KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS,

HYD–32
SAMPLE PAPER 03 FOR PERIODIC TEST II EXAM (2019-20)

SUBJECT: MATHEMATICS(041)

BLUE PRINT FOR PERIODIC TEST - II: CLASS IX

MCQ VSA SA – I SA – II LA
Chapter Total
(1 mark) (1 mark) (2 marks) (3 marks) (4 marks)
Number System 2(2) 2(2) 2(1)* 3(1) 4(1) 13(7)

Polynomials 1(1) 2(2) 2(1) 3(1) 4(1)* 12(6)

Coordinate Geometry 2(2) 1(1) -- 3(1) 4(1) 10(5)

Linear Equation in two
1(1) 2(2) 2(1)* 6(2) -- 11(6)
variables
Lines and Angles 2(2) 1(1) 2(1) 3(1)* 4(1) 12(6)

Triangles 1(1) 1(1) 2(1) 3(1)* 4(1) 11(5)

Quadrilaterals 1(1) 1(1) 2(1) 3(1) 4(1)* 11(5)

Total 10(10) 10(10) 12(6) 24(8) 24(6) 80(40)

MARKING SCHEME FOR PERIODIC TEST - II

NO. OF
SECTION MARKS TOTAL
QUESTIONS
MCQ 1 10 10
VSA 1 10 10
SA – I 2 6 12
SA – II 3 8 24
LA 4 6 24
GRAND TOTAL 80

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 KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS,
HYD–32
SAMPLE PAPER 03 FOR PERIODIC TEST II EXAM (2019-20)
SUBJECT: MATHEMATICS MAX. MARKS : 80
CLASS : IX DURATION : 3 HRS
General Instructions:
(i). All questions are compulsory.
(ii). This question paper contains 40 questions divided into four Sections A, B, C and D.
(iii). Section A comprises of 20 questions of 1 mark each. Section B comprises of 6 questions of 2
marks each. Section C comprises of 8 questions of 3 marks each and Section D comprises of 6
questions of 4 marks each.
(iv). There is no overall choice. However, an internal choice has been provided in two questions of 2
marks each, two questions of 3 marks each and two questions of 4 marks each. You have to attempt
only one of the alternatives in all such questions.
(v). Use of Calculators is not permitted

SECTION – A
Questions 1 to 20 carry 1 mark each.

1. The graph of the linear equation in two variables y = mx is

(a) a line parallel to x – axis (b) a line parallel to y – axis
(c) a line passing through the origin (d) not a straight line

2. A linear equation in two variables has

(a) no solution (b) only one solution
(c) only two solutions (d) infinitely many solutions

3. Point (5, 0) lies on the:

(a) I quadrant (b) II quadrant (c) x – axis (d) y – axis
1
4. On rationalizing the denominator of , we get
2 3
(a) 2  3 (b) 3  2 (c) 2  3 (d)  3  2

5  is:
2
5. The value of  2
(a) 7  25 (b) 1 52 (c) 7  210 (d) 7  2 10

6. On dividing x3 + 3x2 + 3x +1 by x we get remainder:

(a) 1 (b) 0 (c) – 1 (d) 2

7. ABCD is a rhombus such that ACB = 400, then ADB

= (a) 450 (b) 500 (c) 400 (d) 600

8. In a right angled triangle, is the longest side.

(a) perpendicular (b) hypotenuse (c) base (d) none of these

9. The angle which is two times its complement is

(a) 600 (b) 300 c) 450 (d) 720

10. If x + 2 is a factor of x3 + 2ax2 +ax – 1 then the value of a is:

2 3 3 5
(a) (b)
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 3 1
(c) (d) 2
2

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11. Write the coordinates of the point lying on y-axis with y-coordinate –3.

12. If – 1 is a zero of the polynomial p(x) = ax3 – x2 + x + 4, then find the value of ‘a’.

13. Write an irrational number between 2 and 3 .

14. Factorize: 12x2 – 7x + 1

15. Simplify:  2 5 6  8
5

16. In ΔABC, AB = 5 cm, BC = 8 cm and CA = 7 cm. If D and E are respectively the mid-points
of AB and BC, determine the length of DE.

17. Can all the angles of a quadrilateral be acute angles? Give reason for your answer.

18. The angles of triangle are (x + 100), (2x – 300) and x0. Find the value of x.

19. At what point the graph of the linear equation x + y = 5 cuts the x-axis?

20. Write the linear equation such that each point on its graph has an ordinate 3 times its abscissa.

SECTION – B
Questions 21 to 26 carry 2 marks each.

21. One angle of a quadrilateral is of 1080 and the remaining three angles are equal. Find each of
the three equal angles.
22. In the below figure, PR > PQ and PS bisects  QPR. Prove that  PSR >  PSQ.

23. At what point does the graph of the linear equation x + y = 5 meet a line which is parallel to the
y-axis, at a distance 2 units from the origin and in the positive direction of x-axis.
OR
Write 3x + 2y = 18 in the form of y = mx + c. Find the value of m and c. Is (4, 3) lies on this
linear equation?

24. Without actually calculating the cubes, find the value of (28)3 + (–15)3 + (–13)3

25. Simplify 5  2 3 by rationalizing the denominator.

52 3
OR
Simplify: 8242  5 50  398

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26. In the adjoining figure, find the value of
x
P
0
45 B
A

300
C Q D
1300

SECTION – C
Questions 27 to 34 carry 3 marks each.

27. Plot the following points and write the name of the figure thus obtained : P(–3, 2), Q (–7, –3),
R (6, –3), S (2, 2).
28. Show that the bisectors of angles of a parallelogram form a rectangle.

29. Solve the equation 2y + 9 = 0, and represent the solution(s) on (i) the number line,(ii) the
Cartesian plane.

30. In the below figure, if QT  PR, TQR = 40° and SPR = 30°, find x and y.

OR
In the above right sided figure, PQ and RS are two mirrors placed parallel to each other. An
incident ray AB strikes the mirror PQ at B, the reflected ray moves along the path BC and strikes
the mirror RS at C and again reflects back along CD. Prove that AB || CD.

31. If x + y = 12 and xy = 27, find the value of x3 + y3.

p
32. Show that 1.23535353……. can be expressed in the form of , where p and q are integers and
q
q0.

33. The taxi fare in a city is as follows: For the first kilometre, the fare is Rs 8 and for the subsequent
distance it is Rs 5 per km. Taking the distance covered as x km and total fare as Rs y, write a
linear equation for this information, and draw its graph.

34. AD is an altitude of an isosceles triangle ABC in which AB = AC. Show that (i) AD bisects BC

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 (ii) AD bisects A.

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 OR
Line-segment AB is parallel to another line-segment CD. O is the mid-point of AD (see the
below figure). Show that (i) AOB  DOC (ii) O is also the mid-point of BC.

SECTION – D
Questions 35 to 40 carry 4 marks each.

35. Prove that the sum of any two sides of a triangle is greater than twice the median drawn to
the third side.

36. If polynomials ax3 + 3x2 – 3 and 2x3 – 5x + a leaves the same remainder when each is divided
by x – 4, find the value of a.
OR
Verify : (i) x3 + y3 = (x + y) (x2 – xy + y2) (ii) x3 – y3 = (x – y) (x2 + xy + y2)

3 2 3 2
37. Simplify 3  2 by rationalizing the denominator.
3 2

38. Prove that “The line segment joining the mid-points of two sides of a triangle is parallel to the
third side and half of it.”
OR
Show that the quadrilateral formed by joining the mid-points the sides of a rhombus, taken in
order, form a rectangle.

39. Three vertices of a rectangle are (4, 2), (– 3, 2) and (– 3, 7). Plot these points and find the
coordinates of the fourth vertex.

40. In the above right sided figure, the side QR of  PQR is produced to a point S. If the bisectors of
1
PQR and PRS meet at point T, then prove that QTR = QPR.
2

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