# Grade-7 Maths Sample Paper 2024

# Grade- 7 Maths Sample Paper 2024

**General Instructions:**

General Instructions:

This question paper contains two Parts A and B. Both Part A and B have internal choices. **Part – A :**

1. It consists of two sections-I & II

2. Section I has 6 questions on the Case Study. Each case study has four sub-parts.

3. Section-II has 16 questions (Questions No. 7 to 22) of 1 mark each. Internal choice is

provided in 5 questions. **Part – B :**

1. Questions No. 23 to 28 are Short Answer Questions (Type-I) of 2 marks each.

2. Questions No. 29 to 34 are Short Answer Questions (Type-II) of 3 marks each.

3. Questions No. 35 to 36 are Long Answer Type Questions of 5 marks each.

4. Internal choice is provided in 2 questions of 2 marks, 2 of 3 marks, and 1 of 5 marks.

**Part – A (Section – I)**

** Part – A (Section – I)**

*Case study-based questions are compulsory. Each case study has four *

*case-based sub-parts. Each sub-part carries 1 mark. (4×6=24)*

**Q1. A rational number is a number that can be expressed in the form p/q, where p and q are integers and q≠ 0****. For example 2,3/1,1/2,-1/2, 0, etc. By multiplying the numerator and denominator of a rational number by the same non-zero integer, we obtain another rational number equivalent to the given rational number. Observe the number line and answer the following questions:**

i) R represents which rational number?

(a) negative (c) positive

(b) zero (d) none of these

ii) Which rational number is represented by S?

(a)-4/3 (b) -5/3 (c) 5/3 (d) None of these

**Q2. Take a stone, tie it at one end of the string, and swing it in the air holding the other end of the string. The stone will move in a circle. Thus, a circle is the path of a point that moves so that its distance from a fixed point in the given plane, remains constant. This fixed point is called the center of the circle and the constant distance is called the radius. The perimeter of a circle i.e. the length of the boundary of a circle is called the circumference of the circle.**

i) The diameter of a circle of radius 5.6 cm is________.

(a) 5.6 cm (b) 10.12 cm (c) 11.2 cm (d) none of these

ii) The circumference of a circle of diameter 7 cm is __________.

(a) 44 cm (b) 22 cm (c) 38.5 cm (d) 77 cm

iii) The area of a circle of radius 4.9 cm is ____________.

(a) 7546 cm2 (b) 754.6 cm2 (c) 75.46 cm2 (d) 7.546 cm2

iv) There are ____________ a number of center/centers in a circle.

(a) 4 (b) 0 (c) 1 (d) uncountable

**Q3. If interest is calculated uniformly on the original principal throughout the loan period, it is called Simple interest (SI). A borrower should return the principal amount (he/she has borrowed) and the interest to the lender. This money is called an amount. **

(i) Find the simple interest to be paid at the end of 3 years if the principal is Rs. 200 at 12% per annum.

(a) Rs. 24 (b) Rs. 48 (c) Rs. 72 (d) None of these

(ii) Find the simple interest to be paid at the end of 3 years if the principal is Rs. 500 at the rate of 5% per annum.

(a) Rs. 25 (b) Rs. 32 (c) Rs. 75 (d) None of these

(iii) Amount = ______ + ______ .

(a) Principal + S.I. (b) Principal – S.I.

(c) Can’t say (d) None of these

(iv) Choose the correct formula to find out time (T) in years.

**Q4. Expressions are defined as numbers, symbols and mathematical operations (such as +, -, × and ÷) grouped together that show the value of something. In algebra, a term is either a single number or variable or numbers and variables multiplied together. Terms are separated by + or – signs or sometimes by division. A coefficient is a number used to multiply a variable (2x means 2 times x, so 2 is a coefficient). Variables on their own (without a number next to them) have a coefficient of 1 (x is really 1x). **

i) Identify the numerical coefficient of the term (other than constants) in the expression: 5 – 3t^{2}

(a) 2 (b) –3 (c) 5 (d) –5

ii) Identify the term/terms which contains x in the expression 13y^{2} – 8yx.

(a) 13y^{2} (b) –8yx

(c) Both (a) and (b) (d) None of these

iii) Identify the coefficient of y^{2} in the expression 8 – xy^{2}.

(a) 8 (b) –x (c) x (d) None of these

iv) Which of the following is the pair of like terms?

(a) –29x, –29y (b) 14xy, 42yx

(c) 4m^{2}p, 4mp^{2} (d) None of these

**Q5. The heights of 10 girls were measured in cm and the results are as follows: 135, 150, 139, 128, 151, 132, 146, 149, 143, 141.**

- i) What is the height of the tallest girl?

(a) 151cm (b) 152 cm (c) 150 cm (d) None of these

- ii) What is the range of the data?

(a) 15 cm (b) 23 cm (c) 50 cm (d) None of these

iii) What is the mean height of the girls?

(a) 151cm (b) 141.4 cm (c) 155.5 cm (d) None of these

iv) How many girls are higher than the mean height?

(a) 11 (b) 5 (c) 10 (d) None of these

**Q6. Standard Form of any number can be expressed as a decimal number between 1.0 and 10.0 including 1.0 multiplied by a power of 10. Such a form of a number is called its standard form. The exponential form is a shortcut way of writing repeated multiplication involving base and exponents. In this form, the power represents the number of times we are multiplying the base by itself.**

i) The exponential form of b × b × b × b is _____________.

(a) b^{4} (b) 4^{b} (c) 4b (d) none of these

ii) The standard form of the 5,00,00,000 is _________.

(a) 0.05 × 10^{7} (b) 5 × 10^{10} (c) 5 × 10^{7} (d) none of these

iii) The exponential form of 615 ÷ 610 after simplification is __________.

(a) 6^{4 } (b) 6^{5} (c) 6^{15} (d) none of these

iv) The exponential form of 2° + 3° + 4° after simplification is ______ .

(a) 1 (b) 9° (c) 3 (d) none of these

**(Section – II)**

**Fill ups / True-False / MCQ : ** **(1×16=16)**

Q7. The ratio of 15 kg to 210 g is ……………………

OR

The ratio of 30 days to 36 hours is……………………

Q8. The rational number whose numerator is the smallest three-digit number and denominator is the largest four-digit number is…………..

OR

The lowest form of [65/84] is……….

Q9. The product of two negative rational numbers is ______ .

Q10. The area, in square meters, of a rectangle whose length = 5.5 m and breadth = 2.4 m is…………..

OR

The area, in square centimeters, of a square whose side 1.2 cm is…….

Q11. The mode of scores 19, 25, 23, 20, 9, 20, 15, 10, 5, 16, 25, 20, 24, 12, 20 in mathematics test (out of 25) of 15 students is ………..

Q12. The range of the data 130, 132, 135, 137, 139, 140, 142, 143, 145, 148 is……….

OR

The mean of the first five whole numbers is………..

Q13. What is the coefficient of x in the expression 4x + 3y?

(a) 1 (b) 2 (c) 3 (d) 4

Q14. Which of the following pair of terms is a pair of like terms?

(a) 3x, 2xy (b) –xy^{2}, –2xy^{2}

(c) -6x^{2}, 20x^{2}y (d) 8x^{2}, 7y.

OR

Add: a + b – 1, b – a + 1, 1 – 2b

(a) 1 (b) –1 (c) 2 (d) none of these

Q15. The value of 7^{3} is 243. T/F

Q16. The value of (–2) × (–3)^{3} is 54. T/ F

Q17. The sum of the numbers p and 5 is 11. The equation is p+ 5 = 11. T/F

Q18. There can be more than one mode for a given data. T/ F

Q19. An equation form for statement: one-fourth of n is 3 more than 2 is ___.

(a) n/4-2=3 (b)n/4+2=3

(c) n/2-4=3 (d) n/2+4=3

Q20. The solution of the equation m/3= 3 is _____.

(a) 3 (b) 6 (c) 9 (d) 12

Q21. Solve for x: 18 – (2x –12) = 8x

(a) 15 (b) 26 (c) 3 (d)13/5

Q22. An arithmetic mean of a and b is ……….

**(Part – B)**

**Short Answer Questions (Type-I): (2×6=12)**

Q23. In a computer lab, there are 3 computers for every 6 students. How many computers will be needed for 24 students?

OR

Find 15% of 250.

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