MRSM Trial 2025 Add Maths Paper 2, Question 14Index Numbers

Solved on video in English · Form 4, Index Numbers · 6:20 video

The question

(a)

Table 3 shows the number of students according to all courses in a college, with the number of students in 2024 and 2025, the index of the number of students in 2025 (2024 = 100), and the participation percentage. Accounting: 2024 = 220, 2025 = 242, index = 110, participation = b. Culinary: 2024 = x, 2025 = 84, index = 105, participation = 25. Electronic: 2024 = 90, 2025 = y, index = 90, participation = 15. Automotive: 2024 = 160, 2025 = 178, index = z, participation = c.

(a) Find the values of x, y and z.

(b)

Table 3: the accounting course had 220 students in 2024 and 242 in 2025 (index 110, base 2024).

(b) It is given that the number of students for the accounting course decreases by 12% from 2023 to 2025. Calculate the index for the number of students for the accounting course in 2024 based on 2023.

(c)(i)

Table 3 gives participation percentages b (Accounting), 25 (Culinary), 15 (Electronic) and c (Automotive), with 2025 indices (2024 = 100) of 110, 105, 90 and 111.25 respectively. The college organizes a motivational seminar with these participation percentages.

(c)(i) If b is 2 times c, calculate the composite index of the students' participation in the seminar in 2025 based on 2024.

(c)(ii)

The composite index of the students' participation in the seminar in 2025 based on 2024 is 106.

(c)(ii) It is given that the total number of students who participate in the seminar in 2026 is expected to increase by 15% compared to 2025. Find the percentage change of the total number of students' participation in the seminar from 2024 to 2026.

MRSM Trial 2025 Add Maths Paper 2, Question 14: the question as drawn in Eduly's video6:20

Part (a)

Step 1

Using index I = (Q₁/Q₀) × 100. Culinary: (84/x) × 100 = 105 → x = 84/1.05 = 80.

Why this step

Put the compared year (2025) on top and the base year (2024) at the bottom. Flipping them is the common slip that ruins x, y and z.

2 more steps, each with the reason for it, in the full solution

Final answer

x = 80, y = 81, z = 111.25

Where students lose marks

Watch out: don't invert the index formula. The new-year count goes on top (Q₁) and the base-year count at the bottom (Q₀).

Part (b)

2 more steps, each with the reason for it, in the full solution

Final answer

80

Where students lose marks

Watch out: don't apply the 12% to 2024 or 2025. Work back from 2025: 2023 count = 242 ÷ 0.88 = 275.

Part (c)(i)

3 more steps, each with the reason for it, in the full solution

Final answer

Ī = 106

Where students lose marks

Watch out: solve b + c = 60 with b = 2c first, and use the participation percentages, not student counts, as weights.

Part (c)(ii)

3 more steps, each with the reason for it, in the full solution

Final answer

21.9% increase

Where students lose marks

Watch out: multiply 1.06 × 1.15 instead of adding 6% + 15%, then subtract 100 from the index to get the percentage change.

Watch every step of this question solved on video (6:20), with the reason behind each step and a box that checks your own answer.

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