Class 9 Maths questions with answers

120 NCERT Class 9 Maths questions with answers, chapter by chapter, from Orienting Yourself: The Use of Coordinates to Predicting What Comes Next: Exploring Sequences and Progressions.

How to teach Class 9 Maths · Class 9 Maths common misconceptions

• Chapter 1: Orienting Yourself: The Use of Coordinates

  15 questions, 2 with pictures · The coordinate plane, its axes and its origin · Points that lie on one of the axes · Reflecting a point or a shape in an axis · The four quadrants and their sign patterns · Which distance each coordinate measures · Distance between points on a line parallel to an axis · The distance between any two points · Why the pair is ordered: (x, y) and (y, x)

• Chapter 2: Introduction to Linear Polynomials

  15 questions · What an expression is built from: terms, coefficients and constants · The degree of a polynomial, and what each degree is called · What makes a pattern linear: the constant difference · What makes a polynomial linear · Evaluating a polynomial: the input-output view · Writing the rule for a pattern: an + b · Linear growth and decay, and the sign of the slope · Reading a line: y = ax + b, its slope and its y-intercept

• Chapter 3: The World of Numbers

  15 questions · What zero does, and the one thing it may not do · Brahmagupta's rules: fortunes, debts and their products · Telling a rational number from an irrational one · What makes a number rational: the form $p/q$ · Equivalent fractions and lowest terms · Absolute value, and the distance between two numbers · Density: there is always another rational in between · Predicting a decimal expansion, and turning it back into $p/q$

• Chapter 4: Exploring Algebraic Identities

  15 questions · The square of a sum: $(a + b)^2 = a^2 + 2ab + b^2$ · An identity holds for every value; an equation need not · Splitting the middle term: $x^2 + (a + b)x + ab = (x + a)(x + b)$ · The difference of two squares: $a^2 - b^2 = (a + b)(a - b)$ · The square of a difference: $(a - b)^2 = a^2 - 2ab + b^2$ · The square of three terms: $(a+b+c)^2 = a^2+b^2+c^2+2ab+2bc+2ca$ · Cubes: $(a \pm b)^3$, and $x^3 \pm y^3$ as a product · Simplifying a rational expression: only a common FACTOR cancels

• Chapter 5: I'm Up and Down, and Round and Round

  15 questions, 2 with pictures · A circle is the locus of points at a fixed distance from its centre, and every diameter is a line of symmetry · Two points admit infinitely many circles; three non-collinear points admit exactly one · The circumcentre is where the perpendicular bisectors of the sides meet, and the triangle's angles decide where it sits · In one circle, equal chords subtend equal angles at the centre, and equal angles at the centre give equal chords · The line from the centre to a chord's midpoint is perpendicular to it, and the perpendicular from the centre bisects it · A chord's length and its distance from the centre determine each other through the right triangle on the radius · An arc subtends twice the angle at the centre that it subtends at any point on the rest of the circle · Four points are concyclic when a segment subtends equal angles from the same side, and then opposite angles are supplementary

• Chapter 6: Measuring Space: Perimeter and Area

  15 questions, 2 with pictures · The perimeter of a shape is the total length of its border, and knowing it does not tell you the area · The ratio of circumference to diameter is the same for circles of every size, and that constant is pi · Pi is irrational, so 22/7 and 3.14 are approximations and no fraction is ever exact · An arc is the fraction of the circumference named by its central angle, so it depends on the radius too · A rectangle's area is the product of its sides, and a parallelogram's is base times perpendicular height · A triangle's area is half base times perpendicular height, so equal bases and equal heights give equal areas · Heron's formula gives a triangle's area from its three sides, and Brahmagupta's generalises it to cyclic 4-gons · A circle encloses pi r squared, and a sector takes the fraction of that area its angle names

• Chapter 7: The Mathematics of Maybe: Introduction to Probability

  15 questions · A probability is a number from 0 to 1, and the words impossible, less likely, even chance, more likely and certain name places on that scale · Experimental probability is the number of times the event happened divided by the number of trials, and that fraction is the relative frequency · A multi-step experiment has one outcome for each path through its tree, and a path's probability is the product along its branches · When the outcomes are equally likely, the probability of an event is the number of favourable outcomes divided by the number of possible outcomes · A relative frequency measured on a sample estimates the same proportion in the whole population, so a population count comes from multiplying · Each trial of a random experiment starts afresh, and a short run of results need not match the theoretical probability · A random experiment is one whose possible outcomes are known in advance but whose next result is not · The sample space lists every possible outcome exactly once, and an event is any collection of those outcomes

• Chapter 8: Predicting What Comes Next: Exploring Sequences and Progressions

  15 questions · A sequence is an ordered list of terms, and in the notation for a term the subscript names the position and not the value · An explicit rule computes a term straight from its position, and asking whether a number is a term means solving for that position · A recursive rule builds each term out of the terms before it, so it needs a starting value and has to be worked through step by step · An arithmetic progression is a sequence whose consecutive terms differ by the same amount, and its nth term is the first term plus n minus one differences · Turning a real situation into a sequence means deciding which quantity is the first term and what the question is actually counting · The sum of the first n natural numbers is n times n plus one, all halved, and a sum over part of the range is a difference of two such sums · A geometric progression multiplies by the same number each time, and its nth term is the first term times the ratio raised to n minus one · A geometric progression can shrink as well as grow, its points never lie on a straight line, and a shrinking one approaches zero without ever reaching it