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Class 10 Half Yearly Term 1 sample model Paper Download CBSE Pattern

Class 10 half yearly sample paper pdf

Class 10 half yearly sample paper maths

Class 10 term 1 sample paper 


TERM I EXAMINATION 

MATHEMATICS (Code No.041)

 

CLASS: X                 MAX. MARKS: 80                                                                     

TIME: 3Hours

 

GENERAL INSTRUCTIONS:

 1. This Question Paper has 5 Sections A, B, C, D and E.

 2. Section A has 20 MCQs carrying 1 mark each

3. Section B has 5 questions carrying 02 marks each.

4. Section C has 6 questions carrying 03 marks each.

 5. Section D has 4 questions carrying 05 marks each.

 6. Section E has 3 case based integrated units of assessment (04 marks each) with sub- parts of the values of 1, 1 and 2 marks each respectively.

7. All Questions are compulsory. However, an internal choice in 2 Qs of 5 marks, 2 Qs of 3 marks and 2 Questions of 2 marks has been provided. An internal choice has been provided in the 2marks questions of Section E

8. Draw neat figures wherever required. Take Ο€ =22/7 wherever required if not stated.

_________________________________________________________________

                                                SECTION – A                                                (20 x 1=20)

1) The sum of the exponents of prime factors in the prime factorization of 196  is

 (a) 3                                 b)4                               c)5                               d)2

 

2) The first term of AP is p and the common difference is q, then its10th term is

    (a)  π‘ž+9𝑝                       b)𝑝−9π‘ž                                   c)𝑝+9π‘ž                         d)2𝑝+9π‘ž

 

3) The ratio between the LCM and HCF of 5, 15, 20 is:

 (a) 9 : 1                (b) 4 : 3                        (c) 11 : 1                      (d) 12 : 1

 

4) The quadratic equation   x2 – 4x + 6 = 0 has

(a)Two distinct real roots                                    (b)two equa lreal roots

      (c)No real roots                                         (d)more than 2realroots

 

     5) Zeroes of p(z) = z2 – 27 are:

               (a)  2√3, 3√3    (b)  3√3, -3√3    (c)  √3 ,- √3     (d)  2√2,- 2√2

 

     6) The pair of equations ax + 2y = 7 and 3x + by = 16 represent parallel lines if
        (a) a = b           (b) 3a = 2b    (c) 2a = 3b       (d) ab = 6

     7)  The 21st term of the A.P., whose first two terms are 3 and 4, is: 

  (a)  17             (b)  137          (c)  143                       (d)  -143.

   8) The roots of the quadratic equation π‘₯2−0.04=0are

        a)  ±0.2                             b)±0.02                       c)0.4                           d)2

°

   9) If 3π‘₯+4𝑦∶π‘₯+2𝑦 =94 then 3π‘₯+5𝑦∶3π‘₯𝑦 is

        a)  41                               b)14                           c)71                           d)17

 


10) The values of x and y in the given figure are

 

 

 

11) If Ξ±, Ξ² are roots of the equation x2 + 5x + 5 = 0, then equation whose roots are Ξ± + 1 and Ξ² + 1 is

(a)      x2 + 5x – 5 = 0              (b) x2 + 3x + 5 = 0                 (c) x2 + 3x + 1 = 0      (d) none of these 12)

 

12) Theπ‘›π‘‘β„Ž term of the APπ‘Ž,3π‘Ž,5π‘Ž,…is

            a)  π‘›π‘Ž                     b)(2𝑛−1)π‘Ž                   c)(2𝑛+1)π‘Ž                   d)2π‘›π‘Ž

13)  If x = a, y = b is the solution of the pair of equations x – y = 2 and x + y = 4, then the respective values of a and b are
      a) 3, 5               (b) 5, 3                    (c) 3, 1                    (d) –1, –3

14) The pair of equations x = 4 and y = 3 graphically represents lines which are

a)parallel         (b) intersecting at (3, 4)       (c) coincident                (d) intersecting at (4, 3)

 

15) The perimeters of two similar triangles are 25 cm and 15 cm respectively. If one side of first triangle is 9 cm., what is the corresponding side of the other triangle?

(a) 5.4       (b) 3.5 (c) 5.5 (d) 4.5

16)
In figure DE || BC. If BD = x – 3, AB = 2x. CE = x – 2 and AC = 2x + 3. Find x.

a.    3                        (b) 4                            (c) 9                                        (d) none of these

 

17) In the figure, AP = 3 cm, AR = 4.5 cm, AQ = 6 cm, AB = 5 cm and AC = 10 cm. Find the length of AD.


(a) 6.5                     (b) 7.5                         (c) 5.5                         (d) 4.5

 

18) The value of k for which the equation x2 + 2(k + 1)x + k2 = 0 has equal roots is

      (a) – 1                           (b) ½                               (c) 1                (d) none of these

 

19)   In the following questions, a statement of assertion (A) is followed by a statement of Reason (R). Choose the correct answer out of the following choices.

Assertion (A): For no value of n, where n is a natural number, the number 6n ends with the digit

zero.

Reason (R): For a number to end with digit zero, its prime factors should have 2 and 5.

a.      Both A and R are true and R is the correct explanation of A.

b.      Both A and R are true but R is not the correct explanation of A.

c.      A is true but R is false.

d.     A is false but R is true.

20)    Assertion (A): The roots of the quadratic equation x2 + 2x + 2 = 0 are imaginary

Reason (R): If discriminant D = b2 – 4ac < 0 then the roots of quadratic equation ax2 + bx + c = 0 are not real i.e. imaginary.

a.      Both A and R are true and R is the correct explanation of A.

b.      Both A and R are true but R is not the correct explanation of A.

c.      A is true but R is false.

d.     A is false but R is true.

                                                                                                                                                     half yearly sample paper class 10 

half yearly question paper class 10                                              

 

SECTION – B                                       (5x 2=10)

 

21)  Can we have any n N, where 6 n ends with the digit zero?

 

 

 

22) Find a quadratic polynomial whose zeroes are 1/4 and -1

 

23)  In the below Figure, ABCD is a rectangle. Find the values of x and y.

 

 

24)  The sum of the squares of three consecutive positive integers is 50. Find the integers.

25)   Find the 31st term of an A.P. whose 11th term is 38 and the 16th term is 73.

 

SECTION – C                                                            (6x 3=18)

26)  Prove that √5 is an irrational number.

 

27) Find the zeroes of p(x) = x2  2x – 8. quadratic polynomials and verify the relationship between the zeroes and their coefficients.

28)  The sum of the digits of a two digit number is 9. The number obtained by reversing the order of digits of the given number exceeds the given number by 27. Find the given number.

 

29) How many three digit numbers are divisible by 7?

 

30) Solve for x : 4x2 2(a2 + b2) x + a2 b2 = 0.

 

 

31) In the figure, if LM || CB and LN || CD, prove that AM/AB = AN/AD:

 

SECTION – D                                       (8x 4=32)

32)     If the sum of the first n terms of an AP is 4n − n2, what is the first term (that is S1)? What is the sum of the first two terms? What is the second term? Similarly find the 3rd, the 10th and the nth terms.

33)  A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of stream. 5

[or]

Two water taps together can fill a tank in 9 ΰ¬· hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

34)  State and prove Basic Proportionality theorem.

35)  On a morning walk three persons step off together and their steps measure 40 cm, 42 cm, 45 cm, what is the minimum distance each should walk so that each can cover the same distance in complete steps?

(b) There are 576 boys and 448 girls in a school that are to be divided into equal sections of either boys or girls alone. Find the total number of sections thus formed.

 

 

SECTION – E

36) Raj and Ajay are very close friends. Both the families decide to go to Ranikhet by their own cars. Raj’s car travels at a speed of x km/h while Ajay’s car travels 5 km/h faster than Raj’s car. Raj took 4 hours more than Ajay to complete the journey of 400 km.

 

(a) What will be the distance covered by Ajay’s car in two hours?

 (i) 2(x + 5) km      (ii) (x – 5) km   (iii) 2(x + 10) km    (iv) (2x + 5)km

(b) Which of the following quadratic equation describe the speed of Raj’s car?

   (i) x2 – 5x – 500 = 0   (ii) x2 + 4x – 400 = 0   (iii) x2 + 5x – 500 = 0   (iv) x2 – 4x + 400 = 0

(c) What is the speed of Raj’s car?

  (i) 20 km/hour    (ii) 15 km/hour   (iii) 25 km/hour     (iv) 10 km/hour

(d) How much time took Ajay to travel 400 km?

  (i) 20 hours   (ii) 40 hours   (iii) 25 hours   (iv) 16 hours

37)  A Mathematics Exhibition is being conducted in your School and one of your friends is making a model of a factor tree. He has some difficulty and asks for your help in completing a quiz for the audience.

Observe the following factor tree and answer the following:

(i)     What will be the value of x?

(ii)     What will be the value of y?

(iii)      What will be the value of z?

(iv)      Write the prime factorisation of 13915.

38) Manpreet Kaur is the national record holder for women in the shot-put discipline. Her throw of 18.86m at the Asian Grand Prix in 2017 is the maximum distance for an Indian female athlete. Keeping her as a role model, Sanjitha is determined to earn gold in Olympics one day. Initially her throw reached 7.56m only. Being an athlete in school, she regularly practiced both in the mornings and in the evenings and was able to improve the distance by 9cm every week. During the special camp for 15 days, she started with 40 throws and every day kept increasing the number of throws by 12 to achieve this remarkable progress.

(i) How many throws Sanjitha practiced on 11th day of the camp?

(ii) What would be Sanjitha’s throw distance at the end of 6 weeks?

(or)

 When will she be able to achieve a throw of 11.16 m?

(iii) How many throws did she do during the entire camp of 15 days ?



Class 10 term 1 sample paper 

Class 10 term 1 sample paper maths

sample paper class 10

sample paper class 10 maths

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