MATH 42’s mathematical capabilities are being enhanced and expanded permanently — the mathematics coverage described below represents the coverage on September 1st 2016.

Should you have special mathematical requirements, which are not listed below, please ask us about it with a given example.

## Step-by-Step Solutions

### Term Transformation

- Simplyfing and expanding
- Factorization (Factoring out, application of the binomial formulas)
- Transforming powers and roots
- Adding fractions, multiplying fractions, reducing fractions, expanding fractions
- Computing the gcd and the lcm
- Trigonometric transformations (Is being enhanced)
- Logarithmic transformations (Is being enhanced)

### Functions

- Roots
- Y-axis intersection
- Domain of definition
- Extremes (Maximums, Minimums)
- Inflexion points
- Curve sketching
- Derivatives:
- factor rule, sum rule,
- product rule, quotient rule
- chain rule

- Integration:
- Fundamental Integrals
- integrate by substitution
- integrate by parts
- partial fraction decomposition

### Equations

- Linear equations
- Quadratic equations:
- Completing the square, quadratic formula
- pq-formula

- Special equations of higher degree
- Linear systems of equations
- Non-linear system of equations

### Matrices

- Adding matrices
- Multiplying matrices
- Transposing matrices
- Inverting matrices
- Computing determinants
- Computing characteristic polynomials
- Computing eigenvalues
- Computing eigenspaces
- Computing kernels
- Computing ranks
- Cross-product
- Gaussian elimination

## Exercises

The Assessment Center of MATH 42 provides exercises to the 3 following topics:

- Transformation of expressions
- Functions
- Equations

## Graphical Display

- Graphical curve sketching
- Domain, asymptotes
- roots
- intersection with the y-axis
- extremes
- inflexion points

- Derivatives
- Asymptotical functions
- Intersections between functions
- Deskewing of the graph