
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e:rand([-1,1]);
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f:rand([-1,1]);
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c:a*e;
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d:b*f;
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cf1:(rand(3)+2)*(-1)^rand([-1,1]);
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cf2:(rand(3)+2)*(-1)^rand([-1,1]);
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ta:expand((cf1*x+c)*(cf2*x+d));</text>
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<text><![CDATA[<p>[[feedback:prt1]]<br></p>]]></text>
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</specificfeedback>
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<questionnote format="moodle_auto_format">
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<text>\[{@(cf1*x+c)*(cf2*x+d)@} = {@ta@}.\]</text>
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<text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Correct answer, well done.]]></text>
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<text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Your answer is partially correct.]]></text>
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</prtpartiallycorrect>
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<prtincorrect format="html">
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<text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Incorrect answer.]]></text>
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<decimals>.</decimals>
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<scientificnotation>*10</scientificnotation>
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<truescore>1.0000000</truescore>
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<text><![CDATA[<p>Your answer is algebraically equivalent to the correct answer but you need to leave the answer as a polynomial (multiply out the brackets!)</p>]]></text>
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<testcase>1</testcase>
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<value>ta</value>
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<testcase>2</testcase>
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<name>ans</name>
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<value>(cf1*x+c)*(cf2*x+d)</value>
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