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MODEL PAPER - 1
1
CONTINUOUS & COMPREHENSIVE EVALUATION
SUMMATIVE ASSESSMENT
MODEL PAPER - 1
MATHEMATICS - PAPER - I
X CLASS
Max Marks : 40]
[Time : 2 : 45 hrs
SECTION - I
Note : 1.
2.
7×1=7M
Answer all the following questions.
Each question carries one mark
.
d
a
1.
Determine “K” if K + 2, 4K – 6 and 3K – 2 are three consecutive terms of an A.P.
2.
Represent the following situation in the form of quadratic equation.
b
a
r
e
d
y
H
“The product of two consecutive numbers is 56”
3.
Why are 2, –3 zeroes of the polynomial
p(n) = x2 + x – 6
4.
4
Find the value of log
343
5.
State one nature of the roots of quadratic equation x2 – 7x + 12 = 0
6.
In what ratio is the segment joining the points (–3, 2) and (6, 1) divided by y-axis.
7.
Draw venn diagrams to show A – B and B – A
Note : 1.
2.
,
B
E
C
D
SECTION - II
6 × 2 = 12 M
Answer the following questions.
Each question carries two mark
8.
How can you say that the points A(1, 2), B(–3, 4) and C(7, –1) are collinear
9.
The point (1, 4) is the centroid of a triangle, two of whose vertices are (4, –8) and (–9, 7). Find
the third vertex.
10.
Determine the 25th term of an A.P. whose 9th term is –6 and common difference is
11.
Find the sum and the product of the roots of
5
4
3 x2 + 9x + 6 3 = 0
12.
Prove that
2 + 3 is an irrational number..
13.
If A = {3, 4, 5, 6, 7} B = {1, 6, 7, 8, 9}. Then verify n(A  B) = n(A) + n(B) – n(A  B)
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MATHEMATICS - PAPER - I
2
SECTION - III
Note : 1.
2.
14.
4 × 4 = 16 M
Internal choice is given in each question.
Each question carries four mark
(a) Find the co-ordinates of the points of tri-section of a segment joining A(–3, 2), B(9, 5).
(OR)
(b) If the area of the triangle formed with the vertices (x, 2x) (–2, 6) and (3, 1) is 5 sq. units find
“x”.
15.
(a) Find the value of K for which the equation (K – 12) x2 + 2(K – 12) x + 2 = 0 has equal roots.
(OR)
(b) A mathematics text book has a total of 1400 pages. It is broken up into two parts the second
part of the book has 50 pages more than the first part. How many pages are in each part of
the book.
16.
(a) (i)
Which term in the A.P. 5, 2, –1 ..... is –22 ?
(ii) Find the sum to 20 terms of the following A.P.
3, 5, 7, 9, .....
b
a
r
e
d
y
H
.
d
a
(OR)
(b) (i)
Write the formula for the nth term of a G.P. Hence find the 10th tern if 1 –
,
B
E
C
D
(ii) Show that 2 log
17.
1
1
+
+ .....
4 16
5
128
5
+ log
+ log = 0
8
125
2
(a) Draw the graph of y = x2 – x – 12 and find it’s zeroes.
(OR)
(b) Check equations 2x + 3y = 1, 3x – y = 7 are unique solutions, infinitely and many solutions
or no solutions. Solve them graphically.
SECTION - IV
Note : 1.
2.
18.
10 ×
1
=5M
2
Choose the correct answer.
Each question carries
1
2
mark.
Roots of the quadratic polynomial representing in one following.
(a) Complex numbers
(b) Real and equal
(c) Real and unequal
(d) All of these
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(
)
MODEL PAPER - 1
19.
Distance between the points (0, 0) and (a sin, acos) is.
(a) 1
20.
If
22.
(b) 0
1
3
(c) x2 + 3
(b) 5 only
b
a
r
e
d
y
H
(c) any prime
(b) –1
(c) 2
.
d
a
,
B
E
C
D
(c) Unique
(
)
(
)
(
)
(
)
(
)
(
)
(d) 2 or 5 only
(d) –3
If two straight lines intersect each other then their solutions.
(b) Finite
)
(d) x2 – 3
The slope of the line joining the points A(2, 5) and Q(x, 3) is 2 then x = _________
(a) Do not exist
26.
(b) x2 – 9
(
1
3
In the rational form of a terminating decimal number prime factor of the denominator is
(a) 1
25.
(d)
A quadratic polynomial, the sum of whose zeroes is “O” and one zero is 3, is
(a) 2 only
24.
(c) –3
)
(d) 4
1 1 1
+ ,
+ ... is
3
9 27
(b) 3
(a) x2 – 9
23.
(c) 2
(
(d) none of these
2
7
, x,
are in G.P. Then x =
7
2
The common ratio of G.P 1,
(a)
(c) a2
(b) a
(a) 1
21.
3
(d) Infinite
Which of the following statements is false ?
(a) The coefficient of x2 in the polynomial x3 – 6x2 + 7x + 10 is – 6
(b) The degree of constant term is zero
(c) The degree of the polynomial
(d)
27.
3 x2 – 4x + 6 is 2
1
is a quadratic polynomial
x  7x  12
2
If the system of equations has 2x + 3y = 5, 4x + ky = 10 infinitely many solutions then K = _________
(
(a) 1
(b)
1
2
(c) 6
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(d) 3
)