Expressions using Letter-Numbers — Mastery

Q1. A shopkeeper sells pens at Rs x each and notebooks at Rs y each. If Abha buys 8 pens and 3 notebooks, the expression for her total cost is

• A. 8x + 3y
• B. 8 + x + 3 + y
• C. 8y + 3x
• D. 11(x + y)

Q2. Radha cycles 5 km a day in week 1, and adds z km a day every week. How many km will she have cycled in total after 3 weeks?

• A. 35 + 7z
• B. 105 + 21z
• C. 5 + 3z
• D. 15z + 5

Q3. A train from Yahapur to Vahapur stops at three stations at equal distances. Each leg between stations takes t minutes. The train halts for 2 minutes at each of the three stations. Which expression gives the total travel time?

• A. 3t + 2
• B. 4t + 2
• C. 4t + 6
• D. 3t + 6

Q4. Parthiv's matchstick L-pattern uses 2 sticks per L. How many sticks does he need to make 45 Ls?

• A. 47
• B. 43
• C. 45
• D. 90

Q5. If c × 35 + j × 60 is the total-cost expression for Ketaki's coconut-jaggery laddus, what does she earn when she sells 10 coconuts and 5 kg jaggery?

• A. Rs 350
• B. Rs 650
• C. Rs 300
• D. Rs 950

Q6. If the expression 2n gives the number of matchsticks for n Ls, how many sticks are needed for 9 Ls?

• A. 18
• B. 11
• C. 20
• D. 29

Q7. Using the formula 4q for the perimeter of a square (Example 4), what is the perimeter of a square whose side is 7 cm?

• A. 11 cm
• B. 14 cm
• C. 28 cm
• D. 47 cm

Q8. For the Yahapur-to-Vahapur train, total time is 4t + 6 minutes. If t = 4 minutes, the total travel time is

• A. 10 minutes
• B. 16 minutes
• C. 20 minutes
• D. 22 minutes

Q9. From Figure it Out Q5, the expression w + 2 becomes 4w + 20 along one path. What is the value of 4w + 20 when w = 0?

• A. 0
• B. 20
• C. 24
• D. 40

Q10. Consider the sequence 4, 8, 12, 16, 20, 24, … (multiples of 4). The algebraic expression for the nth term of this sequence is

• A. 4n
• B. n + 4
• C. 4 + 4n
• D. 4 - n

Q11. The perimeter of a rectangle with length l and breadth b is l + b + l + b. Its simplest form is

• A. lb
• B. 4lb
• C. 2l + 2b
• D. l + b

Q12. The expression 18c + 11d cannot be simplified further. The reason is that

• A. 18 and 11 are different numbers
• B. c and d are both letters
• C. There is no negative sign in the expression
• D. c and d are different letter-numbers, so 18c and 11d are unlike terms

Q13. Example 5 totals pencils sold over three days as 5c + 3c + 10c, and erasers as expression with d. The expression 18c + 11d represents

• A. Total pencils minus total erasers
• B. Total money earned from pencils and erasers over three days
• C. Total number of items sold
• D. Average price per item

Q14. Simplify 4(x + y) - y. The result is

• A. 4x + y
• B. 4x - y
• C. 4x + 3y
• D. 4xy - y

Q15. Simplify the expression 3a + 9b - 6 + 8a - 4b - 7a + 16.

• A. 4a + 5b + 10
• B. 11a + 5b - 22
• C. 3a + 5b + 16
• D. 4a + 13b - 22

Q16. A Class 7 teacher in Lucknow wants to introduce letter-numbers for the first time. Which opening activity is the MOST effective?

• A. Write the rule 'a letter stands for a number' on the board and ask students to copy it
• B. Give 20 evaluation sums like 'find 3x when x = 5' for homework
• C. Tell students that algebra is hard and they must memorise the steps
• D. Begin with 'Shabnam is 3 years older than Aftab' and ask students to express Shabnam's age in many ways

Q17. A student writes '3d = 36 when d = 6'. The BEST teacher response is

• A. Mark the answer wrong and move on to the next sum
• B. Tell the student to memorise that 3d is not 36
• C. Skip the digit-pasting cases and only set d = 0 or 1 in future
• D. Ask the student to read 3d aloud as '3 times d' and substitute step by step

Q18. Students in Patna repeatedly simplify 5 - (2 - 6z) as 3 - 6z. The MOST effective re-teaching strategy is

• A. Insist that students memorise four bracket rules and recite them daily
• B. Tell students to drop the bracket and copy the inside as it is
• C. Skip bracket questions until Class 8
• D. Show that 5 - (2 - 6z) = 5 - 2 + 6z by substituting a value like z = 1 and matching both sides

Q19. After students see Aftab's age denoted by 'a', a teacher wants them to grasp that 'a' is a number, not a label. The BEST follow-up prompt is

• A. 'Write a in cursive five times'
• B. 'Why is a a vowel?'
• C. 'Memorise that a stands for Aftab'
• D. 'If a = 18, what is a + 3? If a = 25, what is a + 3?'

Q20. Apply the distributive property to expand 3(3a - 3b). The result is

• A. 3a - 3b
• B. 6a - 6b
• C. 9a + 9b
• D. 9a - 9b

Q21. A number machine takes two inputs (a, b) and outputs 2a - b. Consider these statements: I. For inputs (5, 2), the output is 8. II. For inputs (8, 1), the output is 15. III. For inputs (10, 11), the output is 31.

• A. I and II only
• B. I and III only
• C. II and III only
• D. All three

Q22. A number machine gives output 5 for inputs (5, 2), 7 for (8, 1), and 18 for (9, 11). Which formula fits all three?

• A. a + b
• B. a × b
• C. a + b - 2
• D. 2a - b

Q23. Matchstick-triangle pattern, the number of matchsticks at Step y is 2y + 1. How many matchsticks are needed at Step 33?

• A. 33
• B. 66
• C. 67
• D. 99

Q24. Figure it Out Q12shows a row of squares sharing sides — 1 square uses 4 matchsticks, 2 squares use 7, 3 squares use 10. The expression for w squares is

• A. 4w
• B. w + 3
• C. 4w - 1
• D. 3w + 1

Q25. On Somjit's saree border, Design C appears at every multiple of 3 — positions 3, 6, 9, … . The general expression for the nth occurrence of Design C is

• A. n + 3
• B. 3n
• C. 3n - 1
• D. 3n - 2

Q26. Assertion (A): On Somjit's saree border, the nth occurrence of Design B is at position 3n - 1. Reason (R): Design B occurs at positions 2, 5, 8, 11, 14, … — that is, one less than each multiple of 3.

• 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, R is false.
• D. A is false, R is true.

Q27. In a November 2024 calendar, a 2 × 2 square has top-left date 'a'. The two diagonal sums are both

• A. a + 8
• B. 2a + 4
• C. 2a + 8
• D. 4a + 8

Q28. In the extended calendar grid, a plus-shape uses five cells: a centre cell and its four edge-neighbours (above, below, left, right). If the centre is 15, the sum of the five cells is

• A. 30
• B. 60
• C. 75
• D. 90

Q29. In the endless 4-column grid of Figure it Out Q15 (numbers 1, 2, 3, 4 in row 1; 5, 6, 7, 8 in row 2; …), the number in row r and column c is

• A. r + c
• B. 4r + c
• C. 4(r - 1) + c
• D. 4c + r

Q30. A straight rope cut once gives 2 pieces, folded once and cut gives 3 pieces, folded twice and cut gives 5 pieces. The expression for the number of pieces when the rope is folded r times and cut is

• A. r + 2
• B. 2r + 1
• C. 2r - 1
• D. r × 2