List of top Mathematics Questions asked in CBSE Class IX

AD and BC are equal perpendiculars to a line segment AB (see Fig). Show that CD bisects AB.

ABCD is a quadrilateral in which AD = BC and ∠ DAB = ∠ CBA (see Fig. 7.17). Prove that 

(i) ∆ ABD ≅ ∆ BAC 

(ii) BD = AC 

(iii) ∠ ABD = ∠ BAC.

In quadrilateral ACBD, AC = AD and AB bisects ∠ A (see Fig. 7.16). Show that ∆ ABC ≅ ∆ ABD. What can you say about BC and BD?

In Fig. 5.10, if AC = BD, then prove that AB = CD. 

Consider two ‘postulates’ given below :

(i) Given any two distinct points A and B, there exists a third point C which is in between A and B. 

(ii) There exist at least three points that are not on the same line. 

Do these postulates contain any undefined terms? Are these postulates consistent? 

Do they follow from Euclid’s postulates? Explain.

Which of the following statements are true and which are false? Give reasons for your answers. 

(i) Only one line can pass through a single point. 

(ii) There are an infinite number of lines which pass through two distinct points. 

(iii) A terminated line can be produced indefinitely on both the sides. 

(iv) If two circles are equal, then their radii are equal. 

(v) In Fig., if AB = PQ and PQ = XY, then AB = XY

Check which of the following are solutions of the equation x – 2y = 4 and which are not: 

(i) (0, 2) 

(ii) (2, 0) 

(iii) (4, 0) 

(iv) \((\sqrt 2 , 4 \sqrt2) \)

(v) (1, 1)

Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case: 

(i) 2x + 3y = 9.35 

(ii) x – \(\frac{y}{5}\)– 10 = 0 

(iii) –2x + 3y = 6 

(iv) x = 3y 

(v) 2x = –5y 

(vi) 3x + 2 = 0 

(vii) y – 2 = 0

The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement. 

(Take the cost of a notebook to be ` x and that of a pen to be ` y).

See Fig.3.14, and write the following: 

(i) The coordinates of B. 

(ii) The coordinates of C. 

(iii) The point identified by the coordinates (–3, –5).

(iv) The point identified by the coordinates (2, – 4). 

(v) The abscissa of the point D. 

(vi) The ordinate of the point H. 

(vii) The coordinates of the point L. 

(viii) The coordinates of the point M.

Write the answer of each of the following questions: 

(i) What is the name of horizontal and the vertical lines drawn to determine the position of any point in the Cartesian plane?

(ii) What is the name of each part of the plane formed by these two lines? 

(iii) Write the name of the point where these two lines intersect