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Chapter 1 Mathematics as the science of patterns |
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2 |
(46) |
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1.1 Number patterns: sequences, series and sigma notation |
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5 |
(5) |
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1.2 Arithmetic sequences and series |
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10 |
(5) |
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1.3 Geometric sequences and series |
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15 |
(9) |
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1.4 Conjectures and proofs |
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24 |
(1) |
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1.5 Mathematical induction |
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25 |
(6) |
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31 |
(7) |
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38 |
(10) |
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Chapter 2 Mathematics as a language |
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48 |
(48) |
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2.1 Relations and functions |
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50 |
(4) |
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2.2 Special functions and their graphs |
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54 |
(16) |
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2.3 Operations with functions |
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70 |
(9) |
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2.4 Transformations of graphs of functions |
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79 |
(17) |
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Chapter 3 The long journey of mathematics |
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96 |
(70) |
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3.1 Introduction to complex numbers |
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97 |
(12) |
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3.2 Operations with complex numbers |
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109 |
(9) |
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3.3 Polynomial functions: graphs and operations |
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118 |
(13) |
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3.4 Polynomial functions: zeros, sum and product |
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131 |
(9) |
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3.5 Polynomial equations and inequalities |
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140 |
(13) |
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3.6 Solving systems of equations |
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153 |
(13) |
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Chapter 4 Modeling the real world |
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166 |
(66) |
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4.1 Limits, continuity and convergence |
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168 |
(12) |
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4.2 The derivative of a function |
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180 |
(9) |
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4.3 Differentiation rules |
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189 |
(16) |
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4.4 Exploring relationships between f,f' and f" |
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205 |
(3) |
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4.5 Applications of differential calculus: kinematics |
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208 |
(3) |
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4.6 Applications of differential calculus: economics |
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211 |
(4) |
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4.7 Optimization and modeling |
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215 |
(3) |
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4.8 Differentiation of implicit functions |
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218 |
(3) |
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221 |
(11) |
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Chapter 5 Aesthetics in mathematics |
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232 |
(46) |
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234 |
(4) |
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5.2 Properties of exponents and logarithms |
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238 |
(5) |
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5.3 Euler's number and exponential functions |
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243 |
(5) |
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5.4 Invariance and the exponential function - a different approach to Euler's number |
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248 |
(1) |
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249 |
(9) |
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5.6 Logarithmic functions and their behavior |
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258 |
(3) |
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5.7 Derivatives of exponential and logarithmic functions |
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261 |
(6) |
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5.8 Angles, arcs and areas |
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267 |
(11) |
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Chapter 6 Exploring randomness |
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278 |
(64) |
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6.1 Classification and representation of statistical data |
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280 |
(8) |
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6.2 Measures of central tendency |
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288 |
(3) |
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6.3 Measures of dispersion |
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291 |
(8) |
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6.4 Theoretical probability |
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299 |
(7) |
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6.5 Probability properties |
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306 |
(2) |
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6.6 Experimental probability |
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308 |
(4) |
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6.7 Conditional probability |
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312 |
(6) |
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318 |
(3) |
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6.9 Probability tree diagrams |
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321 |
(5) |
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326 |
(16) |
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Chapter 7 The evolution of calculus |
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342 |
(40) |
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7.1 Integration as anti-differentiation |
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344 |
(8) |
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352 |
(3) |
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7.3 Geometric significance of the definite integral |
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355 |
(27) |
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Chapter 8 Ancient mathematics and modern methods |
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382 |
(52) |
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8.1 The right-angled triangle and trigonometric ratios |
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384 |
(5) |
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8.2 The unit circle and trigonometric ratios |
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389 |
(9) |
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8.3 Compound angle identities |
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398 |
(3) |
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8.4 Double angle identities |
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401 |
(2) |
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8.5 Graphs of trigonometric functions |
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403 |
(6) |
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8.6 The inverse trigonometric functions |
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409 |
(3) |
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8.7 Solving trigonometric equations |
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412 |
(3) |
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415 |
(3) |
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418 |
(5) |
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423 |
(11) |
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Chapter 9 The power of calculus |
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434 |
(60) |
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9.1 Derivatives of trigonometric functions |
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436 |
(14) |
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9.2 Related rates of change with trigonometric expressions |
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450 |
(5) |
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9.3 Integration of trigonometric functions |
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455 |
(6) |
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9.4 Integration by substitution |
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461 |
(5) |
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466 |
(6) |
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9.6 Special substitutions |
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472 |
(8) |
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9.7 Applications and modeling |
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480 |
(14) |
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Chapter 10 Modeling randomness |
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494 |
(60) |
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10.1 Discrete random variables and distributions |
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496 |
(7) |
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10.2 Binomial distribution |
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503 |
(10) |
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10.3 Poisson distribution |
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513 |
(7) |
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10.4 Continuous random variables |
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520 |
(12) |
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532 |
(12) |
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10.6 Modeling and problem solving |
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544 |
(10) |
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Chapter 11 Inspiration and formalism |
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554 |
(74) |
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11.1 Geometric vectors and basic operations |
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556 |
(7) |
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11.2 Introduction to vector algebra |
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563 |
(8) |
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11.3 Vectors, points and equations of lines |
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571 |
(12) |
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583 |
(9) |
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11.5 Vector (cross) product and properties |
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592 |
(4) |
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11.6 Vectors and equations of planes |
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596 |
(3) |
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11.7 Angles, distances and intersections |
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599 |
(14) |
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11.8 Modeling and problem solving |
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613 |
(15) |
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Chapter 12 Multiple perspectives in mathematics |
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628 |
(32) |
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12.1 Complex numbers as vectors |
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630 |
(3) |
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12.2 Complex plane and polar form |
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633 |
(5) |
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12.3 Operations with complex numbers in modulus-argument form |
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638 |
(5) |
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12.4 Powers and roots of complex numbers: De Moivre's theorem and applications |
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643 |
(7) |
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12.5 Mathematical connections |
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650 |
(10) |
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660 |
(12) |
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13.1 About the exploration |
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660 |
(1) |
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13.2 Internal assessment criteria |
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661 |
(5) |
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13.3 How the exploration is marked |
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666 |
(1) |
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666 |
(1) |
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667 |
(1) |
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668 |
(1) |
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669 |
(3) |
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Chapter 14 Prior learning |
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672 |
(82) |
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673 |
(24) |
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697 |
(22) |
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719 |
(26) |
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745 |
(9) |
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Chapter 15 Practice Papers |
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754 |
(6) |
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754 |
(3) |
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757 |
(3) |
Answers |
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760 |
(51) |
Index |
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811 |
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