Interactive quiz

ESAT Mathematics 1 — 14 introductory exercises

Two original questions for each of the seven ESAT Mathematics 1 guide areas, with worked answers.

14 randomly selected questions Pass mark: 60%

Instructions

Questions and options are shuffled. One point for a correct answer, zero for an error or omission. Read the explanation after submission. This is a teaching selection; consult the linked PDF for the full material.

Ratio. Two groups are in the ratio 3:5 and contain 64 people altogether. How many are in the first group?

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Numbers. What is the prime factorisation of 84?

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Numbers. Which is greater, −0.3 or −1/4?

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Statistics. Four numbers have mean 8. Three are 4, 7 and 10. What is the fourth?

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Units. What is the most suitable unit for the volume of water in a swimming pool?

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Algebra. Solve 3(x−2)=2x+5.

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Units. A car travels 250 km in 5 hours. What is its average speed?

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Probability. A bag has 3 red and 2 blue balls. If two are drawn without replacement, what is the probability both are red?

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Algebra. Which product equals x²−9?

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Statistics. What is the median of 2, 5, 7, 9 and 100?

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Geometry. What is the area of a circle with radius 3 cm?

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Ratio. A price rises by 20% and then falls by 20%. What fraction of the original price remains?

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Probability. When two fair dice are rolled, what is the probability that their sum is 7?

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Geometry. A rectangle has sides of 6 cm and 8 cm. How long is its diagonal?

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