Examius
🇮🇳 CBSE Class 9 · subject
CBSE Class 9 Mathematics Syllabus
The Mathematics syllabus for CBSE Class 9 in full: 6 chapters and 12 topics, every one listed below, plus 51 Mathematics flashcards with answers.
Mathematics syllabus: all 6 chapters
Expand any chapter to see its topics and sub-topics.
-
Number Systems
2 topics- Real Numbers
- Rationalization
-
Algebra
2 topics- Polynomials
- Linear Equations in Two Variables
-
Coordinate Geometry
2 topics- Cartesian System
- Plotting a Point in the Plane
-
Geometry
2 topics- Lines and Angles
- Triangles
-
Mensuration
2 topics- Areas
- Surface Areas and Volumes
-
Statistics & Probability
2 topics- Statistics
- Probability
CBSE Class 9 Mathematics flashcards — 51 questions with answers
What is a rational number?
A number that can be written in the form p/q where p and q are integers and q is not equal to 0.
What is an irrational number?
A number that cannot be written in the form p/q (with integers p, q and q not 0). Its decimal expansion is non-terminating and non-recurring (e.g., square root of 2, pi).
How can you tell from its decimal expansion whether a number is rational?
A rational number has a decimal expansion that is either terminating or non-terminating but recurring (repeating).
A terminating decimal p/q (in lowest terms) terminates only when q has what prime factors?
Only the prime factors 2 and/or 5 (i.e., q is of the form 2^m x 5^n).
How many rational numbers lie between any two given rational numbers?
Infinitely many.
What is the result of adding or multiplying a non-zero rational number with an irrational number?
The result is always irrational.
State the law of exponents for a^m x a^n.
a^m x a^n = a^(m+n).
State the law of exponents for (a^m)^n.
(a^m)^n = a^(mn).
What is a^m divided by a^n equal to?
a^(m-n).
How do you rationalise the denominator of 1/(a + sqrt(b))?
Multiply numerator and denominator by the conjugate (a - sqrt(b)), giving (a - sqrt(b))/(a^2 - b).
What is the rationalising factor of sqrt(a)?
sqrt(a) itself, since sqrt(a) x sqrt(a) = a.
What is the value of a^0 for any non-zero a?
1.
What is a polynomial in one variable?
An algebraic expression of the form a_n x^n + ... + a_1 x + a_0, where the powers of the variable are whole numbers and the coefficients are real numbers.
What is the degree of a polynomial?
The highest power of the variable that appears in the polynomial.
Name a polynomial by degree: degree 1, degree 2, and degree 3.
Degree 1 = linear, degree 2 = quadratic, degree 3 = cubic.
What is the degree of a non-zero constant polynomial?
Zero.
State the Remainder Theorem.
If a polynomial p(x) is divided by (x - a), the remainder is p(a).
State the Factor Theorem.
(x - a) is a factor of polynomial p(x) if and only if p(a) = 0.
What is a zero (or root) of a polynomial p(x)?
A value of x for which p(x) = 0.
Expand (a + b)^2 and (a - b)^2.
(a + b)^2 = a^2 + 2ab + b^2; (a - b)^2 = a^2 - 2ab + b^2.
Show the other 31 Mathematics flashcards
Give the identity for a^3 + b^3.
a^3 + b^3 = (a + b)(a^2 - ab + b^2).
What does a^3 + b^3 + c^3 - 3abc factor into?
(a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca).
What is the general form of a linear equation in two variables?
ax + by + c = 0, where a and b are not both zero.
How many solutions does a linear equation in two variables have?
Infinitely many solutions.
What does the graph of a linear equation in two variables look like?
A straight line; every point on the line is a solution of the equation.
What is the graph of the equation y = k (a constant)?
A straight line parallel to the x-axis.
What is the graph of the equation x = k (a constant)?
A straight line parallel to the y-axis.
In the Cartesian system, what are the x-axis and y-axis called and where do they meet?
The horizontal x-axis and vertical y-axis; they meet at the origin (0, 0).
What are the coordinates of a point called and in what order are they written?
The abscissa (x-coordinate) and the ordinate (y-coordinate), written as (x, y).
State the sign of coordinates in each of the four quadrants.
Q1: (+, +), Q2: (-, +), Q3: (-, -), Q4: (+, -).
What are the coordinates of any point on the x-axis and on the y-axis?
On the x-axis the y-coordinate is 0, so (x, 0); on the y-axis the x-coordinate is 0, so (0, y).
How do you plot the point (3, -2) in the plane?
Move 3 units right along the x-axis, then 2 units down parallel to the y-axis; the point lies in the fourth quadrant.
What is the measure of a straight angle and of a complete angle?
A straight angle is 180 degrees; a complete angle is 360 degrees.
Define complementary and supplementary angles.
Two angles are complementary if their sum is 90 degrees, and supplementary if their sum is 180 degrees.
What is the Linear Pair Axiom?
If a ray stands on a line, the sum of the two adjacent angles formed is 180 degrees; conversely, if the sum is 180 degrees the non-common arms form a line.
What can you say about vertically opposite angles?
When two lines intersect, the vertically opposite angles are equal.
When a transversal cuts two parallel lines, what is the relation between corresponding angles and between alternate interior angles?
Corresponding angles are equal and alternate interior angles are equal (co-interior angles are supplementary).
State the Angle Sum Property of a triangle.
The sum of the three interior angles of a triangle is 180 degrees.
State the Exterior Angle Property of a triangle.
An exterior angle of a triangle equals the sum of the two interior opposite angles.
List the four main congruence rules for triangles.
SAS, ASA, AAS, and SSS (plus RHS for right triangles).
What does the RHS congruence rule state?
Two right triangles are congruent if the hypotenuse and one side of one equal the hypotenuse and corresponding side of the other.
In a triangle, what is the relationship between the larger angle and the side opposite it?
The side opposite the larger angle is longer; equivalently, the larger angle is opposite the longer side.
State the Triangle Inequality.
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
State the property of angles and sides in an isosceles triangle.
Angles opposite to equal sides are equal, and sides opposite to equal angles are equal.
What is the formula for the area of a triangle using Heron's formula?
Area = sqrt(s(s-a)(s-b)(s-c)), where s = (a+b+c)/2 is the semi-perimeter.
What does it mean for two figures to lie on the same base and between the same parallels, and what is the area relation?
Parallelograms on the same base and between the same parallels are equal in area; a triangle has half the area of a parallelogram on the same base and between the same parallels.
Give the formula for the curved surface area and total surface area of a right circular cylinder.
CSA = 2(pi)rh; TSA = 2(pi)r(h + r).
Give the curved surface area and volume of a right circular cone.
CSA = (pi)rl (where l is slant height); Volume = (1/3)(pi)r^2 h.
Give the surface area and volume of a sphere of radius r.
Surface area = 4(pi)r^2; Volume = (4/3)(pi)r^3.
How do you find the mean, median, and mode of ungrouped data?
Mean = sum of observations divided by number of observations; Median = the middle value when data is arranged in order; Mode = the most frequently occurring observation.
What is the empirical (experimental) definition of the probability of an event E?
P(E) = (number of trials in which E happened) / (total number of trials), and 0 <= P(E) <= 1.
CBSE Class 9 Mathematics FAQ
What is in the CBSE Class 9 Mathematics syllabus?
CBSE Class 9 Mathematics is split into 6 chapters: Number Systems, Algebra, Coordinate Geometry, Geometry, Mensuration and Statistics & Probability. Together they contain 12 topics.
How many chapters are in CBSE Class 9 Mathematics?
6 chapters, containing 12 topics. The largest chapter is Number Systems, with 2 topics.
Are there flashcards for CBSE Class 9 Mathematics?
Yes — a 51-card Mathematics deck, printed in full in the flashcards section of this page and available in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.