JSUNIL TUTORIAL, SAMASTIPUR, BIHAR Sample Question Paper Class 10 Mathematics SA-1

JSUNIL TUTORIAL, SAMASTIPUR, BIHAR
Sample Question Paper
Class 10 Mathematics SA-1
Section-A
1. ABC is right angled at A. The value of tan B . tan C is _______
(a) tan B
(b) tan C
(c) 0
(d) 1
2. If the mean of 2, 4, 6, 8, 10, x, 14, 16 is 9 then the value of x is
(a) 10
(b) 11
(c) 12
(d) 13
3. The relationship in mean, median and mode is
(a) Mode = 2 median – 3 mean
(b) Mode = 2 median - mean
(c) Mode = 3 median + 2 mean
(d) Mode = 3 median – 2 mean
4. If x = tan 2° · tan 36° · tan 54° · tan 88° then the value of x is ______
(a) 45°
(b) 1
(c) 2
(d) 90°
5. Which of these numbers always ends with the digit 6? Where n is a natural number.
(a) 4n
(b) 2n
(c) 6n
(d) 8n
6. For a pair to be consistent and dependent the pair must have
(a) no solution
(b) unique solution
(c) infinitely many solutions (d) none of
these
7. Graph of every linear equation in two variables represents a ___
(a) point
(b) straight line
(c) curve
(d) triangle
8. If in ABC, AB = 6 cm, BC = 12cm and CA= 6 √3 cm then the measure of A is
(a) 30°
(b) 45°
(c) 60°
(d) 90°
9. The area of two similar triangles are in the ratio 9 : 16. The corresponding sides must be in
the
ratio ______
(a) 9 : 16
(b) 16 : 9
10. If sin (90 – ) cos = 1 and
(a) 90°
(c) 3 : 4
(d) 4 : 3
is an acute angle then = ____
(b) 60°
(c) 30°
(d) 0°
Section-B
11.A man goes 10 m due north and then 30 m due east. Find his distance from the starting
place.
12. Prove that 5+ 3 is an irrational
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13. If cot θ = 5/8, Evaluate [1 – sin2θ]/[1 – cos2θ]
14. If sum of the zeroes of the quadratic polynomial is 12 and product of them is 5, find the
polynomial.
15. In a triangle ABC, DE//BC and AD = 1 cm, BD = 2 cm. What is the ratio of the area of
triangle ABC to the area of triangle ADE?
16. In fig. DE II BC, AD/AB = 2/3 and AC = 18cm, find AE.
A
D
E
B
C
17.Find the median when mean = 20 and mode = 18.
18. Find the value of k for which the following system of equations has infinitely many
solutions.
2x + 3y = 4
( k + 2 )x + 6y = 3k + 2
Section-c
19. Check whether 12n can end with the digit 0 for any natural number n.
20. ABC is an isosceles triangle with AC = BC. If AB2 = 2AC2, prove that ABC is a right triangle.
21. Without using trigonometric tables, find the value of :
[sin 390 ] / [cos510 ]
– 3 ( sin2210 + sin2690 ) + 2sin2300
22. The difference of squares of two numbers is 180. The square of the smaller number is
8 times the larger number. Find the two numbers.
23. Find the missing frequencies f1 and f2 in the following frequency distribution table, it is
given that the mean of the distribution is 56.
C.I
0 - 20
20 - 40
40 - 60
60 - 80
80 - 100 100 - 120
Total
f
16
f1
25
f2
12
90
24. Prove
1
sin A
1
sin A
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sec A
10
tan A
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JSUNIL TUTORIAL, SAMASTIPUR, BIHAR
25. If one zero of the polynomial p(x)=3x3 – 5x2 – 11x – 3 is
1
, then find the other zeros of the
3
polynomial.
26. Two trains leave a railway station at the same time. The first train travels due west and the
second train due north. The first train travels 5 km/h faster than the second train. If after two
hours, they are 50 km apart, find their average speeds.
27. Prove that
28. Solve by factorization
sec
tan
1
tan
sec
1
m
x
2
n
n
1
m
cos
1
.
sin
2x .
Section-D
29. In a right triangle, prove that the ratio of areas of two similar triangles is equal to the ratio of
squares of their corresponding altitudes.
Apply the above theorem Solve the following:
ABC is a triangle and PQ is a straight line meeting AB in P and AC in Q. If AP=1cm, PB=3cm,
AQ=1.5cm, QC=4.5 cm. Prove that area of ∆APQ is one sixteenth of the area ∆ABC.
30. For the following frequency distribution, draw a cumulative frequency curve of more than
type and hence obtain the median value.
Class
0-10
10-20
20-30
30-40
40-50
50-60
60-70
15
20
23
17
11
9
interval
5
frequency
31. Prove that in a right angled triangle, the square of the hypotenuse is equal to the sum of the
squares on the other two sides.
33. In
ABC is an acute angled triangle. If tan (A + B – C) = 1 and sec (B + C – A) = 2 find A, B
,and < C
34. Show that the square of any positive integer is of the form 5q, 5q + 1, 5q + 4 for some
positive integer q.
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