List of top Mathematics Questions asked in CBSE Class IX

(Street Plan) : A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East-West direction.

All the other streets of the city run parallel to these roads and are 200 m apart. There are 5 streets in each direction. Using 1cm = 200 m, draw a model of the city on your notebook. Represent the roads/streets by single lines. There are many cross- streets in your model. A particular cross-street is made by two streets, one running in the North - South direction and another in the East - West direction. Each cross street is referred to in the following manner : If the 2nd street running in the North - South direction and 5th in the East - West direction meet at some crossing, then we will call this cross-street (2, 5). Using this convention, find: 

(i) how many cross - streets can be referred to as (4, 3). 

(ii) how many cross - streets can be referred to as (3, 4).

Which one of the following options is true, and why? y = 3x + 5 has 

(i) a unique solution, 

(ii) only two solutions, 

(iii) infinitely many solutions

Write the following in decimal form and say what kind of decimal expansion each has : 

(i) \(\frac{36}{100}\)  (ii) \(\frac{1}{11}\) (iii) \(4\frac{1}{8}\)

(iv) \(\frac{3}{13}\)  (v) \(\frac{2}{11}\)  (vi) \(\frac{329}{400}\)

∆ABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB (see Fig. 7.34). Show that ∠ BCD is a right angle.

In Fig, ∠ ABC = 69°, ∠ ACB = 31°, find ∠ BDC.

Represent the marks of the students of both the sections on the same graph by two frequency polygons. From the two polygons compare the performance of the two sections.

ABC and DBC are two isosceles triangles on the same base BC (see Fig). Show that ∠ABD = ∠ACD.

Factorise each of the following: 

(i) 8a ³ + b ³ + 12a 2b + 6ab² 

(ii) 8a ³ – b ³ – 12a 2b + 6ab2 

(iii) 27 – 125a ³ – 135a + 225a ² 

(iv) 64a ³ – 27b ³ – 144a 2b + 108ab2 

(v) 27p ³ – \(\frac{1}{ 216}\) – \(\frac{9 }{ 2}\) p² + \(\frac{1 }{4}\) p

In ∆ ABC, AD is the perpendicular bisector of BC (see Fig. 7.30). Show that ∆ ABC is an isosceles triangle in which AB = AC.

Find the value of the polynomial 5x – 4x ² + 3 at 

(i) x = 0 (ii) x = –1 (iii) x = 2

Expand each of the following, using suitable identities: 

(i) (x + 2y + 4z) 2 (ii) (2x – y + z) ² (iii) (–2x + 3y + 2z) ² 

(iv) (3a – 7b – c) ² (v) (–2x + 5y – 3z) ² (vi) [ \(\frac{1 }{ 4}\) a - \(\frac{1 }{ 2}\) b + 1]²

Write four solutions for each of the following equations: 

(i) 2x + y = 7 

(ii) πx + y = 9 

(iii) x = 4y

Simplify each of the following expressions: 

(i) (3 + √3)(2 + √2) 

(ii) (3 + √3)(3 - √3) 

(iii) (√5 + √2 )² 

(iv) (√5 - √2)(√5 + √2)