Higher Level Files: Page Number

Higher Level Files:

Page Number File Type File Name iii pdf Prelim summary iii pdf Chapter 1 summary iii pdf Chapter 2 summary iii pdf Chapter 3 summary iii pdf Chapter 4 summary iii pdf Chapter 5 summary iii pdf Chapter 6 summary iv pdf Chapter 7 summary iv pdf Chapter 8 summary iv pdf Chapter 9 summary iv pdf Chapter 10 summary iv pdf Chapter 11 summary iv pdf Chapter 12 summary iv pdf Chapter 13 summary iv pdf Chapter 14 summary v pdf Chapter 15 summary v pdf Chapter 16 summary v pdf Chapter 17 summary v pdf Chapter 18 summary v pdf Chapter 19 summary v pdf Chapter 20 summary v pdf Answers summary v pdf Index summary 4 video 1.1: Proof of irrationality 14 pdf Exercise 1.1 Worked Solutions 19 pdf Exercise 1.2 Worked Solutions 23 pdf Exercise 1.3 Worked Solutions 25 pdf Exercise 1.4 Worked Solutions 26 Autograph Equivalence 1 27 Autograph Equivalence 2 28 Autograph Equivalence 3 30 Autograph Factors of Quadratics 35 pdf Exercise 1.5 Worked Solutions 39 Autograph Midpoint 39 Autograph Parallel Lines 39 Autograph Perpendicular Lines 39 Autograph Distance between Two Points as Radius of a Circle 40 Autograph Distance 1 40 Autograph Distance 2 42 Autograph Solving Equations 45 Quiz 1.1 Straight Lines Interactive 45 pdf Exercise 1.6 Worked Solutions 45 pdf 1.1 Straight Lines Answers 45 pdf 1.1 Straight Lines Quiz 45 pdf Chapter 1 Summary 45 pdf Chapter 1 Test 49 Autograph Vertical Line Test 1 49 Autograph Vertical Line Test 2 51 Autograph Domain and Range 1 52 Autograph Domain and Range 2 55 Autograph Range of a Cubic 56 pdf Exercise 2.1 Worked Solutions 57 Autograph Composite Functions 1 60 Autograph Composite Functions 2 61 pdf Exercise 2.2 Worked Solutions 61 pdf 2.2 Example composite functions 66 Autograph Inverse 1 66 Autograph Inverse 2 66 Autograph Inverse 3 66 Autograph Inverse 4 66 Autograph Inverse Functions 68 pdf 2.3 Example inverse functions 69 pdf Exercise 2.3 Worked Solutions 70 Autograph Transformations of Functions 74 Autograph Vertical Reflection 1 75 Autograph Horizontal Reflection 1 75 Autograph Horizontal Reflection 2 75 Autograph Vertical Reflection 2 82 Autograph Reciprocal Plotter 83 Autograph Modulus Plotter 85 pdf Exercise 2.4 Worked Solutions 85 pdf Chapter 2 Summary 86 Autograph Translation 89 pdf Chapter 2 Practice Question Solutions 89 pdf 2.1 Functions Answers 89 pdf 2.1 Functions Quiz 89 pdf Chapter 2 Test 89 video 1.6: Golden ration 97 pdf 3.1 Example synthetic substitution 98 pdf Exercise 3.1 Worked Solutions 100 Autograph Completing the Square 100 video 3.2: Completing the square 106 Autograph Quadratic Formula 108 Autograph Quadratic Factoring 112 pdf Exercise 3.2 Worked Solutions 116 Autograph Polynomial Zeros 125 Quiz 2.1/3.1 Functions and Quadratics Interactive 125 pdf Exercise 3.3 Worked Solutions 125 pdf 3.1 Polynomials and Quadratics Answers 125 pdf 3.1 Polynomials and Quadratics Quiz 127 Autograph Rational Function Asymptotes 127 Autograph Rational Functions 127 Autograph Geometric Sequence with Sum 131 pdf Exercise 3.4 Worked Solutions 131 pdf 3.4 Rational Functions Answers 131 pdf 3.4 Rational Functions Quiz 133 pdf 3.5 Example equations with radicals 137 Autograph Modulus 144 pdf Exercise 3.5 Worked Solutions 144 pdf Inequalities Answers 144 pdf Inequalities Quiz 149 pdf Exercise 3.6 Worked Solutions 149 pdf Chapter 3 Summary 150 Autograph A Line Meeting a Parabola 150 pdf Chapter 3 Practice Question Solutions 150 pdf Chapter 3 Test 154 pdf Exercise 4.1 Worked Solutions 156 pdf 4.2 Example arithmetic means 156 pdf 4.2 Formula 157 pdf Exercise 4.2 Worked Solutions 160 excel 4.4: Paying off a mortgage 161 pdf 4.3 Example compound interest 164 pdf Exercise 4.3 Worked Solutions 167 Autograph Arithmetic Sequence with Sum 167 pdf 4.4 Example arithmetic series 167 pdf 4.4 Formula arithmetic series 168 pdf 4.4 Example geometric series partial sums 168 pdf 4.4 Formula geometric series partial sums 169 pdf 4.4 Formula infinite geometric series 170 pdf 4.4 Example infinite geometric series 174 Quiz 4.1 Sequences and Series Interactive 174 pdf Exercise 4.4 Worked Solutions 174 pdf 4.1 Sequences and Series Answers 174 pdf 4.1 Sequences and Series Quiz 175 pdf 4.5 Example with and without replacement 178 pdf 4.5 Example permutations 179 pdf 4.5 Example combination vs permutations 183 pdf Exercise 4.5 Worked Solutions 184 pdf 4.6 Example Pascals triangle 187 pdf 4.6 Example binomial theorem 190 pdf Exercise 4.6 Worked Solutions 192 pdf 4.7 Example mathematical induction 192 video 4.7: Example 40 196 pdf 4.7 Example induction 200 pdf Exercise 4.7 Worked Solutions 200 pdf Binomial Theorem and Induction Answers 200 pdf Binomial Theorem and Induction Quiz 200 pdf Chapter 4 Summary 205 excel 4.9: Solution to question 47 205 pdf Chapter 4 Practice Question Solutions 205 pdf Chapter 4 Test 216 pdf Exercise 5.1 and 5.2 Worked Solutions 218 Autograph Definition of e 221 Autograph Exponential Decay Model 221 Autograph Exponential Equation Solution 221 Autograph Exponential Growth Model 224 pdf Exercise 5.3 Worked Soutions 227 Autograph Exponential Logarithmic Function 227 Autograph Inverse Graphs 234 pdf Exercise 5.4 Worked Soutions 243 pdf Exercise 5.5 Worked Soutions 243 pdf Chapter 5 Summary 245 Quiz 5.1 Exponential and Logarithmic Functions Interactive 245 pdf Chapter 5 Practice Question Solutions 245 pdf 5.1 Exponential and Logarithmic Functions Answers 245 pdf 5.1 Exponential and Logarithmic Functions Quiz 245 pdf Chapter 5 Test 256 pdf Exercise 6.1 and 6.2 Worked Solutions 266 pdf Exercise 6.3 Worked Solutions 274 pdf 6.4 Example Gaussian elimination 276 pdf Exercise 6.4 WorkedSolutions 276 pdf Chapter 6 Summary 278 pdf Chapter 6 Practice Question Solutions 278 pdf 6.1 Matrices Answers 278 pdf 6.1 Matrices Quiz 281 Autograph Radian Degree Conversion 281 Autograph Radian Measure 288 pdf Exercise 7.1 Worked Solutions 290 Autograph Unit Circle Definitions 297 Autograph Unit Circle Symmetries 1 297 Autograph Unit Circle Symmetries 2 300 pdf Exercise 7.2 Worked Solutions 301 Autograph Cosine Curve 301 Autograph Sine Curve 308 Media 7.1 Equations of Graphs 308 Media 7.1 Equations of Graphs 308 Autograph Sine Modelling 309 video 7.3: horizontal translation identities 309 video 7.3: complementary angles 310 Autograph Tan Curve 313 pdf Exercise 7.3 Worked Solutions 315 video 7.4: trigonometric equations 317 video 7.4: verifying trig equation cos 318 video 7.4: solving trigonometric equations 322 pdf Exercise 7.4 Worked Solutions 323 Autograph Pythagorean Identity 325 video 7.5: verifying trigonometric equation solution 330 Autograph Sine Double Angle Formula 1 330 Autograph Sine Double Angle Formula 2 335 pdf Exercise 7.5 Worked Solutions 345 pdf Exercise 7.6 Worked Solutions 345 pdf Chapter 7 Summary 349 pdf Chapter 7 Practice Question Solutions 349 pdf 7.1 Trigonometry Answers 349 pdf 7.1 Trigonometry Quiz 349 pdf Chapter 7 Test 360 pdf Exercise 8.1 Worked Solutions 369 pdf Exercise 8.2 Worked Solutions 370 Autograph Sine Rule 370 Autograph Sine Rule 376 Autograph Cosine Rule 1 376 Autograph Cosine Rule 2 378 video 8.4: how to avoid losing precision on GDC 382 pdf Exercise 8.3 and 8.4 Worked Solutions 382 pdf 8.4 Example Herons formula 383 Autograph Tangent and Gradient of Line 383 Autograph Tangent and Gradient the Same 393 pdf Exercise 8.5 Worked Solutions 393 pdf Chapter 8 Summary 396 Autograph Maximising Triangular Area 397 Quiz 8.1 Triangle Trigonometry Interactive 397 pdf Chapter 8 Practice Question Solutions 397 pdf 8.1 Triangle Trigonometry Answers 397 pdf 8.1 Triangle Trigonometry Quiz 397 pdf Chapter 8 Test 400 Autograph Displacement Vectors 400 Autograph Vector Equality 401 Autograph Position Vectors and Coordinates 401 Autograph Vector Magnitude 403 Autograph Combining Vectors 406 Autograph Vector Sum 406 pdf 9.2 Example parallel vectors 409 pdf Exercise 9.1and 9.2 Worked Solutions 410 Autograph Unit Vectors 410 pdf 9.3 Example direction angle 411 pdf 9.3 Example unit vectors 413 pdf 9.3 Example inclined plane 415 Autograph Moving Ships 415 pdf 9.3 Example navigation 419 Autograph Scalar Product Definition 419 pdf Exercise 9.3 Worked Solutions 420 Autograph Scalar Product Zero 420 pdf 9.4 Formula scalar product 422 pdf 9.4 Example angle between vectors 425 pdf Exercise 9.4 Worked Solutions 425 pdf Chapter 9 Summary 427 pdf Chapter 9 Practice Question Solutions 427 pdf 9.1 Vectors in Two Dimensions Answers 427 pdf 9.1 Vectors in Two Dimensions Quiz 427 pdf Chapter 9 Test 436 pdf 10.1 Example complex numbers 438 pdf 10.1 Example zeros of polynomials 440 pdf Exercise 10.1 Worked Solutions 442 pdf 10.2 Example complex number operations 445 Autograph Complex Multiplication 447 pdf 10.2 Summary polar form 448 pdf 10.2 Example polar form 449 pdf Exercise 10.2 Worked Solutions 450 Autograph De Moivre's Theorem 451 pdf 10.3 Example complex powers 453 pdf 10.3 Example complex roots 455 Autograph Roots of Unity 457 pdf 10.3 Formula complex powers 459 pdf Exercise 10.3 Worked Solutions 459 pdf Chapter 10 Summary 462 pdf Chapter 10 Practice Question Solutions 462 pdf 10.1 Complex Numbers Answers 462 pdf 10.1 Complex Numbers Quiz 462 pdf Chapter 10 Test 468 pdf 11.1 Example frequency distribution 470 video 11.1: histogram 470 video 11.1: cumulative frequency distribution demonstration 470 video 11.1: cumulative frequency 473 Autograph Histograms 479 pdf Exercise 11.1 Worked Solutions 482 pdf 11.2 Example central values 486 pdf Exercise 11.2 Worked Solutions 490 video 11.3: one variable statistics 491 pdf 11.3 Example box plot 492 Autograph Box and Whiskers 1 492 Autograph Box and Whiskers 2 493 video 11.3: box plot graph for data 493 video 11.3: one variable statistics grouped 494 video 11.3: ogive 497 Autograph Data Sampling 1 501 video 11.3: multiple graphs 505 pdf Exercise 11.3 Worked Solutions 505 pdf Chapter 11 Summary 515 Quiz 11.1 Statistics Interactive 515 pdf Chapter 11 Practice Question Solutions 515 pdf 11.1 Statistics Answers 515 pdf 11.1 Statistics Quiz 515 pdf Chapter 11 Test 520 pdf 12.2 Example probability 525 pdf Exercise 12.1 and 12.2 Worked Solutions 528 pdf 12.3 Example probability 531 pdf 12.3 Example probability 2 537 pdf Exercise 12.3 Worked Solutions 539 pdf 12.4 Example probability 542 pdf 12.4 Example probability 2 545 pdf 12.4 Example probability 3 552 pdf Exercise 12.4 Worked Solutions 555 excel 12.5: Bayes theorem calculator 558 pdf 12.5 Example Bayes theorem 561 pdf Exercise 12.5 Worked Solutions 562 pdf Chapter 12 Summary 570 Quiz 12.1 Probability 570 pdf Chapter 12 Practice Question Solutions 570 pdf 12.1 Probability Answers 570 pdf 12.1 Probability Quiz 570 pdf Chapter 12 Test 573 video 13.1: limit of functions 573 video 13.1: limit of indeterminate form 574 Autograph Limit of sine(x) over x 580 pdf Exercise 13.1 Worked Solutions 581 Autograph Tangent and Velocity 583 Autograph Chords and Tangents 583 Autograph Derivative Definition: Different Limits 583 Autograph Derivative Definition the Standard case 583 Autograph Derivative Definition: Discontinuity 583 Autograph Derivative Definition: No Limit 585 video 13.2: numerical derivative 586 pdf 13.2 Example differentiation from first principles 588 Autograph Turning Points 589 video 13.2: numerical derivative on graph screen 590 video 13.2: tangent to curve 590 video 13.2: tangent at turning point 591 video 13.2: verifying slope with nDeriv 592 Autograph Plotting a Gradient Function 592 Autograph Gradient Function Trace 592 video 13.2: using nDeriv to verify derivative 598 pdf Exercise 13.2 Worked Solutions 606 Autograph Function with First and Second Derivatives 609 Autograph Second Derivative 609 Autograph Points of Inflection: No Inflection 609 Autograph Points of Inflection: Inflections Not Found 614 pdf Exercise 13.3 Worked Solutions 615 video 13.4: finding equations of tangents 617 Autograph Tangent and Normal 620 pdf Exercise 13.4 Worked Solutions 620 pdf Chapter 13 Summary 625 Quiz 13.1 Differentiation 625 pdf Chapter 13 Practice Question Solutions 625 pdf 13.1 Differentiation Answers 625 pdf 13.1 Differentiation Quiz 625 pdf Chapter 13 Test 630 pdf 14.1 Example vectors 636 pdf Exercise 14.1 Worked Solutions 640 pdf 14.2 Example direction cosines 644 pdf Exercise 14.2 Worked Solutions 645 Autograph Vector Product 646 pdf 14.3 Example vector product 647 video 14.3: Finding the area of a parallelogram 652 pdf Exercise 14.3 Worked Solutions 653 Autograph Equation of a Line 653 Autograph Parametric Lines in 3D 654 Autograph Vector Equation of a Straight Line 658 pdf 14.4 Summary lines in 3D 663 Autograph Modelling Motion with Parametric Equations 670 Quiz 9.1/14 Vectors 670 Autograph Three Point Plane 670 pdf Exercise 14.4 Worked Solutions 672 Autograph Vector Equation of a Plane 677 pdf 14.5 Summary planes equations 685 Autograph Three Planes without a Unique Intersection 685 pdf 14.5 Example intersecting planes 686 Autograph A Sphere Cut by Planes 687 pdf Exercise 14.5 Worked Solutions 688 pdf Review Exercise Worked Solutions 689 pdf Chapter 14 Summary 699 pdf Chapter 14 Practice Question Solutions 699 pdf 14.1 Vectors in Three Dimensions Answers 699 pdf 14.1 Vectors in Three Dimensions Quiz 699 pdf Chapter 14 Test 706 Autograph Chain Rule 716 pdf Exercise 15.1 Worked Solutions 716 pdf 15.1 Example higher derivatives 717 Autograph Derivative of cos kx 717 Autograph Derivative of sin kx 718 video 15.2: exploring derivative tan 723 video 15.2 exploring derivative ex 724 excel 15.2: Exponential function 724 Autograph Exp x 729 Quiz 15.1/15.2 Differentiation II Interactive 729 pdf Exercise 15.2 Worked Solutions 729 pdf 15.1 Chain Product and Quotient Rules Answers 729 pdf 15.1 Chain Product and Quotient Rules Quiz 735 Autograph Derivative of ln x 735 video 15.3: exploring derivative of ln 736 Autograph Product Rule 1 737 Autograph Product Rule 2 745 pdf Exercise 15.3 Worked Solutions 752 pdf Exercise 15.4 Worked Solutions 752 pdf 15.3 Implicit Differentiation Answers 752 pdf 15.3 Implicit Differentiation Quiz 753 video 15.5: using minimum function 755 video 15.5: Example - finding minimum length 756 video 15.5: checking endpoints 757 video 15.5: mininum function vs derivative 761 pdf Exercise 15.5 Worked Solutions 761 pdf Chapter 15 Summary 770 pdf Chapter 15 Practice Question Solutions 770 pdf Chapter 15 Test 773 pdf 16.1 Example integrals 775 pdf 16.1 Example integrals 2 779 pdf 16.1 Example integrals 3 781 pdf Exercise 16.1 Worked Solutions 784 pdf 16.2 Example integrals 786 pdf 16.2 Example integrals 2 787 pdf Exercise 16.2 Worked Solutions 787 pdf 16.2 Example two definite integrals 792 pdf 16.3 Example integrals 794 Quiz 16.1 Integration 794 pdf Exercise 16.3 Worked Solutions 794 pdf 16.1 Integration Techniques Answers 794 pdf 16.1 Integration Techniques Quiz 795 Autograph Area Function 795 Autograph Sum of Rectangles 809 pdf Exercise 16.4 Worked Solutions 810 pdf 16.5 Example partial fractions 812 Autograph Area Under Sine Curve 812 Autograph Designer Curve Area Investigation 812 Autograph Integration of Constant m 812 Autograph Integrating Powers of x 812 pdf Exercise 16.5 Worked Solutions 812 video 16.6: areas 813 Autograph Integration of cos kx 813 Autograph Integration of exp(kx) 813 Autograph Integration of the Line mx 813 Autograph Integration of 1/x 813 Autograph Integrating Over Zeroes 813 video 16.6: areas 2 814 pdf 16.6 Example areas 815 Autograph Area Between Curves 816 video 16.6: areas 3 819 pdf Exercise 16.6 Worked Solutions 820 pdf 16.7 Example volumes 821 Autograph Volume of Revolution Slices 822 Autograph Volume of Revolution 1 822 Autograph Volume of Revolution 2 826 pdf Exercise 16.7 Worked Solutions 828 pdf 16.8 Example motion 835 pdf Exercise 16.8 Worked Solutions 835 pdf Applications Answers 835 pdf Applications Quiz 845 pdf Exercise 16.9 Worked Solutions 845 pdf Chapter 16 Summary 853 pdf Chapter 16 Practice Question Solutions 853 pdf Chapter 16 Test 862 pdf 17.1 Example random variables 864 video 17.1: Demonstration - variance and standard deviation 864 video 17.1: expected value 864 video 17.1: expected value 2 869 pdf Exercise 17.1 Worked Solutions 871 Autograph Binomial Distribution 871 video 17.2: Extra question - binomial distribution 872 pdf 17.2 Example binomial distribution 873 video 17.2: binomial distribution 874 video 17.2: binomial distribution 2 874 video 17.2: binomial distribution 3 876 video 17.2: binomial distribution 4 881 pdf Exercise 17.2 Worked Solutions 882 Autograph Data Sampling 2 884 pdf 17.3 Example Poisson distribution 884 video 17.3: poisson distribution 885 Autograph Poisson Distribution 885 video 17.3: poisson distribution 2 886 Autograph Data Sampling 3 887 pdf 17.1 Discrete Distributions Answers 887 pdf 17.1 Discrete Distributions Quiz 889 pdf Exercise 17.3 Worked Solutions 896 pdf Example continuous distributions 901 pdf Exercise 17.4 Worked Solutions 902 video 17.5: normal distribution 904 Autograph Standard Normal Distribution 907 video 17.5: normal distribution 2 907 video 17.5: normal distribution 3 910 video 17.5: inverse normal 911 video 17.5: normal distribution 4 911 video 17.5: normal distribution 5 912 video 17.5: normal distribution 6 913 Autograph Parameters of the Normal Distribution 916 pdf Exercise 17.5 Worked Solutions 916 pdf Continuous Distributions Answers 916 pdf Continuous Distributions Quiz 916 pdf Chapter 17 Summary 916 pdf Chapter 17 Test 921 Quiz 17 Probability Distributions Interactive 921 pdf Chapter 17 Practice Question Solutions