0580/42 Oct/Nov 2021, Question 1: Unit Conversions

Part (ai) · 2 marks

Using 450 trees and the ratio 8:7:3, show the apple tree count is 200.

1. 1Total parts = 8 + 7 + 3 = 18
2. 2One part = 450 ÷ 18 = 25
3. 3Apple trees = 25 × 8 = 200

Answer450/(8 + 7 + 3)×8

Part (aii) · 1 mark

Find how many plum trees Malena has.

1. 1Plum trees = 25 × 3 = 75

Answer75

Part (aiii) · 2 marks

Calculate the extra pear trees needed to raise their number by 32%.

1. 1Total parts = 8 + 7 + 3 = 18
2. 2Pear trees = 7/18 × 450 = 175
3. 3Extra pear trees = 32/100 × 175 = 56

Answer56

Part (aiv) · 3 marks

With 48.5 kg per tree and 165 g per apple, find total apples from 200 trees to nearest 1000.

1. 148.5 kg = 48 500 g
2. 2Apples per tree = 48 500 ÷ 165 = 293.93…
3. 3Total = 293.93… × 200 = 58 787.8…
4. 4≈ 59 000 apples (nearest 1000)

Answer59 000

Part (bi) · 1 mark

Write three million and seventy-five thousand in figures.

1. 13 075 000

Answer3 075 000

Part (bii) · 1 mark

Express the answer from part (b)(i) in standard form.

1. 13 075 000 = 3.075 × 10⁶

Answer3.075 × 10⁶

Part (c) · 2 marks

Given 37.7 kg in 2020 is 16% more than 2019, find the 2019 mass per plum tree.

1. 12019 mass × 1.16 = 37.7
2. 22019 mass = 37.7 ÷ 1.16 = 32.5 kg

Answer32.5

Part (d) · 2 marks

Calculate the value of $1800 invested at 2.1% compound interest for 15 years.

1. 1Value = 1800 × (1 + 2.1/100)¹⁵
2. 2= 1800 × 1.021¹⁵ = 2458.43…
3. 3≈ $2460

Answer2460 or 2458. …

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