Sec 2 Mathematics Direct & Inverse Proportion topical questions

Three identical notebooks cost $4.50.

1. (a)Find the cost of one notebook.[1]
2. (b)Find the cost of seven notebooks.[1]
3. (c)How many notebooks can be bought for $13.50?[1]

y is directly proportional to x, and y = 15 when x = 5.

1. (a)Find the constant k.[1]
2. (b)Write the equation linking y and x.[1]
3. (c)Find y when x = 12.[1]

A pancake recipe needs 200 g of flour to make 12 pancakes.

1. (a)How much flour is needed for 18 pancakes?[2]
2. (b)How many pancakes can be made from 500 g of flour?[1]

y is directly proportional to x, and y = 9 when x = 3.

1. (a)Find the constant k.[1]
2. (b)Write the equation linking y and x.[1]
3. (c)Find x when y = 21.[1]

Four packets of noodles feed 10 pupils at a camp.

1. (a)How many packets are needed for 25 pupils?[1]
2. (b)How many pupils can 14 packets feed?[1]
3. (c)State the unit rate in pupils per packet.[1]

y is inversely proportional to x, and y = 8 when x = 3.

1. (a)Find the constant k.[1]
2. (b)Find y when x = 6.[1]
3. (c)Find x when y = 12.[1]
4. (d)Explain what stays constant as x and y change.[1]

A construction team of 6 workers builds a wall in 15 days.

1. (a)Find the total number of worker-days the wall needs.[1]
2. (b)How long would 9 workers take?[2]
3. (c)How many workers are needed to finish in 6 days?[1]

A car covers a fixed journey at 60 km/h in 4 hours.

1. (a)Find the distance of the journey.[1]
2. (b)How long would the journey take at 80 km/h?[1]
3. (c)What average speed covers the journey in 5 hours?[1]
4. (d)Which type of proportion links speed and time here, and why?[1]

Two rules are compared: y = 5x and y = 20/x.

1. (a)Describe the graph of y = 5x.[1]
2. (b)Describe the graph of y = 20/x.[1]
3. (c)Which of the two graphs passes through the origin, and why?[1]
4. (d)Give one point (other than (2, 10)) on the graph of y = 20/x.[1]

y is inversely proportional to x², and y = 5 when x = 2.

1. (a)Find the constant k.[1]
2. (b)Find the value of y when x is 4.[1]
3. (c)Find x when y = 20.[2]

Six helpers pack 1 200 goodie bags for a HDB block party in 4 hours.

1. (a)Find the total helper-hours needed.[1]
2. (b)How long would 8 helpers take?[2]
3. (c)How many helpers are needed to finish in 2 hours?[1]

Set A gives the pairs (1, 3), (2, 6), (4, 12). Set B gives the pairs (1, 24), (2, 12), (4, 6).

1. (a)Identify the type of proportion in Set A and state its constant.[2]
2. (b)Identify the type of proportion in Set B and state its constant.[2]
3. (c)Predict the value paired with x = 8 in Set B.[1]

A car’s braking distance d (in metres) is proportional to the square of its speed v (in m/s). At 10 m/s the braking distance is 20 m.

1. (a)Find the constant of proportionality.[2]
2. (b)Find the braking distance at 15 m/s.[2]
3. (c)What happens to the braking distance if the speed doubles?[1]

A catering team of 4 cooks prepares a banquet in 3 hours. Each extra cook is billed $35 per hour.

1. (a)Find the total cook-hours of work the banquet needs.[1]
2. (b)The client wants the job done in 2 hours. How many cooks are needed?[2]
3. (c)Find the extra cost of hiring the larger team for the 2-hour job.[2]

The pressure P (in kPa) of a fixed amount of gas is inversely proportional to its volume V (in litres). The pressure is 300 kPa when the volume is 2 L.

1. (a)Write the equation linking P and V.[2]
2. (b)Find P when V = 5.[1]
3. (c)Find V when P = 75.[1]
4. (d)Explain why V = 0 cannot occur.[1]