8th Mathematics Annual Exam 2018-19

8th Mathematics Annual Exam (2018-19)

School Name: Venkateshwar Global School, Sector 13, Rohini, Delhi 110085 India
Time: 3 hour
M.M. 80 marks
Date: 05/02/2019
Subject: Mathematics
Class: VIII

General Instructions:

1. All questions are compulsory.
2. Do you work neatly.
3. Do not scribble on the question paper.
4. Write your name and section on the question paper.

Section A [1×6 = 6]

Question: 1. Identify the variance: Number of people and fixed quantity of food that will last.

Question: 2. Find the number of sides of a regular polygon if the measure of each exterior angle is 60°.

Question: 3. If one the diagonal of a square is 10 cm, find the area of the square.

Question: 4. Write down the abscissa and ordinate of the point P (-3, 5).

Question: 5. Factorize: x² – 8x + 16.

Question: 6. Find the curved surface area of a cubical water tank of side 2.1 m.

Section B [2×10 = 20]

Question: 7. A table marked at Rs. 20,000 is available at Rs. 18,000. Find the discount given on the table and the discount percentage.

Question: 8. In how much time will Rs. 5000 amount to Rs. 6655 at 10% p.a. compounded annually?

Question: 9. If the length and breadth of a rectangle are (x² – 5x + 3) units and (5x – 2) units respectively, find its area.

Question: 10. Factorize: 6a² 17a + 12.

Question: 11. A metallic pipe whose internal and external radius are 3 cm and 4 cm has a length of 1.1 m. Find the volume of the metal used.

Question: 12. Construct a parallelogram whose adjacent sides are 7 cm and 5 cm with 70º as included angle.

Question: 13. If 9 men can mow a field in 4 days, in how many days can 6 men mow the same field?

Question: 14. If the altitude of parallelogram is doubled and base is halved, what happens to the area?

Question: 15. Plot the points A (-1,3), B (0,2), C (1,1) and D (2,0). Are the points co-linear?

Question: 16. In the figure given below, PQRS is a Rhombus, state the length of PQ and ∠Q. Give reasons.

Section C [3×10 = 30]

Question: 17. Rajneesh sold her watch at a profit of 7%. If he has sold it for Rs. 294 more, he would have got a 10% profit. Find the cost price of the watch.

Question: 18. A shopkeeper was selling all his items at 25% discount. During the off – season, he offered 20% discount over and above the existing discount. If Surveer bought a washing machine, which was marked Rs. 20,000, how much did she pay for it?

Question: 19. A field is in the form of a kite. Its perimeter is 200m. If one of its sides is 40m, what are the lengths of the other two sides of the field?

Question: 20. Find the product using suitable identities. Also, mention the identities used.
(a) 99³  (b) 105 × 106

Question: 21 A can do a piece of work alone in 12 days and B can do it alone in 6 days. How long will they take to finish it, if they work together?

Question: 22. Complete the table of values and make a graph to represent these points.

Question: 23. If x + 1/x = 3, find the value of x² + 1/x²

Question: 24. The dimensions of the cuboid are in the ratio 5:2:1. Its volume is 1250 cubic metres. What is its total surface area?

Question: 25. Construct a rhombus PQRS in which PQ = 7.5 cm, and ∠PQR = 80°.

Question: 26. The length, breadth and height of a hall are 12 m, 8 m and 10 m, respectively. The hall has a door of area 4 m × 1.5 m and a window of area 1.5 m × 1 m. Find the cost of painting the four walls at the rate of Rs. 100 per square meter.

Section D [4×6 = 24]

Question: 27. ABCD is a Rhombus. Find the values of x,y,z and also find AD if CB = 7 cm. Give reasons for your answer. (Refer to figure given)

Question: 28. Simplify: (2a + 3b)³ + (2a – 3b)³. Mention the identities used.

Question: 29. Find the area of the following field. The measurements are in metres.

Question: 30. A well is dug 10 m deep and has a diameter of 1.4 m. The sand taken out is spread over a rectangular plot of dimension 11 m by 14 m to raise the level of the ground. What will be the height by which the ground is raised?

Question: 31. Construct a quadrilateral PQRS, given PQ = 6 cm, QR = 5.6 cm, Rs = 2.7 cm, ∠Q = 45° and ∠R = 90°. Mention the steps of construction.

Question: 32. The given graph describes the distances of a car from a city P at different times when it is travelling from City P to City Q, which are 350 km apart. Study the graph and answer the following:

1. How far did the car go in the first hour?
2. How much time did the car took to travel between 200 km to 350 km?
3. Did the car stop for some duration at any place? Justify your answer.
4. How much time will the whole journey take to reach city Q from P without stopping anywhere?