Quadratic Equations — Concept Maps
Punjab Board · Class 10 · Mathematics
3 concept maps of Quadratic Equations for Punjab Board Class 10 Mathematics, each also written out as a text outline.
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Process to identify if an equation is quadratic
The map in words
- Given Equation
- Expand all brackets
- Move all terms to LHS
- Combine like terms
- Is highest power 2?
- No: Not a Quadratic
- Yes: Is a ≠ 0?
- No: Not a Quadratic
- Yes: Quadratic Equation: ax² + bx + c = 0
- Is highest power 2?
- Combine like terms
- Move all terms to LHS
- Expand all brackets
Mind map showing various real-life applications of quadratic equations
The map in words
- root((Quadratic Equations
- Applications))
- Geometry
- Rectangle areas
- Triangle dimensions
- Circle problems
- Number Theory
- Sum and product
- Consecutive integers
- Digit problems
- Age Problems
- Parent-child ages
- Multiple persons
- Product conditions
- Motion
- Speed and time
- Distance calculations
- Acceleration
- Geometry
Step-by-step process for solving quadratic equations by factorisation
The map in words
- Quadratic Equation ax² + bx + c = 0
- Step 1: Split middle term bx
- Find factors of ac that sum to b
- Step 2: Rewrite equation with split terms
- Step 3: Factor by grouping
- Get form: Factor1 × Factor2 = 0
- Step 4: Apply Zero Product Rule
- Solve Factor1 = 0
- Root 1
- Verify by substitution
- Root 1
- Solve Factor2 = 0
- Root 2
- Solve Factor1 = 0
- Step 4: Apply Zero Product Rule
- Get form: Factor1 × Factor2 = 0
- Step 3: Factor by grouping
- Step 2: Rewrite equation with split terms
- Find factors of ac that sum to b
- Step 1: Split middle term bx
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