NCERT Exemplar Problems Solutions Class 10 Maths PDF form free download. Summative Assessment 1 and Summative Assessment 2. NCERT Exemplar books are also available to download. These exemplar problems solutions are updated for the CBSE examination 2016 – 2017. Also download sample papers, assignments, test papers, Board Papers, notes, practice material and NCERT solutions for all subjects.
Chapter 1: Real Numbers
- Euclid’s Division Lemma: Given two positive integers a and b, there exist unique integers q and r satisfying a = bq + r, 0 ≤ r < b.
- Euclid’s Division Algorithm to obtain the HCF of two positive integers, say c and d, c > d.
- Fundamental Theorem of Arithmetic: Every composite number can be expressed as a product of primes, and this expression (factorisation) is unique, apart from the order in which the prime factors occur.
- Let p be a prime number. If p divides square of a, then p divides a, where a is a positive integer.
- Square root of 2, 3, 5 are irrational numbers.
- The sum or difference of a rational and an irrational number is irrational.
- The product or quotient of a non-zero rational number and an irrational number is irrational.
- For any two positive integers a and b, HCF (a, b) × LCM (a, b) = a × b.
Chapter 2: Polynomials
- Geometrical meaning of zeroes of a polynomial: The zeroes of a polynomial p(x) are precisely the x-coordinates of the points where the graph of y = p(x) intersects the x-axis.
- Relation between the zeroes and coefficients of a polynomial: If α and β are the zeroes of a quadratic polynomial ax2 + bx + c, then α + β = -b/a and αβ = c/a.
- The division algorithm states that given any polynomial p(x) and any non-zero polynomial g( x), there are polynomials q(x) and r(x) such that p(x) = g(x) q(x) + r(x), where r(x) = 0 or degree r(x) < degree g(x).
Chapter 3: Pair of Linear Equations in Two Variables
Chapter 4: Quadratic Equations
Chapter 5: Arithmetic Progressions
Chapter 6: Triangles
Chapter 7: Coordinate Geometry
Chapter 8: Introduction to Trigonometry and its Applications
Chapter 9: Circles
Chapter 10: Constructions
Chapter 11: Area Related to Circles
Chapter 12: Surface Areas and Volumes
Chapter 13: Statistics and Probability