Class7_questionbank

Tatachem DAV Public School Mithapur | Class 7

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Tatachem DAV Public School, Mithapur

Model Question Bank for SA-II 2014-2015

Class 7

1. Exponents and Powers

1. Reciprocal of

is ……………………. where ; m is integer

2. If x be any non-zero rational number and m, n be any positive integers then,

…………………. if m < n.

3. Every number, large or small can be expressed in the form …………….

4. Write the base and exponent of

.

5. Express

in exponential form.

6. Express 1.8 × 1.8 ×1.8 ×1.8 ×1.8 ×1.8 ×1.8 in exponential form.

7. Find the reciprocal of

.

8. Evaluate:

9. Simplify

and express the result as a rational number.

10. Find the value of

11. Evaluate:

12. By what number should (-12)-1 should be divided so that the quotient may be equal

to (-4)-1?

13. If

14. Find the value of x so that

15. Express the product of 2.5 × 105 and 2.1 × 10-3 in the form k ×10n.

16. Write 1.235 × 105 in usual form.

17. Write 0.00729 in the form k ×10n where ≤k< 0 and n is an integer.


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2. Algebraic Expressions

. Algebraic expression with two terms is called a …………………………………..

. ………………. of variables follows the rule of exponents.

. Product of (A+B)(C+D)=……………………………………….

4. Find the product 4y2(xy-x2) and then evaluate it for x=-2, y=3.

5. Find the product of the following.

a. (5x+3)(2x+4)

b. (m2n-5)(6-mn2)

c. (7y-2)(5y2-3y+2)

d. (0.1a – 0.2c)(a+c+ac)

6. Simplify the following

a. ab(a2-b2)+b3(a-2b)

b. (7abc+b2)(7-bc)+c(2b3-9ab)

c.

d. (p2+q2+r2)(pq+qr)

7. Find the HCF of 2x3y2, 10x2y3, 14 xy.

8. Find the HCF of the terms and factorise : 20x3-40x2+80x

9. Factorise the following

a. 2ax + bx + 2ay + by

b. (x + y)(2x + 3y) – (x + y)(x + 1)

c. 4(p + q)(3a – b) + 6(p + q)(2b – 3a)

d. a2 + 2a + ab + 2b

3. Linear Equation in One Variable

1. The standard form of linear equation in one variable x is _____________ where a and b

are ________________ and a ______0.

2. Finding a solution to a word problem involves _______ steps.

3. Solve the following equations

a.

b. 3x + 2(x+2)= 20 –(2x-5)


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c.

d.

e. 0.6x + 0.8 = 0.28x + 1.16

f.

g.

h.

4. A number when added to its two thirds is equal to 55. Find the number.

5. The sum of two numbers is 99. If one exceeds the other by 9, find the numbers.

6. The length of a rectangle is 16 cm less than twice its breadth. If the perimeter of the

rectangle is 100 cm, find its length and breadth.

7. Find two consecutive positive integers whose sum is 63.

8. A piggy bank contains Rs 370 in the notes of denominations of 10 and 50. If the

number of 10 rupee notes is one more than that of 50 rupee notes, find the number of

notes of each type.

9. In a class of 49 students, number of girls is

of the boys. Find the number of boys in

the class.

0. Present age of Veena’s mother is four times Veena’s age. Five years hence, her age

will be years more than Veena’s age. Find their present ages.

11. A man travelled 2/5th of his journey by train, 1/3rd by taxi, 1/6th by bus and

remaining 10 km on foot. Find the length of his total journey.

12. The numerator of a fraction is 6 less than the denominator. If 3 is added to the

numerator, the fraction becomes equal to

Find the original fraction.

4. CONGRUENT TRIANGLES

. Symbol ________ is used to indicate ‘congruent to’.

2. Two figures are congruent, if they have exactly the same ___________ and _________.

3. Two circles are congruent, if they have the __________ radii.

4. Explain SAS, RHS, SSS and ASA congruence conditions with appropriate diagrams.


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5. When two triangles are said to be congruent?

6. In fig 1, it is given that AB=CD and AD=BC. Prove

that ∆ADC≅∆CBA.

7. In fig 2, PS = RS and PQ = RQ

i. Is ∆PQS ≅ ∆RQS?

ii. State the three pairs of matching parts you have used to

answer (i)

iii. ∠P = …………..

8. If ∆PQR is an isosceles triangle such that PQ=PR, then

prove that the altitude PS from P on QR, bisects QR. (fig 3)

9. Find the three pairs of corresponding parts to ensure that

∆PQO ≅ ∆SRO by ASA congruence condition.

10. In fig 4, AO = BO and ∠A = ∠B.

i) Is ∠AOC = ∠BOD ? Why?

ii) Is ∆AOC = ∆BOD by ASA congruence condition?

iii) State the three facts you have used to answer (ii)

iv) Is ∠ACO = ∠BDO ? Why?

Fig 1

Fig 3

Fig 2

Fig 4


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11. Show that the bisector of the vertical angle of an isosceles triangle bisects the base

at right angles.

12. In fig 5, PQR and SQR are two triangles on a common

base QR such that PQ = SR and PR=SQ.

(i) Is ∆PSQ≅∆SPR? By which congruence condition?

(ii) State the three pairs of corresponding parts you have used

to answer (i).

(iii) If ∠SRP=40° a ∠QPS=110° the f ∠PSQ.

13. Show that in an isosceles triangle, angles opposite to equal sides are equal.

14. In fig 6, ABC is an isosceles triangle in which AB=AC. Also D

is a point such that BD=CD. Prove that AD bisects ∠A and ∠D.

15. Fill in the blanks to make the following statements true.

(i) If PQ=YZ, ∠Q = ∠Z and QR = ZX, then ∆PQR ≅ ___________ by SAS congruence condition.

(ii) If ∆ABC ≅ ∆EFD then side BC = side _____________ and ∠A = ____________________.

5. PERIMETER AND AREA

1. A curve is called ________________ if it does not cross itself.

2. A plane figure is called ________________ if it is made up of line segments only.

3. The magnitude of a plane region is called its ___________.

4. The length of a closed figure is called the __________________.

5. Perimeter of a rectangle = __________________.

6. Area of a square = _____________________.

7. 1 km2 = __________ hectares

Fig 5

Fig 6


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8. 1 hectare = ____________ m2

9. A rectangular garden 78 metres long and 35 metres broad has a uniform path 1 metre

wide all around it on the outside. Find the area of the path.

10. 1m wide path is built inside a square park of side 30 m along its sides. Find the area

of the path. Calculate the cost of constructing the path at the rate of Rs 70 per m2.

11. A rectangular plot of land is 300 m long and 250 m broad. It has two hands, each 3

metres wide running midway within it one parallel to the length and the other parallel to

the breadth. Find the area of the roads. Also calculate the cost of constructing the roads

at Rs 50 sq. metre.

12. The height of parallelogram is 3 dm. If the area is 240 cm2, find the base of ∥gm .

13. One side and corresponding altitude of a parallelogram are 50 cm and 8 cm. If the

other altitude is 4 cm, find the length of other pair of parallel sides.

14. The area of rhombus is 119 cm2 and its perimeter is 56 cm. Find its altitude.

15. Area of a ∥gm is 625 m2. Find the length of sides of ∥gm if altitudes corresponding to

sides are 20 m and 25 m.

16. Find the area of rhombus whose diagonals are d1 and d2 units.

17. ∆ABC is right angled at A. AD is perpendicular to BC. If AB = 5 cm, BC=13 cm and

AC = 12 cm, find the area of ∆ABC. Also find the length of AD.

18. A diagonal of quadrilateral is 40 m long and the

perpendiculars to it from the opposite corners are 8 m

and 10 m respectively. Find its area.

19. Find the circumference of a circle whose diameter is 4.2 cm.

20. In the given fig, ST =5 cm, QR = 9 cm. The area of the larger

triangle is 50 cm2. What is the area of shaded region?


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21. A wire is in the form of a circle of radius 35 m. It is now bent in the form of an

equilateral triangle. Find the sides of triangle.

22. The radius of a wheel of a bus is 0.70 m. How many revolutions will it make in

covering 22 km?

23. The diameter of a circular park is 140 m. Around it on the outside, a path having the

width of 7 m is constructed. If the path has to be fenced from inside and outside at the

rate of Rs 7 per metre, find its total cost.

24. Find the area of circle whose

(i) radius is 14 cm

(ii) diameter is 42 cm

(iii) circumference is 264 m

25. If the perimeter of a semi-circular park is 72 m, find its area and radius.

26. A horse is tied to a pole with 21 m long string. Find the area where the horse can

graze.

27. Two concentric circles have radii of 14 cm and 7 cm respectively. Find the area of

space between them.

28. A paper is in the form of a rectangle PQRS in which

PQ=10 cm and QR = 7 cm. Two semi-circular portions

with QR and PS as diameters are cut-off. Find area of

remaining part.

29. The sum of circumferences of 4 small circles is equal to the circumference of a

bigger circle. Find the ratio of the area of the bigger circle to that of the smaller circle.

30. Find the area of the square that can be inscribed in a circle of radius 8 cm.


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31. Find the area of unshaded portion of given fig, the

shaded portions being semi-circular regions.

32. A design on the wall of room consists of 1000 tiles of the shape of parallelogram. If

altitude and base of tiles are 10 cm and 4 cm respectively, find the cost of polishing the

design at the rate of Rs 1.50 per dm2.

33. Write down the formula of following

(a) Area of an equilateral triangle

(b) Area of cross paths

(c) Area of parallelogram

(d) Area of a rhombus

6. DATA HANDLING

1. What is data?

2. How data is organized?

3. What is mean, median and mode?

4. What is a bar graph?

5. The weights (in kg) of 10 students of a class are

43.5, 49.5, 52, 43, 47, 44.5, 38.5, 40, 47, 38

(i) What is the mean weight?

(ii) What is the range of the weights of the students?

(iii) Find the number of students having weight more than the mean weight.

6. The average salary of 9 workers in a factory is Rs 2,800 per month. If the salary of the

manager is Rs 5,000 per month, find the average monthly salary paid to all the

employees.


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7. The mean of 9 observations was found to be 35. Later on, it was discovered that an

observation 81 was misread as 18. Find the correct mean of the observation.

8. The mean of 5 numbers is 27. If one number is excluded, their mean is 25. Find the

excluded number.

9. Find the median of the following data: 11, 39, 43, 45, 25, 46, 43, 42, 37

10. The following number of goals were scored by a team in a series of 10 matches:

2, 3, 5, 4, 0, 1, 3, 3, 3, 4

Find the median of these scores.

11. Find the mode of the following observations: 25, 14, 28, 17, 18, 14, 25, 14, 17, 14

12. The following table shows sale of shirts having different sizes from a certain shop in

a month. Find the mode.

Size 38 39 40 42 44

No. od Shirts 24 31 23 14 7

13. In January 2007, the number of children in 10 families of a locality are;

4, 3, 4, 0, 2, 2, 5, 2, 1, 3

Find the mean, median and mode.

At the end of the year, two families having children 0 and 1 vacated the house. As a

result, two more families having children 2 and 5 got the vacant accommodation. Find

the new mean, median and mode.


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14. Study the bar graph and answer the following questions:

(a) What does graph represent?

(b) Name the music album that had the highest sale.

(c) Which music album had the least sale?

(d) What is the total sale of all the albums put together?

15. A bicycle shop owner sold the following number of bicycles each day in particular

week. Present this information in the form of a bar graph.

Day Monday Tuesday Wednesday Thursday Friday Saturday

No. of cycles sold 35 30 44 25 10 25

16. The following data gives the number of Mathematics and Science books bought by a

library during different years.

Year 2003 2004 2005 2006 2007

Mathematics 350 400 520 600 650

Science 300 380 400 450 600

Draw a double bar graph.


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17. Study the bar graph and answer the questions that follow:

(a) What does the bar graph represent?

(b) In which two sections are the number of girls equal?

(c) Which section has the highest number of girls?

(d) How many sections have more number of girls than boys?

7. VISUALISING SOLIDS

1. How many vertices, edges and faces will a cuboid have? What is the shape of its

faces?

2. Name all the vertices, edges and faces of the given pyramid.

3. Consider the given figure. It shows a cube surmounted by a

pyramid. How many faces, edges and vertices does it have?

Name its edges, faces and vertices. Also state the faces which

are triangles and which are squares.


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4. A dice is a cube with dots or numbers on its faces in such a manner that the sum of

the dots on its opposite faces is always seven. If there are four dots on one face, then on

the opposite face there will be 3 dots. Given below are two nets to make a dice. Put the

numbers in the blanks to get a dice in each case.

5. A ________________ is a solid which has four faces as triangle.

6. A ________ is an outline which we can fold to make a solid.

7. Solid shapes have ________ dimensions.

8. In ____________ sketch, the dimensions tally with those of the solid.

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