iGCSE Mathematics (0580) :E1.13 Use a calculator efficiently.iGCSE Style Questions Paper 4

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Question

(a) In 2018, Gretal earned $$32000.$
(i) She paid tax of 24% on these earnings.
Work out the amount she paid in tax in 2018.
(ii) In 2019, Gretal’s earnings increased by 7%.
Work out her earnings in 2019.

(b) Gretal invests $$5000$ at a rate of 2% per year compound interest.
Calculate the value of her investment at the end of 3 years.

(c) One month, Gretal spent a total of $$360$ on presents.
She spent $\frac{1}{5}$ of this total on presents for her parents.
She spent $\frac{2}{3}$of the remaining money on presents for her friends.
She spent the rest of the money on presents for her sisters.
Calculate the percentage of the $$360$ that she spent on presents for her sisters.

(d) Arjun earned $$36515$ in 2019.
This was an increase of 9% on his earnings in 2018.
Work out his earnings in 2018.

(e) Arjun and Gretal each pay rent.
In 2018, the ratio of the amount each paid in rent was Arjun : Gretal = 5 : 7.
In 2019, the ratio of the amount each paid in rent was Arjun : Gretal = 9 : 13.
Arjun paid the same amount of rent in both 2018 and 2019.
Gretal paid $$290$ more rent in 2019 than she did in 2018.
Work out the amount Arjun paid in rent in 2019.

▶️ Answer/Explanation

(a)(i) Answer: $$7680$

Multiply earnings by tax rate: $32000 \times 0.24 = 7680$.

(a)(ii) Answer: $$34240$

7% increase: $32000 \times 1.07 = 34240$.

(b) Answer: $$5306.04$

Compound interest formula: $5000 \times (1.02)^3 ≈ 5306.04$.

(c) Answer: $26.67\%$

Parents: $72$, friends: $192$, sisters: $96$. $\frac{96}{360} \times 100 ≈ 26.67\%$.

(d) Answer: $$33500.46$

2018 earnings: $\frac{36515}{1.09} ≈ 33500.46$.

(e) Answer: $$6525$

Solve ratios: $5x = 9y$ and $13y – 7x = 290$. $x = 1305$, so Arjun paid $5x = 6525$.

Question

(a) Anvi buys a new car.

(i) The price of the car is $28,240.
She is given a 7.5% discount.

Calculate the amount she pays.

(ii) The fuel tank in the new car has a capacity of 45 litres.
This is 72% of the capacity of the fuel tank in her old car.

Calculate the capacity of the fuel tank in her old car.

(b) Aadi buys a new car costing $28,000.
He pays for the car using a finance plan.
The finance plan is:

A deposit
47 equal monthly payments of $330
A final payment of $11,490

Using this finance plan, Aadi pays a total of $31,900 for the car.

Calculate the deposit paid as a percentage of $28,000.

(c) A car travels 64 km and uses 2.5 litres of fuel.
It then travels 128 km and uses 6 litres of fuel.

Calculate the rate at which the car uses fuel during the whole journey.
Give your answer in litres per 100 km.

(d) At the start of 2021 the value of a car was $46,500.
At the end of 2021 the value of the car was 20% less.
At the end of 2022 the value of the car was 15% less than its value at the end of 2021.

Calculate the value of the car at the end of 2022.

▶️ Answer/Explanation

Solution

(a)(i) $26,122

Calculate 7.5% discount: $28,240 × 0.075 = $2,118. Subtract from original price: $28,240 – $2,118 = $26,122.

(a)(ii) 62.5 litres

Let old capacity be x. 72% of x = 45 litres → x = 45 ÷ 0.72 = 62.5 litres.

(b) 17.5%

Total payments minus installments: $31,900 – ($330 × 47) – $11,490 = $4,900 deposit. As percentage: ($4,900 ÷ $28,000) × 100 = 17.5%.

(c) 4.43 litres per 100 km

Total fuel used: 2.5 + 6 = 8.5 litres. Total distance: 64 + 128 = 192 km. Rate: (8.5 ÷ 192) × 100 ≈ 4.43 litres per 100 km.

(d) $31,620

End of 2021 value: $46,500 × 0.80 = $37,200. End of 2022 value: $37,200 × 0.85 = $31,620.

iGCSE Mathematics (0580) :E1.13 Use a calculator efficiently.iGCSE Style Questions Paper 4

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