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X Mathematics SA I Sample Paper 1

Total marks of the paper:

90

Total time of the paper:

3.5 hrs

General Instructions: 1. All questions are compulsory. 2. The question paper consists of 34 questions divided into four sections A, B, C, and D. Section – A comprises of 8 questions of 1 mark each, Section – B comprises of 6 questions of 2 marks each, Section – C comprises of 10 questions of 3 marks each and Section – D comprises of 10 questions of 4 marks each. 3. Question numbers 1 to 8 in Section – A are multiple choice questions where you are to select one correct option out of the given four. 4. There is no overall choice. However, internal choice has been provided in 1 question of two marks, 3 questions of three marks each and 2 questions of four marks each. You have to attempt only one of the alternatives in all such questions. 5. Use of calculator is not permitted. 6. An additional 15 minutes has been allotted to read this question paper only.

Questions:

1]

The decimal expansion of the rational number after A.

will terminate

[Marks:1]

one decimal place

B. two decimal places C. three decimal places D. more than three decimal places 2]

For some integer 'm' every odd integer is of form:

[Marks:1]

A.

m

B. m + 1 C. 2 m D. 2m + 1 3] If one of the zeroes of the quadratic polynomial (k - 1) x2 + 1 is -3, then the value of k is

[Marks:1]

A. B. C. D. 4]

The lines representing the linear equations 2x - y = 3 and [Marks:1]

4x - y = 5: A.

intersect at a point

B. are parallel C. are coincident D. intersect at exactly two points 5]

The mean of 6 numbers is 16. With the removal of a number the mean of remaining numbers is 17. The number removed is: A.

2

[Marks:1]

B. 22 C. 11 D. 6 6]

If x = 3 sec2θ- 1, y = tan2θ - 2 then x - 3y is equal to A.

[Marks:1]

3

B. 4 C. 8 D. 5 7]

If cos θ + cos2 θ = 1, the value of (sin2 θ + sin4 θ) is A.

[Marks:1]

0

B. 1 C. -1 D. 2 8]

If ABC ~ RQP,

A = 80°,

B = 60°, the value of

A.

P is

[Marks:1]

60°

B. 50° C. 40° D. 30° 9]

Use Euclid's division algorithm to find H.C.F. of 870 and 225.

[Marks:2]

10]

Solve 37x + 43y = 123, 43x + 37y = 117. OR [Marks:2]

x+

= 6, 3x -

= 5.

11]

are the roots of the quadratic polynomial p (x) = x2 - (k + 6)x + 2 [Marks:2]

(2k - 1). Find the value of k, if

.

12]

In fig., AB

BC, GF

BC, DE

BC. Prove that

ADE ~ GCF.

[Marks:2]

13] [Marks:2]

If cot

14]

=

, find the value of

Find the median class and the modal class for the following

[Marks:2]

distribution. C.I. f

135 140 4

140-145 7

11

15]

Show that 5 +

is an irrational number. OR

Prove that

16]

[Marks:3]

is an irrational number.

If Îą and ďŁ¨ are the zeroes of the quadratic polynomial f(x)= x2-2x+1, find [Marks:3]

a quadratic polynomial whose zeroes are

17]

and

.

If in a rectangle, the length is increased and breadth is reduced each by 2 metres, the area is reduced by 28 sq mtrs.If the length is reduced by 1 metre and breadth is increased by 2 metres, the area is increased by 33 sq mtrs. Find the length and breadth of the rectangle.

[Marks:3]

OR A leading library has a fixed charge for first three days and an additional charge for each day thereafter. Bhavya paid Rs 27 for a book kept for seven days, while Vrinda paid Rs 21 for a book kept for five days. Find the fixed charge and the charge for each extra day. 18]

For what values of a and b does the following pairs of linear equations have an infinite number of solutions: 2x + 3y = 7; a (x + y) -b (x - y) = 3a + b - 2

[Marks:3]

19]

In figure, XY || QR,

and PR = 6.3 cm. Find YR.

[Marks:3]

20]

Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.

[Marks:3]

21] [Marks:3]

Find the value of

22]

[Marks:3]

In triangle ABC, right angled at B, AB = 5 cm, ACB = 30째. Find the length of BC and AC.

23]

If mean of the following data is 86, then what is the value of p? Wages 50-60 60-70 70-80 (in [Marks:3] Rs.) Number 5 of workers

24]

3

4

Find the modal age of 100 residents of a colony from the following data : Age 0 in yrs. (mor e than or equal to)

10

20

30

[Marks:3]

No. of Persons

100 90 75

25] A number of the form 15n, where n this statement.

26]

27]

N (the set of natural numbers), can never end with a zero. Justify [Marks:4]

Solve the equations 2x âˆ’ y +6 = 0 and 4x + 5y âˆ’ 16 = 0 graphically. Also determine the coordinate of the vertices of the triangle formed by these lines and the x-axis.

The remainder on dividing x3 + 2x2 + kx + 3 by x - 3 is 21. Sanju was asked to find the quotient. He was a little puzzled and was thinking how to proceed. His classmate gunjan helped him by suggesting that he should first find k and then proceed further.

[Marks:4]

[Marks:4]

Explain how the question was solved.

28] In triangleABC, D is the mid-point of BC and AE

BC. If AC > AB. Show that: AB2 = AD2 - BC x DE

[Marks:4]

+ OR In a right angled triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides.

29]

In figure,

ABC is right angled at C. DE

3 cm and DC = 2 cm, then prove that the lengths of AE and DE.

AB. If BC = 12 cm. AD = and hence find [Marks:4]

30]

Prove that: [Marks:4]

OR

Prove that:

= sec A + tan A

31] [Marks:4]

If sec θ + tan θ = p, show that

= sin θ.

32] [Marks:4]

33]

For the data given below draw less than ogive curve.

Marks

0 - 10

10 - 20 [Marks:4]

Number of 7 students

34]

10

In the distribution given below 50% of the observations is more than 14.4. Find the values of x and y, if the total frequency is 20.

Class Interval Frequency

[Marks:4]

0-6

6 - 12 4

x

12 - 18