1<!DOCTYPE html> 2<html> 3 <head> 4 <meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> 5 <meta name="google-site-verification" content="g_ot9mbIi8h4Uh1Q0JJeLT6QKG5mSLEJTI5vKyRMdrQ" /> 6 <meta name=viewport content="width=device-width, initial-scale=1"> 7 <title> 8 Maths Answers - Notes, Questions, Online Self-Test etc for Secondary Maths 9 </title> 10 <link rel="stylesheet" href="standard.css" type="text/css" /> 11 </head> 12 <body> 13 <div class="padded"> 14 <div> 15 <div class="home" style="float: left;"> 16 <img width=45 src='favicon.png' style='display: block; margin-left: auto; margin-right: auto;' /> 17 </div> 18 <div class="home" style="float: right;"> 19 <img width=45 src='favicon.png' style='display: block; margin-left: auto; margin-right: auto;' /> 20 </div> 21 <h1> 22 Maths Answers 23 </h1> 24 <div style="clear:both;"></div> 25 </div> 26 <p> 27 Here you will find notes, practice questions and solutions for GCSE, detailed notes for A-Level, and you can test your maths skills online. 28 </p> 29 <p> 30 The material on this site has been accumulated over many years of maths teaching. It is made available here in the hope that it may be of some use to teachers or students. Note that all the pdfs are "editable pdfs" - they can be opened by Adobe Reader and used as they are, but if you want to edit them, you can open them with <a href="http://libreoffice.org">LibreOffice</a> or <a href="http://openoffice.org">Apache OpenOffice</a> (both of which are free) and they can be edited as normal documents. For more detail, see <a href="fullintro.html">here</a> 31 </p> 32 <p> 33 If you have any comments or queries, you can contact me at <a href="mailto:[email protected]" target="_top">[email protected]</a> though I don't guarantee to reply promptly! 34 </p> 35 <p> 36 <span style="color:red; font-family:script; font-weight:bold">WHAT'S NEW:</span> 37 </p> 38 <h3>Polyominoes</h3> 39 <p style="text-align: center;"><img src="investigations/polyominoes/images/pentomino%20puzzle.png" width="50%"/></p><p>Fill a variety of shapes with pieces made from squares, like a jigsaw. If you get stuck, you can check whether the pieces you have placed so far are correct, or get some pieces placed for you. There are puzzles in three different sizes:</p> 40 <p><strong><a href="investigations/polyominoes/index.html?size=4" target="_blank">Tetrominoes</a>:</strong> Use 10 shapes each made of 4 squares. There are 10 different puzzles available.</p> 41 <p><strong><a href="investigations/polyominoes/index.html?size=5" target="_blank">Pentominoes</a>:</strong> Use 12 shapes each made of 5 squares. There are 20 different puzzles available.</p> 42 <p><strong><a href="investigations/polyominoes/index.html?size=6" target="_blank">Hexominoes</a>:</strong> Use up to 35 shapes each made of 6 squares. There are 10 different puzzles available.</p> 43 <p></p> 44 </div> 45 <div class="padded"> 46 <h2> 47 Year 7-11 (GCSE) Notes and Worksheets 48 </h2> 49 <p>These are available topic by topic 50 <a href="./gcse"> 51 here. 52 </a> 53 </p> 54 <p>There is also a page with various 55 <a href="./gcserev"> 56 Revision Sheets and Answers 57 </a> 58 </p> 59 </div> 60 <div class="padded"> 61 <h2> 62 Problem Solving 63 </h2> 64 <p>A couple of sheets of extension questions, aimed at encouraging brighter students to think through a problem, are available 65 <a href="./problemsolving"> 66 here. 67 </a> 68 </p> 69 </div> 70 <div class="padded"> 71 <h2> 72 <a href="olympics2/" target="_blank">Maths Olympics</a> 73 </h2> 74 <p> 75 Anyone is welcome to enter the Maths Olympics 76 <a href="olympics2/" target="_blank"> here.</a> This is a collection of "events" (topics). If you enter an event, you will be given ten questions to answer. Get them all right, and you get a gold medal. One wrong, silver, two wrong, bronze. You also get a time for the event.<br /><br /> 77 You will need to make up a user name for yourself so that you can keep track of what medals you have won. Why not try for a complete set? (If you aren't sure what (English) school year you are in, just choose "not at school".) 78 </p> 79 </div> 80 <div class="padded"> 81 <h2> 82 A Level Core Maths Notes and Worksheets 83 </h2> 84 <p>These are available 85 <a href="./core"> 86 here. 87 </a> 88 </p> 89 </div> 90 <div class="padded"> 91 <h2> 92 A Level Statistics Notes and Worksheets 93 </h2> 94 <p>These are available 95 <a href="./stats"> 96 here. 97 </a> 98 </p> 99 </div> 100 <div class="padded"> 101 <h2> 102 A Level Further Pure Maths Notes and Worksheets 103 </h2> 104 <p>These are available 105 <a href="./furtherpure"> 106 here. 107 </a> 108 </p> 109 </div> 110 <div class="padded"> 111 <h2> 112 Online Demonstration Software 113 </h2> 114 <p>These are tools for demonstrating various mathematical concepts. So far there is just one: 115 </p> 116 <p> 117 <a href="./demos/norbinpo"> 118 Graphs of Probability Distributions 119 </a><br /> 120 Use this tool to see how good an approximation a Poisson or Normal distribution is to a Binomial distribution, etc. 121 </p> 122 </div> 123 <div class="padded"> 124 <h2> 125 Mathematical Puzzles 126 </h2> 127 <p> 128 <a href="puzzles">Here</a> you will find Number Puzzles, Algebra Puzzles, Shapes Puzzles and Miscellaneous Puzzles for various age groups. 129 </p> 130 <p> 131 A collection of <a href="christmaspuzzles">Christmas puzzles</a> of various kinds. 132 </p> 133 </div> 134 <div class="padded"> 135 <h2> 136 Online Games and Investigations 137 </h2> 138 <h3>Polyominoes</h3> 139 <p style="text-align: center;"><img src="investigations/polyominoes/images/pentomino%20puzzle.png" width="50%"/></p><p>Fill a variety of shapes with pieces made from squares, like a jigsaw. If you get stuck, you can check whether the pieces you have placed so far are correct, or get some pieces placed for you. There are puzzles in three different sizes:</p> 140 <p><strong><a href="investigations/polyominoes/index.html?size=4" target="_blank">Tetrominoes</a>:</strong> Use 10 shapes each made of 4 squares. There are 10 different puzzles available.</p> 141 <p><strong><a href="investigations/polyominoes/index.html?size=5" target="_blank">Pentominoes</a>:</strong> Use 12 shapes each made of 5 squares. There are 20 different puzzles available.</p> 142 <p><strong><a href="investigations/polyominoes/index.html?size=6" target="_blank">Hexominoes</a>:</strong> Use up to 35 shapes each made of 6 squares. There are 10 different puzzles available.</p> 143 <p> </p> 144 <h3><a href="games/squares/index.html" target="_blank">Squares</a></h3> 145 <p>Place four counters at the corner of a square before your opponent!</p> 146 <p>This is a game I invented over 30 years ago. Originally it was played with counters on a paper board. Then around 1985 I wrote a version which ran on a Research Machines Nimbus (in text mode!), a few years later I converted it to Windows, and now finally we have the online version.</p> 147 <p>There is also the <a href="games/squares/SquaresChallenge.html" target="_blank">Squares Challenge</a>, which looks at the number of possible winning squares on different size game boards.</p> 148 <h3><a href="games/dominate/index.html" target="_blank">Dominate</a></h3> 149 <p>Drag dominos onto a board so that the dots add up to the correct totals.</p> 150 <p>I didn't invent this game, but I haven't been able to find any trace of it for many years. It's a really nice puzzle game, so I decided it was due for a revival. For more of a challenge, choose a harder level.</p> 151 <h3><a href="games/tangrams/index.html" target="_blank">Tangrams</a></h3> 152 <p>Choose a shape, and then fill it with the seven "Tans".</p> 153 <p>This is an ancient puzzle which originated in China and spread to the Western world in the early 19th century.</p> 154 <h3><a href="games/flipit/index.html" target="_blank">Flipit</a></h3> 155 <p>Can you turn all the counters blue?</p> 156 <p>I didn't invent this game. But my version gives the option to set up a particular starting position, and return to it at any point. It also keeps a record of the moves made, which helps with working out the strategy to use in solving the game.</p> 157 </div> 158 <div class="padded"> 159 <h2> 160 Investigations 161 </h2> 162 <h3><a href="investigations/tessellations/index.html">Tessellations</a></h3> 163 <p>A page introducing tessellations, with a worksheet for an investigation into semi-regular tessellations, and examples created using each of the tools below</p> 164 <p style="text-align: center;"> 165 <img width="50%" src="investigations/tessellations/tess1.png" /> 166 </p> 167 <p><span style="color:red; font-family:script; font-weight:bold">NEW:</span></p> 168 <h3><a href="investigations/tessellate/index.html" target="_blank">Tessellate!</a></h3> 169 <p>An online tool for designing tessellations out of regular polygons.</p> 170 <p style="text-align: center;"> 171 <img width="50%" src="investigations/tessellations/tessellate.png" /> 172 </p> 173 <ul> 174 <li>Click on the polygons on the left to add them to the canvas.</li> 175 <li>Then drag them and rotate them to start forming your tessellation.</li> 176 <li>Form groups of tiles which can be added with a single click to speed up the creation process.</li> 177 <li>Full instructions for use are available by clicking the help button in the program.</li> 178 <li>Or watch a <a href="https://www.youtube.com/watch?v=ZfiIApLdn_8" target="_blank">Youtube video</a> showing how to use it.</li> 179 </ul> 180 <h3><a href="investigations/tessmaker/index.html" target="_blank">TessMaker</a></h3> 181 <p>An online tool to help with the design of tessellations, for example in the style of <a href="http://www.mcescher.com/gallery/symmetry/" target="_blank">Maurits Escher</a>.</p> 182 <p style="text-align: center;"> 183 <img style="width:40%; margin-right:5%;" src="investigations/tessellations/tessmaker.png" /> 184 <img width="40%" src="investigations/tessellations/tessmaker2.png" /> 185 </p> 186 <ul> 187 <li>Start by choosing a type of tile (parallelogram, kite, etc) and how the tiles will fit together (by rotating, reflecting, etc).</li> 188 <li>Then add extra points and drag them around to make an interesting shape.</li> 189 <li>Decorate the shape using the drawing tools.</li> 190 <li>Then click the tessellation tab to see the completed tessellation</li> 191 <li>Full instructions for use are available by clicking the help button in the program.</li> 192 <li>Or watch a <a href="https://www.youtube.com/watch?v=n81ie1JM-ac" target="_blank">Youtube video</a> showing how to use it.</li> 193 </ul> 194 <h3><a href="investigations/recdecs/index.html" target="_blank">Recurring and non-recurring decimals</a></h3> 195 <p>An investigation into the decimal expansion of 1/n for different values of n ,with hints and s
195ome answers. There are also a couple of tools to help with working out long recurring decimals, and prime factorisation of large integers.</p> 196 </div> 197 </body> 198</html>
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