Class 7 – EXPRESSIONS USING LETTERS-NUMBERS

Class VII Maths – Practice Paper 10

PRACTICE PAPER

Class 7 – EXPRESSIONS USING LETTERS-NUMBERS

SECTION – A

1. If the side length of a regular pentagon is p, and the side length of a square is q, which of the following expressions represents the total perimeter of the two figures?
(a) 5p + q (b) 5p + 4q (c) p + q + 9 (d) 5p + 4

(b) 5p + 4q

2. A rope is 50 meters long. A piece of length x meters is cut from it. The remaining length is then divided into two equal parts. Which expression represents the length of each part?
(a) (50 − x)×2 (b) 50/2 − x (c) (50 − x) / 2 (d) 50 – (x/2)

(c) (50 − x) / 2

3. The cost of a notebook is ₹n and the cost of a pen is ₹p. If you buy 3 notebooks and 5 pens, and the shopkeeper gives a discount of ₹10, the total amount to be paid is represented by:
(a) 3n + 5p − 10 (b) 3n × 5p − 10 (c) 3(n − 10) + 5p (d) 10 − (3n + 5p)

(a) 3n + 5p − 10

4. Simplify the expression 7a − 3b + 2a + 5b.
(a) 9a − 8b (b) 9a + 2b (c) 5a + 8b (d) 5a − 2b

(b) 9a + 2b

5. What is the value of the expression 15 − 2x when x = −4?
(a) 23 (b) 7 (c) 11 (d) -23

(a) 23

6. An expression for the perimeter of a rectangle with length l and breadth b is 2l+2b. Which other expression is also equivalent to this?
(a) l × b (b) 2(l × b) (c) l + b + l + b (d) 2l × 2b

(c) l + b + l + b

7. The algebraic expression for “3 less than 10 times a number y” is:
(a) 3 − 10y (b) 10(y − 3) (c) 10y − 3 (d) 3y − 10

(c) 10y − 3

8. Which of the following pairs are unlike terms?
(a) 7x and 3x (b) 2ab and 5ba (c) 10p and 11q (d) 4y² and 6y²

(c) 10p and 11q

9. Assertion (A): The simplified form of the expression 5(2w + 3x + 4w) is 30w + 15x.
Reason (R): The distributive property is used to multiply the number outside the bracket with each term inside the bracket.
(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.

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

10. Assertion (A): The expressions 10y − 3 and 10(y − 3) are equal.
Reason (R): Algebraic expressions with different operations on the same variables can have the same values for some specific values of the variable.
(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.

(d) A is false but R is true.

SECTION – B

11. Find the value of the expression 2p − 3q + 5 when p = 4 and q = −1.

2(4) − 3(−1) + 5 = 8 − (−3) + 5 = 8 + 3 + 5 = 16.

12. The perimeter of a regular hexagon is given by the expression 6s. If the side of the hexagon is increased by 2 cm, write a new expression for its perimeter.

New side length = s + 2
New perimeter = 6(s + 2) or 6s + 12.

13. Simplify the expression 12m − (3m + 4n) + 2n.

12m − 3m − 4n + 2n = (12m − 3m) + (−4n + 2n) = 9m − 2n.

14. A shopkeeper sells x kg of sugar at ₹50 per kg and y kg of rice at ₹40 per kg. He spent ₹20 on transport. Write an algebraic expression for his total cost.

Cost of sugar = 50x
Cost of rice = 40y
Total cost = 50x + 40y + 20.

SECTION – C

15. Simplify the expression (40x + 75y) − (6x + 10y) by grouping like terms and then find the value of the simplified expression if x = 2 and y = 3.

40x + 75y − 6x − 10y = 34x + 65y
Substitute x=2, y=3:
34(2) + 65(3) = 68 + 195 = 263.

16. A number machine takes in two numbers, a and b, as inputs. The output is given by the formula 3a + 5b. If the output is 31 and the value of b is 4, find the value of a.

3a + 5(4) = 31
3a + 20 = 31
3a = 11
a = 11/3.

17. A school has p classrooms, each with 20 students. On a particular day, q students are absent from each classroom. Write an expression for the total number of students present on that day.

Students present in each classroom = 20 − q
Total students present = p(20 − q) or 20p − pq.

SECTION – D

18. Simplify the following expression and find its value if x = −2 and y = 5.
5(2x − 3y) + 3(4y − 6x) − (x + y)

= 10x − 15y + 12y − 18x − x − y
= −9x − 4y
Substitute x = −2, y = 5:
= −9(−2) − 4(5)
= 18 − 20 = −2.

SECTION – E (Case Study Based Questions)

19. Case Study 1: A travel agent offers different packages for a trip. The cost of one person’s travel is ₹c, and the cost of one night’s stay is ₹n. The agent charges an additional service fee of ₹100 for each booking.
(a) Write an expression for the total cost for a group of 5 people staying for 3 nights.
(b) If the travel cost per person is ₹2000 and the stay cost per night is ₹1500, what is the total cost for a group of 4 people staying for d nights?

(a) 5c + 15n + 100

(b) 4×2000 + 4×d×1500 + 100
= 8000 + 6000d + 100
= 6000d + 8100.

20. Case Study 2: In a calendar month, a 2×2 grid of dates is selected. Let the first date in the top-left corner be ‘a’. The dates in the grid can be represented as: a, a + 1 a + 7, a + 8

a a + 1
a + 7 a + 8

(a) Show that the sum of the diagonal dates is always equal.
(b) If the sum of the two diagonal pairs in such a 2×2 grid is 56, find the dates in the grid.

(a) First diagonal: a + (a + 8) = 2a + 8
Second diagonal: (a + 1) + (a + 7) = 2a + 8
Both are equal.

(b) 2a + 8 = 56
2a = 48
a = 24
Dates: 24, 25, 31, 32.

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