Quadratic Formula
Secondary · AlgebraGiven: x²−5x+6=0
Formula: x=[−b±√(b²−4ac)]/(2a)
Formula: x=[−b±√(b²−4ac)]/(2a)
Substitute: x=[5±√(25−24)]/2
Answer: x=3 or x=2
MATHEMATICS · FORMULA LIBRARY
Standard Mathematics Formulas
A structured cross-level reference from primary/foundation mathematics through secondary, intermediate/HSC-equivalent, undergraduate and postgraduate/advanced mathematics. English terminology is paired with Bangla labels where useful. Use the level selector first, then narrow by topic.
How to use this library
Select a study level, choose a topic, and use the formula with its meaning, conditions, common error and practice guidance. The worked examples and self-check section are provided to help you move from understanding a formula to applying it independently.
How to Learn from a Formula
Use each formula as a learning unit: understand its meaning, verify its conditions, apply it in a worked example, then retrieve and practise it independently.
1 · Understand
Identify the concept, formula type, symbols and mathematical meaning.
2 · Check conditions
Confirm domain, restrictions, units and angle conventions before substitution.
3 · Apply
Follow Given → Required → Formula → Substitution → Calculation → Answer.
4 · Retrieve
Close the answer and solve a fresh problem without looking first.
Worked Examples
Pythagorean Theorem
School · GeometryGiven: legs 6 cm and 8 cm.
Formula: c²=a²+b²
Formula: c²=a²+b²
Calculation: c²=36+64=100
Answer: c=10 cm
Power Rule
HSC · CalculusGiven: f(x)=x⁵
Rule: d(xⁿ)/dx=nxⁿ⁻¹
Rule: d(xⁿ)/dx=nxⁿ⁻¹
Apply: f′(x)=5x⁴
Answer: 5x⁴
Conditional Probability
HSC · ProbabilityGiven: P(A∩B)=0.2, P(B)=0.5.
Formula: P(A|B)=P(A∩B)/P(B)
Formula: P(A|B)=P(A∩B)/P(B)
Calculation: 0.2/0.5=0.4
Answer: 0.4
Practice & Self-Check
1 · Area
Find the area of a circle with radius 7 cm.
Answer: 49π cm².
2 · Explain
Why must a≠0 in the quadratic formula?
Answer: Otherwise the equation is not quadratic.
3 · Differentiate
Find f′(x) for f(x)=3x⁴−2x²+7.
Answer: 12x³−4x.
4 · Select a method
A right triangle has legs 9 and 12. Which theorem finds the hypotenuse?
Answer: Pythagorean theorem.
5 · Check a condition
Can the ordinary power rule integrate x⁻¹?
Answer: No; use ∫1/x dx=ln|x|+C.
6 · Coordinate geometry
For y=2x+3, identify slope and y-intercept.
Answer: m=2 and c=3.
Curriculum note: Bangladesh's NCTB publishes school and higher-secondary textbook lists, including Bangla and English-version materials. This library is a cross-level formula reference, not a substitute for a specific board, university or examination syllabus. Verify the applicable syllabus and notation before exam use. NCTB 2026 textbook list ↗