y is inversely proportional to x. When x = 4, y = 9. Find y when x = 6.
(1)
2
In the relationship y = k/x, x = 3 and y = 20. Find the value of k.
(1)
3
p is inversely proportional to q. When q = 5, p = 10. Find p when q = 2.
(1)
4
In y = k/x, x = 8 and y = 5. Find k.
(1)
5
a is inversely proportional to b. When b = 7, a = 6. Find a when b = 21.
(1)
6
m and n are inversely proportional. When m = 12, n = 3. Find n when m = 4.
(1)
7
y = 24/x. Find y when x = 6.
(1)
8
State whether the number of days needed to build a wall and the number of identical builders (working at the same steady rate) are directly proportional or inversely proportional.
(1)
9
Two quantities x and y are inversely proportional. When x = 5, y = 8. Find y when x = 20.
(2)
10
r is inversely proportional to s. When s = 9, r = 4. Find s when r = 12.
(2)
11
y is inversely proportional to x2. When x = 2, y = 18. Find y when x = 3.
(2)
12
The variable c is inversely proportional to d. When d = 0.5, c = 16. Find c when d = 4.
(2)
13
w is inversely proportional to t. When t = 3, w = 14. Find w when t = 8. Give your answer as a decimal.
(2)
14
Two variables g and h are inversely proportional. When g = 15, h = 4. Find h when g = 6.
(2)
15
A printing company assigns identical printers to a job. The time taken is inversely proportional to the number of printers used, assuming each printer works at the same rate and the same total work is required. It takes 8 printers 15 hours to complete the job. How many hours would 12 printers take to complete the same job?
(3)
16
The force needed to balance a see-saw is inversely proportional to the distance from the pivot. A force of 45 N balances the see-saw at a distance of 2 m from the pivot. What force is needed to balance it at a distance of 5 m from the pivot?
(3)
17
A charity divides a fixed amount of money equally among a number of families. The amount each family receives is inversely proportional to the number of families sharing the money. If 6 families each receive 150 pounds, how much would each family receive if there were 9 families instead?
(3)
18
The number of tiles needed to cover a floor of fixed area is inversely proportional to the area of one tile. Using tiles of area 0.25 m2, 96 tiles are needed. How many tiles of area 0.4 m2 are needed to cover the same floor?
(3)
19
The time taken for identical machines to complete a printing order is inversely proportional to the number of machines used, assuming a fixed total amount of work and each machine works at the same rate. Using 5 machines, the order takes 18 hours. Find how many machines are needed to complete the same order in 3 hours.
(4)
20
A water tank is filled by a number of identical pipes working together. The time to fill the tank is inversely proportional to the number of pipes used, assuming a fixed tank volume and each pipe delivers water at the same steady rate. It takes 4 pipes 6 hours to fill the tank. A larger job requires the time to be reduced to 1.5 hours using the same type of pipes. How many pipes are needed, and how many more pipes is this than the original 4?
(4)
Mark scheme · KS3.M-R8D Inverse Proportion: Fluency and Exam Drill
Question 1
B1 y = 6 cao
Answer: y = 6
Question 2
B1 k = 60 cao
Answer: k = 60
Question 3
B1 p = 25 cao
Answer: p = 25
Question 4
B1 k = 40 cao
Answer: k = 40
Question 5
B1 a = 2 cao
Answer: a = 2
Question 6
B1 n = 9 cao
Answer: n = 9
Question 7
B1 y = 4 cao
Answer: y = 4
Question 8
B1 Inversely proportional (oe)
Answer: Inversely proportional
Question 9
M1 find k = 5*8 = 40 or state y = k/x
A1 y = 2 cao
Answer: y = 2
Question 10
M1 find k = 9*4 = 36
A1 s = 3 cao
Answer: s = 3
Question 11
M1 find k = y*x2 = 18*4 = 72
A1 y = 8 cao
Answer: y = 8
Question 12
M1 find k = 0.5*16 = 8
A1 c = 2 cao
Answer: c = 2
Question 13
M1 find k = 3*14 = 42
A1 w = 5.25 cao
Answer: w = 5.25
Question 14
M1 find k = 15*4 = 60
A1 h = 10 cao
Answer: h = 10
Question 15
M1 use inverse proportion: k = printers*time = 8*15 = 120 or state time = k/printers