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1. Unit 21
Formula
Presentation 1 Using Formula
Presentation 2 Constructing Formulae
Presentation 3 Negative Numbers
Presentation 4 Temperature Differences
Presentation 5 Substitutions into Formulae
Presentation 6 More Complex Formulae
Presentation 7 Changing the Subject
Presentation 8 Pendulums

2. Unit 21
Formula
21.1 Using Formula

3. Question
What are the perimeter length and area if and
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The perimeter length, P, and area, A, of a rectangle
are given by the formulae
where l is the length and w the width of the rectangle.
Solution
(b)
l
w4cm
8 cm
Solution
(a)
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4. Unit 21
Formula
21.2 Constructing Formula

5. When repairing air conditioning systems, an
emergency engineer charges a basic fee of J$3000
plus J$1200 per hour.
Question
Find a formula for calculating the engineer's charge
for repair work which takes n hours.
Solution
Let C = Charge
So C = fixed charge + hourly charge × no. of hours
C = J$3000 + J$1200 × n
C = J$3000 + J$1200n
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Question
What does the engineer charge in total if the repair
takes 6 hours?
Solution
C = J$3000 + J$1200 × 6
C = J$3000 + J$7200
C = J$10200
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? ?
?

6. Unit 21
Formula
21.3 Negative Numbers

7. Rules to remember
Calculate
- x - = +
- x + = -
+ x - = -
+ x + = +
- ÷ - = +
- ÷ + = -
+ ÷ - = -
+ ÷ + = +
4 + (−10) = −6 −6 + 8 = 2
−4 − 5 = −9 −6 + (−7) = −13
(−40) ÷ (5) = −8 (−24) ÷ (3) = −8
(−40) ÷ (−5) = 8 (−6) × 7 = −42
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8. Unit 21
Formula
21.4 Temperature Differences

9. Use information given on the above to answer these questions.What is the difference in temperature between
Kingston and Singapore 4 Kingston and London 25
Kingston and Vancouver 29 London and New York 3
London and Sydney 26 Lima and Kingston 0
Oslo and Kingston 30 Moscow and Kingston 34
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10. Unit 21
Formula
21.5 Substitution in Formula

11. l = (40 + 0.02T) cm
The length of a metal rod changes with temperature according
to formula above; where T is the temperature in ˚C
Question
What is the length of the rod when
(a) T = 50˚C (b) T = −10˚C
(a) l = (40 + 0.02 x 50) cm
= (40 + 1) cm
= 41cm
Solution
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(b) l = (40 + 0.02 x −10) cm
= (40 + −0.2) cm
= 39.8cm
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12. Unit 21
Formula
21.6 More Complex Formula

13. The formula gives the focal
length f for a lens
Question
What is the value of f, if u = 10cm and v = 8cm
Solution
? ?
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Hence ?

14. Unit 21
Formula
21.7 Changing the Subject

15. The formula that connects ˚Celsius (C) and
˚Fahrenheit (F) is
Question
Rewrite the formula in the form C = ......
Solution
Take 32 from both sides of the formula
Multiply by 5
throughout
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Divide by 9
throughout
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So

16. Unit 21
Formula
21.8 Pendulums

17. Problem
Make l the subject of this equation.
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The period of revolution, T, of a pendulum of length l
is given by the formula when G is a constant.
Solution
Divide both sides by to give
Square both sides
Multiply both sides by G to give
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