Class 7 Sample Paper Maths (Half Yearly)

SAMPLE
PAPER
Half Yearly Examination

Prepared For
NCERT BASED SYLLABUS
Applicable For
CBSE BOARD AND STATE BOARD USING NCERT

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HALF YEARLY EXAMINATION
SAMPLE QUESTION PAPER

Class - VII Subject – Mathematics
Time – 3 Hours Maximum Marks- 80

Attempt all questions. However there are internal choices. Rough work to be done in the right margin.
General Instructions
1. The Question paper contains two parts :-Part – I& Part – II.
2. Both parts have internal choices.
3. Part I consists of two sections.
4. Section 1 has 16 questions of 1 mark each. Internal choice is there in 5 questions.
5. Section 2 has 4 questions on case study. Each case study has case based 5 sub parts. Examinee has to be
attempt any 4 sub parts out of 5 i.e. 16 marks.
6. Question no. 21 to 26 are very short answer type questions of 2 marks each i.e. 12 marks.
7. Question no. 27 to 33 are short answer type questions of 3 marks each i.e. 21 marks.
8. Question no. 34 to 36 are long answer type questions of 5 marks each i.e. 15 marks.
9. Internal choices is provided in 2 questions of 2 marks, 2 questions of 3 marks each and 1 question of five
marks.

Part - I
Section – A (1 x 16=16)
1. Write the additive identity and multiplicative identity for integers.
2. Find : 70 × (–19) + (–1) × 70 using distributive property.
3. Evaluate : 13 ÷ [(–2) + 1]
OR
3. What must be subtracted from –7 to obtain –15 ?
4. Write four equivalent fractions of .

5. Find (a) of 40 and (b) of 48.
6. Arrange in descending order :
, , ,
OR
6. Simplify : –

7. Write the equation for the statements :
(a) If you subtract 5from 6 times a number, you get 7.
(b) One third of a number plus 5 is 8.

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8. The runs scored by 11 members of a cricket team are
25, 39, 53, 18, 65, 72, 0, 46, 31, 08, 34. Find the median score.
9. Find the mean of the numbers :
7.6, 6.8, 8.5, 9.4, 5.9, 6.4, 9.1 and 4.7.
OR
9. Find the mean of first five prime numbers.
10. Find the angle which is its own compliment.
11. Find the angle which is double of its supplement.
12. In ABC, A = 35o, B = 65 o, find the measure of C.
13. Two angles of a triangle are equal and the third angle measures 70o. Find the measure of each of the
unknown angles.
OR
13. Draw a triangle in which two altitudes of the triangle are two of its sides.
14. State the correspondence between the vertices, sides and angles of the pair of congruent triangles if
ABC EFD.
15. When are two circles congruent ?
OR
15. When are all squares congruent ?
16.

Applying congruence criterion, if these triangles are congruent, write the steps in symbolic form.
Part - I
Section – B (4 x 4=16)
CASE STUDY BASED
Attempt any four subparts out of five subparts.
17. Read the passage and answer four out of five questions given below :-
In a class of strength 60, 20 students like Mathematics, 15 students like Physics, 25 students like
chemistry.
(i) The fraction of students who like Mathematics is
(a) (b) (c) (d)
(ii) The fraction of students who like Physics is

(a) (b) (c) (d)
(iii) The fraction of students who like Chemistry is

(a) (b) (c) (d)

(iv) The fraction is

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(a) > (b) < (c) = (d) None of these
(v) Find the fraction of students who like both Mathematics and Physics

(a) (b) (c) (d)

18. The marks in a subject for 12 students are as follows :-
31, 37, 35, 38, 42, 23, 17, 18, 35, 25, 35, 29
For the given data,
(i) The mean is
(a) 25 (b) 30.41 (c) 33 (d) 35
(ii) The mode is
(a) 25 (b) 30.41 (c) 33 (d) 35
(iii) The median is
(a) 25 (b) 30.41 (c) 33 (d) 35
(iv) The Range is
(a) 25 (b) 30.41 (c) 33 (d) 35
(v) How many students have marks more than mean marks ?
(a) 7 (b) 6 (c) 8 (d) 5
19. An equation is a mathematical sentence that uses an equality sign to show that two expressions have
the same value. To solve an equation that contains a variable, that makes the equation true,this value
of the variable is called the solution of the equation. Read the problems carefully and solve the
equations :
(i) The solution of the equation 3x + 5 = 0 is
–
(a) (b) –5 (c) (d) 5
(ii) –1 is not a solution of the equation
(a) x + 1 = 0 (b) x – 1 = 2 (c) 2y + 3 = 1 (d) 2p + 7 = 5
(iii) 2x + _____ = 11 has the solution –4
(a) 19 (b) 28 (c) 18 (d) 29
(iv) One fourth of a number is 20 less than the number itself. The number is
(a) (b) (c) (d)
(v) 9 added to twice a number gives 13. The number is -
(a) 2 (b) 4 (c) 3 (d) 1
20. From the figure, name of the pair of angles asked -

(i) The corresponding angles are -

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(a) (a, e) (b) (b, c) (c) (a, d) (d) (e, f)
(ii) The pair of co-interior allied angles are -
(a) (e, h) (b) (d, e) (c) (a, d) (d) (f, g)

(iii) The pair of interior alternate angles are -
(a) (a, h) (b) (b, g) (c) (d, f) (d) (c, f)
(iv) The pair of vertically opposite angles are -
(a) (b, d) (b) (f, g) (c) (g, h) (d) (c, f)
(v) The linear pair of angles are -
(a) (d, e) (b) (c, f) (c) (a, b) (d) (d, f)

Part - II
Section – C (2x 6 = 12)
21. Match the following :
Column I Column II
(a) a ÷ (–1) (i) a
(b) 1÷a (ii) 1
(c) (–a) ÷ (–a) (iii) Not an integer
(d) a ÷ (+1) (iv) –a
OR
21. When the integers 10, 0, 5, –5, –7 are arranged in descending or ascending order, then find out the
integer which will be in the middle.

22. Find 2 ÷ 2
23. Find the probability of getting a number greater than 2 on throwing a die once.
24. 9 added to twice a number gives 13. Find the number.
25. Solve : 3 (x + 3) – 2 (x – 1) = 5 (x – 5)
OR
25. Solve : 16 (3x – 5) – 10 (4x – 8) = 40
26. In the Figure, AO = OB
A = B

Show that AOC BOD.

Section – D (3x7 = 21)
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27. Simplify : 118 – [121 ÷ (11 × 11) – (–4) – {3 –9 – 2}]

28. The cost of 5 kg of sugar is Rs. 101 , find its cost per kg.
OR
28. The product of two numbers is 20 . If one of the numbers is 6 , find the other.
29. Rahul’s father is thrice as old as Rahul. After 12 years he will be just twice his son. Find their present
ages.
30. State the property that is used in the following statements :-

(i) If a || b, then 1 = 5.
(ii) If 4 = 6, then a || b.
(iii) If 4 + 5 = 180, then a || b.
31. If the sides of a triangle are produced in order, prove that the sum of the exterior angles so formed is
360o.
32. Prove the Angle Sum Property that the sum of the angles of a triangle is 180o.
33. In figure, PL OA, PM  OB such that PL = PM. Prove that PLO PMO giving suitable reasons.

OR
33. In the figure, AB = CD, AD = BC, Prove that ADCCBA.

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Section – E (5 x 3 = 15)
34. In a public library, the librarian made the following observations in particular week.
Days Mon Tues. Wed. Thurs. Fri. Sat.
Newspaper Readers 350 400 500 450 550 450
Magazine Readers 200 450 300 250 100 50
(i) Draw a double bar graph choosing an appropriate scale.
(ii) On which day, the number of readers in the library was maximum ?
(ii) What is the mean number of magazine readers per day ?
35. PQRS is a quadrilateral in which diagonals PR and QS intersect in O. Show that (PQ+ QR+ RS+SP) >
(PR+QS).

36. The diagonals of a rhombus measure 16 cm and 30 cm. Find its perimeter.

OR

In the adjoining figure, p ∥q.Find the unknown angles, a, b, c, d, e, f.

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