Interactive quiz

INVALSI mathematics 2014–15: 18 questions

Eighteen questions adapted from the 2014–15 INVALSI grade-10 paper, with worked solutions.

18 randomly selected questions Pass mark: 60%

Instructions

Questions and answers are shuffled. One point for a correct answer and zero for a wrong or blank answer. Worked solutions appear after submission. This is an adapted selection, not the complete official paper.

D28a. A yoghurt pot weighs 125 g and 11% is vanilla preparation. Approximately how many grams is that?

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D28b. Yoghurt contains 16.3 g of carbohydrates per 100 g. How much is in a 125 g pot, rounded to one decimal place?

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D25. In 300 rolls of a fair six-sided die, about how often should the result exceed 4?

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D2. For which real numbers is x²+1≥0 true?

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D17. A laundrette opens for nine hours daily. Each load needs 10 minutes to fill, a 33-minute cycle and five minutes to empty. What is the maximum number of complete loads per machine?

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D11a. Which ratio defines π for every circle?

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D18b. Two independent side effects affect 2% and 7% of patients respectively. What percentage experience both?

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D12a. One day’s temperatures are −8, −10, −10, −3, +1, −1, −3 and −6 °C. What is the temperature range?

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D8a. A call costs €0.15 connection plus €0.12 per minute or part-minute. What is the charge for 7 minutes 10 seconds?

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D16. If the ratio of the edge lengths of two cubes is 5, what is the ratio of their volumes?

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D9a. The counts of pupils living 100–499 m, 500–999 m, 1000–1499 m, 1500–1999 m and 2000–2499 m from school are 2, 8, 5, 7 and 3. How many live less than 1 km away?

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D4c. A tank starts with 100 m³; it gains 5 m³ and loses 7 m³ each week. After how many weeks is it empty?

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D12b. Temperatures measured at regular intervals are −8, −10, −10, −3, +1, −1, −3 and −6 °C. What is their arithmetic mean?

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D9b. With frequencies 2, 8, 5, 7 and 3 in the distance bands 100–499 m, 500–999 m, 1000–1499 m, 1500–1999 m and 2000–2499 m, what percentage lives less than 1.5 km away?

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D7. A 2.5 m pole casts a 0.8 m shadow. At the same time an obelisk casts a 6.4 m shadow. How tall is it?

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D11b. What does it mean that π is irrational?

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D22. An urn contains 23 red and 17 blue balls. After two blue balls are removed without replacement, what is the probability the third is blue?

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D23. In a test, 20 students have an average score of 85 and another 80 average 65. What is the overall average for all 100 students?

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