IGCSE Number Ratio & Basic Proportion Past Paper Questions

Higher June 2025 Paper 1R Q11

EdexcelCurrent spec5 marksPercentages Ratio & Basic Proportion

11 Zhou invests some money for 2 years.
He invests $2500 with Bank A and $3000 with Bank B.

Bank A

Invests $2500

amount of money invested : total amount of interest after 2 years = 20 : 3

Bank B

Invests $3000

4% per year compound interest for 2 years

Zhou receives more interest from Bank A than from Bank B.

How much more?

(5)

Mark scheme

Scheme	Marks
2500 ÷ 20 × 3 (= 375) oe or 125 × 3 (=375) or 7500 ÷ 20 (= 375) 3000 ÷ 20 × 3 (= 450) oe or 150 × 3 (= 450) or 9000 ÷ 20 (= 450)	M1
for 0.04 × 3000 (= 120) or 0.04 × 2500 oe (= 100) or 1.04 × 3000 oe (= 3120) or 1.04 × 2500 oe (= 2600) or 3000 × 1.04² (= 3244.8) or 2500 × 1.04² (=2704)	M1
1.04 × “3120” oe (= 3244.8) 1.04 × “2600” oe (= 2704)	M1
eg “3244.8” – 3000 (= 244.8) or “2704” – 2500 (= 204)	M1
Correct answer scores full marks (unless from obvious incorrect working) Answer: 130.2(0)	A1
	(5)
	(5 marks)

Notes

M1: for a method to find the interest for Bank A
2875 or 3450 implies this method mark

M1: for finding 4% or 104% of 3000 or 2500

M1: for completing method to find the total amount for Bank B

M1: for a complete method to find the interest for Bank B

OR M2 for 3000 × 1.04² (= 3244.8) or 2500 × 1.04² (=2704) or 3000 × 1.04³ (= 3374.59) or 2500 × 1.04³ (= 2812.16)

SC: if none of the 2^nd or 3^rd M marks gained award SCM1 for
0.08 × 3000 oe or 240 or 1.08 × 3000 or 3240 or 0.08 × 2500 oe or 200 or 1.08 × 2500 or 2700 or 3000 × (1 – 0.04)² (= 2764.8(0)) or 2500 × (1 – 0.04)² (= 2304)

accept (1 + 0.04) or $\left(1 + \dfrac{4}{100}\right)$ as equivalent to 1.04 throughout

Higher June 2025 Paper 2 Q6

EdexcelCurrent spec4 marksRatio & Basic Proportion

6 Pau, Sam and Tia share £240 in the ratios $3 : 4 : 5$

Sam and Tia each give £10 of their share to Pau.

Work out the ratios of the amounts of money that Pau, Sam and Tia now have.
Give your answer in its simplest form.

(4)

Mark scheme

Scheme	Marks
240 ÷ (3 + 4 + 5) (= 20) or $240 \times \dfrac{3}{3 + 4 + 5}(= 60)$ oe or $240 \times \dfrac{4}{3 + 4 + 5}(= 80)$ oe or $240 \times \dfrac{5}{3 + 4 + 5}(= 100)$ oe	M1
For two of (Pau:) 3 × “20” + 10 + 10 ( = 80) or “60” + 10 + 10 ( = 80) (Sam:) 4 × “20” – 10 ( = 70) or “80” – 10 ( = 70) (Tia:) 5 × “20” – 10 ( = 90) or “100” – 10 ( = 90)	M1
80, 70 and 90 or eg 9 : 7 : 8 oe or eg 4 : 3.5 : 4.5 oe	M1
Working not required, so correct answer scores full marks (unless from obvious incorrect working) Answer: 8 : 7 : 9	A1
	(4)
	(4 marks)

Notes

M1: for a correct method to find the value of one share

NB (240 ÷ 3 =) 80, (240 ÷ 4 =) 60 and (240 ÷ 5 =) 48 scores M0

M1: for the correct values for 2 of the people after S and T give P £10

M1: for all 3 of 80, 70, and 90 correct (ignore units)

or

for the correct values for the final ratio in the wrong order (ignore units)

or

for the correct values for the final ratio unsimplified (ignore units)

A1: other orders are acceptable if labelled correctly