Challenging Questions Mathematics – Compulsory Part Learning Unit: Equations of circles Question M0-13-03 Let \(C\) be the circle \((x – h)^2 + (y – k)^2 = r^2\) and \(L\) be the tangents to \(C\) with slope \(m\). Find the equations of \(L\) in terms of \(h, k, r\) and \(m\). # More challenging questions will... » read more
Challenging Questions Mathematics – Compulsory Part Learning Unit: Equations of circles Question M0-13-02 Let \(C\) be the circle \(x^2 + y^2 – 2x + 6y + 1 = 0\) and \(L\) be the line \(x + y = 4\). # More challenging questions will be updated # Answer
Challenging Questions Mathematics – Compulsory Part Learning Unit: Equations of circles Question M0-13-01 Consider two circles, \(C_1: x^2 + y^2 – 6x – 8y = 0\) \(C_2: x^2 + y^2 – 18x + 8y + 72 = 0\) # More challenging questions will be updated # Answer
Challenging Questions Mathematics – Compulsory Part Learning Unit: More about probability Question M0-16-10 A bag contains 2 white balls (W) and 2 red balls (R). # More challenging questions will be updated # Answer
Challenging Questions Mathematics – Compulsory Part Learning Unit: More about probability Question M0-16-09 In a school, \(\frac{1}{8}\) of the students travel by bus, \(\frac{3}{8}\) by car, and the remaining students walk to school. The probabilities of being late are as follows: # More challenging questions will be updated # Answer
Challenging Questions Mathematics – Compulsory Part Learning Unit: More about probability Question M0-16-08 We have n bags with the following compositions: A ball is drawn randomly from bag 1 and placed in bag 2. Then, a ball is drawn randomly from bag 2 and placed in bag 3. This process continues until a ball is... » read more
Challenging Questions Mathematics – Compulsory Part Learning Unit: More about probability Question M0-16-07 Ben and Ron play a badminton match consisting of multiple rounds. In each round, the probability of Ben winning is \(0.6\). # More challenging questions will be updated # Answer
Challenging Questions Mathematics – Compulsory Part Learning Unit: More about probability Question M0-16-06 Consider \(r\) distinct balls distributed uniformly at random into \(n\) distinct boxes, where \(n>r\). Calculate the probability that at least one box contains two or more balls. # More challenging questions will be updated # Answer
Challenging Questions Mathematics – Compulsory Part Learning Unit: More about probability Question M0-16-05 Given five line segments with lengths 1, 2, 3, 4, and 5 units, three segments are selected at random. What is the probability that these three segments can form a triangle? # More challenging questions will be updated # Answer
Challenging Questions Mathematics – Compulsory Part Learning Unit: More about probability Question M0-16-04 Two people, Ben and Ron, take turns rolling a fair six-sided die. Ben rolls first, and Ron rolls second. The first player to roll a one (1 dot) wins the game. # More challenging questions will be updated # Answer
Challenging Questions Mathematics – Compulsory Part Learning Unit: More about probability Question M0-16-03 In a lucky draw, there are 24 tickets. The tickets are drawn at random, one by one, without replacement. The person who draws a ticket labeled X, Y, or Z wins a prize. Please express your answers as fractions. # More challenging... » read more
Challenging Questions Mathematics – Compulsory Part Learning Unit: More about probability Question M0-16-02 There are \(50\) teachers in a school. Among them, \(30\) teachers are male, while \(20\) teachers are female. In addition, \(8\) English teachers are male and \(5\) English teachers are female. A school committee of \(4\) teachers is formed by selecting them... » read more