Interactive quiz

INVALSI mathematics 2013–14: 18 questions

Eighteen questions adapted from the 2013–14 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.

D5a. For someone aged x, the recommended maximum heart rate is 220−x beats per minute. Effective training is between 70% and 90% of this rate. Which interval describes y?

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D21. Starting with a square of area 64 cm², three times join the midpoints of the current square’s sides to form a new square. What is the final side length?

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D12c. In the same survey of 1,500 women, 367 employed and 407 unemployed women give a negative rating. What is the probability of selecting a negative rating?

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D13. y is inversely proportional to x². If y=4 at x=2, what is y at x=8?

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D10b. Monthly salaries and frequencies are: €1,000 (12 people), €1,300 (145), €1,800 (20), €3,500 (8), €5,000 (6). What is the median?

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D4b. A gym charges €60 up front plus €5 per visit. With €200, what is the maximum number of visits?

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D4c. A gym charges a €60 membership fee plus €5 per visit. Which formula gives the total cost C for n visits?

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D22a. For eight hours of parking you can choose A: €15 flat, B: €1 per hour, or C: first hour free then €1.20 for each later hour. Which is cheapest?

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D9. Of 1,000 students, 60% join a race. Then 30% of the runners leave, followed by 40% of those still running. How many finish?

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D22b. Parking costs €1 per hour (B), or the first hour is free and later hours cost €1.20 each (C). After how many whole hours are the prices equal?

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D20. A machine produces 14 defective parts per 1,200 parts. At the same rate, how many defective parts are expected among 2,150, rounded to the nearest whole number?

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D18. A trapezoid circumscribed around a circle of radius 5 cm has area 120 cm². What is the sum of its two parallel bases?

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D1. If k is a negative integer, which of 5+k, 5k, 5−k and 5^k is certainly the greatest?

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D6. Is n²+n+1 prime for every positive integer n?

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D19. Of 100 students, 82 follow football, 26 basketball and 10 neither. How many follow both?

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D17. For which value of k does the equation (2k−3)x+1−k=0 have the solution x=1?

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D12a. In a survey, 450 employed and 276 unemployed women give a positive rating; 367 employed and 407 unemployed give a negative rating. How many positive ratings are there?

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D24. If 0<a<1, what is the correct order of a², a and √a?

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