Class 10 Maths questions with answers

210 NCERT Class 10 Maths questions with answers, chapter by chapter, from Real Numbers to Probability.

How to teach Class 10 Maths · Class 10 Maths common misconceptions

• Chapter 1: Real Numbers

  15 questions, 4 with pictures · Prime factorisation and the Fundamental Theorem of Arithmetic · Deciding whether a situation needs the HCF or the LCM · Which digit a power can end with · Finding the HCF and the LCM from prime factorisations · The relation between the HCF, the LCM and the product of the numbers · Proving that the square root of a prime is irrational · Irrationality of sums, differences and multiples involving a surd

• Chapter 2: Polynomials

  15 questions, 3 with pictures · The degree of a polynomial, and what the degree allows · The value of a polynomial at a number, and when that value is zero · Reading the zeroes of a polynomial off its graph · The zeroes and the coefficients of a polynomial · Building a quadratic polynomial from its zeroes · Finding the zeroes of a quadratic polynomial

• Chapter 3: Pair of Linear Equations in Two Variables

  15 questions, 3 with pictures · The three cases, and the ratio test that tells them apart · Turning a situation into a pair of equations, and solving it · A pair of linear equations, and what a solution is · Reading a pair of linear equations as two lines · Finding an unknown coefficient from the condition · Solving a pair algebraically: substitution and elimination

• Chapter 4: Quadratic Equations

  15 questions · A root of a quadratic equation · Finding the roots by factorising · What makes an equation quadratic · Turning a situation into a quadratic and solving it · Choosing a coefficient to force a given nature · The discriminant and the nature of the roots

• Chapter 5: Arithmetic Progressions

  15 questions · Locating a term in the list · What makes a list an arithmetic progression · The link between the sum and the terms · The nth term of an AP · The sum of the first n terms · Recovering the first term and the common difference · Three terms in AP and the arithmetic mean

• Chapter 6: Triangles

  15 questions, 6 with pictures · Proportionality in a fuller figure · Matching the right vertices and sides · The Basic Proportionality Theorem · The converse of the proportionality theorem · Justifying a step in a similarity argument · The similarity criteria · What similarity means · Using similar triangles to find a length

• Chapter 7: Coordinate Geometry

  15 questions · The distance formula · Naming a figure from its distances · Reading a point on the plane · The mid-point, and what bisects what · An unknown found from a distance condition · Recovering the ratio · The section formula

• Chapter 8: Introduction to Trigonometry

  15 questions, 1 with pictures · All the ratios from one of them · Recovering the angle from its ratio · The six ratios of an acute angle · The values at 0°, 30°, 45°, 60° and 90° · The three Pythagorean identities · Proving an identity, and using one under a condition · sin (A + B) is not sin A + sin B

• Chapter 9: Some Applications of Trigonometry

  15 questions, 15 with pictures · Setting up the right triangle: the line of sight, the angle and the ratio · The eye above the ground: adding the observer's height, elevation above and depression below · One height, two positions on the same side: the observer or the object moves · Two triangles on a shared base: a part on top of a known height · One height, two positions on opposite sides: widths of roads and rivers

• Chapter 10: Circles

  15 questions, 5 with pictures · A circle touching all the sides of a figure: equal tangent segments around a polygon · Where a line meets a circle: secant, tangent, and how many tangents a point admits · The radius at the point of contact: the right angle and the angles that follow from it · Two tangents from an external point: equal lengths, the bisected angle, and the supplementary pair · The right triangle made by a tangent: lengths from Pythagoras, and the chord that touches an inner circle

• Chapter 11: Areas Related to Circles

  15 questions, 1 with pictures · The whole circle and its named parts: sector, segment, quadrant, and the fraction of the disc · The area of a sector, from the angle, from the arc, and from the thing that sweeps it · The length of an arc, and the perimeter of a sector that includes the two radii · A segment is a sector less its triangle · The part left over: the major sector, the ring, and a region cut out of a larger shape

• Chapter 12: Surface Areas and Volumes

  15 questions, 10 with pictures · Capacity, the part that is left over, and how many smaller solids a larger one holds · Surface area of a combination: the faces that disappear where two solids are joined · Surface area when a piece is scooped out, and the largest solid that fits inside another · The basic solids the chapter builds with, and the measurement each formula needs · Volume of a combination: unlike areas, volumes simply add

• Chapter 13: Statistics

  15 questions · The mean of grouped data: the direct, assumed-mean and step-deviation methods · The modal class and the mode of grouped data · Cumulative frequency, and locating the median class · The median formula, and recovering a missing frequency from a stated median · Which average answers the question, and how the three are related

• Chapter 14: Probability

  15 questions · What a probability is, the values it can take, and the complement · One card from a deck of fifty-two · One object drawn from a bag or a lot · One throw of a die, or one number chosen from a list · Two coins, two dice, and writing down the whole sample space