IB SL - Algebra
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Surds, indices and number types
  • Understanding of indices including negative indices, fractional indices, simplifying indices.
  • Types of number: real, rational, irrational.
  • Simplifying and writing exact numbers by use of surds.
 
Quadratics
  • Factorizing and solving quadratics.
  • Using the quadratic formula to solve a quadratic equation.
  • Using the discriminate to find the nature of roots of a quadratic.
  • Completing the square.
  • Graphing quadratics, showing intercepts and the vertex.
  • Finding the coordinates of the vertex of the quadratic equation.
 
Graphing functions, domains and range
  • Substituting, solving and inverse functions.
  • Composite functions.
  • Domains and ranges of functions.
  • Concept of a one-to-one function, many-to-one, one-to-many functions.
  • Understand that a function only has an inverse if it is one-to-one.
  • Graphing functions on a GDC.
  • Inverse functions graphically, reflections in the line y=x.
  • Solving functions graphically.
  • Graphing functions, finding points of intersection, and other features such as asymptotes.
 
Binomial expansions and combinations
  • Counting principles, using the ! sign.
  • Combinations and using the combination formula.
  • Pascal's triangle.
  • Expanding brackets (a + b) ^n
 
Logarithms and the natural exponential
  • Laws of logarithms and exponents.
  • Using the change of base.
  • Graphing logarithms and their inverses.
  • The natural exponential (e) function.
  • The natural logarithm (ln) function.
  • Using logarithms to solve problems.
 
Series: arithmetic and geometric
  • Arithmetic series: sum of and next term.
  • Geometric series: sum of and next term.
  • Using the sigma sign, for arithmetic and geometric series.
  • Solving problems involving savings schemes and mortgage payments.
 
Transformation of curves
  • Reflections in the lines y=x, x-axis, y-axis.
  • Translations vertically or horizontally.
  • Stretches of curves with either the y-axis or the x-axis invariant.