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Summary Mathematics 114 summaries R218,00
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  2.  
  3. Stellenbosch University (SUN)
  4.  
  5. Mathematics 144 (MATH114)

Summary

Summary Mathematics 114 summaries
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Aesthetic digital concise summaries of all the theory and some examples you need to know for mathematics 114. The whole semester's content for mathematics 114 is summarised. Self-study: Revision of coordinate geometry & straight lines These are topics that you should be familiar with from school...

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  • No
  • All chapters covered in mathematics 114
  • June 1, 2022
  • 80
  • 2021/2022
  • Summary

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Numbers
•

IR : real numbers

•
IN :
integers ( -2 , 1,0 )

④ rational numbers of
: → ratio
integers
•




→
decimal representation is always repeating
0,50
'
e-
g z
=




É =

0,6666 =
0,5
•
Irrational numbers > cannot be expressed as ratio of integers 11T
,
B
,
1091027
•

IN : natural numbers : [ 1. 2,3 . . . }




°:"^°ᵗ°^"Mb"[)
•
W : whole : 0
, 1,2 3,4 , . . -




± "" " "

if acb then btc (
•
ate <
symbol representing
◦
a
very large number
positive
$




u w Proof by contradiction (§ < 1)
it is between a and b
x exists if
o
{ xlacxcb }
o


Open : Ca , b) =



y g
⑧

{
⑧

Closed : [a ,b] = xla≤ ✗ ≤ b}
, t
a b




solving inequalities : 4x < 2×+1 ≤ 3×+2 / split
,
1




Absolute values

191 ≥ 0 for number a.
every

191=9 if a ≥ 0


191 = -

a if 9<0




az = 1011 for all values of a
,
as a must be ≥ 0 .

, properties
lab / lallbl 13×-21
e. g.
just
=
•
*


b≠0 191
§
•
= 191 =

i




{
/ by
= 1011 = a if a ≥o
a if a < 0
Ian / 1AM NEZ
-


• =

,


•
1×1 =
9 if I = -1-9

•
txt < a if -
a < ✗ < a


•

1×1 > g if ✗ c- a or x > a




e.
g. with
inequalities :




0<1×-51 < É } split

9




{
<
a txt 1×1
0<1×-51 1×-51 < É

X -
5 > 0 or
-



t < x -
S <
{

x -

5 < 0
{ < ✗ <
¥
0 °
i. ✗ < 5 Or × > 5 >
◦
<
I ,

4 'z 5 5
;
i. ✗ E ( 45 5) ,
U / 5. ¥ )

triangle inequality
latbl ≤ 101 -1lb /




and radians
trigonometry
180
✗

radian *
> degree
^




9,0° /
0° 30° 45° 60° 180° 360°
Cosa
Degrees
¥
=




IT IT IT ± 10,1) PE
0 IT 21T
Radians 3- and r=t
6- -4 ( cosy sino )
p⊖ ,
( x , y) : ✗ = ( 050
length of arc


( 1 radian = where a = r
A
a = TO I -1,07
5 OF Poll ,O )
< >
Pit
C
T
Sino =

?
tano =
y
1)
Pgp
co , -




, I
I ≤ 1 I I
[ Oso ≤ and ≤ Sino
-


≤ v
-




COSO =
¥

,Trigonometric identities


•
( 0sec / ⊖ ) = I

Sino I I
'
4 3
• Sec ⊖ = I
z z
COS ⊖ I
,
I
•
cot ⊖ = = COS -0
tano Sino
IT
I
¥
sin ⊖ I
• tan -0 = 3

( 050



PYTHAGOREAN IDENTITIES CO -
FUNCTIONS


(0520--1 Simo 1 (¥ ⊖)
=

cos
-
=
Sino
÷ sink
sin (
÷ cosy
Iz ⊖ )
OSOS
-
= [


L



Sec 20 = I + tan 20 [ 0sec 20
=
1+101-20


EVEN AND ODD DOUBLE ANGLES



[OSC -
⊖) = COSQ sin C- F) =
-
Sino
sin 20 =
Zsinocoso

↳ function ↳ odd function

{
even
cosz⊖ = cos 20 -
sin2⊖

^ ix. 4) 2<0520--1
I -
2sin2⊖
)⊖
>
1- ⊖

CX, -

y
✓




Graphs

or • @




6 • • •




v
↓
o 6 @




0 • @




>

, sets and logic
Week 2

* sets and logic NOT in calculus book

SETS

Basic concept of
•

a set.




•
count no .
elements in a set with finitely many elements .




•
understand what it means :




something is an element of a set


E symbol
when one set is a subset of another set

C
symbol
difference between something being an element of a set us .
subset of a set


Definition of intersection ( n) and union ( U)
•




•
An interval is a set of real numbers

•
Use of interval notation

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