Class 7 Mathematics

Sample Paper 1

Time: 3 hrs                                                         Max. Marks: 80

General Instructions

1. The paper is divided into four sections A to D. Each section is compulsory.

2. Section A consists of Multiple-Choice Questions containing 1 Mark each from question 1to 11.

3. Section B consists of Very Short Answer Type Questions containing 4 Marks each from question 12 to 14 having sub-parts.

4. Section C consists of Short Answer Type Questions containing 3 Marks each from question 15 to 23.

5. Section D consists of Long Answer Type Questions containing 5 Marks each from question 24 to 29.

 

Section A (Multiple Choice Questions)

 

Q.1. The median of the data 2, 3, 1, 8, 4, 7, 11, 12, 10 is

(a) 6

(b) 8

(c) 9

(d) 7

Q.2. In the given figure, the value of x is

(a) 45°

(b) 40°

(c) 50°

(d) 30°

Q.3. The product of 25 × (−15) and 10 × (−2) is

(a) 2560

(b) 2500

(c) 7500

(d) −6000

Q.4. If ∆ABC is a right-angled triangle in which right angled at C. If AC = 6 cm and BC = 8 cm, then the length of AB is

(a) 12 cm

(b) 9 cm

(c) 10 cm

(d) 11 cm

Q.5. Two candidates contested an election. One candidate got 30% of the total votes and still lost by 500 votes, then the total number of votes casted is equal to

(a) 1150

(b) 1250

(c) 1100

(d) 950

Q.6. If  then m is equal to

(a) 3

(b) 2

(c) −3

(d) 4

Q.7. Simplified value of  is

(a)

(b)

(c) 2

(d) 3

Q.8. The mean of the first ten natural numbers is

(a) 2.5

(b) 14

(c) 5.5

(d) 3

Q.9. In a right-angled triangle, at least one angle is equal to

(a) 45°

(b) 60°

(c) 90°

(d) 180°

Q.10. In the given figure, find the value of x.

(a) 30°

(b) 60°

(c) 75°

(d) 45°

Q.11. In the given figure, the value of x and y are

(a) 120°, 30°

(b) 130°, 40°

(c) 120°, 40°

(d) 90°, 40°

 

Section B (Very Short Answer Type Questions)

 

Q.12. Answer the following questions:

(i) Find the value of expression.

4(3x − 2) + 2x + 10, if x = 2 .

(ii) The rainfall (in mm) in a city on 7 days of a certain week was recorded as follows:

(a) Find range of the rainfall in above data.

(b) Find mean rainfall of the week.

(iii) Draw the net diagram of a cone.

(iv) Draw an isometric sketch of a cuboid given below (oblique sketch).

Q.13. Fill in the blanks.

(i)

(ii)

(iii) In the given figure,

x = ______

y = ______

z = ______

(iv) If 2(m + 4) + 3(2m + 6) = 12, then m = ______

Q.14.  

(i) Simplify 2a − 4b − 2ab − 2(a + 2b − 4ab).

(ii) Simplify

(iii) Find the area of the given triangle.

(iv) Express the following in exponential form.

x × x × x × x × y × y × y × a × a × a × a

 

Section C (Short Answer Type Questions)

 

Q.15. Draw ∆ABC in which BC = 4 cm, ∠B= 35° and ∠C = 105°. Measure ∠A and write down all steps of construction.

Q.16. Draw nets to make a tetrahedron.

Q.17. The value of a machine depreciates 10% every year. If the present value of the machine is ₹ 200000. What will be its value after 2 years?

Q.18. The simple interest on a certain sum for 3 year at 4% per annum is ₹ 102 more than the simple interest on the same sum for 2 year at 5% per annum. Find the sum.

Q.19. The diagonal of a square is 1352 cm. Find the length of the sides of the square.

Q.20. Find the perimeter of a rectangle whose breadth is 18 cm and a diagonal is 30 cm.

Q.21. In the adjacent figure, D and E are two points on the sides AB, AC of ∆ABC respectively such that DE || BC. If ∠B = 30° and ∠A = 40° ,then find x°, y° and z°.

Q.22. In ∆ABC, ∠A = 80° and AB = AC. Find ∠B and ∠C.

Q.23. In the adjacent figure, given that LM = MN, OM = MR, ML ^ PO and MN ^ PR. Prove that PO = PR.

 

Section D (Long Answer Type Questions)

 

Q.24. A die is thrown 100 times and outcomes are noted as given below:

Find the probability of getting number

(i) 2

(ii) 5

(iii) 4

(iv) less than 2

Q.25. The following data gives the amount of loans (in ₹ crores) disbursed by a bank during 1992-1997

(a) Represent the above data with the help of a bar graph.

(b) Find the difference between maximum amount of loan and minimum amount of loan disbursed by the bank.

Q.26. A housing society decided to construct a rectangular park for making aware their residence about good health and benefit of walking. If the rectangular park has 3 m wide path for running outside. Also, the length and breadth of the remaining rectangular part of the park are 130 m and 60 m respectively. Find the area of the path. What is the value depict here?

Q.27. If the area of a rhombus is 88 cm² and one of its diagonals is 8 cm. Find its perimeter.

Q.28. A square park has each side 50 m. At each conner of the park, there is a flower bed in the form of a quadrant of radius 7 m, as shown in the figure. Find the area of remaining part of the park.

Q.29. The inner circumference of a circular race track 7 m wide is 440 m. Find the radius of the outer circle.

 

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