| IB HL - Functions, Algebra and Complex numbers |
 |
|
| |
| 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
|
| |
| Permutations |
|
| |
| Factor and remainder |
- Factor theorems.
- Remainder theorems.
|
| |
| 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.
|
| |
| Mathematical induction |
- Proof by mathematical induction. Apply to series, and later to trigonometric equations, complex numbers and calculus functions.
|
| |
| 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.
|
| |
| Inequalities |
- Solving linear inequalities by use of algebra and graphically.
- Solving quadratic inequalities by use of a combination of graphs and algebra.
- Solving inequalities with absolute values (modulus sign), graphically and by use of algebra.
|
| |
| Complex numbers |
- Understanding of the complex number in cartesian form (a +ib). The real and imaginary parts.
- Writing a complex number in the modulus form.
- Representing a complex number graphically by use of an Argand diagram.
- Sum, product, and quotient of a complex number.
- Understanding of De Moivre's theorem.
- Using De Moivre's theorem to find roots of complex equations.
|
| |
| |
