Skip to content

HTTPS clone URL

Subversion checkout URL

You can clone with
or
.
Download ZIP
Newer
Older
100644 102 lines (101 sloc) 5.764 kB
d103285 @beneater Split measuring_segments into 4 exercises
beneater authored
1 <!DOCTYPE html>
2 <html data-require="math graphie expressions">
3 <head>
4e4cb9b @beneater lint: tabs->spaces and jQuery->$ for exercises
beneater authored
4 <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
5 <title>Segment addition</title>
6 <script src="../khan-exercise.js"></script>
d103285 @beneater Split measuring_segments into 4 exercises
beneater authored
7 </head>
8 <body>
9 <div class="exercise">
4e4cb9b @beneater lint: tabs->spaces and jQuery->$ for exercises
beneater authored
10 <div class="problems">
11 <div>
12 <div class="vars">
13 <var id="POINTS">randFromArray([ [ "A", "B", "C" ], [ "J", "K", "L" ], [ "C", "J", "T" ] ])</var>
14 <var id="SEG_1">POINTS[ 0 ] + POINTS[ 1 ]</var>
15 <var id="SEG_2">POINTS[ 1 ] + POINTS[ 2 ]</var>
16 <var id="SEG_TOTAL">POINTS[ 0 ] + POINTS[ 2 ]</var>
17 <var id="COEF_1">randRangeNonZero( 2, 9 )</var>
18 <var id="CONST_1">randRangeNonZero( 2, 9 )</var>
19 <var id="COEF_2">randRangeNonZero( 2, 9 )</var>
20 <var id="CONST_2">randRangeNonZero( 2, 9 )</var>
21 <var id="X">randRange( 1, 9 )</var>
22 <var id="TOTAL">( COEF_1 * X + CONST_1 ) + ( COEF_2 * X + CONST_2 )</var>
23 <var id="GIVEN">shuffle([
24 [ BLUE, SEG_1 + " = " + COEF_1 + "x + " + CONST_1 ],
25 [ GREEN, SEG_2 + " = " + COEF_2 + "x + " + CONST_2 ],
26 [ "purple", SEG_TOTAL + " = " + TOTAL ]
27 ])</var>
28 </div>
29 <div class="problem">
30 <div class="graphie" id="number-line">
31 init({
32 range: [ [ -1, 11 ], [ -1, 1 ] ]
33 });
34 line( [ 0, 0 ], [ 10, 0 ] );
35 style({ stroke: "#000", fill: "#000" });
36 graph.points = raphael.set();
37 graph.points.push( circle( [ 0, 0 ], 0.10 ) );
38 graph.points.push( circle( [ 10 * ( COEF_1 * X + CONST_1 ) / TOTAL, 0 ], 0.10 ) );
39 graph.points.push( circle( [ 10, 0 ], 0.10 ) );
40 label( [ 0, 0 ], POINTS[ 0 ], "below" );
41 label( [ 10 * ( COEF_1 * X + CONST_1 ) / TOTAL, 0 ], POINTS[ 1 ], "below" );
42 label( [ 10, 0 ], POINTS[ 2 ], "below" );
43 </div>
44 <p>
45 If:<br />
46 <span id="given0"><code>\qquad <var>GIVEN[ 0 ][ 1 ]</var></code></span>,<br />
47 <span id="given1"><code>\qquad <var>GIVEN[ 1 ][ 1 ]</var></code></span>, and<br />
48 <span id="given2"><code>\qquad <var>GIVEN[ 2 ][ 1 ]</var></code></span>,
49 </p>
50 </div>
51 <p class="question">Find <code><var>SEG_2</var></code>.</p>
52 <div class="solution" data-forms="integer"><var>COEF_2 * X + CONST_2</var></div>
53 <div class="hints">
54 <div>
55 <div class="graphie" data-update="number-line">
56 style({ stroke: BLUE, strokeWidth: 3 });
57 line( [ 0, 0 ], [ 10 * ( COEF_1 * X + CONST_1 ) / TOTAL, 0 ] );
58 style({ stroke: GREEN, strokeWidth: 3 });
59 line( [ 10 * ( COEF_1 * X + CONST_1 ) / TOTAL, 0 ], [ 10, 0 ] );
60 graph.points.toFront();
61 $( "#given0" ).css({ "color": GIVEN[ 0 ][ 0 ] });
62 $( "#given1" ).css({ "color": GIVEN[ 1 ][ 0 ] });
63 $( "#given2" ).css({ "color": GIVEN[ 2 ][ 0 ] });
64 </div>
65 <p>From the diagram, we can see that the total length of <code>\purple{<var>SEG_TOTAL</var>}</code> is the sum of <code>\blue{<var>SEG_1</var>}</code> and <code>\green{<var>SEG_2</var>}</code>:</p>
66 <p><code>\qquad \blue{<var>SEG_1</var>} + \green{<var>SEG_2</var>} = \purple{<var>SEG_TOTAL</var>}</code></p>
67 </div>
68 <div>
69 <p>Substitute in the expressions that were given for each length:</p>
70 <p><code>\qquad \blue{<var>COEF_1</var>x + <var>CONST_1</var>} + \green{<var>COEF_2</var>x + <var>CONST_2</var>} = \purple{<var>TOTAL</var>}</code></p>
71 </div>
72 <div>
73 <p>Combine like terms:</p>
74 <p><code>\qquad<var>COEF_1 + COEF_2</var>x + <var>CONST_1 + CONST_2</var> = \purple{<var>TOTAL</var>}</code></p>
75 </div>
76 <div>
77 <p>Subtract <code><var>CONST_1 + CONST_2</var></code> from both sides:</p>
78 <p><code>\qquad<var>COEF_1 + COEF_2</var>x = <var>TOTAL - CONST_1 - CONST_2</var></code></p>
79 </div>
80 <div>
81 <p>Divide both sides by <code><var>COEF_1 + COEF_2</var></code> to find <code class="hint_pink">x</code>:</p>
82 <p><code class="hint_pink">\qquad x = <var>X</var></code></p>
83 </div>
84 <div>
85 <p>Substitute <code class="hint_pink"><var>X</var></code> for <code class="hint_pink">x</code> in the expression that was given for <code><var>SEG_2</var></code>:
86 <p><code class="hint_green">\qquad <var>SEG_2</var> = <var>COEF_2</var>(\pink{<var>X</var>}) + <var>CONST_2</var></code></p>
87 </div>
88 <div>
89 <p>Simplify:</p>
90 <p><code>\qquad \green{<var>SEG_2</var> = <var>COEF_2 * X</var> + <var>CONST_2</var>}</code></p>
91 </div>
92 <div>
93 <p class="final_answer">Simplify to find <code>\green{<var>SEG_2</var>}</code>:</p>
94 <p><code>\qquad \green{<var>SEG_2</var> = <var>COEF_2 * X + CONST_2</var>}</code></p>
95 </div>
96 </div>
97 </div>
98 </div>
d103285 @beneater Split measuring_segments into 4 exercises
beneater authored
99 </div>
100 </body>
101 </html>
Something went wrong with that request. Please try again.