Page 22 - Mathematics_Form_Two

Rates and variations

3. The height h of a cone varies directly (c) d varies directly as y and the
as its volume V and inversely as the square root of z.
square of its radius r. Write a formula 11. The heating cost H for a house
for the height of the cone. varies directly with its size S in
4. If y varies directly as x − 1 and square metres and inversely with
2
inversely as x + d and x = 2, d = 4 the efficiency rating E of the heating
FOR ONLINE READING ONLY
when y = 1, find the value of x when system. If H = 50,000 shillings for
Mathematics for Secondary Schools 5. If two typists in a typing pool can 12. The shipping cost C varies directly
y = 2 and d = 1.
a house of 200 square metres with
an efficiency rating of 4, find k and
the heating cost for a house of 250
type 210 pages in 3 days, how many
square metres with an efficiency
typists working at the same speed
rating of 5.
will be needed to type 700 pages in
2 days?
6. Suppose x varies directly as y and
2
and inversely with the number
inversely as p. If x = 2, when y = 3
of packages n. If the cost is TShs
and p = 1, find the value of y when with the mass W of the package
x = 4 and p = 5. 7,000,000 for a package weighing
7. If V varies directly as the square of 20 kg, and 6 packages, find k and
x and inversely as y , and if V = 18 the cost of a package weighing 30
when x = 3 and y = 4, find the kg with 5 packages.
value of V when x = 5 and y = 2.
8. Use a mathematical software to draw Chapter summary
the following curves. Assume that 1. A rate gives the change of one quantity
the constant of proportionality is 1. with respect to another quantity.
1 __
(a) y ∝ 2. Exchange rate is the conversion rate
x
1 __
(b) y ∝ between different currencies.
x 3. Variation is the relationship in which
2
1
_
(c) y ∝ the change in one quantity results in
_
√ x
9. The following table shows the values a proportional change in the other.
of y for some selected values of x. 4. If y = kx, then y varies directly with
The variables x and y are connected x, or y is directly proportional to x.
by the relation, ʻ y varies inversely as The constant k is called a constant of
x̕ . Calculate the missing values of y. proportionality.

x 5 10 15 20 5. If y varies as 1 , then y is inversely

x
y a 3 b 1.5 proportional to x.

10. Express each of the following 6. If a quantity varies as the product of
relations as an equation using k as a two or more quantities, then it varies
constant of proportionality. jointly with other quantities.
(a) c varies directly as p and q , and 7. If both direct variation and inverse
inversely as s. variation occur at the same time, then
(b) d varies jointly as t and r . it is called a combined variation.
2

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Student's Book Form Two

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MATHEMATIC F2 v5.indd 16