MATHEMATICS ASSIGNMENT – IX STEPS … A T C Y Prog r am _________________________________________________________________________________
ASSIGNMENT ON NUMBER SYSTEMS Directions for questions 1 – 15: State true or false. 1.
There are infinitely many natural numbers between 1 and 2.
2.
The difference between any two consecutive natural numbers is one.
3.
There are infinitely many rational numbers.
4.
All real numbers are rational numbers.
5.
Every point on the real number line can be written in the from n , where ‘n’ is a natural number.
6.
Every real number is either rational or irrational.
7.
The sum of two irrational numbers is always irrational.
8.
Every irrational number can be converted into a rational number.
9.
5 3 and 10 3 are rationalizing factors of each other.
10.
Every irrational number has a unique rationalizing factor.
11.
The product of am and an is amn.
12.
If (–a)n = an, then ‘n’ is an even number.
13.
All prime numbers are odd numbers.
14.
All decimal numbers with non–terminating decimal parts are irrational numbers.
15.
If ‘a’ and ‘b’ are two consecutive integers and ‘a’ lies to the right of ‘b’, then a – b > 0.
16.
Write two integers which are not whole numbers.
17.
Insert one rational number between 3 and 4.
18.
Insert 3 rational numbers between 4 and 5.
19.
Insert 4 rational numbers between
20.
Express 3 and –2 in the form of
21.
Give two irrational numbers whose sum is rational.
22.
Give two irrational numbers whose sum is irrational.
23.
Give two irrational numbers whose difference is (i) rational (ii) irrational.
24.
Give two irrational numbers whose product is (i) rational (ii) irrational.
25.
Give two irrational numbers whose quotient is (i) rational (ii) irrational.
26.
Locate
27.
Locate the points representing
2 and
2 3 and . 5 5
p , where p and q are integers and q ≠ 0. q
3 on the number line. 2 + 1 and
2 –1 on the number line.
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MATHEMATICS ASSIGNMENT – IX STEPS … A TC Y P r og r am _________________________________________________________________________________
Construct a square root spiral starting from
29.
Classify the following rational number into numbers with (i)
terminating decimal expansion
(ii)
non–terminating decimal expansion.
(a)
1 4
(b)
1 3
(c)
2 upto
5.
28.
3 5
(d)
3 7
3 3 and 35 24
30.
Find the decimal representation of
31.
State which of the following fractions are convertible into terminating decimals, doing actual division. (a)
33 18
(b)
4 25
(c)
5 15
(d)
5 13
32.
Write two numbers whose decimal expansion are non–terminating and non repeating.
33.
Convert the following decimal numbers into rational number in the form (i) 0.08
34.
(ii) 1.205
(iii) 0.001
p . q
(iv) 3.2125
Convert the following decimal numbers into rational numbers in the form p/q. (i) 0. 312
(ii) 0. 092
(iii) 0.12345
Find four irrational number between
36.
Find four irrational numbers between 4 and 5.
37.
Classify the following numbers as rational or irrational 26
(ii)
324
(v) 2.21 347
(iv) 0.934984…..
(v) 4.02121121112………..
1 2 and . 3 3
35.
(i)
(iv) 0.4
(iii) 0.125
38.
Visualize 2.34 on the number line using successive magnification.
39.
Visualize 4. 3 on the number line upto three decimal places using successive magnification.
40.
Find the sum of (3 + 4 3 + 5 2 )
41.
Simplify:
42.
(i)
(5 2 + 7 3 ) – (3 2 + 2 3 )
(ii)
(iii)
5 3 ×7 3 ×2 2×3 2
(iv)
6 3 2 3
Find the simplest rationalizing factors of the following irrationals. (i)
43.
5 2 × 2 10 × 5 15
8
(ii) 3 18
(iii) 5 12
(iv) 7 7
Rationalize the denominators of the following. (i)
1 3
(ii)
2 3− 2
(iii)
1 3 −1
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MATHEMATICS ASSIGNMENT – IX STEPS … A T C Y Prog r am _________________________________________________________________________________
44.
If a = 3 12 + 2 18 and b = (i) a + b
45.
(ii) a – b
(iii) 2a + 3b
(iv) 5a – 4b
Rationalize the denominators (i)
46.
2 + 3 , find the value of
5 3
(ii)
10 − 3
3 2 6− 2
Evaluate (i)
4–5 × 48 ÷ 47
(ii)
57 × 53 ÷ 5–2
(iii)
(32)3 × (3–2)2
(iv)
⎛ 56 ⎞ 1 ⎜ ⎟ × × ⎝ 28 ⎠ 1
(v)
(625) −3 / 4
(vi)
⎛ 1 ⎞ ⎜ ⎟ ⎝ 32 ⎠
(iii)
181/2 × 81/2
2
0
47.
9 ⎛2⎞ ⎜ ⎟ × ⎝ 5 ⎠ 16
−3 / 5
Evaluate (i)
(243)3/5 ÷ (64)–1/4
(iv)
81 / 2 81 / 3
48.
Find the point representing
3.5 on the number line geometrically.
49.
Find the point representing
42 on the number line geometrically.
50.
Find the point representing
35 on the number line geometrically.
51.
In the following figure, AB = 7 units, BC = 5 units and AC is the diameter of the semicircle. What is the value of ‘x’?
D a
A
52.
x
b
B
7
5
C
In the figure, PQ = 12, QS = 6 and PR is the diameter of the semicircle. Find PR. S x
P
6
12
y
Q
R
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MATHEMATICS ASSIGNMENT – IX STEPS … A TC Y P r og r am _________________________________________________________________________________
53.
In the figure, ‘O’ is the origin of the number line ‘ l ’. AB = 1 unit and AB ⊥ l . The semi circle with centre origin and radius OB intersects the line at ‘C’ and ‘D’. Find the numbers represented by ‘C’ and ‘D’. B x 1 A O
D
54.
3
2
1
C
Look at the square root spiral shown below. Given that P1P2 = P2P3 = P3P4 = P4P5 = 1 unit. Find the length of the segment OP5.
P5 P4 P3 P2
O
55.
2
3
P1 5
4
In the figure, ‘O’ is the centre of the number line ‘ l ’. AB ⊥ l and CD ⊥ l . AB = 1 unit, the arc with centre ‘O’ and radius OB intersects the line at ‘C’. CD = 2 units, the arc with centre ‘O’ and radius OD intersects the line at ‘E’. Find the number that represents the point E. Check whether E represents a natural number. D B
O
56.
2A C
1
E
In the figure, ‘O’ is the centre of the number line ‘ l ’, OA = 6 and OC = 7. An arc with centre ‘O’ and radius OC intersects the perpendicular on A and ‘B’. Find AB. B
O
1
2
3
4
5
6 A
7 C
l
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MATHEMATICS ASSIGNMENT – IX STEPS … A T C Y Prog r am _________________________________________________________________________________
57.
In the figure, ‘O’ is the centre of the number line ‘ l ’. A semi circle is drawn with centre ‘O’ and radius 10 units. The semi circle intersects the perpendiculars at the points A and B, respectively represent –6 and 5, at D and C. Calculate the area of the quadrilateral ABCD. (Take
3 =1.732) C
D
–12 –10 –8 –6 –4 –2 A
O 2
4 5 6 B
8
10 12
l
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MATHEMATICS ASSIGNMENT – IX STEPS … A TC Y P r og r am _________________________________________________________________________________
NUMBER SYSTEMS ANSWER KEY 1.
False
2.
True
3.
True
40.
5
4.
False
5.
False
6.
True
41.
(i)
2 2 +5 3
(ii)
500 3
7.
False
8.
True
9.
True
(iv)
1260
(iv)
3
10.
True
11.
True
12.
True
(i)
2
(ii)
2
13.
False
14.
False
15.
True
(iii)
3
(iv)
7
20.
⎛6 −4⎞ ⎟ ⎜ , ⎝2 2 ⎠
(i)
3 3
(ii)
2( 3 +
(iii)
3 +1 2
16.
(–2, –3)
21.
(3– 5 , 4 + 5 )
22.
( 2,
23.
(i)
3+ 5,2+
(ii) 24.
(i)
25.
(i) 2 , – 2 , 2 ,
29.
(i) (a), (c)
30.
[0.125, 0. 0857143 ]
31.
(b)
33.
(i)
2 25
(ii)
(iii)
1 1000
(i)
34.
37.
42.
43.
3)
2)
(i)
7 3+7 2
3+ 5,2+2 5
(ii)
5 3+5 2
2 5,
(iii)
15 3 + 15 2
(iv)
26 3 + 26 2
45.
(i)
5( 30 + 3) 7
(ii)
3( 3 + 1) 2
46.
(i)
4–4
(ii)
512
241 200
(iii)
32
(iv)
9 100
(iv)
257 80
(v)
1 125
(vi)
8
104 333
(ii)
92 999
47.
(i)
216
(iii)
4115 3333
(iv)
2 5
51.
35
52.
15
53.
10 , – 10
54.
2 5
(v)
110563 49950
55.
7 , No
56.
13
(i)
Irrational
(ii)
Rational
(iii)
Rational
(iv)
Irrational
(v)
Irrational
5
44.
5
(ii) 2 3 , 2 3
(ii)
(b), (d)
(ii) 12
(iii)
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