10 Case-based Questions
A. Students of Winkee Wee school visit a plant nursery with their class teachers. In the nursery, they see that the plants are kept in rows where the number of plants in each row follows a pattern.
Based on the above information, answer the following questions.
(i) There are 3 plants in the first row, 6 in the second row, and 9 plants in the third row. If the same pattern is followed, how many plants will be in the ninth row?
(a) 18
(b) 27
(c) 36
(d) 9
(ii) How many total plants would be there in the 25th row?
(a) 50
(b) 65
(c) 75
(d) 100
B. Bob, the builder, is building a museum made of glass. He starts the construction by placing 1 glass block in the first row, 4 glass blocks in the second row, 9 glass blocks in the third row, and so on.
Based on the above information, answer the following questions.
(i) If Bob continues the same pattern, then how many glass blocks will be in the 7th row?
(a) 18
(b) 27
(c) 36
(d) 49
(ii) How many glass blocks are needed to construct the 9th row?
(a) 64
(b) 81
(c) 100
(d) 121
C. A group of friends is counting the number of stars they see each night. On the first night, they see 5 stars. Each subsequent night, they see 2 more stars than the previous night.
(i) How many stars will they see on the 4th night?
(a) 11
(b) 14
(c) 15
(d) 16
(ii) If this pattern continues, how many stars will they see on the 10th night?
(a) 20
(b) 21
(c) 24
(d) 23
Answer (1)
Let's analyze and solve each part of the question step by step:
Part A: Plant Nursery Pattern
(i) The pattern of the number of plants in each row increases by 3 each time: 3, 6, 9, 12, etc. This can be expressed mathematically as an arithmetic sequence where the nth term, a n , can be given by: a n = 3 n So, for the 9th row: a 9 = 3 × 9 = 27 Therefore, the number of plants in the ninth row is (b) 27 .
(ii) Similarly, for the 25th row: a 25 = 3 × 25 = 75 Thus, there would be (c) 75 plants in the 25th row.
Part B: Glass Blocks for Museum Construction
The pattern of the glass blocks follows the sequence of perfect squares: 1, 4, 9, 16, etc. The nth term, b n , is: b n = n 2
(i) For the 7th row: b 7 = 7 2 = 49 There are (d) 49 glass blocks in the 7th row.
(ii) For the 9th row: b 9 = 9 2 = 81 Therefore, 81 glass blocks are needed for the 9th row, so the answer is (b) 81 .
Part C: Counting Stars
The number of stars follows an arithmetic sequence starting at 5 and increasing by 2 each night.
(i) The number of stars seen on the 4th night is:
Night 1: 5 stars
Night 2: 7 stars
Night 3: 9 stars
Night 4: 11 stars
Thus, the number of stars on the 4th night is (a) 11 .
(ii) To find the number of stars on the 10th night, use the formula for the nth term of an arithmetic sequence: a n = 5 + ( n − 1 ) × 2 a 10 = 5 + ( 10 − 1 ) × 2 = 5 + 18 = 23 Therefore, they will see (d) 23 stars on the 10th night.
These calculations help us understand how patterns work and how mathematical sequences can predict outcomes.
