SSS2 Math Quiz 19.3 – Geometric progressions

If ‘y’ varies directly as ‘x’ and inversely as ‘z’, and y = 10 when x = 4 and z = 2, find y when x = 8 and z = 4.

If ‘p’ is directly proportional to the square of ‘q’ and inversely proportional to ‘r’, and p = 12 when q = 3 and r = 2, find p when q = 2 and r = 3.

The volume of a gas ‘V’ varies directly with its temperature ‘T’ and inversely with its pressure ‘P’. If V = 40 liters when T = 300 K and P = 2 atmospheres, find V when T = 240 K and P = 3 atmospheres.

The time ‘t’ taken to complete a journey varies directly with the distance ‘d’ and inversely with the speed ‘s’. If t = 3 hours when d = 180 km and s = 60 km/h, find t when d = 240 km and s = 80 km/h.

The force of attraction ‘F’ between two objects varies directly with the product of their masses ‘m₁’ and ‘m₂’ and inversely with the square of the distance ‘d’ between them. If F = 10 N when m₁ = 2 kg, m₂ = 3 kg, and d = 1 m, find F when m₁ = 4 kg, m₂ = 6 kg, and d = 2 m.

The cost of painting a wall ‘C’ varies directly with its area ‘A’ and the cost of paint per square meter ‘p’. If C = $60 when A = 15 m² and p = $4/m², find C when A = 20 m² and p = $5/m².

The electrical resistance ‘R’ of a wire varies directly with its length ‘L’ and inversely with the square of its diameter ‘d’. If R = 10 ohms when L = 50 m and d = 2 mm, find R when L = 100 m and d = 4 mm.

The time ‘t’ taken to fill a swimming pool varies directly with its volume ‘V’ and inversely with the flow rate ‘F’ of the water. If t = 6 hours when V = 120 m³ and F = 20 m³/hour, find t when V = 180 m³ and F = 30 m³/hour.

The number of days ‘d’ it takes to complete a project varies directly with the amount of work ‘W’ and inversely with the number of workers ‘n’. If d = 10 days when W = 300 units and n = 6 workers, find d when W = 450 units and n = 9 workers.

The kinetic energy ‘KE’ of an object varies directly with its mass ‘m’ and the square of its velocity ‘v’. If KE = 50 joules when m = 2 kg and v = 5 m/s, find KE when m = 4 kg and v = 10 m/s.

The amount of money earned (E) is directly proportional to the number of hours worked (h) and the hourly rate (r). If John earns $120 after working 8 hours at $15/hour, how much will he earn if he works 10 hours at $18/hour?

The force (F) needed to stretch a spring is directly proportional to the extension (x) and the spring constant (k). If a force of 10 N stretches a spring by 0.2 m and the spring constant is 50 N/m, what force is needed to stretch the same spring by 0.5 m?

The time (t) it takes to fill a tank is directly proportional to the volume of the tank (V) and inversely proportional to the flow rate (r). If it takes 3 hours to fill a 600-liter tank at a flow rate of 200 liters/hour, how long will it take to fill a 900-liter tank at a flow rate of 300 liters/hour?

The gravitational force (F) between two objects is directly proportional to the product of their masses (m1 and m2) and inversely proportional to the square of the distance (d) between them. If the force between two objects is 100 N when their masses are 5 kg and 10 kg and the distance between them is 2 m, what will be the force if the masses are doubled and the distance is halved?

The volume of a gas (V) is directly proportional to its temperature (T) and inversely proportional to its pressure (P). If the volume of a gas is 20 liters at a temperature of 300 K and a pressure of 2 atmospheres, what will be the volume if the temperature is increased to 360 K and the pressure is decreased to 1.5 atmospheres?

The intensity of light (I) is directly proportional to the power of the source (P) and inversely proportional to the square of the distance (d) from the source. If the intensity of light is 50 units at a distance of 2 meters from a 100-watt bulb, what will be the intensity at a distance of 4 meters from a 200-watt bulb?

The number of days (d) it takes to complete a task varies directly with the amount of work (w) and inversely with the number of people (p) working on it. If it takes 5 people 10 days to complete 200 units of work, how long will it take 8 people to complete 320 units of work?

The resistance (R) of a wire is directly proportional to its length (L) and inversely proportional to its cross-sectional area (A). If a wire of length 10 meters and cross-sectional area 0.5 mm² has a resistance of 2 ohms, what will be the resistance of a wire of the same material with a length of 20 meters and a cross-sectional area of 0.25 mm²?

The frequency (f) of a vibrating string is directly proportional to the square root of the tension (T) in the string and inversely proportional to its length (L). If a string has a frequency of 440 Hz when the tension is 100 N and the length is 0.5 m, what will be the frequency if the tension is increased to 144 N and the length is kept the same?

The amount of heat (Q) required to raise the temperature of a substance is directly proportional to its mass (m), its specific heat capacity (c), and the change in temperature (ΔT). If 1000 J of heat is required to raise the temperature of 2 kg of a substance with a specific heat capacity of 400 J/kg°C by 1.25°C, how much heat is required to raise the temperature of 3 kg of the same substance by 2°C?