KENDRIYA VIDYALAYA IIT CAMPUS, CHENNAI-36X – MATHEMATICS (MODEL QP) –REVISION EXAM

TIME: 3 Hours MAX. MARKS: 80

GENERAL INSTRUCTIONS:1) All questions are compulsory.2) The question paper consists of 30 questions divided into four sections, A, B, C and D.

Section-A comprises of 6 questions of 1 mark each. Section-B comprises of 6 questions of 2 marks each. Section-C comprises of 10 questions of 3 marks each. Section-D comprises of 8 questions of 4 marks each.

3) All questions in Section-A are to be answered in one word, one sentence or as per the exact requirement of the question.

4) Use of calculator is not permitted.

SECTION – A

1) Find the next term of the sequence √2 , √8 , √18 .

2) What is the angle of elevation of the Sun when the length of the shadow of a vertical pole is equal to its height?

3) Find the discriminant of √3 x2−2√2 x−2√3=0 .4) Find the distance between the points (sin, cos) and (cos, sin)

5) State Euclid’s Division Lemma.

6) State and Prove Basic Proportionality Theorem

SECTION – B

7) Show that 5−2√3 is an irrational number.

8) Find the quadratic polynomial whose zeroes are √2 + 3 and √2 - 3.

9) Find the value of ‘k’ if the following system of equations 2x + 3y = 6 and 4x – ky = 10 has no solution

10) The mid-point of a line segment joining the points (a , 2) and (3 , 6) is (2 , 4). Find the numerical value of ‘a’.

11) How many two digit numbers are divisible by 7?

12) Prove that the parallelogram circumscribing a circle is a rhombus.

SECTION – C

13) Find the roots of the equation 5x2 – 6x – 2 = 0 by the method of completing the square.

14)

A fraction becomes

911 , if 2 is added to both the numerator and the denominator. If, 3 is

added to both the numerator and the denominator it becomes

56

.find the fraction.

15) If A, B and C are the interior angles of a triangle ABC, then show that

tan(B+C2 )=cot( A

2 ).

OR

If sin (A – B) =

12 , cos (A + B) =

12 , 0° < A + B 90°, A > B, find A and B.

16) A quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB + CD = AD + BC

17) Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60°.

18) A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30°.

19) Find the value of k if the points A(2, 3), B(4, k) and C(6, –3) are collinear.

OR

If the points A(6, 1), B(8, 2), C(9, 4) and D(p, 3) are the vertices of a parallelogram, taken in order, find the value of p.

20) Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is

some integer.

OR

Consider the numbers 14n, where n is a natural number. Check whether there is any value of n for which 14nends with the digit zero.

21) Divide 6x4 – 44x2 +6 x -3 by x2 -3x +1 and verify the division algorithm.

22) In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes.

OR

Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.

SECTION – D

23)

Solve:

x+3x−2

− 1−xx

= 174

, x≠2 , x≠0

OR

A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in Rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was Rs 750. Find the number of toys produced on that day.

24) Draw the graphs of the equations x – y + 1 = 0 and 3x + 2y – 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region.

25) In a school, students thought of planting trees in and around the school to reduce air

pollution. It was decided that the number of trees, that each section of each class will plant, will be the same as the class, in which they are studying, e.g., a section of Class I will plant 1 tree, a section of Class II will plant 2 trees and so on till Class XII. There are three sections of each class. How many trees will be planted by the students? What value is depicted from this question?

26) “The length of the two tangents drawn from an external point to a circle are equal” – Prove.

OR

“The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides” - Prove.

27)

Construct a triangle similar to a given ∆ABC such that each of its sides is ( 2

3 )rd

of the corresponding sides of ∆ABC, given that BC = 7.5 cm, B = 50 and C = 60.

28) The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. Prove that the height of the tower is 6 m.

OR

From a point P on the ground the angle of elevation of the top of a 10 m tall building is 30°. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from P is 45°. Find the length of the flagstaff and the distance of the building from the point P.

29) If the vertices of a triangle are (1, 3), (4, p) and (9, 7) and its area is 15 sq.units. Find the value(s) of ‘p’.

30)

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PRE BOARD MODEL PAPER 2017-2018

I.ONE MARK

1. Who was proclaimed the germen emperor in 1871?2. What was vernacular pren act?3. How can the resources are classified on the basis of origin.4. Give example of horizontal and vertical power shaving?5. What is average income of precipitin income?6. What is trade heavier? Explain?7. On what basis the section are classified in to public and private sector?

II. ANSWER THE FOLLOWING IN BRIEF

1. What changes did Napoleon introduce to make the administrative system more efficient on the territarin ruled by him?

2. “Gandhi said the fight for shavaj” is a fight for the liberty of speech liberty of press and freedom of association.

3. Which is the most widely spread and important soil of Indra? State any three characterization of this type of soli?

4. Difference between perimeter and intensive subsistence farming?5. Difference between a federal form of government and a victory one? Explain with example?6. Distinguish between overlapping and cross cutting?7. “Democratic government is a legitimate government” explain?8. Why is the issue of sustainability important for development?9. Explain money as a medium of exchange?10. What are the advantages of depositing money in the banks?11. How does foreign trade play an important role in integrating the markets across the

countries? Explain.

III. ANSWER THE FOLLOWING IN LONG

1. How to create more employment in rural areas? Explain with example.2. Describe any five functions political parties perform in a democratic set up? 3. State any provisions of the Indian constitution which makes it a secular state?4. “Agriculture and industry are not exclusive of each other. They more hard in hand” explain.5. Explain the methods of traditional rain water harvesting techniques in India.6. Explain the various land reclamation projects launched in Bombay? Which helped in its

expansion?7. What is the limitation of CDM of 1930?

IV. MAP

1. A place associated with the calling off the NCM.2. A place where the congress session was held in 1927 to 19293. I own one belt 4. Coal mining petroleum mining areas.