Transcript Int 1 Unit 3 Revision

Int 1 Unit 3 Nab
Formula
Multiply Bracket
Multiply Bracket plus letter
Factorise
s+7=13
a+4 > 11
3z=14
5t>20
y=2x+3 Draw Line
Trig Side
Trig Angle
Big to Standard Form
Small to Standard Form
Standard Form to Big
Standard Form to Small
Light Years
What is a Formula
The RHS of the formula is interpreted then
the letters are replaced by numbers
m
=
F=
ma
m xa
F=
F=
F=
a
7
7
x
21
3
=
3
Formula
u=
7
a=
v=
7u
v=
7
3
4a at
xt 3
+
x
+
v=
v=
t=
4
+
19
12
BoDMas
Multiply before Add
Multiply out Brackets
Simply multiply everything inside the bracket
by what is outside the bracket
6 ( a +
=
6 x
=
6a
7 )
6x
+
42
Two “answers one for each term inside the brackets
The + between the a and 7 tells you to subtract the answers
Multiply out Brackets
Simply multiply everything inside the bracket
by what is outside the bracket
5( x =
5 x
=
5x
3 )
5x
-
15
Two “answers one for each term inside the brackets
The - between the x and 3 tells you to subtract the answers
Simply multiply everything inside the bracket by what is outside the bracket
3 ( 2c + 9 )
x
3
x
3
+ 5c
3 x 2xc
6cx c
= 6
3x
=
All Maths “sums” involve BODMAS. ( B ) first
Two answers, one for each term
The + between the 2c and 9 tells you there is a
+ between the answers
27
Simply multiply everything inside the bracket by what is outside the bracket
3 ( 2c +
=
=
6c
11c
9 )
+ 27
+
+ 5c
+ 5c
6c +5c =
27
The brackets equal 6c + 27
Three
terms now
The
expression
has been simplified to 11c + 27
The 1st and last terms are letter terms the middle a number
A letter
term plus
a number
Hide
the middle
term
and addterm
the two letter terms
11c
Simply multiply everything inside the bracket by what is outside the bracket
5 ( 3b - 7 )
x
5
x
5
+ 4b
5 x 3xb
15bx b
= 15
5x
=
All Maths “sums” involve BODMAS. ( B ) first
Two answers, one for each term
The - between the 3b and 7 tells you there is a
- between the answers
35
Simply multiply everything inside the bracket by what is outside the bracket
5 ( 3b -
=
=
7 )
15b - 35
19b
-
+ 4b
+ 4b
15b +4b = 19b
35
The brackets equal 15b -35
Three
terms now
The
expression
has been simplified to 19b - 35
The 1st and last terms are letter terms the middle a number
A letter
term plus
a number
Hide
the middle
term
and addterm
the two letter terms
Factorisation
2d
+
x
x
=
(
8
+
)
Factorising is the opposite
of multiplying the contents
of a bracket
Need to find a number that
you can multiply something to
get 2d and 8.
Find a common factor
by a number ( or a term )
Factorising
2d
+
2d is one term
8
8 is the 2nd term
=
2
(
2
d
x
+
)
4
2
x
Concentrate on the number part
of each … 2 and 8
2x4=8
2d
8
2 x d
2 x 4
2 is a COMMON FACTOR of 2d and 8
s + 7 = 13
s
+ 7
s
Letters to the left
= 13
= 13
- 7
= 6
Change from
+ 7 to - 7
= 6
Numbers to the right
d - 9 = 28
d
- 9
d
Letters to the left
= 28
= 28
+ 9
= 37
Change from
- 9 to + 9
= 37
Numbers to the right
3z = 14
3z
14
=
3 xz
=
14
z
=
14
x3
÷3
z
=
14
3
Opposite of Multiply is
Letter on the left
Divide
Numbers on the right
4g = 21
4g
21
=
4 xg
=
21
g
=
21
x4
÷4
g
=
21
4
Opposite of Multiply is
Letter on the left
=
5.25
Divide
Numbers on the right
a + 4 > 11
a
+ 4
a
> 11
> 11
- 4
> 7
Solve in the same way as equation but replace = with >
Letters to the left
Change from
+ 4 to - 4
Numbers to the right
f-9<5
f
- 9
f
< 5
< 5
+ 9
< 14
Solve in the same way as equation but replace = with >
Letters to the left
Change from
- 9 to + 9
Numbers to the right
5t > 20
5t
20
>
5 xt
>
20
t
>
20
x5
÷5
t
>
4
Opposite of Multiply is
Letter on the left
Divide
Numbers on the right
6d < 42
6d
42
<
6 xd
<
42
d
<
42
x6
÷6
d
<
7
Opposite of Multiply is
Letter on the left
Divide
Numbers on the right
y=2x-3
2
Y=
-3
x
x
0
1
Y
-3
-1
2
1
3
4
3
5
x
Y
x=
0
Y=
2x0-3
-3
( 0 , -3)
x=
1
Y=
2x1-3
-1
( 1 , -1)
1
( 2 , 1)
x=
2
Y=
2x2-3
x=
3
Y=
2x3-3
3
( 3 , 3)
x=
4
Y=
2x4-3
5
( 4 , 5)
=
0
2–3=3
-1
x=0
x=1
y=
2
x
0
x1
-
3
X
X
X
X
X
y=3x+1
3
Y=
X
+1
x
x
0
1
Y
-3
-1
2
1
3
4
3
5
X
x
Y
x=
0
Y=
3x0+1
1
( 0 , 1)
x=
1
Y=
3x1+1
4
( 1 , 4)
x=
2
Y=
3x2+1
7
( 2 , 7)
x=
3
Y=
3x3+1
10
( 3 , 10)
x=
4
Y=
3x4+1
13
( 4 , 13)
=
0
3 + 1 = 14
x=1
x=0
y=
y= 33
xx
1x0
x
+
1
X
X
X
SohCahToa


C
H
S

=
13
Opp
61°
Sin
b
T
H
A

SOH
=
b
O
A
O
Hyp

=
61°
=
13 x Sin 61
b
Opp
13
Hyp
=
=
11.37
=
Identify sides then click letters in SohCahToa
b on its own. Opposite of Div is mult
SohCahToa

=
Opp
51°
A
T
H

TOA
Tan 51°
e
Adj = 12
C
H
=
e
O
A
O
S


=
=
e
Opp
12
Adj
12 x Tan 51
=
=
14.819
Identify sides then click letters in SohCahToa
No
51° Adj
SohCahToa


Hyp
Cos
9
c°
c°
Adj = 5
=
Adj
9
Hyp
Cos-1 (0.55556...)
cos-1 Ans
0.55555556
56.2510114
c°
5
5 ÷9
=
0.556
=
56.3
Move Cos to other side --- > Cos-1
Opp
No
=
c°


CAH
=
A
T
H
C
H
S
=
O
A
O
Adj
sin
cos
SHIFT
tan
√ ² C x
÷
5 6 7 8 9
+
-
On
0 1 2 3 4
.
=
Ans
(-)
Big to Standard Form
4
3
6
2
0
4
3
6
2
x 10
Move your finger, from point, until you get a
whole number less than 10
Copy figure then add a point
Copy other figure until all that is to be copied is zeros
Add x 10
4
4
3
3
6
6
2
2
0
x 10
4
213
Count number of places from new position to old position
This number goes above the 10 to indicate how often
you multiply by 10
7
5
7
9
9
3
5
0
0
0
0
x 10
3
9
9
5
5
0
3
0
0
x 10
5
3
6
5
0
6
3
0
2
2
3
5
5
x 10
6
6
x 10
2
1
Small Numbers
0
0
0
0
5
5
3
3
6
6
2
2
x 10
-2
-3
-4
-1
Ignore the zeros at the front then cover
until you get a number less than 10
Copy figure, add a point then other figure until all that is left are zeros
Add x 10
The original position of the point is to THE LEFT
Count …. 1 to left …. -1 …. 2 to left ….. -2 and so on
-4
0.0005362 = 5.363 x 10
0
0
0
0
0
0
2
4
2
4
0
0
x 10
6
6
4
4
-3
6
6
x 10
-5
SF to normal
=
4
3
6
2
4
3
6
2
x 10
0
0
7
0
0
Start as if there were no figures after point
You have to multiply by 10 seven times.
Instead of adding 7 zeros put 7 underlines
The “lines” show where the point should go
Copy other figure until all that is to be copied is zeros
Fill remaining places with zeros
3
3
3
3
x 10
0
0
3
4
8
4
3
4
8
4
0
5
0
x 10
1
Add Point then other figures
Small to normal
7
=
0
0
0
0
0
0
0
0 7
8
8
0
0
3
x 10
-8
3
Start as if there were no figures after point
Positive means GO RIGHT ….. Negative means GO LEFT
Need 8 underline going left starting under the 7 …. -8 …. 8 to LEFT
The “lines” show where the point should go
Put zeros above the lines
Copy other figure until all that is to be copied is zeros
Small to Normal
0
0
0
0
0
0
5 to the left of “line”
0
0
8
5
9
3
8
5
9
3
8
9
8
9
x 10
x 10
3 to the left of “line”
-5
-3
Light Years
Distances in the solar system are vast.
Distance from the Sun to Pluto is
59 400 000 000 km or 5.95 x 1010 km
To make sense of distance people often use
time. For these extremely large distances
scientists use the time that Light takes to go
from one point to another
As a comparison light takes about 1.27 seconds to go from
the Moon to Earth.
Light takes 4 Hours and 2 minutes to go from Pluto to the Earth
About 22 000 times the time so about 22000 the distance
Light Years
Proxima Centauri is the closest star to the Solar
System. It is 4.22 Light years away
If it was possible to build a craft which could travel at the speed of
light it would take over 4 years to get to this star. 4 hours into the
journey it would pass Pluto having completed about 1 / 365 part of
the journey
1 Light Year is 9.467 x 1012 km
Distance to Proxima Centauri
is 4.22 Light Year
4.22x9.47 x 1012 = 4.22 x 9.47
4.22 x 9.467
x 10x
12
4.22
E
12
12
Light
Year
9.467
x 10
km
4.22 x
=3.995 x 1013 km
7 Light Year
7x9.47 x 1012 =
7 x 9.467
7
7 x 9.47
x 10x
E
12
12
32 x 9.467
7x
=6.629 x 1013 km
32 Light Year
32x9.47 x 1012 =
32
32 x 9.47
x 10x
E
12
12
Light
Year
9.467
x 10
km
12
12
Light
Year
9.467
x 10
km
32 x
=3.0304 x 1014 km
0
(-)
Ans
On
C √ ²
7 8 9 x
√ ² C x
÷
5 6 7 8 9
+
-
On
0 1 2 3 4
.
=
Ans
(-)
Test
0
4
5 6 ÷
1
2 3
0
.
-
= +