Easy Mathematics

A target is an object used in various shooting sports to test the accuracy of various firearms (pistols, darts, bows and arrows, etc.). The center of the target is called the bullseye, and shooters try to make the bullet land as close to the bullseye as possible. The image below shows the standard five-color ten-ring target used in World Archery competitions, with a diameter of 80cm. The scores from the outermost ring to the bullseye range from 1 to 10. a) If a shooter can obtain all scores from 1 to 10 with equal probability in one shot, find the radius r of the bullseye. b) Assume the spacing between each ring is the same. A shooter shoots the target independently three times, obtaining a score X. Find the expected value of X.

Randomly choose 2 numbers in the interval [0, 1]. Determine the probability that their product is more than 0.4

In a farming simulation game, an animal has equal chance to produce a product at anytime between 30 and 40 second after you fed them. a) When you fed an animal, determine the probability that you receive 2 product after 1 minute 10 seconds. b) When you fed 5 animals, what is the expected number of product you will receive in 38 seconds? c) At the beginning of a game, a player has 20 chickens which produce eggs, each player is required to receive 32 eggs within t seconds, otherwise he loses the game. i) When t = 75, determine the probability that the player loses the game. ii) You should ensure that each player has 95% of winning chance, determine the least integer value of t that satisfies the requirement.

In a farming simulation game, an animal has equal chance to produce a product at anytime between 30 and 40 second after you fed them. a) When you fed an animal, determine the probability that you receive 2 product after 1 minute 10 seconds. b) When you fed 5 animals, what is the expected number of product you will receive in 38 seconds? c) At the beginning of a game, you have 20 chickens which produce eggs, you are required to receive 32 eggs within t seconds. i) When t = 75, determine the probability that you lose the game. ii) You should ensure that each player has 95% of winning chance, determine the least integer value of t that satisfies the requirement.

Randomly choose an arithmetic progression that formed using the integers from 1 to 100 (inclusive). Find the probability that this sequence has exactly 20 terms.

Randomly choose an arithmetic progression that formed using the integers from 1 to 100 (inclusive). Find the probability that this sequence has exactly 20 terms.

Gao Kao 2026 (2) 新高考二卷

Gao Kao 2026 （1） 新高考一卷