Study Guide

Objective

The student :
- is familiar with the concept of functions
- is able to solve equations algebraically, graphically and numerically ( Equations with roots and absolute values, equations with complex solutions,
exponential equations , equations with logarithms ,trigonometric equations )
- Is able to apply a variety of mathematical models in problem solving.

Content

The concept of functions, graphs, inequalities
Equations with roots
Equations containing absolute values
Equations with complex solutions
Complex numbers ; rectangular form, polar form and power form
Power functions, power equations
Exponential functions and equations
Logarithms, equations with logarithms
Problems with exponential change
Trigonometric functions, graphs
Trigonometric equations

Application according to specific education may occur.

Evaluation scale

H-5

Assessment criteria, satisfactory (1)

Is able to extract information from graphs and understand basic properties about different types of functions
Is able to solve simple exponential equations
Is able to solve simple trigonometric equations
Knows complex numbers and can perform simple calculations with them
Have some understanding of how to use a mathematical model and how it can be solved.
Master basic use of a calculation software.

Assessment criteria, good (3)

Is able to draw graphs for different types of functions and can define the domain and the range for the functions.
Master the solution of ordinary exponential and logarithm equations
Is able to rewrite trigonometric expressions and can solve common trigonometric equations
Master the transformation of complex numbers between different forms
Have a good understanding of how to use a mathematical model and how it can be solved.
Master the use of calculation software.

Assessment criteria, excellent (5)

Master the basic properties of functions and can solve inequalities
Master the solution of more demanding equations and problems containing exponential functions and logarithms
Master the solution of more demanding trigonometric equations.
Can apply complex numbers to solve more complicated problems
Can design and solve more complicated models.
Master advanced use of calculation software.

Qualifications

Functions and equations 1,
Geometry and vectors