SPM 2024 Add Maths Paper 2, Question 15Index Numbers

Solved on video in English and Bahasa Melayu · Form 4, Index Numbers · 6:35 video

The question

(a)

Table 4 shows information for four ingredients used to produce a type of biscuit.

Table 4:

  • Ingredient A: price 2022 = x (RM), price 2023 = 2.10 (RM), price index 2023 (base 2022) = 130, weightage = n
  • Ingredient B: price 2022 = 2.00 (RM), price 2023 = 2.40 (RM), price index 2023 (base 2022) = y, weightage = m + n
  • Ingredient C: price 2022 = 0.90 (RM), price 2023 = 1.44 (RM), price index 2023 (base 2022) = 160, weightage = m/3
  • Ingredient D: price 2022 = 1.20 (RM), price 2023 = z (RM), price index 2023 (base 2022) = 150, weightage = 2n

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

Find the value of x, of y and of z.

(b)(i)

(b) The composite index for the production cost of the biscuit in the year 2023 with 2022 as the base year is 135.

(i) Find the ratio of ingredient A to ingredient B used.

The composite index for the production cost of the biscuit in the year 2023 with 2022 as the base year is 135.

Find the ratio of ingredient A to ingredient B used.

(b)(ii)

(b)(ii) The production cost of 200 biscuits in the year 2022 is RM25. The price of each ingredient is expected to increase by 20.25% from the year 2023 to the year 2025. In the year 2025, the box used to fit 40 biscuits is expected to cost RM1.50 per unit.

In the year 2025, if RM45 is allocated to produce 200 biscuits including the purchase of the box, determine whether or not the allocation is enough.

In the year 2025, if RM45 is allocated to produce 200 biscuits including the purchase of the box, determine whether or not the allocation is enough.

Part (a)

Step 1

Use the price index formula: I = (Q₁/Q₀) × 100, where Q₁ is the price in the given year and Q₀ is the base-year price.

Why this step

An index compares this year with the base year, so the base-year price always goes at the bottom of the fraction.

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

Final answer

x = 1.62, y = 120, z = 1.80

Where students lose marks

Watch out: give x to 2 decimal places, so x = 1.62, not 1.615.

Part (b)(i)

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

Final answer

A : B = 2 : 5

Where students lose marks

Watch out: give the answer as a ratio 2 : 5, not as a fraction 2/5.

Part (b)(ii)

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

Final answer

Not enough: total RM48.09 > RM45

Where students lose marks

Watch out: apply the index to the base-year cost RM25, not a 2025 cost, and give the ingredient cost to 2 d.p. (RM40.59).

Watch every step of this question solved on video (6:35), with the reason behind each step and a box that checks your own answer.

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