Senior secondary model school
Bhirdana
MATHEMATICS
Class 09 - Mathematics
Time Allowed: 2 hours and 30 minutes Maximum Marks: 80
Section A
1. Which of the following is an irrational number: [1]
a) 3.141141114 ... b) 3.14444 ...
c) 3.14 d) 3.141414...
2. Which of the following is a polynomial in one variable? [1]
– –
a) √2x 2
− √3x +6 b) x + 2
x
+3
−
c) 3√x + 2
+5 d) x10 + y5 + 8
√x
3. Zero of the polynomial p(x) =2x + 5 is [1]
a) b)
2 5
5 2
c) −5
2
d) −2
4. In which quadrant does the point (-2, -5) lie? [1]
5. Express y in terms of x in the equation 5x - 2y = 7. [1]
a) y = 5x−7
2
b) y =
7−5x
c) y = d)
7x+5 5x+7
y =
2 2
6. If (4, 19) is a solution of the equation y = ax + 3, then a = [1]
a) 4 b) 6
c) 3 d) 5
7. How many lines pass through two points? [1]
a) many b) three
c) two d) only one
8. Two distinct points in a plane determine line(s). [1]
a) Three b) Unique
c) One d) Two
9. How many lines can pass through a single point? [1]
10. Use the given figure to match Column-I with Column-ll, if AB || CD. [1]
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_
Column-I Column-II
(a) Corresponding angles (i) ∠ 1 = ∠ 7
(b) Alternate interior angles (ii) ∠ 4 + ∠ 5 = 180°
(c) Alternate exterior angles (iii) ∠ 1 = ∠ 5
(d) Co-interior angles (iv) ∠ 4 = ∠ 6
a) (a) - (iv), (b) - (ii), (c) - (i), (d) - (iii) b) (a) - (iii), (b) - (iv), (c) - (i), (d) - (ii)
c) (a) - (iv), (b) - (i), (c) - (ii), (d) - (iii) d) (a) - (iii), (b) - (ii), (c) - (iv), (d) - (i)
11. In the given figure (not drawn to scale), if AB || CD, then x and y respectively are ________. [1]
a) 40°, 30° b) 30°, 45°
c) 90°, 30° d) 50°, 77°
12. Two straight lines AB and CD cut each other at O. If ∠ BOD = 63°, then∠ BOC = [1]
a) 117° b) 17°
c) 153° d) 63°
Section B
13. State True or False: [2]
(a) Irrational numbers cannot be represented by points on the number line. [1]
(b) Remainder Theorem states that Dividend = (Divisor × Quotient) + Remainder. [1]
14. Fill in the blanks: [2]
(a) π is an ________ number. [1]
(b) The y-coordinate is also called the ________. [1]
Section C
15. Rationalize the denominator of 1
[3]
√5+√2
16. Factorise: 2y3 + y2 - 2y - 1 [3]
17. In fig find the vertices' co-ordinates of △ABC [3]
2/5
18. In the given figure, if OX = 1
2
XY, PX =
1
2
XZ and OX = PX, show that XY = XZ. [3]
OR
Factories
4x²+9y²+16z²+12xy+24yz+16xz
19. In fig POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. [3]
Prove that ∠ ROS =
1
2
(∠ QOS − ∠POS)
Section D
20. Find the decimal expansions of 10
3
,
7
8
and 1
7
. [4]
21. If x =
5−√3
and y =
5+√3
,show that x − y = −
10√3
. [4]
5+√3 5−√3 11
22. Verify that x 3
+ y
3
+ z
3
− 3xyz [4]
1 2 2 2
= (x + y + z) [(x − y) + (y − z) + (z − x) ]
2
OR
It is given that √xyz=64°and xy is produced to point p. Draw a figure from the given information.If ray yq bisects
√zyp . Find √xyq and reflex √qyp.
23. Factories by division method [4]
X³-3x²-9x-5
24. In a line segment AB point C is called a mid-point of line segment AB, prove that every line segment has one [4]
and only one mid-point.
25. In the given figure, AB || CD || EF, ∠DBG = x, ∠EDH = y , ∠AEB = z , ∠EAB = 90
∘
and [4]
∠BEF = 65
∘
. Find the values of x, y and z.
3/5
Section E
26. Verify that x3
+ y
3
+ z
3
− 3xyz =
1
2
(x + y + z) [(x − y)
2 2
+ (y − z)
2
+ (z − x) ] [5]
27. write the following: [5]
i. The coordinates of B.
ii. The coordinates of C.
iii. The point identified by the coordinates (-3, -5).
iv. The point identified by the coordinates (2, - 4).
v. The abscissa of the point D.
vi. The ordinate of the point H.
vii. The coordinates of the point L.
viii. The coordinates of the point M.
28. Find five different solutions of the equation: 3y = 4x [5]
29. In the adjoining figure, name: [5]
i. Six points
ii. Five line segments
iii. Four rays
iv. Four lines
v. Four collinear points
4/5
30. In the given figure, if AB || CD, CD || EF and y: z = 3: 7, find x. [5]
5/5
