Page 18 - Mathematics_Form_Two
P. 18
Rates and variations
10. The time t in seconds that Mary 2. Find and describe real-life examples
takes to return home from school of such variations using daily
varies inversely with her average practices such as formulas.
speed v in metres per second. If 3. Share your final observations and
Mary gets back home in half an discuss the examples you discovered.
hour at an average speed of 10 m/s; Joint variation
FOR ONLINE READING ONLY
(a)
write and sketch the graph of
Mathematics for Secondary Schools (b) if Mary wants to get back home area of a triangle. It is given by
the equation.
Consider a formula for finding the
1
in 15 minutes, what must be
Area = ×base×height. In this equation,
2
her average speed?
the area of a triangle varies directly as the
why the graph in (a) does not
(c)
product of its base and height. Variable
cross either axes?
relationships of this nature are known as
(d) what happens to t as v joint variations. This specific variation
increases? As v decreases? can be generally expressed as
How does t and v vary?
Area ∝ base height. ×
11. The intensity of light varies inversely
as the square of the distance from the A joint variation occurs when a variable
light source. If the intensity from a is directly or inversely proportional to
light source 90 cm away is 12 lumen, the product of two or more variables.
how far should the light source be so Mathematically, if a variable z varies
that the intensity is 4 lumen? jointly as x and y, the general formula for
joint variation can be written as:
Joint and combined variations z ∝ xy ⇒ z = kxy
In some activities, one variable can Example 1�11
depend on several other variables to
operate effectively. Such relationships Suppose y varies directly as x and z.
are described by joint and combined Given x = 4, z = 2, and y = 24, find:
variations. Engage in Activity 4.5 to (a) The variation equation connecting
explore more about joint and combined x, y, and z.
variations in real-life activities. (b) The value of y when x = 5 and
z = 6 .
Activity 1�5: Discovering joint and
combined variations in daily life Solution
1. Explore the concepts of joint and (a) Since y ∝ x and y ∝ z, it follows that
combined variations using books y ∝ xz,
and online resources. y = kxz.
12
Student's Book Form Two
11/10/2024 20:11:09
MATHEMATIC F2 v5.indd 12
MATHEMATIC F2 v5.indd 12 11/10/2024 20:11:09
