Page 14 - Mathematics_Form_Two

Rates and variations

3. If x varies directly as y and x = 30 (b) If yes, calculate the constant
when y = 40, find the value of x of proportionality and find the
when y = 16. equation that describes the
4. A mason can build 100 metres of relationship.
fence in 20 hours. How long will it 11. The volume of a sphere varies as the
take 5 masons with the same ability cube of its radius. Three solid spheres
FOR ONLINE READING ONLY
3 __
5 __
of diameters m, 2 m, and m are
Mathematics for Secondary Schools 6. If 8 men can assemble 16 machines 12. When observing two buildings
to build 875 metres of fence?
2
2
melted and combined to form a new
5. If x varies directly as 2y + 7 and
solid sphere. Find the diameter of the
x = 5 , when y = 4, find the value
new sphere.
of y when x = 6.
simultaneously, the length of each
in 12 days, how long will it take 15
with its height. If a 5 floor building
men of the same ability to assemble
has a shadow of length 20 m, how
100 machines? building's shadow varies directly
7. If y varies directly as the square root many floors of a building would form
of x, and y = 12 when x = 4, find a shadow of length 32 m?
the value of y when x = 9. 13. The resistance of a wire varies as
8. If y varies directly as x and y = 8 the square of the diameter of its
cross-section. Find the percentage
when x = 3, find the value of y change in the resistance when the
when x = 18. diameter is (a) doubled (b) reduced

9. Two variables x and y that vary by 20%.
directly have corresponding values 14. Two variables A and x are related by
as shown in the following table. the formula A ax= n . The following
x 3 5 6 8 set of data was generated based on
this formula.
y 17 34 58 x 1 2 3 4

(a) Find the rule connecting x and y . A 0.5 2 4.5 8

(b) Fill in the missing values. (a) Find the values of a and n.

(c) Draw a graph which shows that (b) Find the value of A when x = 5.
y ∝ x for k = 1. 15. A precious stone worth
Tshs 15,600,000 is accidentally
10. Study the following table and answer dropped and broken into three
the questions that follow. pieces. The weights of the pieces

Hours 2 3 4 5 are in the proportions of 2:3:5,
worked respectively. If the value of the

Earning 1,150 1,725 2,300 2,875 precious stone varies directly as
(Tsh) the cube of its weight, calculate
(a) Do earnings vary directly as the the value of the remaining stone in
percentage.
number of hours worked?

8
Student's Book Form Two

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MATHEMATIC F2 v5.indd 8 11/10/2024 20:11:08
MATHEMATIC F2 v5.indd 8