| Introduction |
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vii | |
| How to use your enhanced online course book |
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ix | |
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1 Measuring space: accuracy and geometry |
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2 | (42) |
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1.1 Representing numbers exactly and approximately |
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4 | (9) |
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13 | (15) |
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1.3 Three dimensional geometry |
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28 | (11) |
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39 | (3) |
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Modelling and investigation activity |
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42 | (2) |
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2 Representing and describing data: descriptive statistics |
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44 | (38) |
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2.1 Collecting and organizing data |
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46 | (5) |
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51 | (8) |
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2.3 Ways in which you can present data |
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59 | (7) |
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66 | (9) |
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75 | (5) |
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Modelling and investigation activity |
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80 | (2) |
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3 Dividing up space: coordinate geometry, Voronoi diagrams, vectors, lines |
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82 | (58) |
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3.1 Coordinate geometry in 2 and 3 dimensions |
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84 | (2) |
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3.2 The equation of a straight line in 2 dimensions |
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86 | (10) |
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96 | (8) |
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104 | (8) |
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3.5 The scalar and vector product |
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112 | (6) |
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3.6 Vector equations of lines |
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118 | (12) |
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130 | (4) |
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Modelling and investigation activity |
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134 | (2) |
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Paper 3 question and comments |
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136 | (4) |
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4 Modelling constant rates of change: linear functions and regressions |
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140 | (64) |
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142 | (13) |
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155 | (13) |
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168 | (10) |
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4.4 Arithmetic sequences and series |
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178 | (12) |
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190 | (8) |
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198 | (4) |
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Modelling and investigation activity |
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202 | (2) |
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5 Quantifying uncertainty: probability |
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204 | (28) |
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5.1 Reflecting on experiences in the world of chance. First steps in the quantification of probabilities |
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206 | (6) |
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5.2 Representing combined probabilities with diagrams |
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212 | (4) |
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5.3 Representing combined probabilities with diagrams and formulae |
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216 | (5) |
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5.4 Complete, concise and consistent representations |
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221 | (5) |
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226 | (4) |
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Modelling and investigation activity |
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230 | (2) |
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6 Modelling relationships with functions: power and polynomial functions |
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232 | (56) |
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234 | (11) |
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6.2 Problems involving quadratics |
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245 | (14) |
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6.3 Cubic functions and models |
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259 | (9) |
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6.4 Power functions, direct and inverse variation and models |
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268 | (13) |
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281 | (5) |
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Modelling and investigation activity |
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286 | (2) |
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7 Modelling rates of change: exponential and logarithmic functions |
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288 | (50) |
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7.1 Geometric sequences and series |
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290 | (12) |
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7.2 Financial applications of geometric sequences and series |
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302 | (8) |
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7.3 Exponential functions and models |
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310 | (10) |
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7.4 Laws of exponents -- laws of logarithms |
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320 | (9) |
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329 | (3) |
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332 | (4) |
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Modelling and investigation activity |
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336 | (2) |
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8 Modelling periodic phenomena: trigonometric functions and complex numbers |
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338 | (34) |
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340 | (3) |
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8.2 Sinusoidal models: ∞(x)=a sin (b(x-c))+d |
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343 | (9) |
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8.3 Completing our number system |
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352 | (4) |
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8.4 A geometrical interpretation of complex numbers |
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356 | (8) |
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8.5 Using complex numbers to understand periodic models |
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364 | (4) |
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368 | (2) |
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Modelling and investigation activity |
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370 | (2) |
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9 Modelling with matrices: storing and analysing data |
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372 | (54) |
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9.1 Introduction to matrices and matrix operations |
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324 | (53) |
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9.2 Matrix multiplication and Properties |
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377 | (6) |
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9.3 Solving systems of equations using matrices |
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383 | (8) |
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9.4 Transformations of the plane |
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391 | (11) |
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402 | (4) |
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9.6 Representing steady state systems |
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406 | (7) |
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9.2 Eigenvalues and eigenvectors |
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413 | (9) |
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422 | (2) |
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Modelling and investigation activity |
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424 | (2) |
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10 Analyzing rates of change: differential calculus |
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426 | (46) |
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10.1 Limits and derivatives |
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428 | (14) |
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10.2 Differentiation: further rules and techniques |
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442 | (13) |
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10.3 Applications and higher derivatives |
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455 | (7) |
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462 | (10) |
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Modelling and investigation activity |
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470 | (2) |
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11 Approximating irregular spaces: integration and differential equations |
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472 | (2) |
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11.1 Finding approximate areas for irregular regions |
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474 | (13) |
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11.2 Indefinite integrals and techniques of integration |
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487 | (11) |
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11.3 Applications of integration |
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498 | (17) |
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11.4 Differential equations |
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515 | (4) |
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11.5 Slope fields and differential equations |
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519 | (7) |
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526 | (4) |
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Modelling and investigation activity |
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530 | (2) |
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12 Modelling motion and change in two and three dimensions |
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532 | (38) |
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535 | (5) |
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12.2 Motion with variable velocity |
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540 | (7) |
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12.3 Exact solutions of coupled differential equations |
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547 | (9) |
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12.4 Approximate solutions to coupled linear equations |
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556 | (7) |
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563 | (5) |
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Modelling and investigation activity |
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568 | (2) |
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13 Representing multiple outcomes: random variables and probability distributions |
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570 | (52) |
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13.1 Modelling random behaviour |
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572 | (8) |
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13.2 Modelling the number of successes in a fixed number of trials |
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580 | (7) |
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13.3 Modelling the number of successes in a fixed interval |
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587 | (6) |
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13.4 Modelling measurements that are distributed randomly |
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593 | (8) |
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13.5 Mean and variance of transformed or combined random variables |
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601 | (3) |
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13.6 Distributions of combined random variables |
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604 | (12) |
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616 | (4) |
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Modelling and investigation activity |
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620 | (2) |
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14 Testing for validity: Spearman's, hypothesis testing and /2 test for independence |
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622 | (68) |
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14.1 Spearman's rank correlation Coefficient |
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625 | (4) |
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14.2 Hypothesis testing for the binomial probability, the Poisson mean and the product moment correlation coefficient |
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629 | (9) |
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14.3 Testing for the mean of a normal distribution |
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638 | (12) |
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14.4 Χ2 test for independence |
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650 | (2) |
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14.5 Χ2 goodness-of-fit test |
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652 | (18) |
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14.6 Choice, validity and interpretation of tests |
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670 | (14) |
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684 | (4) |
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Modelling and investigation activity |
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688 | (2) |
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15 Optimizing complex networks: graph theory |
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690 | (46) |
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692 | (7) |
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15.2 Graph theory for unweighted graphs |
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699 | (8) |
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15.3 Graph theory for weighted graphs: the minimum spanningtree |
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708 | (6) |
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15.4 Graph theory for weighted graphs: the Chinese postman problem |
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714 | (6) |
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15.5 Graph theory for weighted graphs: the travelling salesman problem |
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720 | (9) |
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729 | (5) |
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Modelling and investigation activity |
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734 | (2) |
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736 | (14) |
| Practice exam paper 1 |
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750 | (6) |
| Practice exam paper 2 |
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756 | (5) |
| Practice exam paper 3 |
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761 | (4) |
| Answers |
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765 | (84) |
| Index |
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849 | |
