X Practice Paper 1

8/12/2019 X Practice Paper 1

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Demo Paper Mathematics

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SUMMATIVE ASSESSMEnT SAI)ModEl PrAcTIcE PAPEr dEMo

Key features of Model Practice Papers:

Summative Assessment Papers are based on the syllabus

prescribed by the CBSE Board for SA IExamination.

They are prepared exactly as per the sample papers suggested by

the CBSE Board.

The questions are selected in such a way that students get

acquainted with each and every concept of the prescribed syllabus

for SA I.

All the questions provided in the papers, are supported with detailed

and authentic solutions.

The Summative Assessment papers will give you chance to

practice more and more before the commencement of actual

examination, for obtaining high scores.

Class X MATHEMATICS


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Class X MATHEMATICS

SUMMATIVE ASSESSMENT (SA I)

MODEL PRACTICE PAPER - DEMO

2011 2012

Time allowed: 3 hours Maximum Marks: 80

General Instructions:

(i) All questions are compulsory.

(ii) The question paper consists of 34 questions divided into four sections A, B, C

and D.

(iii) Section A contains 10 questions of 1 mark each, which are multiple choice type

questions, Section B contains 8 questions of 2 marks each, Section C contains

10 questions of 3 marks each, and Section D contains 6 questions of 4 marks

each.

(iv) There is no overall choice in the paper. However, internal choice is provided in

one question of 2 marks. 3 questions of 3 marks and two questions of 4 marks.

(v) Use of Calculators is not permitted.


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SECTION A

Question numbers 1 to 10 carry 1 mark each. For each of the questions 1-10, four

alternative choices have been provided of which only one is correct. You have to

select the correct choice.

Q1. Which of the following relation is false?

(a) HCF ( ) 17 (b) LCM ( ) HCF ( )

(c) LCM ( ) 12121 (d) None of these.

Q2. Which one of the following is true?

(a) Sum of two irrational numbers is a rational number.

(b) Sum of rational and irrational numbers is a rational number.

(c) Product of two different irrational number is an irrational number.

(d) Product of rational and irrational numbers is a rational number.

Q3. Which of the following statement is false?

(a) A real number is zero of a polynomial if .

(b) A fourth degree polynomial is called a biquadratic polynomial.

(c) A Polynomial of degree zero is called a constant polynomial.

(d) None of these.

Q4. If the product of zeros of a polynomial is 4, then

value of ( is

(a) (b)

(c) (d) None of these.


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Q5. Sum of two numbers is 35 and their difference is 13, then the numbers are

(a) 34, 1 (b) 23, 12

(c) 24, 11 (d) None of these.

Q6. The given pair of linear equations are and , the value of

is

(a) (b)


Q7. In a ABC, D and E are the points on the sides AB and AC respectively such that

AD , DB AE and EC , then relation between

DE and BC is

(a) Parallel (b) Perpendicular

(c) Intersecting (d) None of these.

Q8. In a ABC, D and E are the points on the sides AB and AC respectively such that

DE BC. If AD , DB AE and EC , then

value of is

(a) 1 (b) 2

(c) 3 (d) 4

Q9. If , and then is equal to

(a) (b)



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Q10. Median of a given frequency distribution is found graphically with the help of

(a) Ogive (b) Histogram

(c) Frequency curve (d) None of these.


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SECTION B

Question numbers 11 to 18 carry 2 marks each.

Q11. Find the largest positive integer that will divide 396, 434 and 540 leavingremainders 5, 9 and 13 respectively.

Q12. If the zeros of the polynomial are prove

that .

Q13. Solve: and ; find if .

Q14. Evaluate:

OR

If are the interior angles of a triangle , prove that:

Q15. Given two triangles are , Find E

B

E

C4 cm

3.8 cm 3 cm

D

6 cm 7.6 cm

6

80

8 cmAF

B

E

C4 cm

3.8 cm 3 cm

D

6 cm 7.6 cm

6

80

8 cmAF


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SECTION C


Q19. Find the HCF and LCM of 288, 360 and 834 by prime factorization method.

Q20. Show that 7 is irrational.

OR

Prove that is irrational.

Q21. A man walks a certain distance with certain speed. If he walks an hour

faster, he takes 1 hour less. But, if he walks 1 an hour slower, he takes 3more hours. Find the distance covered by the man and his original rate of

walking.

OR

2 men and 7 boys can finish a piece of work in 4 days while 4 men and 4 boys

can finish it in 3 days. Find the time taken by one man along and that by one

boy alone to finish the work.

Q22. Find the value of and so that is divisible by

Q23. In a right angled at B, if AB 12 and BC 5 ,

Prove that

Q24. Given that , find the value of .


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Q25. is the bisector of If

, find

Q26. If and , prove that .

Q27. If the mean of the following distribution is 16, find the value of .

OR

4 6 10 14

1 3 4 2 2

A

15 cm

22 cm

B D C


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Find the median of the following data:

Q28. The mean of the following frequency distribution is 30. Find the value of .

Class interval Frequency

25.5 34.5 4

35.5 44.5 5

45.5 54.5 6

55.5 64.5 9

65.5 74.5 11

75.5 84.5 12

85.5 94.5 8

95.5 104.5 5

Class 0.5 19.5 20.5 39.5 40.5 59.5 60.5 79.5 80.5 99.5

Frequency 5 10 2 5


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SECTION D


Q29. Applying the division algorithm to find the quotient and remainder on dividing

by .

Q30. In an equilateral triangle the side BC is trisected at D.

Prove that

OR

In figure, D and E trisect BC. Prove that

Q31. Prove that

OR

Prove that

Q32. If and , prove that

A

DB E C


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Q33. Solve:

Q34. Compute the median from the following data:

Mid-value Frequency

115 6

125 25

135 48

145 72

155 116

165 60

175 38

185 22

195 3


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SECTION A

A1. Correct option:d

Explanation: Prime factorization are

HCF ( ) 17, LCM ( ) 12121

and LCM ( ) HCF ( ) are correct.

A2. Correct option: c

Explanation: Product of two different irrational number is irrational number.



Explanation: Given polynomial

product of zeros 4

4


Explanation: Let two numbers are and ,

Then + 35 (i)

and 13 (ii)

SOLUTION OF MODEL PRACTICE PAPER - DEMO


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Adding (i) and (ii) equations after that we get 2 48 or 24

Substituting the value of 24 in (i)

+ 35 or 11

A6. Correct option:a

Explanation: (i)

and (ii)

multiply (i) by , we get

(iii)

Adding equation (ii) and (iii), we get

or

A7. Correct option:a

Explanation: Given, and

and

Hence, (by basic proportional theorem)


A9. Correct option:b


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SECTION B

A11. According to question, largest positive integer is a factor of 396 5, 434 9 and

540 13.

Clearly, required number is the HCF of 391, 425 and 527.

Using the factor tree the prime factorizations of 391, 425 and 527 are as follows:

391 17 23, 425 17 and 527 17 31

HCF of 391, 425 and 527 is 17

Hence, required number is 17.

A12. Given are the zeros of the

Sum of the zeros

1 (i)

Product of the zeros (

(ii)

From (i) and (ii), we get

1 Proved.

A13. Given system of equation is

(i)

(ii)


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Substitute the value of from (ii) in (i), we get

Putting in , we get

Putting , in , we get

0

A14. We have,

OR

In triangle ,we have

Proved.


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A15. In triangles , we have

Therefore, by SSS-criterion of similarity, we have

A D, B F and C E, D 80,F 60

Hence, C E 60 (Since, A + B + C = 180)

A16. In , we have .

By Thales Theorem,

A

E

C

D B

B

E

C4 cm

3.8 cm 3 cm

D

6 cm 7.6 cm

6

80

8 cmAF

B

E

C

4 cm

3.8 cm 3 cm

D

6 cm 7.6 cm

6

80

8 cmAF


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A17. Less than type cumulative frequency distribution:

A18. Given frequency table

Marks obtained 0 15 15 30 30 45 45 60 60 75

Number of Students 10 13 18 5 14

Here, maximum frequency is 18 and the corresponding class is 30 45 .

So, 30 45 is the modal class. We have,

Lower limit of modal class

Size of the class interval

Frequency of the modal class

Frequency of the class preceding the modal class

Frequency of the class succeeding the modal class

Formula of obtain the mode

Daily income

(in rupees)

Number ofWorkers

or Frequency (

Less than

Daily income Number of Workers

or (

150 250 11 250 11

250 350 13 350 24

350 450 7 450 31

450 550 5 550 36

550 650 9 650 45


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SECTION C

A19. Using the factor tree for the prime factorization of 288, 360 and 834

288 ,

360 and

834

HCF of 288, 360 and 834 24 and

LCM of 288, 360 and 834 5760.

A20. Let us assume, on contrary, that 7 is rational.

Suppose 7 , where and are co-primes and .

Rearranging, we get

Since 7, and are integers, is rational, and so is rational. But this

contradicts the fact that is irrational. So we conclude that 7 is irrational.

OR

Assume that is rational.

Then there exist positive integers and such that = ,

Where and are co-prime and .

So, .(i)

Therefore, by theorem is divisible by 7 and so is divisible by 7.

So, we can write for some integer .


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Substituting in (i) we get;

.(ii)

So, by theorem is divisible by 7 and also is divisible by 7.

Therefore, and have at least 7 as a common factor. But this contradicts the

fact and are co-prime. So our assumption that is rational is incorrect

Hence. is irrational.

A21. Let the original speed be and total time taken be hrs. Then,

Distance

According to question, since distance covered in each case is same.

(i)

and, (ii)

adding (i) and (ii), we get

Substituting the value of in (ii), we get

OR

Suppose that one man alone can finish the work in days and one boy alone

can finish it in days. Then,

One mans one days work

One boys one days work

2 mens one days work


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7 boys one days work

Since 2 men and 7 boys can finish the work in 4 days.

(i)

Again, 4 men and 4 boys can finish the work in 3 days.

(ii)

Putting and in equations (i) and (ii), we get

(iii)

(iv)

Substituting the value of in (iii), we get

and


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Therefore, and

Thus, one man alone can finish the work in 20 days one boy alone can finish the

work in 30 days.

A22. If is exactly divisible by , then the remainder

should be zero.

On dividing, we get

Remainder 8

Now, Remainder 8

8)

and 8

and .

8


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A23. By Pythagoras theorem, we have

and .

LHS

RHS Proved.

A24. Let A and B

or


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A25. Let then

Since is the bisector of

A

15 cm

22 cm

B D C


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A26. Since and ; hence

(Alternate Angles)

Now in and

(Both 90)

Hence

From AA-criterion,

Proved.


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A27. Frequency distribution table:

We have 12, 92 + and mean 16

Mean

16

.

OR

65 75 is the median class. (where lise in of 35)

= 65, = 11, = 24, = 10

Median =

4 1 4

6 3 18

10 4 40

2

14 2 28

12 92 +

Classes

(Inclusive form)

Classes

(Exclusive form)

Frequency

( )

Cumulative

frequency ( )

25.5 34.5 25 35 4 4

35.5 44.5 35 45 5 9

45.5 54.5 45 55 6 15

55.5 64.5 55 65 9 24

65.5 74.5 65 75 11 35

75.5 84.5 75 85 12 47

85.5 94.5 85 95 8 55

95.5 104.5 95 105 5 60

= 60


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= 65 + 70.45 (approximate)

A28.

, , given

Class

(Inclusive form)

Class

(Exclusive form)

Frequency Class mark

0.5 19.5 020 5 10 50

20.5 39.5 2040 30 30

40.5 59.5 4060 10 50 500

60.5 79.5 6080 2 70 140

80.5 99.5 80100 5 90 450


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A30. Given: In , be a point on such that

To Prove:

Construction: Draw Join

Proof: In , and we have

and,

So, by RHS criterion of similarity, we have

Thus, we have

and (i)

Since . Therefore, is an acute triangle.

CB

A

D E


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OR

Given, D and E trisect BC

Therefore,

Let

Then, and

In right triangles and we have

, (i)

(ii)

DB E C

A


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and

(iii)

Now,

[From (i) (ii) and (iii)]

Proved.

A31. We have LHS

LHS

LHS

LHS

LHS

LHS

LHS

LHS RHS Proved.

OR

We have, LHS


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LHS

LHS

LHS

LHS (i)

and, RHS

RHS

RHS

RHS

RHS

RHS (ii)

From (i) and (ii)

LHS =RHS Proved.

A32. We have,

[where,


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Now,

Hence,

Proved.

A33. We have, (i)

(ii)

(iii)

From equation (i), we get

Substituting in equation (ii), we get

(iv)

Adding equation (iii) and (iv), we get

Putting in equation (iii), we get

Putting in equation (i), we get

Hence, and .


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X Practice Paper 1

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