This document is a mathematics sample test paper for class 10, consisting of 37 questions divided into four sections: A (1 mark each), B (2 marks each), C (3 marks each), and D (4 marks each). Each section includes a variety of mathematical problems covering topics such as equations, geometry, and algebra. The test is designed to assess students' understanding of key mathematical concepts within a time limit of 3 hours.

1. 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 37questions divided into four sections - A, B, C and D.
Ò Section - A contains 10 questions of 1 mark each,
Ò Section B is of 9 questions of 2 marks each, Section C is of 10 questions of 3 marks each and
Ò section D is of 8 questions of 4 marks each.
Ò The drawing should be maintained as per the given measurements.
SECTION A
1. If the equation 2x2
+ 4x + k = 0 has real and distinct roots, then 4 (
a)k< 4 (b) k > 4 (c) k ≥ 4 (d) k ≤ 4
2. Two lines are given to be parallel. The equation of one of the lines is 4x+3y = 16. then equation
of the second line can be
a)3x+4y = 14 b)8x+6y = 28 c)12x+9y =42 d)-12x = 9y
3. If the area of the triangle formed by the points (k, 4/3) , (-2, 6) and (3, 1) is 5 sq units , then k is
a)3 b)5 c)2/3 d)3/5
4. The area of ∆ABC = 144sq.cm and area of ∆PQR = 25sq.cm. Altitude of ∆ABC = 6cm. If
∆ABC ∆PQR then the corresponding altitude of ∆PQR is __
a)2.5 cm b)5 cm c)12cm d)6cm
5. The number313 -310 is divisble by :
a) 3,15,5 b)3,10 c)2,3,13 d)2,3,10
6. The prime factors of 2*7*11*17*23+23 is
a)7 b)11 c)17 d)23
7. In the triangle, ABC, ABC = 90o
, then which of the following is true _____
a) AB2
= BC 2
+ AC2
b) BC2
= AB2
+ AC2
c) AC2
= 2AB2
+ 2BC2
d) AC2
= AB2
+ BC2
8. A man goes 15m due west and then 8m due north. The distance of the man fro the starting
point is
a)23cm b)23m c)17m d)7m
9. If first term of an AP is a and nth term is b, then its common difference is
a)(b-a)/n+1 (b) (b-a)/n-1 (c) (b-a)/n (d) none of these
10. If p(x,y) is coordinate then y is called as
a)ordinates b)magnitude c)integer d)median
SECTION B
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2. 11. Find the LCM and HCF of 20 and 16 by prime factorization
12. Prove that the number is irrational 7√3
13. Find all the zeroes of f(x)=24
-5x
14. Solve for x, 4√6 +x2
-13 x -2√6 = 0 by using a completing the square.
15. Find the 103th
term of the AP 4, 4 ½, 5, 5 ½, 6 ……..
16. solve for x and y px+qy = p-q; qx-y = p+q
17. If a diagonal of a square is 10√2 cm find its perimeter.
18. In ∆ABC, DE is parallel to BC. AD = 7.5cms. BD = 5.5cm, EC = 5cm find AE.
19. The total height of a plumb line is 16 cm, its radius is 8cm. Find its volume & total surface area.
SECTION C
20. Give the terminating or non terminating decimal expansion of the number
15
3 ,
17
8
21. Two rails are represent by the equation x+2y-4 = 0 and 2x+4y-12 = 0, represent this situation
geometrically
22. on dividing 3x3+4x2+5x-13 by a polynomial g(x) the quotient and remainder were 3x+10 and
16x-43 respectively . Find the polynomial g(x)
23. prove that 5+4√2 is ration or irrational number.
24. solve the equation by substitution method
3x-3 = 3; 9x-3y = 9
25. verify whether the equation as a linear equation x-3y-7 = 0; 3x-3y-15 = 0
26. Find the value of k for which the quadratic equation have equal roots kx(x-2)+6 = 0
27. Triangle ABE = ACD . Show that triangle ADE ~ triangle ABC
28. ABCD is a quadrilateral in which the diagonal AC and BD intersect at O such that
AO
OC =
BO
OD show that the quadrilateral ABCD is a trapezium.
29. Find the points on the y axis whose distances from the points (5, 7) and (8,-3) are in the ratio
1:3.
SECTION D
30. For the following pairs of linear equations intersect at a point, are consistent or inconsistent then
obtain the solution graphically 2x-2y-2 = 0; 4x-4y-5 = 0
31. Half the perimeter of rectangular garden, whose length is 4m more than its width 36m. Find the
dimension of the garden.
32. BY Euclid's algorithm , find the largest number which divides 650 and 1170.
33. Solve the pairs of equations by reducing them to a pair of linear equations.
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3. 1
(3x+ y) +
1
(3x− y) =
3
4
34. If the square of the number is added to 3 times the number, the sum is 28. find the other
number.
35. Find the discrimination of the quadratic equation 2x2-4x+3 = 0and hence find the nature of the
roots.
36. Draw the graph of the equation x-u+1 = 0 and 3x+2y-12 = 0. Determine the coordinates of the
vertices of the triangles formed by these lines and x- axis.
37. The median of the following data is 525. Find x and y if the sum of all frequencies is 100.w
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