1) The document contains multiple choice questions about different types of variations between quantities including direct, inverse, joint and combined variations. 2) It asks the reader to identify equations that represent these different variations, determine unknown values given variations between quantities, and choose statements that correctly describe the variations. 3) It contains questions about direct and inverse variations between time and workers, area of a triangle, volume of a cone, and relationships between multiple variables.

1. Which relations between two quantities
states “If one quantity increases, the other
also increases”?
a. Inverse variation
b. direct variation
c. joint variation
d. combined variation

2. The number of days (d) to finish a certain
task varies inversely as the number (n) of
men working is written as
a. d = kn b. d =
𝑘
𝑛
c. k =
𝑑
𝑛
d. y = kdn

3. The formula for the area of a triangle
A =
1
2
bh is an example of_______.
a. direct variation
b. inverse variation
c. joint variation
d. combined variation

4. If y varies directly as x, and y = 40 when
x= 10, find y when x =12. (2 points)

5. What kind of variation does
p =
𝑘𝑏²
𝑠³
represent?
a. direct b. inverse
c. joint d. combined

6. Which equation below represents
inverse variation?
a. xy =
1
𝑘
b. y =
𝑘
𝑥
c.
1
𝑥𝑦
= k d.
𝑘
𝑥𝑦
=
1
2

7. The volume (V) of a cone varies
jointly as the square of the radius (r)
of its base and its height (h). Which
equation describes the variation
statement?
a. V = kr²h c. V = krh²
b. V =
𝑘𝑟²
ℎ
d. V =
𝑟²ℎ
𝑘

8. If y varies inversely as x and y= 30 when x
=9, find x when y = 540. (2 points)

9. Day 3

10. What is the variation statement for y =
𝑘𝑏
𝑐
?
a. y varies directly as b and c
b. y is inversely proportional to b and c
c. y varies directly as b and inversely as c d.
y varies jointly as b and c

11. Describe the graph at the right.
a. y varies directly as x
b. x varies directly as y
c. y varies inversely as x
d. x varies jointly as y

13. If x varies jointly with y and the square of z. If
x=72 and y= 9 when z=2, find y when x = 36 and
z=3. (2 points)

14. Determine the variation statement for
the given table of values.
y
a. y is proportional to k
b. y varies inversely as x
c. y varies directly as x
d. x varies inversely as y

15. Find the constant of variation when “y
varies inversely as x”
given y=16 and 𝑥 =
1
4
.
a. 6 b. 5 c. 4 d. 2

16. If y varies directly as x and y = 18 when x
= 3, find the equation of variation.
a. y = 3x b. y = 5x
c. y = 6x d. y = 8x

17. If z varies directly as x and inversely as y² and z=5
when x =4 and y=2, find z when x=5 and y=2. (2
points)

18. If s varies directly as t and inversely as v,
then which of the following equations
describes the relation among the three
variables s, t and v?
a. 𝑠 =
𝑥
𝑡𝑣
b. 𝑠 =
𝑘𝑣
𝑡
c.
1
𝑠
=
𝑘𝑡
𝑣
d. 𝑠 =
𝑘𝑡
𝑣

19. What is the equation of variation that
describes the table of values below? Write
your solution in any space of this page or in
a separate sheet of paper.
𝑎. 𝑦 = 6𝑥 c. 𝑥𝑦 = 6
b. 𝑦 =
6
𝑥
d. 𝑥 = 6𝑦

20. What happens to T when h is doubled in the
equation T = 4h?
a. T is halved b. T is tripled
c. T is doubled d. T becomes zero