Polynomials — Class 10 CBSE Mathematics revision notes
A 4-page visual revision sheet for Polynomials, written for Class 10 CBSE Mathematics. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.
What this Polynomials sheet covers
- Introduction
- What counts as a polynomial
- Value at a point, and a zero
- the value of p at x=k
- k is a zero of p exactly when
- zero of the linear ax+b
- check on 2x-6
- Named by degree
- Linear, degree 1
- Quadratic, degree 2
- Cubic, degree 3
- Constant, degree 0
- Geometrical Meaning of the Zeroes of a Polynomial
- Geometrical meaning of the zeroes
- One zero, and none at all
- When a sketch is all you are given
- Relationship between Zeroes and Coefficients of a Polynomial
- Zeroes and coefficients of a quadratic
- for ax^2+bx+c with zeroes α and β
- sum of the zeroes
- product of the zeroes
- check on x^2-5x+6, zeroes 2 and 3
- Where those two relations come from
- a quadratic with zeroes α and β
- multiply the brackets out
- line it up against ax^2+bx+c
- divide by a and there they are
- Building a quadratic from its zeroes
- from sum S and product P
- zeroes 2 and 3
- zeroes -3 and 5
- k=2 gives the same zeroes
- Splitting the middle term
- What the two signs alone tell you
- Expressions rebuilt from sum and product
- squares
- difference, up to sign
- reciprocals
- on x^2-5x+6, zeroes 2 and 3
- One quadratic, worked end to end
- Three shapes worth recognising on sight
- a difference of two squares
- so its zeroes sit either side of 0
- a perfect square, one repeated zero
- and a plain common factor
- When a sentence hides a coefficient
- the zeroes are equal and opposite
- the zeroes are reciprocals
- one of the zeroes is 0
- the two zeroes are the same
- Symbols
- Traps that cost marks
- Tricks that save time
How CapCompass uses this sheet
These notes are not a standalone PDF. CapCompass plans Mathematics chapter by chapter against your real exam dates and free hours, and when the plan reaches Polynomials the sheet opens inside the study block itself — at the page covering the sub-topic that block is on, with the timer still running. Revision arrives at the moment the plan says revise, instead of having to be gone looking for.