List of top Mathematics Questions asked in CBSE Class IX

(i) Represent the information above by a bar graph.
(ii) In the classroom discuss what conclusions can be arrived at from the graph.

Use suitable identities to find the following products: 

(i) (x + 4) (x + 10) 

(ii) (x + 8) (x – 10) 

(iii) (3x + 4) (3x – 5) 

(iv) \((y^ 2 + \frac{3 }{ 2}) (y^ 2 – \frac{3 }{ 2}) \)

(v) (3 – 2x) (3 + 2x)

(i) Represent the given information with the help of a histogram. 
(ii) How many lamps have a lifetime of more than 700 hours?

AB is a line segment and P is its mid-point. D and E are points on the same side of AB such that ∠ BAD = ∠ ABE and ∠ EPA = ∠ DPB (see Fig). Show that 

(i) ∆ DAP ≅ ∆ EBP 

(ii) AD = BE

ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see Fig). Show that 

(i) ∆ ABE ≅ ∆ ACF 

(ii) AB = AC, i.e., ABC is an isosceles triangle.

Factorise each of the following: 

(i) 27y ³ + 125z ³ 

(ii) 64m³ – 343n ³ 

[ Hint : See Question 9. ]

Write the following cubes in expanded form: 

(i) (2x + 1)³ (ii) (2a – 3b) ³ (iii) [\(\frac{3}{2}\) x + 1]³ (iv) [x - \(\frac{2 }{ 3} \)y]³

Factorise: 

(i) 4x ² + 9y ² + 16z ² + 12xy – 24yz – 16xz 

(ii) 2x ² + y ² + 8z ² – 2√2 xy + 4√2 yz – 8xz

Factorise the following using appropriate identities: 

(i) 9x ² + 6xy + y 2 

(ii) 4y ² – 4y + 1 

(iii) x ² – \(\frac{y^2 }{ 100}\)

Evaluate the following products without multiplying directly: 

(i) 103 × 107 (ii) 95 × 96 (iii) 104 × 96