**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 π =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) 𝑞+9𝑝 b)𝑝−9𝑞 c)𝑝+9𝑞 d)2𝑝+9𝑞

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 x^{2} – 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 21^{st} 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 𝑥^{2}−0.04=0are

a)
±0.2 b)±0.02 c)0.4 d)2

°

9) If 3𝑥+4𝑦∶𝑥+2𝑦 =9∶4 then 3𝑥+5𝑦∶3𝑥−𝑦 is

a)
4∶1 b)1∶4 c)7∶1 d)1∶7

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

11) If α, β are roots of the
equation x^{2} + 5x + 5 = 0, then equation whose roots are α + 1
and β + 1 is

(a) x^{2} +
5x – 5 = 0 (b) x^{2} +
3x + 5 = 0 (c) x^{2} + 3x + 1 = 0 (d)
none of these 12)

12) The𝑛^{𝑡}^{ℎ}^{ }term of the AP𝑎,3𝑎,5𝑎,…is

a)
𝑛𝑎 b)(2𝑛−1)𝑎 c)(2𝑛+1)𝑎 d)2𝑛𝑎

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 x^{2} + 2x + 2 =
0 are imaginary

**Reason
(R): **If discriminant D = b^{2} – 4ac < 0 then the roots of
quadratic equation ax^{2} + 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 31**^{st}** term of
an A.P. whose 11**^{th}** term is 38 and the 16**^{th}** term is
73.**

__SECTION – C__** (6x****3=18)**

26) Prove that √5 is an irrational number.

27) Find the zeroes
of *p*(*x*) = *x*2 – 2*x** *–
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 *:
4*x*^{2} – 2(*a*^{2} + *b*^{2}) *x *+
*a*^{2} *b*^{2} = 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 − n ^{2},
what is the first term (that is S_{1})? 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 ଷ ଼ 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) x^{2} – 5x – 500 = 0 (ii) x^{2} + 4x – 400 = 0 (iii) x^{2} + 5x – 500 = 0 (iv) x^{2} – 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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