Practicing Class 7 Maths MCQ and Class 7 Maths Chapter 4 Expressions using Letter Numbers MCQ Questions Online Test with Answers daily helps in time management.
MCQ on Expressions using Letter Numbers Class 7
Expressions using Letter Numbers MCQ Class 7
Class 7 Maths MCQ Chapter 4 Expressions using Letter Numbers
Multiple Choice Questions
Question 1.
Which expression best describes ‘four times a number decreased by 6’?
(a) 4n – 6
(b) 4(n – 6)
(c) 6 – 4n
(d) n – 4 × 6
Answer:
(a) 4n – 6
Question 2.
What is the expression for ‘7 more than half a number y’?
(a) \(\frac{y}{2}\) + 7
(b) \(\frac{7y}{2}\)
(c) 7 + y × 2
(d) y ÷ 2 – 7
Answer:
(a) \(\frac{y}{2}\) + 7
Question 3.
Which of the following best describes the expression 120m + 500?
(a) Total money spent after buying m movie tickets at ₹ 500 each and adding ₹ 120 for popcorn
(b) ₹ 120 per movie for (m + 1) people, plus ₹ 500 booking fee
(c) ₹ 120 per month for m months, plus a ₹ 500 one-time fee
(d) 120 added to the product of m and 500
Answer:
(c) ₹ 120 per month for m months, plus a ₹ 500 one-time fee
Question 4.
Which of the following best describes the expression 5(a – b)?
(a) Multiply 5 by a and then subtract b
(b) Subtract b from a and then multiply the result by 5
(c) Subtract a from b and multiply by 5
(d) Five more than a minus b
Answer:
(b) Subtract b from a and then multiply the result by 5
Question 5.
Expression for the total cost of c chairs at ₹ 120 each and t tables at ₹ 450.
(a) 120c + 450t
(b) c + t × 450
(c) 450(c + t)
(d) 120 + 450
Answer:
(a) 120c + 450t
Question 6.
Which pair of expressions is not always equal in value?
(a) 5u and u + u + u + u + u
(b) 4a – 2a and 2a
(c) 3x and x + x + x
(d) 9s and 9 + s
Answer:
(d) 9s and 9 + s
Question 7.
What is the simplified form of 5x + 3y – 12 + 7x – 6y + 4?
(a) 12x – 3y – 8
(b) 2x – 9y – 16
(c) 12x + 9y – 8
(d) 12x – 3y – 16
Answer:
(a) 12x – 3y – 8
Question 8.
Simplify the expression ‘two times the sum of 3x + 4 and x + 2’?
(a) 8x + 6
(b) 6x + 12
(c) 2(3x + 4 + x + 2)
(d) 8x + 12
Answer:
(d) 8x + 12
Question 9.
Which of the following are like terms?
(a) 3x, 4x, -5xz
(b) x, -xy, xyz
(c) ab, -2ba, 6ab
(d) x, y
Answer:
(c) ab, -2ba, 6ab
Question 10.
What is the value of 4x – x + 2 if x = 5?
(a) 17
(b) 19
(c) 22
(d) 27
Answer:
(a) 17
Question 11.
The sum of (7m – 2n + 11) and (6n – 5 + 4m) is
(a) 11m – 4n + 6
(b) 11m + 4n + 6
(c) 11m – 2n + 16
(d) 3m + 4n + 6
Answer:
(b) 11m + 4n + 6
Question 12.
Subtracting (2c + 5d – 9) from (-3c – 2d + 15) gives
(a) -5c – 7d + 24
(b) -5c – 3d + 6
(c) 5c + 7d – 24
(d) -5c – 7d + 6
Answer:
(a) -5c – 7d + 24
Question 13.
A taxi charges ₹ 15/km and a base fare of ₹ 60. For 8 km, the fare is
(a) ₹ 120
(b) ₹ 180
(c) ₹ 135
(d) ₹ 90
Answer:
(b) ₹ 180
Question 14.
A worker earns ₹ 250 per hour for h hours and receives a ₹ 300 bonus. What is the expression for the total earnings of the worker?
(a) 250h + 300
(b) h + 300 × 250
(c) 250 + 300h
(d) 300h + 250
Answer:
(a) 250h + 300
Question 15.
A parcel delivery costs ₹ x per kg. If the cost is ₹ 25 per kg, what is the total cost for delivering 6 kg?
(a) ₹ 125
(b) ₹ 130
(c) ₹ 150
(d) ₹ 100
Answer:
(c) ₹ 150
Question 16.
If a machine processes 30 units at a rate of 3 minutes per unit, plus an additional 10 minutes for setup, what is the total time required for processing?
(a) 100 minutes
(b) 90 minutes
(c) 70 minutes
(d) 55 minutes
Answer:
(a) 100 minutes
Question 17.
Derive an expression for the total earnings for n items, if the earnings per item is ₹ w.
(a) wn
(b) w + n
(c) w – n
(d) n ÷ w
Answer:
(a) wn
Question 18.
A calendar box has four dates like this
| w | w + 1 |
| w + 7 | ? |
Which of the following options gives the missing value of the date and the sum of the diagonals, respectively?
(a) w + 8; 2w + 8
(b) w + 7; 2w + 7
(c) w + 8; 2w + 9
(d) w + 1; 2w + 1
Answer:
(a) w + 8; 2w + 8
Question 19.
Which expression shows ‘seven more than three times a number y’?
(a) 3y + 7
(b) 7y + 3
(c) y × 3 + 7
(d) 3 + y + 7
Answer:
(a) 3y + 7
Question 20.
Which of the following expressions is equal to the nth term of the pattern 5, 10, 15, 20,…..?
(a) 5 + n
(b) 5n
(c) 5n + 1
(d) n + 5
Answer:
(b) 5n
Question 21.
If a = 4 and b = 6, what is the value of 3a + 2b – 5?
(a) 25
(b) 23
(c) 19
(d) 26
Answer:
(c) 19
Question 22.
Which expression represents the cost of m mangoes at ₹ 15 each and n apples at ₹ 12 each?
(a) 15m + 12n
(b) m + 12n + 15
(c) 12m + 15n
(d) 15 + m + n
Answer:
(a) 15m + 12n
Question 23.
Which pair of expressions is not equal in value?
(a) 3x and x + x + x
(b) 4a – 2a and 2a
(c) 6x + 2 and 2 + 6x
(d) 35 + q and 35q
Answer:
(d) 35 + q and 35q
Assertion-Reason Based Questions
Study the Assertion (A) and Reason (R) statements given below and choose the correct alternative.
Question 1.
Assertion (A): x – 4 is an algebraic expression that shows ‘four less than a number’.
Reason (R): The distributive property states that 2(x – 4) = 2x – 8.
(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.
Answer:
(b) Both A and R are true, but R is not the correct explanation of A.
Question 2.
Assertion (A): In the expression y + 2, 2 is called a constant.
Reason (R): A constant is a fixed number added to or subtracted from a 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.
Answer:
(a) Both A and R are true, and R is the correct explanation of A.
Question 3.
Assertion (A): In 2a + b, both a and b must have the same value.
Reason (R): Variables can take any value depending on the situation.
(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.
Answer:
(d) A is false, but R is true.
Question 4.
Assertion (A): The expression 5(2x + 3) – 3(4x – 5) simplifies to -2x + 34.
Reason (R): To simplify the expression, first apply the distributive property 5(2x + 3) = 10x + 15 and -3(4x – 5) = -12x + 15, then combine like terms.
(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.
Answer:
(d) A is false, but R is true.
Question 5.
Assertion (A): 5abc, 7bac, and -23acb are like terms.
Reason (R): Like terms cannot be added together.
(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.
Answer:
(c) A is true but R is false.
Question 6.
Assertion (A): Subtracting 2x – 3 from 4x + 7 gives 2x + 10.
Reason (R): Subtracting the second polynomial requires removing the brackets, giving 4x + 7 + 2x – 3, which simplifies to 6x + 10.
(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.
Answer:
(c) A is true but R is false.
Question 7.
Assertion (A): Expressions 2 × n and n + n are equal.
Reason (R): Expressions with different symbols are never equal.
(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.
Answer:
(c) A is true but R is false.
Question 8.
Assertion (A): The perimeter of a square is given by P = 4s, where s is the length of a side.
Reason (R): The perimeter of a square is calculated by adding the length of all four sides, each of which is equal to s.
(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.
Answer:
(a) Both A and R are true, and R is the correct explanation of A.
Question 9.
Assertion (A): The total cost of 10 pens at ₹ p each and ₹ 5 delivery is ₹ (10p + 5).
Reason (R): The Delivery charge is deducted from the total cost.
(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.
Answer:
(c) A is true but R is false.
Fill in the blanks.
1. An ______________ is a combination of numbers, letters, and operators representing a real-life situation mathematically.
Answer: algebraic expression
2. A symbol that represents an unknown value in an expression is called a ______________
Answer: variable
3. The expression that shows ‘6 less than twice the number p’ is ______________
Answer: 2p – 6
4. If each star shape has 5 matchsticks, then the total matchsticks used for n stars is ______________
Answer: 5n
5. A square tile costs ₹ x and a border tile costs ₹ y. The cost for 5 square tiles and 2 border tiles is ₹ ______________
Answer: 5x + 2y
6. A shorter way to write ‘7 multiplied by r’ in algebra is ______________
Answer: 7r
7. In the sequence 2, 5, 8, 11, the expression for the nth term is ______________
Answer: 3n – 1
8. The difference between twice a number, a, and the number itself is ______________
Answer: a
9. The simplified form of 2(4a – 5b) + 6b – 3a + 10 is ______________
Answer: 5a – 4b + 10
10. In the expression 3x + 4 – 2x, the like terms are ______________
Answer: 3x and -2x
11. The term without any variable is called a ______________ term.
Answer: constant
12. The constant term in the expression 2x – 6 + 3y is ______________
Answer: -6
13. The simplified form of 18 + 3(5c – 2d) – 6d – 4c – 9 is ______________
Answer: 11c – 12d + 9
14. If y = 4 then the value of 2(y – 1) – y is ______________
Answer: 2
15. The expression 3(k + 2) is equivalent to ______________
Answer: 3k + 6
16. The sum of (-6f + 19 – 8s) and (-23 + 13f + 12s) is ______________
Answer: 7f + 4s – 4
17. A person plays 3 quiz rounds scoring (7p – 3q), (8p – 4q) and (6p – 2q). The total score as an expression is ______________
Answer: 21p – 9q
18. The perimeter of a square with side s is given by ______________
Answer: 4s
19. An expression for ‘the cost of fencing a square garden of side x metres at ₹ 15 per metre is ₹ ______________
Answer: 60x
20. A device takes 5 minutes to start and then cleans y kilograms of rice at a rate of 3 minutes per kilogram. The total time taken is ______________ minutes.
Answer: 5 + 3y
21. A bus travels at a speed of 48 km/h. In t hours, the total distance it covers is ______________ km.
Answer: 48t
22. An online store charges ₹ c per item and a flat delivery fee of ₹ d. For 7 items, the total cost is ₹ ______________
Answer: 7c + d
23. The expression for ‘twice the perimeter of a rectangle’ is ______________
Answer: 4(l + b)
24. A taxi charges ₹ 31 per km and a fixed base fare of ₹ f. For a ride of d km, the total charge is ₹ ______________
Answer: 31d + f
25. A water supplier charges ₹ 40 for each can as a deposit and refunds ₹ 6 per can when returned. If x water cans are delivered and later returned, the actual payment is ₹ ______________
Answer: 34x
26. A paper fan is folded r times and then cut along the fold. The number of pieces of paper strips after cutting along the folds is ______________
Answer: r + 1
State whether the following statements are True or False.
1. Algebraic expressions cannot contain variables.
Answer: False
2. The expression 3x + 2 represents a quantity that is three times a number increased by two.
Answer: True
3. A variable is a fixed number that never changes.
Answer: False
4. The term 5 m means the same as 5 × m.
Answer: True
5. In the expression 10 – a, as the value of a increases, the result also increases.
Answer: False
6. 2yx and -2x are unlike terms.
Answer: True
7. The expressions 13(3x – 4y) is equal to the expression 39x – 4y.
Answer: False
8. An expression cannot have more than one variable.
Answer: False
9. The expression 2a + 3b can be simplified to 5ab.
Answer: False
10. If h = 6, n = 7 then h – (3 – n) = 10.
Answer: True
11. 16a – 5 is equal to 16(a – 5).
Answer: False
12. The perimeter of a rectangle with length l and width w is given by the expression 2(l + w), and this can be simplified to 2l + 2w.
Answer: True
13. The total cost of buying x apples at ₹ 15 per apple and a ₹ 30 delivery fee can be expressed by 15 + 30x.
Answer: False
14. A person saves ₹ 200 every week for x weeks, and the total amount saved can be represented by 200 + x.
Answer: False
15. The perimeter of an equilateral triangle with side length x is given by 3x.
Answer: True
Match the Following Table.
Question 1.
| Expression | Meaning |
| (i) 3(p – 1) | (a) Four times m minus 3 |
| (ii) 5 + 2y | (b) Total of p and twice a number one more than p |
| (iii) 6x | (c) Three times one less than p |
| (iv) 4m – 3 | (d) Cost of x items at ₹ 6 each |
| (v) p + 2(p + 1) | (e) Add 5 to double of y |
Answer:
| Expression | Meaning |
| (i) 3(p – 1) | (c) Three times one less than p |
| (ii) 5 + 2y | (e) Add 5 to double of y |
| (iii) 6x | (d) Cost of x items at ₹ 6 each |
| (iv) 4m – 3 | (a) Four times m minus 3 |
| (v) p + 2(p + 1) | (b) Total of p and twice a number one more than p |
Question 2.
| Expression with Substitution | Value |
| (i) 5x + 2y – 3z (if x = 4, y = 2, z = 1) | (a) 47 |
| (ii) 3(a – 2) + 7b (if a = 6, b = 5) | (b) 21 |
| (iii) 4(m + 9) – 3n + p (if m = -4, n = 3, p = 2) | (c) 19 |
| (iv) 2t + 5(b – 3) (if t = 8, b = 10) | (d) 51 |
| (v) 3f + 2g – 4h (if f = 7, g = 5, h = 3) | (e) 13 |
Answer:
| Expression with Substitution | Value |
| (i) 5x + 2y – 3z (if x = 4, y = 2, z = 1) | (b) 21 |
| (ii) 3(a – 2) + 7b (if a = 6, b = 5) | (a) 47 |
| (iii) 4(m + 9) – 3n + p (if m = -4, n = 3, p = 2) | (e) 13 |
| (iv) 2t + 5(b – 3) (if t = 8, b = 10) | (d) 51 |
| (v) 3f + 2g – 4h (if f = 7, g = 5, h = 3) | (c) 19 |
Case-Based Questions
Question 1.
A mobile company charges ₹ 300 per month as a fixed rental. Additionally, the company charges ₹ 2 per call made during the month.
Now, based on the context, answer the following questions carefully.
(i) Write the algebraic expression for the total monthly cost for n calls.
(ii) Evaluate the total cost if n = 35.
(iii) Write the new expression for the total monthly cost if the plan includes 10 free calls per month.
(iv) What is the total monthly cost for 35 calls if the plan includes 10 free calls per month?
Answer:
(i) 300 + 2n
(ii) ₹ 370
(iii) 300 + 2(n – 10)
(iv) ₹ 350
Question 2.
A plumber charges ₹ r per hour (h) for labour, ₹ x for the cost of parts, and a fixed amount ₹ f for transport. This pricing model helps customers to understand the total cost as a combination of time-based labour, materials used, and travel expenses.
Now, based on the information, answer the following carefully.
(i) Write an expression for the total cost.
(ii) Find the cost for r = ₹ 180, h = 3, x = ₹ 250, f = ₹ 70.
(iii) If the hourly rate increases by ₹ 20, write the new expression for the total cost.
Answer:
(i) rh + x + f
(ii) ₹ 860
(iii) (r + 20)h + x + f
Complete the following table.
Question 1.
| Number | Expression |
| (i) Tanuj is x years old. His father is 4 times older than him. | |
| (ii) Total x pens bought at ₹ 12 each plus y notebook | |
| (iii) Total cost of 5 chocolates at ₹ y each plus ₹ 10 delivery charge | |
| (iv) A number t is tripled and then 4 is subtracted | |
| (v) Total time to walk d km at 10 mins per km plus 5 mins break |
Answer:
| Number | Expression |
| (i) Tanuj is x years old. His father is 4 times older than him. | 4x |
| (ii) Total x pens bought at ₹ 12 each plus y notebook | 12x + y |
| (iii) Total cost of 5 chocolates at ₹ y each plus ₹ 10 delivery charge | 5y + 10 |
| (iv) A number t is tripled and then 4 is subtracted | 3t – 4 |
| (v) Total time to walk d km at 10 mins per km plus 5 mins break | 10d + 5 |
Question 2.
| Expression | Simplified Form | Value if x = 3 |
| (i) 4x + 3x | ||
| (ii) 2x – x + 7 | ||
| (iii) 6x + 4 – 3x – 1 | ||
| (iv) 2(x + 1) + 3(x – 2) | ||
| (v) 5x – 2(2x – 1) | ||
| (vi) 4(x – 1) + x |
Answer:
| Expression | Simplified Form | Value if x = 3 |
| (i) 4x + 3x | 7x | 21 |
| (ii) 2x – x + 7 | x + 7 | 10 |
| (iii) 6x + 4 – 3x – 1 | 3x + 3 | 12 |
| (iv) 2(x + 1) + 3(x – 2) | 5x – 4 | 11 |
| (v) 5x – 2(2x – 1) | x + 2 | 5 |
| (vi) 4(x – 1) + x | 5x – 4 | 11 |
Question 3.
| Situation | Algebraic Expression | Value for Input | Value of the Expression |
| (i) Perimeter of Rectangle | l = 5, b = 3 | ||
| (ii) You order 3 notebooks costing ₹ d each and pay ₹ 20 for delivery | d = 40 | ||
| (iii) A mechanic works h hours, charges ₹ 150/hr, and ₹ x for materials | h = 5, x = 200 | ||
| (iv) Distance travelled by a bus at 60 km/h for t hours | t = 4 | ||
| (v) A cab charges ₹ y per km for 10 km plus ₹ f base fare | y = 12, f = 50 | ||
| (vi) Weight of chocolate if it is cut into n pieces, each weighing 5 g | n = 5 |
Answer:
| Situation | Algebraic Expression | Value for Input | Value of the Expression |
| (i) Perimeter of Rectangle | 2(l + b) | l = 5, b = 3 | 16 units |
| (ii) You order 3 notebooks costing ₹ d each and pay ₹ 20 for delivery | 3d + 20 | d = 40 | ₹ 140 |
| (iii) A mechanic works h hours, charges ₹ 150/hr, and ₹ x for materials | 150h + x | h = 5, x = 200 | ₹ 950 |
| (iv) Distance travelled by a bus at 60 km/h for t hours | 60t | t = 4 | 240 km |
| (v) A cab charges ₹ y per km for 10 km plus ₹ f base fare | 10y + f | y = 12, f = 50 | ₹ 170 |
| (vi) Weight of chocolate if it is cut into n pieces, each weighing 5 g | 5n | n = 5 | 25 g |
Look at the pictures in the table. In each case, two numbers are given at the top. These numbers are used to perform a specific operation, and the result appears at the bottom. Match the pictures with their correct expressions.
Answer:
(i) – (d)
(ii) – (e)
(iii) – (b)
(iv) – (a)
(v) – (c)
In the following questions, letters are replaced by numbers, and a value is given for each expression. However, some of these calculations might be incorrect. Carefully check each one. If you find a mistake, explain what went wrong and then correct it to find the right answer.
1. If x = 9, then 5x – 4 = 40
Answer: Incorrect; 41
2. If y = 3, then 4y + 2 = 14
Answer: Correct
3. If m = – 7, then 10 – m = 3
Answer: Incorrect; 17
4. If a = 6 and b = 2, then a – 2b = 3
Answer: Incorrect; 2
5. If x = 4, then 3(x + 2) = 18
Answer: Correct
6. If q = -3, then 5(q – 1) = 10
Answer: Incorrect; -20
7. If r = 6, then 2(-r – 4) + 3 = 7
Answer: Incorrect; -17
8. If m = -4 and n = 3, then m + 2n = 2
Answer:
Correct
9. If x = 4 and y = -5, then 2y – (7 – 3x) = -15
Answer: Incorrect; -5
Check each simple expression. If there is a mistake, correct it and write the correct, simplest form.
| Expression | Given Simplest Form | Correct Simplest Form |
| (i) 4x + 3x – 2 | 7x | |
| (ii) 6a – (2a + 4) | 4a + 4 | |
| (iii) 5(p – 2) + 3 | 5p – 10 + 3 | |
| (iv) 3(2x + 1) – 2x | 6x + 1 – 2x | |
| (v) 7 – (x – 3) | 7 – x – 3 | |
| (vi) 2b + 3b – (4b – 2) | b + 2 | |
| (vii) 4y – 3(2y + 1) | 4y – 6y – 3 | |
| (viii) 6(m + 2) – 2m | 4m + 12 | |
| (ix) 2(x – 1) + 3(x + 1) | 5x |
Answer:
| Expression | Given Simplest Form | Correct Simplest Form |
| (i) 4x + 3x – 2 | 7x | 7x – 2 |
| (ii) 6a – (2a + 4) | 4a + 4 | 4a – 4 |
| (iii) 5(p – 2) + 3 | 5p – 10 + 3 | 5p – 7 |
| (iv) 3(2x + 1) – 2x | 6x + 1 – 2x | 4x + 3 |
| (v) 7 – (x – 3) | 7 – x – 3 | 10 – x |
| (vi) 2b + 3b – (4b – 2) | b + 2 | b + 2 |
| (vii) 4y – 3(2y + 1) | 4y – 6y – 3 | -2y – 3 |
| (viii) 6(m + 2) – 2m | 4m + 12 | 4m + 12 |
| (ix) 2(x – 1) + 3(x + 1) | 5x | 5x + 1 |
Very Short Answer Type Questions
Question 1.
Write an expression for ‘twice the sum of x and 3’.
Answer:
2(x + 3)
Question 2.
What is the simplified form of 5x + 4 – 2x + 6?
Answer:
3x + 10
Question 3.
Expand 4(m – 3).
Answer:
4m – 12
Question 4.
What does the expression 2a – (a – 4) simplify to?
Answer:
a + 4
Question 5.
If u = 7, what is the value of 6a + 7 – 3a – 1?
Answer:
27
Short Answer Type Questions
Question 1.
A shop charges a refundable deposit of ₹ 50 per helmet and ₹ 100 per jacket. On return, ₹ 8 is deducted for each helmet and ₹ 12 for each jacket as a usage fee. Write and simplify an expression for the total refund if h helmets and j jackets are returned.
Answer:
42h + 88j
Question 2.
Simplify 7p + 3 – 2p – 1 + 4p.
Answer:
9p + 2
Question 3.
A printing shop charges ₹ c per page and ₹ 25 setup fee. Write an expression for 50 pages.
Answer:
50c + 25
Question 4.
Are the expressions 7(x + 2y) and 7x + 9y equal? Justify with an example.
Answer:
No
Question 5.
Meera sells handcrafted items over three weekends. Her earnings were (3a – 2b), (6a + b) and (5a – 3b). Write and simplify an expression for her total earnings from all weekends.
Answer:
14a – 4b
Question 6.
Derive an expression for the nth term of the pattern 4, 7, 10, 13,…
Answer:
3n + 1
Question 7.
A square tile costs ₹ x and a border tile costs ₹ y. Write an expression for the total cost of m square tiles and n border tiles. Find the cost, if m = 4, n = 3, x = 15, y = 10.
Answer:
mx + ny; ₹ 90
Question 8.
Evaluate 3(a + b) – (2a – b) when a = 2, b = 5.
Answer:
22
Question 9.
Rohan earned (8m + 5n) points in Game 1 but lost (3m – 2n) points due to a penalty, and he earned (4m + n) points in Game 2. Write and simplify an expression for his total points after both games and the penalties.
Answer:
(8m + 5n) – (3m – 2n) + (4m + n) = 9m + 8n
Question 10.
A bigger rectangle is split into 3 rectangles as given below. Write the expression that describes the area of the biggest rectangle out of the three rectangles.
Answer:
19p
Long Answer Type Questions
Question 1.
Add the following expressions.
(a) -19a + 23b and 19a – 23b
(b) 5p – 9q + 14 and -3q + 11 + 7p
(c) -4x + 22 – 7y and -13 + 9x + 10y
Answer:
(a) 0
(b) 12p – 12q + 25
(c) 5x + 3y + 9
Question 2.
Subtract the following expressions.
(a) 7a + 12 from 5a – 20
(b) -18x + 21 – 7y from 8y – 16 + 5x
(c) 13g + 11 – 5h from 15 – 11g + 4h
Answer:
(a) -2a – 32
(b) 15y – 37 + 23x
(c) -24g + 9h + 4
Question 3.
A calendar pattern shows that 2 × 2 boxes have equal diagonal sums.
(a) Take the top-left number as a. Write expressions for the other 3 boxes.
(b) Prove they are equal using algebra.
(c) Use your expression to find the diagonal sum if a = 9.
Answer:
(a) a + 1, a + 7 and a + 8
(c) 26