Direct Proportion Equations

y is directly proportional to the square of x. When y = 24, x = 2. Find the value of y when x = 4.

• 6

• 96

• 24

• 2

H varies directly to the cube of c. When H = 40, c = 2. Find H when c = 5.

• 5

• 25

• 625

• 3

H varies directly to the cube of c. When H = 40, c = 2. Find c when H = 5000.

• 5

• 1000

• 10

• 2

A pebble is thrown vertically upwards. It has an initial speed of 𝑢 metres per second. The pebble reaches a maximum height of ℎ metres, before falling vertically downwards. It is known that ℎ is directly proportional to 𝑢 ² . When the pebble is thrown with an initial speed of 10m/s it reaches a maximum height of 5m. Find the initial speed of the pebble if the maximum height reached is 16m.

• 10

• 0.05

• 320

• 17.89

C is directly proportional to the square root of y. When C = 12.8, y = 16. Calculate C when y = 400.

• 3.2

• 20

• 64

• 4

y is directly proportional to x. When y = 270, x = 60. Which of these shows the correct method to calculate the constant of proportionality (k)?

• k = 270 x 60

• k = 270 - 60

• k = 60 / 270

• k = 270 / 60

y is directly proportional to x. When y = 145, x = 15. What is the correct method for calculating the constant of proportionality (k)?

• k = 145 x 15

• k = 145 - 15

• k = 145 / 15

• k = 15 / 145

When x = 15, y = 145. What is the correct method for calculating the constant of proportionality (k)?

• k = 145 x 15

• k = 145 - 15

• k = 145 / 15

• k = 15 / 145

When x = 180, y = 30.

Which is the correct equation linking x and y?

• y = 6x

• x = 6y

The cost C pounds, of hiring a car is directly proportional to the number of days d, it is hired.

When a car is hired for 5 days, the cost is £180.

What is the cost of hiring the car for 20 days?

• £720

• £3.33

• £360

• £33.33

• None of these