vmbo havo vwo
Algebra
What belongs here
Algebra is working with letters: you look for x (and sometimes y) in an equation. Three tools: linear equation, a system of two equations, and quadratic with the quadratic formula. On the Dutch site this topic is also called Algebra.
In which order do you build this?
- Linear: one unknown, balance method
- System: two unknowns, two equations
- Quadratic formula: quadratic, discriminant and roots
Start with the linear equation solver: ax + b = c, or with x on both sides. If a = 0 the x-term vanishes; then there is no unique x left. A system of equations is two of those lines at once: intersection, parallel (no solution) or coincident (infinitely many). The quadratic formula calculator comes after: ax² + bx + c = 0 with a ≠ 0. If a = 0 you fall back to linear — the tool says so too.
Which tool do you pick?
| You see in the sum… | Open |
|---|---|
| One unknown, no x² (e.g. 2x + 3 = 11) | Linear equation solver |
| Two equations with x and y | Systems of equations |
| x², or ax² + bx + c = 0 | Quadratic formula calculator |
Unsure between linear and quadratic: look for an x². Unsure between one equation and a system: count the unknowns and the equations.
What you meet per level
On this hub: which algebra tool fits which kind of sum. The current exam program is on Examenblad. Dutch secondary tracks are named once: vmbo, havo and vwo.
On vmbo algebra is mainly the balance method: the same operation left and right. Typical: 2x + 3 = 11 → x = 4. Negative numbers and decimals are fine. Quadratic equations and systems are not the core of these tools here; start with linear.
On havo, systems and the quadratic formula join in. A system is two lines; the quadratic formula is the standard route when factoring fails. Discriminant D = b² − 4ac tells whether there are 0, 1 or 2 real solutions. Example: x² − 5x + 6 = 0 → D = 1 → x = 2 or x = 3. A graphing calculator plots the parabola; the quadratic formula page computes the roots with steps.
On vwo the same three tools inside a larger sum: first rewrite to ax² + bx + c = 0, or a system you substitute down to one equation. No extra exam rules on this hub. Order stays: master linear, then two equations, then quadratic.
Tools
Linear equation solver
One unknown, no square: isolate x with the balance method. Open this first.
havo vwoSystems of equations
Two lines in the plane: one intersection, none, or the same line forever.
havo vwoQuadratic formula calculator
ax² + bx + c = 0: read D, then both real roots when they exist.
Topics by level
- vmbo, havo and vwo: Linear equation solver · Exponential growth calculator
- havo and vwo: Systems of equations · Quadratic formula calculator · Derivative calculator
- Explore: Linear function simulation · Parabola simulation
- Math A or math B in havo or vwo? Difference between math A and B