HILLS HIGH SCHOOL
Vacation Home Work [ IX MATHEMATICS]
Q1. Find an irrational number between √2 & √3 .
Q2. Insert five rational number between
2
7
3
and
1
1
𝑥
𝑥
Q3. If x = 2 - √5 , find the value of x + , x -
5
.
.
Q4. Simplify : ( √5 + 3) (√2 - 7) .
)⅓ .
Q5. Find the value of (343
Q6. Evaluate : 5⅓ x 5⅔ x 5 .
Q7. Represent √8.9 and √8 on number line by suitable method(s).
Q8. Represent √6 on number line by Spiral method..
Q9. Find two irrational nos. between 0.12 and 0.13.
Q10. Simplify :
1
3+√5
3
+ 2−√3 .
Q11 . Find the values of (i) p & q , if p - q √5 =
𝟐
𝟑+√𝟓
(ii) a& b , if a + b √5 =
𝟐+ √5
𝟑−𝟐√𝟓
.
Q12. Visualise 5.867 and 3.2727 on the no. line, using successive magnification.
𝑝
Q13. Express : 1.54 in the form
.
𝑞
Q14.Determine the value of k , if y – 2 is factor of (i) 2y2 - k y + √𝟑 (ii) ky3 + 3y - 2 .Type equation here.
Q15. Factorise : (i) x3 + 6x2+11x + 6 (ii) x3 – 7x + 6.
Q16. Find the values of a & b so that y3 + 10 y2 +ay +b is exactly divisible by y – 1 and y – 2.
Q17.Factorise :(i) 9p2 + 4q2 + 25r2 +12pq + 20qr + 30pr (ii) 3a2 + b2+ 8c2+2√3b – 4√2bc –2 √6 ca.
Q18. Use suitable identities , find (i) 104x 109
(ii) (97)3
(iii) (104)3 .
Q19. Factorise : (i) 9p2 – 30pq + 25q2 (ii) 8x3 + y3 + 27z 3– 18xyz .
Q20. Without actually calculating the cubes , evaluate : (i) (8)3 – (17)3 + (9)3 (ii)13)3 + (-7)3+ (-6)3 .
Q21. If a + b + c = 9 and ab + bc + ca = 40, then find a2 + b2 + c2 .
15
Q22. Evaluate :
.
√10+√20+√40−√5−√80
.
Q23 Find the remainder ,when f(x) = 4x -12x + 14x – 3, is divided by g(x)= 2x – 1 and verify the result
by actual division.
Q24. Factorise : (m-3n)3 + (3n-p)3 + (p-m)3
.