Direct Proportion - RED
1. A is directly proportional to B. When A=24, B=3.
a) Write an equation linking A and B
b) Calculate A when B = 5
2. A is directly proportional to B. When A=42, B=7.
a) Write an equation linking A and B
b) Calculate A when B = 5
3. A is directly proportional to B. When A=72, B=8.
a) Write an equation linking A and B
b) Calculate A when B = 9
4. A is directly proportional to B. When A=5, B=25. (take care with this question)
a) Write an equation linking A and B
b) Calculate A when B = 5
5. A is directly proportional to B. When A=100, B=4.
a) Write an equation linking A and B
b) Calculate A when B = 10
6. A is directly proportional to B. When A=90, B=15. (take care with this question)
a) Write an equation linking A and B
b) Calculate B when A = 72
7. A is directly proportional to B. When A=15, B=45.
a) Write an equation linking A and B
b) Calculate B when A = 16
2
8. A is directly proportional to B . When A=45, B=3.
a) Write an equation linking A and B
b) Calculate A when B = 4
Direct Proportion - AMBER
2
1. A is directly proportional to B . When A=45, B=3.
a) Write an equation linking A and B
b) Calculate A when B = 4
2
2. A is directly proportional to B . When A=50, B=5.
a) Write an equation linking A and B
b) Calculate A when B = 4
3. A is directly proportional to the square of B. When A=48, B=4.
a) Write an equation linking A and B
b) Calculate A when B = 6
4. A is directly proportional to the square of B. When A=8, B=4. (take care with
this question)
a) Write an equation linking A and B
b) Calculate B when A = 18
5. A is directly proportional to the square root of B. When A=8, B=4.
a) Write an equation linking A and B
b) Calculate B when A = 24
c) Calculate A when B = 49
6. A is directly proportional to the square root of B. When A=24, B=4.
a) Write an equation linking A and B
b) Calculate A when B = 81
c) Calculate B when A = 60
7. A is directly proportional to the cube of B. When A=54, B=3.
a) Write an equation linking A and B
b) Calculate A when B = 4
Direct Proportion - GREEN
1. A is directly proportional to the cube of B. When A=54, B=3.
a) Write an equation linking A and B
b) Calculate A when B = 4
2. A is directly proportional to the cube of B. When A=81, B=3.
a) Write an equation linking A and B
b) Calculate A when B = 4
3. A is directly proportional to the cube root of B. When A=24, B=216.
a) Write an equation linking A and B
b) Calculate A when B = 8
4. The volume, V, of a balloon is proportional to the cube of its radius, r. When the
radius of 10 cm the volume is 4200 cm3.
a) Find a relationship between V and r.
b) Find the volume of a balloon of radius 5 cm.
c) Find the radius of a balloon that has a volume of 8400 cm3.
5. y is directly proportional to the square of x. When y = 5, x = 4.
a) Find the value of y when x = 8.
6. The distance, d km, it is possible to see on a clear day is proportional to the
square root of the height, h m, above sea level.
Standing on a pier, 4 m above sea level, it is possible to see a distance of 10 km.
a) Find a formula for d in terms of h.
Standing on top of the cliffs I can see a distance of 35 km.
b) How high are the cliffs?
ANSWERS
RED
1)
2)
3)
4)
A)
A)
A)
A)
A=8B
A=6B
A=9B
1
A=5B
5) A) A=25B
6) A) A=6B
1
7) A) A=3B
8) A) A=5B2
B)
B)
B)
B)
40
30
81
1
B) 250
B) 12
B) 48
B) 80
AMBER
1)
2)
3)
4)
A)
A)
A)
A)
A=5B2
A=2B2
A=3B2
1
A=2B 2
B) 80
B) 32
B) 108
B) 6
A=2B3
A=3B3
3
A = 4 √𝐵
V=4.2r3
20
d=5√ℎ
B) 128
B) 192
B) 8
B) 525
5) A) A=4√𝐵 B) 36
6) A) A=12√𝐵 B) 108
7) A) A=2B3
B) 128
C) 28
C) 25
GREEN
1)
2)
3)
4)
5)
6)
A)
A)
A)
A)
A)
A)
B) 49
C) 12.6cm (1dp)