This document contains summaries of 8 presentations about formulas: 1. Using formulas to calculate the perimeter and area of a rectangle given the length and width. 2. Constructing a formula to calculate an engineer's charge based on a fixed fee plus an hourly rate multiplied by hours worked. 3. Reviewing rules for performing calculations with negative numbers. 4. Using information provided to calculate temperature differences between various cities. 5. Substituting values into a formula to calculate the length of a metal rod at different temperatures. 6. Substituting values into a more complex formula involving fractions to calculate a focal length. 7. Rewriting a formula connecting Celsius and Fahrenheit

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
?
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
? ?
?
?
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
? ?
? ?
?

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
? ?
? ? ?
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.
?
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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