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Rates and variations questions

Rates and variations questions | form three Basic Mathematics

Find Rates and variations examination questions, form three Basic Mathematics in acaproso.com

# Question
1

The area of a circular sector containing a given angle varies as the square of the radius of the circle. If the area of the sector is 2cm2 when the radius is 1.6cm, find the area of the sector containing the same angle when the radius of the circle is 2.7cm.


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2

Express the following equations as two statements each, using the words ‘varies’ and ‘proportional’.

  1. V(r)=frac{4}{3}pi r^{3}
  2. T(l)=frac{pi}{2sqrt{2}}sqrt{l}
  3. z(t)=frac{1}{t^{2}}

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3

The variables t and z in the following table are related by the formula z=atn where a is a constant and n is a positive integer.

  1. Use the data from the table to determine the values of a and n.
  2. Use the values of a and n obtained in part (a) (i) to complete the following table.
t 1 2 3 4 5
z 0.5 4 13.5    

 


Mathematical Calculation
4

If v varies directly as the square of x and inversely as sqrt{y}, given that v=18 when x=3 and y=16, find the values of v when x=5 and y=4.


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5

Mr. Ogango from Kenya visited Tanzania. He had 5,000 Kenya shillings (Kshs) and wanted to change the money into US dollars. If 1 US dollar was equivalent to 2500 Tanzania shilliings (Tshs) and Ksh 1 was equivalent to Tshs 20, how much US dollars did he get?.


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6

A gardener has found the time t to cut the grass on a square field varies directly as the square of its length (L) and inversely as a number of men(m) doing that job. If 5 men cut grass on a field of side 50m in 3 hours, how many more men are required to cut grass on a field of side 100m in 5 hours? assume that the men are working on the same pace.


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7

Mukasa received Ushs 1,000,000 from his sister in Uganda. How much did he get in Tanzania currency (Tshs) if one Ugandan shilling was equivalent to 0.65 Tanzanian shillings?


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8

The energy (E) stored in an elastic band varies as square of the extension (x). Whn the elastic band is extended by 4cm, the energy stored is 240 joules. what is the energy stored when the extension is 6cm? what is the extension when the stored energy is 60 joules?


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9

In the preparation of fanta orange drink, a bottling filling machine can fill 1,500 bottles in 45 minutes. How many bottles will it fill in 4½ hours?


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10

If X varies directly as Y and inversely as W, find the values of a and b in the table below.

X 8 6 b
Y 4 a 2
W 2 3 4

 


Mathematical Calculation