Pages 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 8289 result(s) returned

Learning outcomes

After studying this course, you should be able to:

  • create simple models, given a clear statement of the problem

  • identify the simplifying assumptions that underpin a model

  • identify the key variables and the parameters of a model

  • apply the input–output principle to obtain a mathematical model, where appropriate.


Author(s): The Open University

License information
Related content

Copyright © 2016 The Open University

2.8 The angles of a triangle

The sum of the angles of any triangle is 180°. This property can be demonstrated in several ways. One way is to draw a triangle on a piece of paper, mark each angle with a different symbol, and then cut out the angles and arrange them side by side, touching one another as illustrated.


Author(s): The Open University

License information
Related content

Copyright © 2016 The Open University

Try some yourself

Question 1

Draw a line of symmetry on each of the shapes below.

2.7 Rotational symmetry

There is another kind of symmetry which is often used in designs. It can be seen, for instance, in a car wheel trim.

Look at the trim on the left. It does not have line symmetry but
Author(s): The Open University

License information
Related content

Copyright © 2016 The Open University

1.4 Parallel lines

Two straight lines that do not intersect, no matter how far they are extended, are said to be parallel. Arrows are used to indicate parallel lines.


Author(s): The Open University

License information
Related content

Copyright © 2016 The Open University

1.3.4 Vertically opposite angles

When two straight lines cross, they form four angles. In the diagram below, these angles are labelled α, β, θ and φ and referred to as alpha, beta, theta and phi. The angles opposite each other are equal. They are called vertically opposite angles. Here α and β are a pair of vertically opposite angles, as are θ and φ. Although such angles are called ‘vertically opposite’, they do not need to be vertically above and bel
Author(s): The Open University

License information
Related content

Copyright © 2016 The Open University

Try some yourself

Question 1

A company carried out a survey, recording how staff in a particular office spent their working time. The table shows the average number of minutes spent in each hour on various activities.

Author(s): The Open University

License information
Related content

Copyright © 2016 The Open University

1.3.3 Drawing a pie chart

You can use the fact that the sum of angles at a point is 360° to draw a pie chart.

Example 4

Over a five-year period a mathematics tutor found that 16 of her students gained distinctions, 32 gained pass grades and 12 failed to complete the course. Draw a pie chart to re
Author(s): The Open University

License information
Related content

Copyright © 2016 The Open University

2.3.1 Try some yourself

Activity 14

A piece of computer software is to be developed by a team of programmers. It is estimated that a team of four people would take a year. Which of the following times is the length of time taken by three program
Author(s): The Open University

License information
Related content

Copyright © 2016 The Open University

Climate change: transitions to sustainability
Human societies have to take urgent action to end their dependences on fossil fuels. We have to alter the whole path of our development and decision making in order to make our societies both environmentally adaptable and sustainable. This free course, Climate change, takes on the task of trying to chart some of the ways in which it might be possible.Author(s): Creator not set

License information
Related content

Except for third party materials and otherwise stated (see http://www.open.ac.uk/conditions terms and conditions), this content is made available under a http://creativecommons.org/licenses/by-nc-sa/2

The frozen planet
This free course is a general introduction to the frozen planet, including the temperature in the polar regions; the energy from the Sun and the seasons; reading and understanding graphs and maps; and how the Arctic and Antarctic regions are defined. First published on Thu, 23 May 2019 as Author(s): Creator not set

Water for life
Atoms, elements and molecules are the building blocks of everything that makes up our world, including ourselves. In this free course, Water for life, you will learn the basic chemistry of how these components work together, starting with a chemical compound we are all very familiar with water. First published on Wed, 17 Jan 2018 as Author(s): Creator not set

Life in the Palaeozoic
Fossils are a glimpse into the distant past and fascinate young and old alike. This free course, Life in the Palaeozoic, will introduce you to the explosion of evolution that took place during the Palaeozoic era. You will look at the many different types of creatures that existed at that time and how they managed to evolve to exist on land. First published on W
Author(s): Creator not set

License information
Related content

Except for third party materials and otherwise stated (see http://www.open.ac.uk/conditions terms and conditions), this content is made available under a http://creativecommons.org/licenses/by-nc-sa/2

Water in the UK
Water is arguably the most important physical resource as it is the one that is essential to human survival. Understanding the global water cycle and how we use water is essential to planning a sustainable source of water for the future. Globally, there are many areas that do not have enough water to support the current population adequately. Decisions will have to be made on the best way to use water in a world where there is climate change. This free course looks at Water in the UK where water
Author(s): Creator not set

License information
Related content

Except for third party materials and otherwise stated (see http://www.open.ac.uk/conditions terms and conditions), this content is made available under a http://creativecommons.org/licenses/by-nc-sa/2

The science of nuclear energy
This free course, The science of nuclear energy, will delve into the science behind nuclear power and explain what happens inside a nuclear reactor and what it means for an element to be radioactive. It will explore some of the risks of producing nuclear power and examine the arguments for and against including it in future energy planning as well as looking at other potential future solutions. Author(s): Creator not set

License information
Related content

Except for third party materials and otherwise stated (see http://www.open.ac.uk/conditions terms and conditions), this content is made available under a http://creativecommons.org/licenses/by-nc-sa/2

Environment: understanding atmospheric and ocean flows
What affects the atmospheric and ocean flows? This free course, Environment: understanding atmospheric and ocean flows, explores the mechanisms that are important; the most rapid carrier is the wind. The basic principle of global atmospheric circulation is simple: warm air rises and cold air sinks. How does this principle affect the atmosphere and flow of water in practical terms? Starting with an iconic environmental icon, the polar bear, you will learn how global flows of water, heat and
Author(s): Creator not set

License information
Related content

Except for third party materials and otherwise stated (see http://www.open.ac.uk/conditions terms and conditions), this content is made available under a http://creativecommons.org/licenses/by-nc-sa/2

1.2 What determines the Earth's GMST?

The Sun is the ultimate source of energy for the Earth's climate. A planet such as the Earth will have a stable temperature as long as there is a balance between the rate at which energy comes in from the Sun and the rate at which it is returned to space by the planet. If the two rates fail to match, the planet will either warm up or cool down until a balance is restored. Thus, it is appropriate to begin with a review of this global balancing act. The heart of the matter is that the energy fl
Author(s): The Open University

License information
Related content

Copyright © 2016 The Open University

Learning outcomes

After studying this course, you should be able to:

  • understand the physical basis of the natural greenhouse effect, including the meaning of the term radiative forcing

  • know something of the way various human activities are increasing emmissions of the natural greenhouse gases, and are also contributing to sulphate aerosols in the troposphere

  • demonstrate an awareness of the difficulties involved in the detection of any unusual global warming ‘signal
    Author(s): The Open University

    License information
    Related content

    Copyright © 2016 The Open University

2.3 Citizens in conversation with nature and experts

Before leaving office in 2008, Sir David King (the ex-Chief Scientific Advisor to the UK Government) introduced an ethical code for scientists. This drew particularly on his experience in working across the scientific–political divide on issues of climate change. The code comprises three attributes of scientific endeavour: rigour, representation and responsibility (Author(s): The Open University

1.4.3 It's all down to connections

For Iris Marion Young, the responsibility of those in North America and Europe towards distant others does indeed rest with their connections to injustices elsewhere, but it would be a mistake to stretch this line of reasoning too far. Although these connections, whether as a consumer, boardroom executive or shop manager, can establish a line of responsibility, as was claimed in Section 3.1, for Young this is only the starting point and not the end point of our involvement. We do not have to
Author(s): The Open University

License information
Related content

Copyright © 2016 The Open University

Pages 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415