Download IX Maths Summer Vacation HW

Summer Vacation Assignment
1. Find a rational number between – 2 and 6.
2. Find a rational number between
−2
3
1
and
4
.
3. Find five rational numbers between 3 and 4.
4. Find five rational numbers between
3
5
4
and .
5
5. Find two rational numbers between 0.12 and 0.13
6. Find two rational numbers between 0.1 and 0.3
7. Find two irrational number between √2 and √3 .
8. Express the following 0.3̅ in the form
𝑝
𝑞
̅̅̅̅ in the form
9. Express the following 0.27
10. Express the following 5.2̅ in the form
, where p and q are integers and q ≠ 0.
𝑝
𝑞
𝑝
𝑞
̅̅̅̅ in the form
11. Express the following 1.27
, where p and q are integers and q ≠ 0.
, where p and q are integers and q ≠ 0.
𝑝
𝑞
12. Express the following 0.123̅ in the form
, where p and q are integers and q ≠ 0.
𝑝
𝑞
, where p and q are integers and q ≠ 0.
13. Express the following 0.404040….. in the form
14. Simplify
a) (3 + √3 )(2 + √2)
b) (5 + √7 )(2 + √5)
c) (5 + √5 )(5 - √5)
d) (3 + 2√2 )(3 - 2√2)
2
e) (√11 - √5 )
2
f) (2√5 - 3√2 )
3
3
g) √4 x √16
12
1
h) √(𝑥 4 )3
𝑝
𝑞
, where p and q are integers and q ≠ 0.
15. Rationalize the denominator of
16. Rationalize the denominator of
17. Rationalize the denominator of
18. Rationalize the denominator of
1
.
2− √3
1
5 + √3
√2
2+√2
1
.
.
.
7+3√2
19. Simplify:
(a)
9
3
2
(b)
2
3
1
5
1
2 . 23
(c) 13 . 17
3
5
(e) √(32)−3
6
(f) √7 . √6
(g)
1
20. If a = 2 + √3 , find the value of a - .
a
1
21. If a = 3 - √2 , find the value of a + a.
22. If x = 3 - 2√2 , find the value of x2 +
23. If x = 2 + √5 , find the value of x2 +
1
𝑥2
1
𝑥2
.
.
1 3
24. If x = 2 - √3 , find the value of (𝑥 − 𝑥)
25. Solve for x
a) 25𝑥−1 = 52𝑥−1 – 100
b) 42𝑥 =
1
32
5
c) 25𝑥 ÷ 2 𝑥 = √(2)20
d) 42𝑥−1 - 16 𝑥−1 = 384
3
1
5
√2 .√5
−3
(d)
81 4
(16)
4
3
(h) √ √22