Practice Questions

Chapter 1: From patterns to generalizations: sequences and series.

  1. Number pattern and sigma notation. Free
  2. Arithmetic and geometric sequences. Free
  3. Arithmetic and geometric series.
  4. Application of arithmetic and geometric patterns.
  5. The binomial theorem.
  6. Proofs.

Chapter Review.

Chapter 2: Representing relationships: introducing functions.

  1. What is a function?
  2. Functional notation.
  3. Drawing graphs of functions.
  4. The domain and range of a function.
  5. Composite functions.
  6. Inverse functions.

Chapter Review.

Chapter 3: Modelling relationships: linear and quadratic functions.

  1. Gradient of a linear function.
  2. Linear functions.
  3. Transformation of functions.
  4. Graphing quadratic functions.
  5. Solving quadratic equations by factorization and completing the square.
  6. The quadratic formula and the discriminant.
  7. Application of quadratics.

Chapter Review.

Chapter 4: Equivalent representations: rational functions.

  1. The reciprocal function.
  2. Transforming the reciprocal function.
  3. Rational function of the form f(x) =(ax+b)/(cx+d).

Chapter Review.

Chapter 5: Measuring change: differentiation.

  1. Limits and convergence.
  2. The derivative function.
  3. Differentiation rules.
  4. Graphical interpretation of the first and second derivatives.
  5. Application of differential calculus: optimization and Kinematics.

Chapter Review.

Chapter 6: Representing data: statistics for univariate data.

  1. Sampling.
  2. Presentation of data.
  3. Measures of central tendency.
  4. Measures of dispersion.

Chapter Review.

Chapter 7: Modelling relationships between two data sets.

  1. Scatter diagrams.
  2. Measuring correlation.
  3. The line of best fit.
  4. Least square regression.

Chapter Review.

Chapter 8: Quantifying randomness.

  1. Theoretical and experimental probability.
  2. Representing probabilities: Venn diagrams and sample spaces.
  3. Independent and dependent events and conditional probability.
  4. Probability tree diagrams.

Chapter Review.

Chapter 9: Representing equivalent quantities: exponential and logarithms.

  1. Exponents
  2. Logarithms.
  3. Derivatives of exponential functions and natural logarithmic functions.

Chapter Review.

Chapter 10: From approximation to generalization: integration.

  1. Antiderivatives and the indefinite integral.
  2. More on indefinite integrals.
  3. Area and definite integrals.
  4. Fundamental theorem of calculus.
  5. Area between two curves.

Chapter Review.

Chapter 11: Relationships in space: geometry and trigonometry in 2D and 3D.

  1. The geometry of 3D shapes.
  2. Right-angled triangle trigonometry.
  3. The sine rule.
  4. The cosine rule.
  5. Application of right and non-right-angled trigonometry.

Chapter Review.

Chapter 12: Periodic relationships: trigonometric functions.

  1. Radian measure, arcs, sectors and segments.
  2. Trigonometric ratios in the unit circle.
  3. Trigonometric identities and equations.
  4. Trigonometric functions.

Chapter Review.

Chapter 13: Modelling change: more calculus.

  1. Derivative with sine and cosine.
  2. Application of derivatives.
  3. Integration with sine, cosine, and substitution.
  4. Kinematics and accumulating change.

Chapter Review.

Chapter 14: Invalid comparisons and informed decisions: probability distributions.

  1. Random variables.
  2. The binomial distribution.
  3. The normal distribution.

Chapter Review.

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