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0580/33 Oct/Nov 2023, Question 3: Dividing in a Given Ratio

Cambridge IGCSE Mathematics 0580 · Paper 33 (Core) · Calculator · 15 marks

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The question, in short

Work through tea-making quantities, ratio sharing of $6875, index and algebra simplifications, LCM from prime factors, and identify an irrational number from a list.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (aia) · 2 marks

Find the simplest fraction of Aneel's 80 tea bags used when he makes 15 cups.

  1. 115/80 = 3/16

Answer3/16

Part (aib) · 2 marks

Find the mass of sugar, in grams, left after 15 cups using 8 g each from 1/2 kg.

  1. 1Sugar used = 15 × 8 = 120 g
  2. 21/2 kg = 500 g
  3. 3Sugar left = 500 − 120 = 380 g

Answer380

Part (aii) · 1 mark

Find total cups made when all 1 litre of milk is used at 40 ml per cup.

  1. 11 litre = 1000 ml
  2. 21000 ÷ 40 = 25 cups

Answer25

Part (b) · 3 marks

Share $6875 between Bobby, Carl and Davood in the ratio 6 : 8 : 11; find each amount.

  1. 16 + 8 + 11 = 25 parts
  2. 21 part = 6875 ÷ 25 = 275
  3. 3Bobby = 6 × 275 = 1650, Carl = 8 × 275 = 2200, Davood = 11 × 275 = 3025

AnswerBobby 1650, Carl 2200, Davood 3025

Part (ci) · 1 mark

Write (3² × 3⁴) ÷ 3⁶ as a single power of 3.

  1. 1(3² × 3⁴)/3⁶ = 3⁶/3⁶ = 3⁰

Answer3⁰

Part (cii) · 1 mark

Write 2⁻⁴ as a decimal value.

  1. 12⁻⁴ = 1/2⁴ = 1/16 = 0.0625

Answer0.0625

Part (di) · 1 mark

Simplify (b⁵)³.

  1. 1(b⁵)³ = b⁵ˣ³ = b¹⁵

Answerb¹⁵

Part (dii) · 1 mark

Simplify (4/m)⁻².

  1. 1(4/m)⁻² = (m/4)² = m²/16

Answerm²/16

Part (e) · 2 marks

Using 30 = 2 × 3 × 5 and 84 = 2² × 3 × 7, find the LCM of 30 and 84.

  1. 1Take the highest power of each prime: 2², 3, 5, 7
  2. 2LCM = 2² × 3 × 5 × 7 = 420

Answer420

Part (f) · 1 mark

From 2/9, √7, 5/4, √16, 2³, identify and ring the irrational number.

  1. 12/9 and 5/4 are fractions, √16 = 4 and 2³ = 8 are integers
  2. 2√7 cannot be written as a fraction, so √7 is irrational

Answer√7

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Also searched as: 0580/33/O/N/23 · 0580_w23_qp_33 · 0580 w23 33 · question 3.
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