The document is a mathematics sample test paper for class X, consisting of 34 questions divided into four sections (A, B, C, D) with varying marks. It includes a mix of theoretical and practical problems involving polynomials, geometry, equations, and areas. Students are instructed to answer all questions and maintain drawings as per the given measurements.

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MATHEMATICS
SAMPLE TEST PAPER (SEMSTER I)
CLASS X
Class:10 Max Mks:90
Time 3hrs No of pages: 3
General Instructions:
Ò All questions are compulsory.
Ò The question paper consists of 34 questions divided into four sections - A, B, C and D.
Ò Section - A contains 8 questions of 1 mark each,
Ò Section B is of 12 questions of 2 marks each, Section C is of 8 questions of 3 marks each and
Ò section D is of 6 questions of 4 marks each.
Ò The drawing should be maintained as per the given measurements.
SECTION A
1. Find the sum of the zero of the polynomial x2
-3
a) 0 b)1 c)4 d)3
2. all squares are ____
a) equal b)opposite c)congruent d)equatorial
3. If alpha and beta are the zeroes of the quadratic polynomial ax2+bx+c , then α+ß is
a)
c
a b)
− c
a c)
− b
a d)
a
c
4. If x > y > 0, x2
+ y2
= 13 and x y = 6, then y =
a)4 (b) 3 (c) 2 (d) none of these
5. What are similar triangles
6. If tangents PA & PB are drawn to a circle such that & chord AC is drawn || to the tangent PB
then
(i) 30
0
(ii) 45
0
(iii) 60
0
(iv) 90
0
7. roots are equal when
a)b2-4ac = 0 (b) b2-4ac >0 (c) b2
-4ac < 0 (d) b2
+4ac = 0
8. General quadratic formula
SECTION B
9. Give the terminating expansion of the number
21
12
10. solve 2x+3y = 22 and 2x-8y = -32 and hence find the value of 'm' for which y= mx+3

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11. solve the pairs of equation
1
2x +
1
3y = 2
12. Use Euclid division algorithm to find the HCF of 196 and 560
13. find the nature of the root 4x2
-4x-1 = 0
14.
In a equilateral triangle ABC , D is a point on side BC such that BD = BC. Prove that 9AD2
=
7AB2
15. Find the area of triangle formed by the vertices A (2,3) ,B (-2,0) and C (4,1)
16. Finds the relation between x and y if the points (x,y) (1,2) and (5,0) are collinear.
17. What is the area of triangle formed by the points (x1, y1 ), (x2, y2 ) and (x3, y3)
18. Find the coordinates of the points which divide the line segment joining A(-5,3) and B (4,8)
into four equal parts
19. Write the pairs of similar triangles in the symbolic form
20. If a line intersect sides AB and AC of a triangle ABC at D and E respectively and is parallel to
BC, prove that
AD
AB =
AE
AC
SECTION C
21. Show that any positive odd integer is of the form 4q+1, where q is some integer.
22. Express each number as a product of its prime factor a)456 b)532
23. Find the quadratic polynomial , the sum and the product of whose zeroes are -3 and 2 ,
receptively.
24. Solve the equation x+y = 5 and 2x-3y = 4 by elimination method
25. The altitude of a right triangle is 7 cm less tan its base. If the hypotenuse is 13cmfind the other
two ides.
26. Find the value of k for which the quadratic equation have equal roots x2
-kx+9 = 0
27.
ABC is a an isosceles triangle right angled at C. Prove that AB2
=2AC2
28. Find the area of quadrilateral whose vertices are (-4,-2) (-3,-5) (4,1) (5,6)
SECTION D
29. Divide 5x2
-x3
+3x+6 by x-1-x2
, and verify the division algorithm.
30. find out whether the lines representing the following pairs of linear equations intersect at a
point, are consistent or inconsistent 5x-3y = 11; -10x+6y = -22. then obtain the solution
graphically
31. use elimination method to find out all possible values of the linear equation
2x+3y = 8; 5x+8y =7
32. sum of the number and its reciprocal is 5
1
5 , find the number.
33. In the figure DE is parallel to OQ and DF is parallel to OR show that EF is parallel to QR.

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34. Find the area of triangle formed by joining the mid points of the sides of the triangle whose
vertices are (1,2) (2,1) and (0,3). Find the ratio of this area to the area of the given triangle.