Page 23 - Mathematics_Form_Two

Rates and variations

Revision exercise 1 9. Suppose y varies directly as x and
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1. If y = kx and y = 8 when x = 7 , find inversely as √ z . If x = 8, y = 16,
the value of k and the value of y when and z = 25, find the value of y when

x = 40. x = 5 and z = 9.
2. If y is directly proportional to x and 10. Determine whether the data in the
FOR ONLINE READING ONLY
y = 10 when x = 4, find the value of y following tables have an inverse
when x = 15 and the value of x when variation relationship. If yes, find
y = 8 . 4. the missing values.

3. If y ∝ x and y = 16. 5 when x = 3 . 5, (a) x y Mathematics for Secondary Schools
find the equation connecting x and 7 10
y. Hence, find the value of x when 9 12
y = 21. 12 15

4. If y is proportional to x and if 6
2
x = 15 when y = 200, find the equation (b) x y
connecting x and y. Find the value of 12 4
y when x = 8 . 5. 6 2
21 7
5. If y ∝ x x and y = 3 . 5 when x = 4, 3
express y in terms of x. What is the
value of y when x = 25 ? (c) x y
1 − 15 − 8

6. If y ∝ , find the values of a, b, and − 8 − 15

x
c in the following table. 10
x a 1.2 8 c 11. A dairy farm dispenses milk into

y 6 b 1.5 0.8 a container at a rate of 45 litres per

minute.
7. Given that y varies directly as x (a) How much milk is dispensed in
and inversely as z. If y = 10 when 2 hours?
x = 8 and z = 5, find the equation (b) How long will it take to empty a
connecting x, y, and z. Find the value 2000 litre tank?
of y when x = 6 and z = 2 . 5. 12. A water pump operates at a flow rate

8. If y varies jointly as x and z , and if of 300 litres per minute.
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y = 13 when x = 2 . 5 and z = , (a) Calculate the total volume of
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find the equation connecting the three water pumped in 2 hours.
variables. Find the value of x when (b) Calculate the time required to
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z = and y = 54. fill a 30,000-litre tank.
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Student's Book Form Two

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MATHEMATIC F2 v5.indd 17