#### Half Yearly Model Question Paper 2019 - 2020

7th Standard

Reg.No. :
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Maths

Time : 02:30:00 Hrs
Total Marks : 60

#### Multiple Choice Question

10 x 1 = 10
1. 3 + $\frac { 4 }{ 100 } +\frac { 9 }{ 1000 }$ =?

(a)

30.49

(b)

3049

(c)

3.0049

(d)

3.049

2. The simplest form of 0.35 is

(a)

$\frac { 35 }{ 1000 }$

(b)

$\frac { 35 }{ 10 }$

(c)

$\frac { 7 }{ 20 }$

(d)

$\frac { 7 }{ 100 }$

3. In the formula, C = 2πr, ‘r’ refers to

(a)

circumference

(b)

area

(c)

rotation

(d)

4. The formula used to find the area of the rectangular path is

(a)

π(R2 − r2 ) sq. units

(b)

(L × B) − (l × b) sq. units

(c)

LB sq. units

(d)

lb sq. units

5. The unit digit of the numeric expression 1071 + 1072 + 1073 is

(a)

0

(b)

3

(c)

1

(d)

2

6. If p(x) and q(x) are two expressions of degree 3, then the degree of p(x) + q(x) is

(a)

6

(b)

0

(c)

3

(d)

Undefined

7. The angles of a triangle are in the ratio 2: 3: 4. Then the angles are

(a)

20, 30, 40

(b)

40, 60, 80

(c)

80, 20, 80

(d)

10, 15, 20

8. In the given figure, AB is parallel to CD. Then the value of b is

(a)

1120

(b)

680

(c)

1020

(d)

620

9. Identify the correct relationship between x and y from the given table.

 x 1 2 3 4 ... y 4 8 12 16 ...
(a)

y = 4x

(b)

y = x + 4

(c)

y = 4

(d)

y = 4 × 4

10. Choose the correct relationship between x and y from the given table.

 x -2 -1 0 1 2 ... y 4 5 6 7 8 ...
(a)

y = x + 4

(b)

y = x + 5

(c)

y = x + 6

(d)

y = x + 7

11. #### Fill in the blanks

5 x 1 = 5
12. The exponential form 149 should be read as_________

()

14 power 9

13. When base is 12 and exponent is 17, its exponential form is___________

()

1217

14. When the unit digit of the base and its expanded form of that number is 9, then the exponent must be ________ power.

()

odd

15. The degree of the term a3b2c4d2 is ________.

()

11

16. Degree of the constant term is _________.

()

0

17. #### Match the following

5 x 1 = 5
18. 2010

19. (1)

0

20. 12111

21. (2)

Sequence: 2, 4, 6, 8… General from: y = 2n

22. 729725

23. (3)

1

24. Match the given patterns of shapes with the appropriate number pattern and its generalization.

25. (4)

9

26. (5)

Sequence: 3, 4, 5, 6,… General form: y = x + 2

10 x 2 = 20
27. Compare the following decimal numbers and find out the smaller number.
0.99, 1.9

28. Represent the following decimal numbers on the number line.
2.1

29. Write the following decimal numbers in words.
0.7

30. A picture is painted on a ceiling of a marriage hall whose length and breadth are 18 m and 7 m respectively. There is a border of 10 cm along each of its sides. Find the area of the border.

31. The cost of fencing a circular race course at the rate of Rs.8 per metre is Rs.2112. Find the diameter of the race course.

32. A goat is tethered with a rope of length 45 m at the centre of the circular grass land whose radius is 52 m. Find the area of the grass land that the goat cannot graze.

33. Simplify and express each of the following in exponential form:
45 x 42 x 44

34. Find the degree of the following terms.
-7ab

35. II. Construct a triangle ABC with given conditions.
(i) AB = 7 cm, AC = 6.5 cm and∠A = 120°.
(ii) BC = 8 cm, AC = 6 cm and ∠C = 40°.
(iii) An isosceles obtuse triangle with equal sides 5 cm

36. Using the given figure, prove that the triangles are congruent. Can you conclude that AC is parallel to DE.

37. Find the trianglular numbers from the Pascal’s Triangle and colour them.

38. Verify whether the following hexagonal shapes form a part of the Pascal’s Triangle.

39. Verify whether the following hexagonal shapes form a part of the Pascal’s Triangle.

5 x 3 = 15
41. The height of a person is 165 cm. Express this height in metre.

42. Two automatic ice cream machines A and B designed to fill cups with 100 ml of ice cream were tested. Two cups of ice creams, one from machine A and one from machine B are weighed and found to be 99.56 ml from machine A and 99.65 ml from machine B. Can you say which machine gives more quantity of ice creams?

43. Find the perimeter of the given shape (Fig.2.9) (Take $\pi =\frac { 22 }{ 7 }$).

44. Express the following numbers in exponential form with the given base:
243, base 3.

45. Simplify and find the degree of the expression
(4m2 + 3n)− (3m+ 9n2 )− (3m2 − 6n2 )+ (5m− n)

46. Can the following angles form a triangle?
(i) 800, 700, 500
(ii) 560, 640, 600

47. In the following figures, polygons are formed by increasing the number of sides using matchsticks as given below.

Find the number of sticks required to form the next three shapes by tabulation and generalisatio

2 x 5 = 5
49. Find the unit digit of the following exponential numbers:
2523

50. Tabulate the 3rd slanting row of the Pascal’s Triangle by taking the position of the numbers in the slanting row as x and the corresponding values as y.

 x 1 2 3 4 5 6 ... y 1 3 6 10 15 21 ...

Verify whether the relationship, y = $\frac { x(x+1) }{ 2 }$ between x and y for the given values is true.