Transcript Unit 8 Number Sequences

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
Unit 21
Formula
21.1 Using Formula
4cm
w
8l cm
Question
The
perimeter length, P, and area, A, of a rectangle
Solution
Solution
are given by the formulae
?
(b) are? the? perimeter
What
and
? length and area if
(a)
? ?
?
?
where l is the length
and w the width of the rectangle.
?
Unit 21
Formula
21.2 Constructing Formula
When repairing air conditioning systems, an
emergency engineer charges a basic fee of J$3000
plus J$1200 per hour.
Question
What
Find adoes
formula
the for
engineer
calculating
charge
theinengineer's
total if the charge
repair
takes
for repair
6 hours?
work which takes n hours.
Solution
?
?
Let C = J$3000
Charge
+ J$1200
×6
So C = J$3000
fixed?charge
+ J$7200
+ ?hourly charge × no. of hours
?
?? + J$1200
C = J$10200
J$3000
× n?
?
C = J$3000 + J$1200n
Unit 21
Formula
21.3 Negative Numbers
Rules to remember
+
+
x
x
x
x
+
+
= +
= = = +
+
+
÷
÷
÷
÷
+
+
= +
= = = +
Calculate
?
4 + (−10) = −6
?
−4 − 5 = −9
?
(−40) ÷ (5) = −8
(−40) ÷ (−5) = 8?
−6 + 8 = 2?
?
−6 + (−7) = −13
?
(−24) ÷ (3) = −8
(−6) × 7 = −42
?
Unit 21
Formula
21.4 Temperature Differences
What
is the difference
Use information
given in
ontemperature
the above tobetween
answer these questions.
Kingston and Singapore
Kingston and Vancouver
London and Sydney
Oslo and Kingston
4?
?
29
?
26
?
30
Kingston and London
London and New York
Lima and Kingston
Moscow and Kingston
?
25
3?
0?
?
34
Unit 21
Formula
21.5 Substitution in Formula
l = (40 + 0.02T) cm
The
length of a metal rod changes with temperature according
Question
to
formula
is when
the temperature in ˚C
What
is theabove;
lengthwhere
of the T
rod
(a) T = 50˚C
(b) T = −10˚C
Solution
(a)
(b)
?? cm
50)
l = (40 + 0.02 x −10)
cm
=
= (40
(40 +
+ ?−0.2)
1)?cm cm
= 39.8cm
??
41cm
Unit 21
Formula
21.6 More Complex Formula
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
?
?
?
?
?
?
Unit 21
Formula
21.7 Changing the Subject
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
So
?
Multiply by 5
throughout
Divide
by 9
throughout
?
?
Unit 21
Formula
21.8 Pendulums
The period of revolution, T, of a pendulum of length l
is given by the formula when G is a constant.
Solution
Problem
Divide
sides by
give
Make lboth
the subject
of this to
equation.
?
Square both sides
?
Multiply both sides by G to give
?
?