Rithvik's Blog 11+

  f(x) = (3x^2 + 5x - 2) * (4x^3 - 2x + 7) What is the value of x when f(x) = 1480

A cylindrical tank has a diameter of 6 meters and a height of 10 meters. The tank is initially filled to 3/4 of its capacity with water. A pipe is connected to the tank and is pouring water into it at a rate of 0.2 cubic meters per minute. At the same time, water is being drained from the tank through another pipe at a rate of 0.1 cubic meters per minute. a) Calculate the total capacity of the tank in cubic meters. b) Determine the rate at which the water level in the tank is rising (or falling) in centimeters per minute, when it is 4/5 full.

  Simplify the following expression: (3x^2 - 2x + 5) - (2x^2 + 4x - 1)

  Solve the following simultaneous equations for x and y: 3x + 2y = 11 2x - y = 4

A bag contains 6 red marbles and 4 blue marbles. Two marbles are drawn from the bag without replacement. a) What is the probability of drawing two red marbles in succession? b) What is the probability of drawing a red marble followed by a blue marble?

Solve the following simultaneous equations: 2x + 3y = 7 4x - y = 5 A geometric sequence has a common ratio of 2. The sum of the first four terms is 30. a) Find the first term of the sequence. b) Find the sum of the first ten terms of the sequence.

Simplify the following expression: (2x^2 + 3x - 5) - (x^2 - 4x + 2) + (5x^2 + 2x + 7)

The equation of a circle is given by (x - 2)^2 + (y + 3)^2 = 25. Determine the centre coordinates and radius of the circle.