Model Question Paper - 2

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Questions:

Fill up / 1 Marks

10 x 1 = 10

Replace the blank with an integer to make it a true statement. 5 x____ = - 35

Replace the blank with an integer to make it a true statement. (-3) x _____ =27

The following statement true:
[2 + 12] + 6 = 2 + [ 12 + ____ ]

The following statement true:
-6 + 8 = 8 + ________

- 4 + [ 15 + (- 3) ] = [ - 4 + 15 ] + ______

[ 13 + (- 12) ] + ______ = 13 + [ (- 12) + (- 7) ]

17 + ______ = 0

-53 + ______ = - 53

Using >, < or =.
21 - 5 ____ 40 - 6

10.

Using >, < or =.
18 - 16 ____ + 2

Multiple Choice Question

22 x 1 = 22

11.

(16) \(\div\) 4 is not same as:

(a)

(-4) \(\div\) 16

(b)

-(16 \(\div\) 4)

(c)

16 \(\div\) (-4)

(d)

-4

12.

\(\frac{5}{12}\)part of what amount will be equal to 3\(\frac{3}{4}\) part of Rs 100?

(a)

Rs 900

(b)

Rs 940

(c)

Rs 875

(d)

Rs 925

13.

How many pieces of 13.2 cm can be cut from a 330 cm long rod?

(a)

(b)

(c)

(d)

14.

In the year 2014, Shantanu gets Rs 3832.5 as his pocket allowance. Find his pockect allowane per day

(a)

Rs 9.5

(b)

Rs 10.5

(c)

Rs 12.5

(d)

Rs 11.5

15.

Which of the following represents \(\frac{1}{3}\)of\(\frac{1}{6}\)?

(a)

\(\frac{1}{3}+\frac{1}{6}\)

(b)

\(\frac{1}{3}-\frac{1}{6}\)

(c)

\(\frac{1}{3}\times \frac{1}{6}\)

(d)

\(\frac{1}{3}\div \frac{1}{6}\)

16.

The product of \(\frac{11}{13}\) and 4 is

(a)

\(3 \frac{5}{13}\)

(b)

\(5\frac{3}{13}\)

(c)

\(13\frac{5}{5}\)

(d)

\(13\frac{5}{3}\)

17.

Pictorial representation of \(3\times \frac{2}{3} \)is

(a)

(b)

(c)

(d)

18.

\(\frac{2}{5}\times 5\frac{1}{5}\) is equaI to

(a)

\(\frac{26}{25}\)

(b)

\(\frac{52}{25}\)

(c)

\(\frac{2}{5}\)

(d)

19.

If \(\bigotimes \) , O and \(\bullet\) represent some integers on the number line, then descending order of these numbers is

(a)

\(\bullet ,\bigotimes ,\oslash ,O\)

(b)

\(\bigotimes ,\bullet ,\oslash ,O\)

(c)

\(O,\oslash ,\bigotimes ,\bullet \)

(d)

\(O,\bullet ,\bigotimes ,\oslash \)

20.

Next three consecutive numbers in the pattern 11, 8, 5, 2, ... are

(a)

0,-3, -4

(b)

-1, -5,-8

(c)

2, -5, -8

(d)

1, -4, -7

21.

Which of the following does not represent an integer?

(a)

0 \(\div\) (-7)

(b)

20 \(\div\) (-4)

(c)

(-9) \(\div\) 3

(d)

(-12) \(\div\) 5

22.

On the following number line, zero is shown by the point.

(a)

(b)

(c)

(d)

23.

(-43) x (-99) + 43 is equal to

(a)

4300

(b)

-4300

(c)

4257

(d)

-4214

24.

The value of (-10) x (-5) + (-7) is

(a)

(b)

-43

(c)

(d)

25.

Which measures of central tendency get affected, if the extreme observations on both the ends of a data a arranged in descending order are removed?

(a)

Mean and mode

(b)

Mean and median

(c)

Mode and median

(d)

Mean, median and mode

26.

If k + 2 = 6, then the value of 4k + 12 is equal to

(a)

(b)

-12

(c)

(d)

-30

27.

If 8m - 8 = 56, then m is equal to

(a)

-4

(b)

-2

(c)

-14

(d)

28.

If 7x + 4 = 39, then x is equal to

(a)

(b)

-4

(c)

(d)

29.

The solution of which of the following equations is neither a fraction not an integer?

(a)

2x + 6 = 0

(b)

3x - 5 = 0

(c)

5x - 8 = x + 4

(d)

4x + 7 = x + 2

30.

If * represents 3 mangoes, then 18 mangoes are represented by

(a)

***

(b)

****

(c)

******

(d)

None of these

31.

The value of 1200 x 2 is

(a)

600 x 20

(b)

2000 + 400

(c)

600 + 600

(d)

None of these

32.

If the sum of two integers a and b is zero, then

(a)

a=0, b=0

(b)

a = -b

(c)

Both (a) and (b) are not zero

(d)

None of these

Generic 5

10 x 5 = 50

33.

Express the following numbers in normal form:
4.0 x 10¹⁰

34.

Express the following numbers in normal form:
5.8 x 10⁵

35.

Express the following numbers in the standard form:
90040000000

36.

Express the following numbers in the standard form:
56,950

37.

Express the following numbers in the standard form:
9585.3

38.

Is (i) 1 + a = 1 and (ii) a + (-1) = -a for any integer a? Take different values of a and
check.

39.

Find 4 x (- 8), 8 x (- 2), 3 x (- 7), 10 x (- 1) using number line.

40.

A shopkeeper gains Rs 1 on each pen and loses 40 paise on each pencil. He sells 45 pens and some pencils losing Rs 5 in all. How many pencils does he sell?

41.

If * is an operation such that for integers a and b, we have a * b = a \(\times\) b + (a \(\times\)a + b \(\times\) b). then find
(i) (-3) * (-5)
(ii) (-6) * 2

42.

If \(\Delta\) is an operation such that for integers a and b, we have a\(\Delta\)b = a \(\times\) b - 2 (a + b) + b (b - a) \(\times\) b \(\times\) b Then, find
(i) 4 \(\Delta\)(-3)
(ii) (-7) \(\Delta\)(-1)
Also, show that 4 \(\Delta\)(-3) \(\neq\) (-3) \(\Delta\) 4 and (-7) \(\Delta\) (-1) \(\neq\) (-1) \(\Delta\) (-7)

Generic 4

2 x 4 = 8

43.

The mean marks (out of 100) of a group of students is 60. If their marks are 85, 62, 36, 48, 72, x, 75 and 39, then find the value of x.

44.

Following are the marks obtained by 25 students in class test (out of 25 marks) in Maths :
18, 13, 18, 16, 8, 5, 13, 5, 18, 18,2,16, 13, 8, 17, 18 5, 2, 13, 8, 19, 16, 8, 20.
How many students obtained marks more than the mean marks?

1 Marks

5 x 1 = 5

45.

What is the additive inverse of (-14)?

46.

What is the additive inverse of 0?

47.

What is the additive inverse of -1?

48.

What is the sum of (-1) and 1?

49.

What is the product of (-1) and 1?

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Answers Key:

Fill up / 1 Marks

10 x 1 = 10

()
5 x (- 7) = - 35

()
(- 3) x (- 9) = 27

()
6 (associative property of addition)

()
-6 (commutative property of addition)

()
(- 4) + [ 15 + (-3) ] = [ (- 4) + 15 ] + (-3) [\(\because\)addition of integers is commutative]

()
[ 13 + (-12) ] + (-7) = 13 + [ (-12) + (- 7) ] [\(\because\) addition of integers is associative]

()
17 + (-17) = 0 [\(\because\) sum of an integer and its additive inverse is zero]

()
(- 53) + 0 = - 53 [ if we add zero to any number, then we get the same number ]

()
<

10.

()
=

Multiple Choice Question

22 x 1 = 22

11.

(a)
(-4) \(\div\) 16

12.

(a)
Rs 900

13.

(a)
25

14.

(b)
Rs 10.5

15.

16.

(a)
\(3 \frac{5}{13}\)

17.

18.

(b)
\(\frac{52}{25}\)

19.

20.

(d)
1, -4, -7

21.

(d)
(-12) \(\div\) 5

22.

(b)
Z

23.

(a)
4300

24.

25.

(a)
Mean and mode

26.

27.

(d)
8

28.

29.

(d)
4x + 7 = x + 2

30.

31.

(b)
2000 + 400

32.

(b)
a = -b

Generic 5

10 x 5 = 50

33.

40000000000

34.

580000

35.

9.004 X 10¹⁰

36.

5.695 x 10⁴

37.

9.5853 x 10³

38.

(i) Let us take a = -1, 1, 2, 3, ...
For a = -1,
L.H.S. = 1 ÷ (-1) = -1 [∵ 1 + 1 = 1]
R.H.S. = 1
i.e. L.H.S. ≠ R.H.S.
For a = 1,
L.H.S. = 1 ÷ a = 1 + 1 = 1
R.H.S. = 1
i.e. L.H.S. = R.H.S.
For a = 2,
L.H.S.= 1 ÷ a = 1 ÷ 2 = \(1\over2\)≠ R.H.S.
For a =3
L.H.S. = 1 ÷ a = 1 ÷ 3 = \(1\over3\)≠ R.H.S.
Thus, 1 ÷ a = 1 is true only for a = 1
(ii) Let us take a = 1, 2, 3, ...
For a = 1,
L.H.S.= a ÷ (-1) = 1 ÷ (-1) = -1
R.H.S.= -a = -1
i.e. L.H.S. = R.H.S.
For a = 2,
L.H.S.= a ÷ (-1) = 2 ÷ (-1) = -2
R.H.S.= a = -2
i.e. L.H.S. = R.H.S.
For a = 3,
L.H.S.= a ÷ (-1) = 3 ÷ (-1) = -3
R.H.S.= -a = -3
i.e. L.H.S. = R.H.S.
For a = 7,
L.H.S. = a ÷ (-1) = 7 ÷ (-1) = -7
R.H.S.= -a = -7
i.e. L.H.S. = R.H.S.
i.e. For every integer, we have a ÷ (-1) = -a

39.

We can write 4 x (- 8) as
4 x (- 8) = (- 8) + (- 8) + (- 8) + (- 8)
It can be represented on the number line as under:

We have, 8 x (- 2) = (- 2) + (- 2) + (- 2) + (-2) + (-2) + (-2) + (-2) + (-2)
It can be represented on the number line as under:

We have, 3 x (-7) = (-7) + (-7) + (-7)
It can be represented on the number line as under:

We have,
10 x (-1) = (-1) + (-1) + (-1) + (-1) + (-1) + (-1) + (-1) + (-1) + (-1) + (-1)
It can be represented on the number line as under:
.

40.

125

41.

(i) 49
(ii) 28

42.

(i) 4\(\Delta\)(-3) = 16, (-3) \(\Delta\) 4 = 18, No,
(ii) (-7) \(\Delta\) (-1) = - 6, (-1) \(\Delta\) (-7) = 42, No

Generic 4

2 x 4 = 8

43.

Total number of students = 8
Sum of the marks obtained =85 + 62 + 36 + 48 + x + 75 + 39 + 72=417+x
\(\therefore \)Mean marks =\(\frac { (417\quad +x) }{ 8 } \)
\(\Rightarrow \)\(\frac { (417\quad +x) }{ 8 } \)=60
\(\Rightarrow \)417 + x = 60 x 8 = 480
\(\Rightarrow \)x = 480 - 417 = 63
Thus, the required value of x = 63

44.

Arranging the observations (marks) in ascending order:
2, 2, 5, 5, 5, 8, 8, 8, 8, 13, 13, 13, 13, 16, 16, 16, 17, 17, 18,18,18,18,18,19,20
Sum of observations
\(2\times2=4\\5\times3=15\\8\times4=32\\13\times4=52\\16\times3=48\\17\times2=34\\18\times5=90\\19\times1=19\\20\times1=20\\\quad\quad\quad\quad\_\_\_\_\\\ Total=314\\ \quad\quad\quad\quad\_\_\_\_\)Number of students = 25
\(\therefore\) Mean marks \(=\frac{Sum\ of\ the\ observations}{Total\ number\ of\ students}\)
\(=\frac{314}{25}=12.5\)
So, the number of students who scored marks more than mean marks is
4 + 3 + 2 + 5 + 1 + 1 = 16.