u | P
s N st c
sic o.za B S
y .c
h s its si
cP o te
uvia | W h y
BS sN st c P
its s ic .za
o BS
y c
| W ALGEBRAP h t eI SURVIVAL
s i a . KIT its
a c o uv | W
B S N
s Course Summary &sPractice Guide t
it s Comprehensive
s i c . za B Sc
W h y s a . co its
| P t e i W
. za S c N o t uv |
o B s s
a . c i ts s i c
o .za
| W P hy t es i a .c its
c o uv W
. z1.a Numbers, Inequalities B S & Absolute
s N Values s t |
. c o s i c za
a i t s .
u vi Fundamental real Wnumber systems and their h yproperties. Key focus ons solving ranges.
a. co
st | P te vi
a c o u
.z
• Sets: Intersection
o (∩) is "common B Sto both"; Union (∪) is "alls elements
c
N together". st a
. c i t s s i . z
va co
• iAbsolute Value Property: |a| = √a². Always non-negative.
W h y s .
u te number. a
st • Inequalities: Flip athe |inequality sign when multiplying c P or dividing by a negative o u vi
.z B S s N s t
o
s i a .c |x| < b ↔ -b < itsx < b | |x| > b ↔ xy<s-bicor x > b
t uv | W
P h e s i a .c
t
s
. za S c N o t uv
o B c s s
s PRACTICE QUESTIONS . c i t s i
te v ia W ys
N o 1. Solve for x:
s tu|3x - 5| ≤ 10 | P h t es
s a c N o
2. Express in interval notation: {x.z∈ ℝ | (x-1)(x-8) / x(x-2)B≥S 0} s
c o s i c s
s . it
o te v ia W h ys s
N tu | P t e
c s s a c o
s i . z B S s N
o
hy s . c
ia & Inverses Wi t s i c
te
2. Functions: Basics v ys
N o
s t u | P h t es
cs a
zGraphs Sc Line Test. N o
sAi function assigns exactly one output to every input. o . must pass the BVertical s
P hy t es i a .c its s ic
S c • Symmetry: Even
N o (f(-x)=f(x), y-axis) vs.tuOdd v (f(-x)=-f(x), origin). | W
P hy
B • Inverses:i c sTo find f⁻¹(x), swap x and y,sthen solve for the newzy.aOnly one-to-one functions S chave N
s o . B s
y c c
P h
inverses.
t es i a . its y si
c o uv | W h
B S s N t
s in most cases. a c P
s c f(g(x)) ≠ g(f(x)) z S
i t i . B
W h ys s . c o
ts
P te ia i y
c o u v | W h
S
PRACTICE
B QUESTIONS N
s st c P
c z a S
its1. Determine the domain y si of f(x) = 1 / √(|x| - 2). c o . B
W h s . i t s
|
c P o t e v ia W
.za B S s N s tu
a
|
its © Wits BSc Physics Notes c
si | Available on stuvia.co.za | Unauthorised copying prohibited .z
y c o
| W
Ph te
s ia.
s N st c
sic o.za B S
y .c
h s its si
cP o te
uvia | W h y
BS sN st c P
its s ic .za
o BS
y c
| W ALGEBRAP h t eI SURVIVAL
s i a . KIT its
a c o uv | W
B S N
s Course Summary &sPractice Guide t
it s Comprehensive
s i c . za B Sc
W h y s a . co its
| P t e i W
. za S c N o t uv |
o B s s
a . c i ts s i c
o .za
| W P hy t es i a .c its
c o uv W
. z1.a Numbers, Inequalities B S & Absolute
s N Values s t |
. c o s i c za
a i t s .
u vi Fundamental real Wnumber systems and their h yproperties. Key focus ons solving ranges.
a. co
st | P te vi
a c o u
.z
• Sets: Intersection
o (∩) is "common B Sto both"; Union (∪) is "alls elements
c
N together". st a
. c i t s s i . z
va co
• iAbsolute Value Property: |a| = √a². Always non-negative.
W h y s .
u te number. a
st • Inequalities: Flip athe |inequality sign when multiplying c P or dividing by a negative o u vi
.z B S s N s t
o
s i a .c |x| < b ↔ -b < itsx < b | |x| > b ↔ xy<s-bicor x > b
t uv | W
P h e s i a .c
t
s
. za S c N o t uv
o B c s s
s PRACTICE QUESTIONS . c i t s i
te v ia W ys
N o 1. Solve for x:
s tu|3x - 5| ≤ 10 | P h t es
s a c N o
2. Express in interval notation: {x.z∈ ℝ | (x-1)(x-8) / x(x-2)B≥S 0} s
c o s i c s
s . it
o te v ia W h ys s
N tu | P t e
c s s a c o
s i . z B S s N
o
hy s . c
ia & Inverses Wi t s i c
te
2. Functions: Basics v ys
N o
s t u | P h t es
cs a
zGraphs Sc Line Test. N o
sAi function assigns exactly one output to every input. o . must pass the BVertical s
P hy t es i a .c its s ic
S c • Symmetry: Even
N o (f(-x)=f(x), y-axis) vs.tuOdd v (f(-x)=-f(x), origin). | W
P hy
B • Inverses:i c sTo find f⁻¹(x), swap x and y,sthen solve for the newzy.aOnly one-to-one functions S chave N
s o . B s
y c c
P h
inverses.
t es i a . its y si
c o uv | W h
B S s N t
s in most cases. a c P
s c f(g(x)) ≠ g(f(x)) z S
i t i . B
W h ys s . c o
ts
P te ia i y
c o u v | W h
S
PRACTICE
B QUESTIONS N
s st c P
c z a S
its1. Determine the domain y si of f(x) = 1 / √(|x| - 2). c o . B
W h s . i t s
|
c P o t e v ia W
.za B S s N s tu
a
|
its © Wits BSc Physics Notes c
si | Available on stuvia.co.za | Unauthorised copying prohibited .z
y c o
| W
Ph te
s ia.
