Home / iGCSE Mathematics (0580) :C1.13 Use a calculator efficiently. iGCSE Style Questions Paper 3

iGCSE Mathematics (0580) :C1.13 Use a calculator efficiently. iGCSE Style Questions Paper 3

Question

A family go on a skiing holiday to America.

(a) The hotel has 840 rooms. 735 rooms are occupied. Calculate the percentage of rooms that are occupied.

(b) The temperature in the hotel is 21°C. The temperature in the hotel is 26.7°C warmer than at the top of the mountain. The temperature at the top of the mountain is 3.2 °C colder than at the bottom of the mountain. Work out the temperature at the bottom of the mountain.

(c) There are two adults and one child in the family. They hire all their equipment. The child skis for 3 days and snowboards for 4 days. Both adults ski for 7 days. All three of them hire a helmet for 7 days. Work out the total cost of the equipment hire for the family.

Ski equipment pricing

(d) A ski lift, when full, takes 4000 passengers per hour. This lift works for 10 hours a day. One day, this lift is 90% full for 3 hours and 75% full for 7 hours. Work out the number of passengers who take the lift that day.

(e) The family buy their lift passes before the holiday for a total of 51400 rupees. In America, the passes cost a total of $684. The exchange rate is 1 rupee = $0.0129. Show that the family save 1620 rupees, correct to the nearest 10 rupees, by buying the passes before their holiday.

(f) The height, h metres, of the mountain is 2642m, correct to the nearest metre. Complete this statement about the value of h. …… ≤ h < …….

▶️ Answer/Explanation

(a) 87.5% – (735÷840)×100 = 87.5% occupancy rate.

(b) −2.5°C – Mountain top: 21-26.7 = -5.7°C. Bottom: -5.7+3.2 = -2.5°C.

(c) 431.90 – Adults: 2×(7×24) + 2×(7×5) = 406. Child: (3×12)+(4×15) = 96. Helmets: 3×7×1.40 = 29.40. Total: 406+96+29.40 = 431.90.

(d) 31,800 – (4000×0.9×3)+(4000×0.75×7) = 10,800 + 21,000 = 31,800 passengers.

(e) 1620 rupees – $684 ÷ 0.0129 = 53,023 rupees. Savings: 53,023 – 51,400 = 1,623 ≈ 1,620 rupees.

(f) 2641.5 ≤ h < 2642.5 – Nearest metre means values within ±0.5m of 2642m.

Question

(a) Tom has a restaurant bill.

Soup$……
Pasta$13.30
Ice cream$4.80
Drinks$3.81
Total cost$25.40

(i) Complete the bill to show the cost of soup.
(ii) Find the cost of drinks as a percentage of the total cost.

(b) (i) Work out \(\frac{2}{5}\) of \($2400\).
(ii) Decrease \($3450\) by 18%.

(c) Amelia invests \($14000\) at a rate of \(1.6%\) per year compound interest.

Calculate the value of her investment at the end of \(5\) years.
Give your answer correct to the nearest dollar.

(d) This conversion graph can be used to change between dollars and Swiss francs.

(i) Use the graph to change

(a) \($80\) to Swiss francs
(b) \(108\) Swiss francs to dollars.

(ii) Explain how you can use the graph to change \($360\) to Swiss francs.

▶️ Answer/Explanation
Solution

(a)(i) Ans: $3.49

Subtract all other items from total: \($25.40 – ($13.30 + $4.80 + $3.81) = $3.49\)

(a)(ii) Ans: 15%

Divide drinks cost by total: \(($3.81 ÷ $25.40) × 100 = 15%\)

(b)(i) Ans: $960

Calculate 2/5 of 2400: \($2400 × (2/5) = $960\)

(b)(ii) Ans: $2829

Decrease amount by 18%: \($3450 × (1 – 0.18) = $3450 × 0.82 = $2829\)

(c) Ans: $15156

Compound interest calculation: \($14000\) × \((1 + 0.016)^5\) = \($14000 × 1.0824 ≈ $15156\)

(d)(i)(a) Ans: 72 Swiss francs

From graph, \($80\) corresponds to 72 Swiss francs.

(d)(i)(b) Ans: $120

From graph, 108 Swiss francs corresponds to \($120\).

(d)(ii) Explanation:

Since \($360\) is beyond the graph’s scale, find \($180\) (half of \($360\)) on the graph, get corresponding Swiss francs, then double that value.

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