IX Standard - 9th - Maths - First Midterm Question Paper - Samacheer Kalvi
I –MID TERM TEST
Class : IX MARKS : 50
Sub: Maths Time:1:30
Hrs
I. Choose the correct Answer: 14x1=14
1. If B⊆ A then n(A∩B) is
(a) n(A–B) (b) n(B) (c)
n(B – A) (d)
n(A)
2. For any three sets A, B and C, ( A-B) ∩( B-C) is equal to
(a) A only (b)
B only (c) C
only (d)
∅
3. Which of the following is correct?
a) ø εø
II. Answer any Ten questions. Q.No
28 is compulsory 10x2=20
15. Find the cardinal number of the following set.
P = {x : x =
3n+2, n∈W and x< 15}
16. Represent AΔB through Venn diagram.
17. (i) If n(A) = 25, n(B) = 40, n(A∪B) = 50 and n(B′) = 25 , find n(A∩B) and
n(U).
18. Convert the following decimal number in the form of , 
(p,q
Z and q
0).
2.124
19. Write the following in scientific notation : ( 0.00000005)3
20. Find the remainder when 3x3 - 4x2+7x-5 is divided by (x+3).
21. Factorise 2x2
– 15x- 27.
22. Find the value of k for which the system of linear equations 8x +5y = 9; kx + 10y= 15 has no solution
23. Find the centroid of the triangle whose vertices are (−5,−5), (1,−4)
and (−4,−2).
24. If (x,3), (6,y), (8,2) and (9,4) are the vertices of a parallelogram
taken in order, then find the value of x and y.
25. Find the value of 8 sin2x cos4x sin6x, when x=15
26. Find the values of tan7
tan 23 tan 60 tan 67 tan 83.
27. What is the probability of drawing a King or a Queen
or a Jack from a deck of cards?
28. The probability of guessing the correct answer to a certain question
is 
. If the probability of not guessing the
correct answer is 
, then find the value of x .
III. Answer any Ten Questions. Q.No 44 is compulsory. 10x5=50
29. If A ={0,2,4.6,8}, B={x:x is a prime number and
x<11)} and C={x:X 
and 5 
x<9} then verify A
(B
C)=(AB)(AC).
30. In a colony, 275 families buy Tamil newspaper, 150
families buy English newspaper, 45 families buy Hindi newspaper, 125 families
buy Tamil and English newspapers, 17 families buy English and Hindi newspapers,
5 families buy Tamil and Hindi newspapers and 3 families buy all the three
newspapers. If each family buy atleast one of these newspapers then find
(i) Number of families buy only one newspaper
(ii) Number of families buy atleast two newspapers
(iii) Total number of families in the colony.
31. Represent the following numbers on the number line.
4.73 upto 4 decimal places.
32. Arrange in ascending order:
, 
, 
.
33. a)What should be added to 2x3+6x2-5x+8 to get 3x3-2x2+6x+15?
b) Expand (a- b +c)2
34. Factorise x3-5x2-2x+24
35. Solve 3x-4y=10 and
4x+3y=5 by the method of
cross multiplication.
36. Find all the three angles of
the ΔABC
37. Verify that the following points taken in order form the vertices of
a rhombus. A(3,–2), B (7,6),C (–1,2), D
(–5, –6)
38. The mid-points of the sides of a triangle are ( 5, 1), ( 3,-5 ) and (
, − 5,- 1). Find the coordinates of the vertices of the triangle.
39. If 3 cot A = 2, then find the value of
40. Find the area of a right triangle whose hypotenuse is
10cm and one of the acute angle is 24 24’
41. 1500 families were surveyed and following data was recorded about
their maids at homes
|
Type of maids |
Only part time |
Only full time |
Both |
|
Number of families |
860 |
370 |
250 |
A family is selected at random. Find the probability that the family
selected has
(i)Both types of maids (ii)Part time maids (iii)No maids
42. Verify (AB)’=A’ B’ using Venn diagrams.
IV. Answer the following. 2x8=16
43. a) Construct the centroid of 
PQR whose sides are PQ
= 8cm; QR = 6cm; RP = 7cm.
(OR)
b) Construct ΔABC
with AB = 5 cm B = 100 and BC = 6 cm. Also locate its circumcentre draw
circumcircle.
44. a) Draw the graph for the following y=4x-1.
(OR)
b) Draw the graph
for the following y=
x+3
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