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Math Problems
Algebra 2
Simplify rational expressions
Rationalise the denomitor
\newline
2
6
−
5
3
5
−
2
5
\frac{2 \sqrt{6}-\sqrt{5}}{3 \sqrt{5}-2 \sqrt{5}}
3
5
−
2
5
2
6
−
5
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Select the expressions that are equivalent to
5
q
+
2
q
5q + 2q
5
q
+
2
q
.
\newline
Multi-select Choices:
\newline
(A)
q
+
4
q
+
2
q
q + 4q + 2q
q
+
4
q
+
2
q
\newline
(B)
q
7
q^7
q
7
\newline
(C)
q
×
7
q \times 7
q
×
7
\newline
(D)
6
q
6q
6
q
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Select the expressions that are equivalent to
2
(
9
m
)
2(9m)
2
(
9
m
)
.
\newline
Multi-select Choices:
\newline
(A)
9
(
2
m
)
9(2m)
9
(
2
m
)
\newline
(B)
2
+
9
m
2 + 9m
2
+
9
m
\newline
(C)
9
m
+
2
9m + 2
9
m
+
2
\newline
(D)
18
m
18m
18
m
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Select the expressions that are equivalent to
6
b
+
5
b
6b + 5b
6
b
+
5
b
.
\newline
Multi-select Choices:
\newline
(A)
b
11
b^{11}
b
11
\newline
(B)
b
+
11
b + 11
b
+
11
\newline
(C)
11
b
11b
11
b
\newline
(D)
9
b
+
b
9b + b
9
b
+
b
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Select the expressions that are equivalent to
3
(
6
x
)
3(6x)
3
(
6
x
)
.
\newline
Multi-select Choices:
\newline
(A)
(
3
x
)
6
(3x)6
(
3
x
)
6
\newline
(B)
18
x
18x
18
x
\newline
(C)
3
+
6
x
3 + 6x
3
+
6
x
\newline
(D)
3
(
x
+
5
x
)
3(x + 5x)
3
(
x
+
5
x
)
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Select the expressions that are equivalent to
3
f
+
6
f
3f + 6f
3
f
+
6
f
.
\newline
Multi-select Choices:
\newline
(A)
9
f
+
f
9f + f
9
f
+
f
\newline
(B)
9
f
9f
9
f
\newline
(C)
8
f
8f
8
f
\newline
(D)
4
f
+
6
f
4f + 6f
4
f
+
6
f
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Which expression is equivalent to
3
r
+
2
r
3r + 2r
3
r
+
2
r
?
\newline
Choices:
\newline
(A)
5
r
5r
5
r
\newline
(B)
r
5
r^5
r
5
\newline
(C)
4
r
4r
4
r
\newline
(D)
r
+
5
r + 5
r
+
5
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Select the expressions that are equivalent to
4
j
+
8
j
4j + 8j
4
j
+
8
j
.
\newline
Multi-select Choices:
\newline
(A)
2
j
+
2
j
+
8
j
2j + 2j + 8j
2
j
+
2
j
+
8
j
\newline
(B)
j
+
12
j + 12
j
+
12
\newline
(C)
j
×
12
j \times 12
j
×
12
\newline
(D)
13
j
13j
13
j
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Question
5
5
5
\newline
Pause
\newline
Zoom
\newline
Look at the graph below.
\newline
What is the solution of
\newline
\left\{\begin{array}{l}2y-3x=9,\4y+3x=12\end{array}\right.?:
\newline
c
2024
2024
2024
Ifluminate Education TM, Inc
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Select all the numbers that are irrational.
\newline
Multi-select Choices:
\newline
(A)
2
\sqrt{2}
2
\newline
(B)
2
3
\frac{2}{3}
3
2
\newline
(C)
0.
8
‾
0.\overline{8}
0.
8
\newline
(D)
π
2
\frac{\pi}{2}
2
π
\newline
(E)
−
4.99
-4.99
−
4.99
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Expand each of the following, using suitable identities:
\newline
(i)
(
x
+
2
y
+
4
z
)
2
(x+2 y+4 z)^{2}
(
x
+
2
y
+
4
z
)
2
\newline
(ii)
(
2
x
−
y
+
z
)
2
(2 x-y+z)^{2}
(
2
x
−
y
+
z
)
2
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Which expression is equivalent to
3
h
+
2
h
3h + 2h
3
h
+
2
h
?
\newline
Choices:
\newline
(A)
5
h
5h
5
h
\newline
(B)
h
5
h^5
h
5
\newline
(C)
4
h
4h
4
h
\newline
(D)
h
+
5
h + 5
h
+
5
Get tutor help
Which expression is equivalent to
3
b
+
6
b
3b + 6b
3
b
+
6
b
?
\newline
Choices:
\newline
(A)
b
+
9
b + 9
b
+
9
\newline
(B)
8
b
8b
8
b
\newline
(C)
b
9
b^9
b
9
\newline
(D)
9
b
9b
9
b
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Select the expressions that are equivalent to
2
q
+
q
2q + q
2
q
+
q
.
\newline
Multi-select Choices:
\newline
(A)
2
q
2q
2
q
\newline
(B)
4
q
−
q
4q - q
4
q
−
q
\newline
(C)
q
+
q
+
q
q + q + q
q
+
q
+
q
\newline
(D)
3
q
3q
3
q
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Select the expressions that are equivalent to
9
k
+
2
k
9k + 2k
9
k
+
2
k
.
\newline
Multi-select Choices:
\newline
(A)
11
k
11k
11
k
\newline
(B)
10
k
+
2
k
10k + 2k
10
k
+
2
k
\newline
(C)
8
k
+
2
k
8k + 2k
8
k
+
2
k
\newline
(D)
5
k
+
7
k
5k + 7k
5
k
+
7
k
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Select the expressions that are equivalent to
9
(
t
+
4
)
9(t + 4)
9
(
t
+
4
)
.
\newline
Multi-select Choices:
\newline
(A)
9
(
4
+
t
)
9(4 + t)
9
(
4
+
t
)
\newline
(B)
13
t
13t
13
t
\newline
(C)
(
t
+
4
)
9
(t + 4)9
(
t
+
4
)
9
\newline
(D)
(
4
+
t
)
9
(4 + t)9
(
4
+
t
)
9
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Select the expressions that are equivalent to
7
(
q
+
4
)
7(q + 4)
7
(
q
+
4
)
.
\newline
Multi-select Choices:
\newline
(A)
(
4
q
)
7
(4q)7
(
4
q
)
7
\newline
(B)
11
q
11q
11
q
\newline
(C)
(
q
+
4
)
7
(q + 4)7
(
q
+
4
)
7
\newline
(D)
4
(
q
+
7
)
4(q + 7)
4
(
q
+
7
)
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Select the expressions that are equivalent to
6
(
u
+
5
)
6(u + 5)
6
(
u
+
5
)
.
\newline
Multi-select Choices:
\newline
(A)
(
u
⋅
5
)
6
(u \cdot 5)6
(
u
⋅
5
)
6
\newline
(B)
30
u
+
6
30u + 6
30
u
+
6
\newline
(C)
6
u
+
30
6u + 30
6
u
+
30
\newline
(D)
30
u
30u
30
u
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Select the expressions that are equivalent to
3
(
m
+
9
)
3(m + 9)
3
(
m
+
9
)
.
\newline
Multi-select Choices:
\newline
(A)
(
m
+
9
)
3
(m + 9)3
(
m
+
9
)
3
\newline
(B)
27
m
27m
27
m
\newline
(C)
27
m
+
3
27m + 3
27
m
+
3
\newline
(D)
12
m
12m
12
m
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Write a factor that you can use to rationalize the denominator of
\newline
2
5
−
8
\frac{\sqrt{2}}{\sqrt{5}-8}
5
−
8
2
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Which equation has both
3
3
3
and
−
3
-3
−
3
as possible values of
x
x
x
? Select all that apply.
\newline
Multi-select Choices:
\newline
(A)
x
2
=
6
x^2 = 6
x
2
=
6
\newline
(B)
x
3
=
6
x^3 = 6
x
3
=
6
\newline
(C)
x
2
=
9
x^2 = 9
x
2
=
9
\newline
(D)
x
3
=
9
x^3 = 9
x
3
=
9
\newline
(E)
x
2
=
27
x^2 = 27
x
2
=
27
\newline
(F)
x
3
=
27
x^3 = 27
x
3
=
27
Get tutor help
Which of the following are polynomials?
\newline
(Select all that apply)
\newline
A
1
2
x
2
+
7
x
+
4
\frac{1}{2} x^{2}+7 x+4
2
1
x
2
+
7
x
+
4
\newline
B
x
−
2
+
23
x
−
99
x^{-2}+23 x-99
x
−
2
+
23
x
−
99
\newline
C
5
x
2
−
12
x
5 x^{2}-12 x
5
x
2
−
12
x
\newline
D
1
x
2
+
5
x
−
12
\frac{1}{x^{2}}+5 x-12
x
2
1
+
5
x
−
12
Get tutor help
Direct Messages - SEQTA Le
\newline
Assessment Master - Exam Wi
\newline
assess.scsa.wa.edu.au/engine/index.php/Ims/index
\newline
School Curriculum
\newline
and Standards
\newline
Authority
\newline
Numeracy
\newline
()
0
0
0
:
11
11
11
:
58
58
58
/
0
0
0
:
50
50
50
:
00
00
00
\newline
31751624
31751624
31751624
\newline
43
43
43
of
45
45
45
\newline
In a board game, two standard dice are thrown.
\newline
The top numbers are then added to determine the number of spaces a player moves.
\newline
To land on a blue space, Ben must throw a total of
8
8
8
or
9
9
9
on his next turn. What is the probability that Ben would land on a blue space?
\newline
2
36
\frac{2}{36}
36
2
\newline
5
36
\frac{5}{36}
36
5
\newline
9
36
\frac{9}{36}
36
9
\newline
10
36
\frac{10}{36}
36
10
\newline
Content copyright WA School Curriculum and Standards Authority
2024
2024
2024
\newline
a
a
a
\newline
Assessment
\newline
Copyright
⊕
\oplus
⊕
SoNET Systems Pty Ltd.
2024
2024
2024
\newline
(.)
\newline
Master
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rom the following equal or
\newline
(
x
+
2
x
,
3
)
=
(
−
1
,
2
x
−
v
)
(x+2 x, 3)=(-1,2 x-v)
(
x
+
2
x
,
3
)
=
(
−
1
,
2
x
−
v
)
Get tutor help
Select all the expressions that are equivalent to
1
1
5
/
1
1
5
11^5/11^5
1
1
5
/1
1
5
.
\newline
Multi-select Choices:
\newline
(A)
1
1
0
11^0
1
1
0
\newline
(B)
11
11
11
\newline
(C)
1
1
1
\newline
(D)
1
1
10
11^{10}
1
1
10
Get tutor help
Select all the expressions that are equivalent to
1
2
2
6
2
\frac{12^2}{6^2}
6
2
1
2
2
.
\newline
Multi-select Choices:
\newline
(A)
2
−
3
2
−
5
\frac{2^{-3}}{2^{-5}}
2
−
5
2
−
3
\newline
(B)
2
2
2
\newline
(C)
(
2
−
2
)
−
1
(2^{-2})^{-1}
(
2
−
2
)
−
1
\newline
(D)
2
2
2^2
2
2
Get tutor help
Select all the expressions that are equivalent to
2
6
×
2
9
2^6 \times 2^9
2
6
×
2
9
.
\newline
Multi-select Choices:
\newline
(A)
(
2
5
)
3
(2^5)^3
(
2
5
)
3
\newline
(B)
1
2
15
6
15
\frac{12^{15}}{6^{15}}
6
15
1
2
15
\newline
(C)
2
54
2^{54}
2
54
\newline
(D)
2
15
2^{15}
2
15
Get tutor help
Select all the expressions that are equivalent to
6
6
2
6
\frac{6^6}{2^6}
2
6
6
6
.
\newline
Multi-select Choices:
\newline
(A)
3
3
3
\newline
(B)
1
3
6
\frac{1}{3^6}
3
6
1
\newline
(C)
3
0
3^0
3
0
\newline
(D)
3
6
3^6
3
6
Get tutor help
Select all the expressions that are equivalent to
8
−
2
×
7
−
2
8^{-2} \times 7^{-2}
8
−
2
×
7
−
2
.
\newline
Multi-select Choices:
\newline
(A)
1
5
6
2
\frac{1}{56^2}
5
6
2
1
\newline
(B)
5
6
4
56^4
5
6
4
\newline
(C)
5
6
−
2
56^{-2}
5
6
−
2
\newline
(D)
5
6
−
4
56^{-4}
5
6
−
4
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Select all the expressions that are equivalent to
(
7
5
)
1
(7^5)^1
(
7
5
)
1
.
\newline
Multi-select Choices:
\newline
(A)
1
7
5
\frac{1}{7^5}
7
5
1
\newline
(B)
1
7
−
5
\frac{1}{7^{-5}}
7
−
5
1
\newline
(C)
7
5
7^5
7
5
\newline
(D)
7
6
7^6
7
6
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Select all the expressions that are equivalent to
(
6
1
)
5
(6^1)^5
(
6
1
)
5
.
\newline
Multi-select Choices:
\newline
(A)
6
5
6^5
6
5
\newline
(B)
1
6
−
5
\frac{1}{6^{-5}}
6
−
5
1
\newline
(C)
1
6
6
\frac{1}{6^6}
6
6
1
\newline
(D)
1
6
5
\frac{1}{6^5}
6
5
1
Get tutor help
Select all the expressions that are equivalent to
3
2
3
2
\frac{3^2}{3^2}
3
2
3
2
.
\newline
Multi-select Choices:
\newline
(A)
1
1
1
\newline
(B)
1
3
0
\frac{1}{3^0}
3
0
1
\newline
(C)
3
0
3^0
3
0
\newline
(D)
3
4
3^4
3
4
Get tutor help
What is the relationship between
\newline
∠
a
\angle a
∠
a
and
\newline
∠
b
\angle b
∠
b
?
\newline
Choose
1
1
1
answer:
\newline
(A) Vertical angles
\newline
(B) Complementary angles
\newline
(C) Supplementary angles
\newline
(D) None of the above
Get tutor help
−
2
x
2
+
10
x
−
8
-2x^2+10x-8
−
2
x
2
+
10
x
−
8
which of the following is equivalent to the given expression
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Which of the following is a solution to the equation
(
x
−
2
)
2
=
25
?
(x-2)^{2}=25 ?
(
x
−
2
)
2
=
25
?
Get tutor help
Divide and simplify.
\newline
3
n
9
+
6
n
5
−
15
n
2
−
3
n
4
\frac{3 n^{9}+6 n^{5}-15 n^{2}}{-3 n^{4}}
−
3
n
4
3
n
9
+
6
n
5
−
15
n
2
Get tutor help
Choase the coroct ansurer
\newline
−
84
,
−
52
,
−
12
is
a)
18
b)
−
18
c)
\begin{array}{lll} -84,-52,-12 & \text { is } \\ \text { a) } \begin{array}{lll} 18 & \text { b) }-18 & \text { c) } \end{array} \end{array}
−
84
,
−
52
,
−
12
a)
18
b)
−
18
c)
is
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3
3
3
. The greatest common factor of
200
×
3
200 \times 3
200
×
3
and
2
×
300
2 \times 300
2
×
300
is
\newline
A)
2
×
3
2 \times 3
2
×
3
\newline
B)
20
×
30
20 \times 30
20
×
30
\newline
C)
23
×
100
23 \times 100
23
×
100
\newline
D)
200
×
300
200 \times 300
200
×
300
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K
M
h
undefined
KM^{\overrightarrow{h}}
K
M
h
and
N
P
h
undefined
NP^{\overrightarrow{h}}
N
P
h
are parallel lines. Which angles are adjacent angles?
\newline
/
M
L
O
/_{MLO}
/
M
L
O
and
/
M
L
J
/_{MLJ}
/
M
L
J
\newline
/
K
L
O
/_{KLO}
/
K
L
O
and
/
N
O
L
/_{NOL}
/
NO
L
\newline
/
K
U
/_{KU}
/
K
U
and
/
P
O
L
/_{POL}
/
PO
L
\newline
/
N
O
L
/_{NOL}
/
NO
L
and
/
M
L
O
/_{MLO}
/
M
L
O
Get tutor help
K
M
undefined
\overleftrightarrow{K M}
K
M
and
N
P
undefined
\overleftrightarrow{N P}
NP
are parallel lines.
\newline
Which angles are adjacent angles?
\newline
∠
M
L
O
\angle M L O
∠
M
L
O
and
∠
M
L
\angle M L
∠
M
L
\newline
∠
K
L
O
\angle K L O
∠
K
L
O
and
∠
N
O
L
\angle N O L
∠
NO
L
\newline
∠
K
U
\angle K U
∠
K
U
and
∠
P
O
L
\angle P O L
∠
PO
L
\newline
∠
N
O
L
\angle N O L
∠
NO
L
and
∠
M
L
O
\angle M L O
∠
M
L
O
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Figure I and Figure II are similar figures.
\newline
Figure I
\newline
Figure II
\newline
Which proportion must be true?
\newline
R
S
A
B
=
T
U
C
D
T
U
A
B
=
U
V
A
F
\frac{R S}{A B}=\frac{T U}{C D} \quad \frac{T U}{A B}=\frac{U V}{A F}
A
B
RS
=
C
D
T
U
A
B
T
U
=
A
F
U
V
\newline
Option
1
1
1
\newline
Option
2
2
2
\newline
S
T
E
F
=
W
R
C
D
W
V
A
B
=
S
T
E
F
\frac{S T}{E F}=\frac{W R}{C D} \quad \frac{W V}{A B}=\frac{S T}{E F}
EF
ST
=
C
D
W
R
A
B
WV
=
EF
ST
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For \#
5
5
5
\& \#
6
6
6
, graph the linear equation. Then des
\newline
5
5
5
.)
y
=
3.5
y=3.5
y
=
3.5
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Step
2
2
2
: If the rational number is not in its simplest form, first find Then divide both the numerator and denominator by their HCF to expres Example
1
1
1
: Express (i)
2
−
7
\frac{2}{-7}
−
7
2
\newline
(ii)
4
10
\frac{4}{10}
10
4
\newline
(iii)
2
3
\frac{2}{3}
3
2
and
\newline
(iv)
17
49
\frac{17}{49}
49
17
in their standard Solution: (i)
2
−
7
\frac{2}{-7}
−
7
2
is not in the standard form as its denominator is negat
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b) Find the general solution of
cos
θ
+
Cos
3
θ
+
cos
5
θ
=
0
\cos \theta+\operatorname{Cos} 3 \theta+\cos 5 \theta=0
cos
θ
+
Cos
3
θ
+
cos
5
θ
=
0
\newline
OR
\newline
Prove that:
tan
−
1
x
−
tan
−
1
y
=
tan
−
1
x
−
y
1
+
x
y
\tan ^{-1} x-\tan ^{-1} y=\tan ^{-1} \frac{x-y}{1+x y}
tan
−
1
x
−
tan
−
1
y
=
tan
−
1
1
+
x
y
x
−
y
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(a)
\newline
(
1
1
1
)
\newline
(c) (
0
0
0
) :
\newline
(D)
\newline
(a)
\newline
(
0
0
0
)
\newline
⋮
\vdots
⋮
\newline
1
1
1
\newline
→
I
\rightarrow I
→
I
\newline
Nilai dari
cos
7
5
∘
−
sin
16
\cos 75^{\circ}-\sin 16
cos
7
5
∘
−
sin
16
aq
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Simplify the rational expression.
\newline
2
q
2
−
q
r
−
3
r
2
2
q
2
−
9
q
r
+
9
r
2
\frac{2q^{2}-qr-3r^{2}}{2q^{2}-9qr+9r^{2}}
2
q
2
−
9
q
r
+
9
r
2
2
q
2
−
q
r
−
3
r
2
\newline
(
q
+
r
)
/
(
k
+
3
r
)
(q+r)/(k+3r)
(
q
+
r
)
/
(
k
+
3
r
)
\newline
Cannot be simplified
\newline
(
a
+
r
)
(
q
−
3
r
)
(a+r)(q-3r)
(
a
+
r
)
(
q
−
3
r
)
\newline
(
q
+
r
)
(
q
+
3
r
)
(q+r)(q+3r)
(
q
+
r
)
(
q
+
3
r
)
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d)
lim
x
→
0
e
x
−
e
−
x
−
2
x
x
−
sin
x
\lim _{x \rightarrow 0} \frac{e^{x}-e^{-x}-2 x}{x-\sin x}
lim
x
→
0
x
−
s
i
n
x
e
x
−
e
−
x
−
2
x
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Find the measures of
∠
E
A
F
,
∠
D
A
E
\angle E A F, \angle D A E
∠
E
A
F
,
∠
D
A
E
, and
∠
C
A
D
\angle C A D
∠
C
A
D
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Date
\newline
15
/
4
/
2024
15 / 4 / 2024
15/4/2024
\newline
Q
1
1
1
) Simplify by rationalising the denominator:
\newline
(a)
5
+
6
5
−
6
\frac{5+\sqrt{6}}{5-\sqrt{6}}
5
−
6
5
+
6
\newline
(b)
7
+
3
5
7
−
3
5
\frac{7+3 \sqrt{5}}{7-3 \sqrt{5}}
7
−
3
5
7
+
3
5
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(c) Use your graph to solve these simultaneous equations.
\newline
y
=
x
+
2
and
y
=
−
3
x
−
2
y=x+2 \text { and } y=-3 x-2
y
=
x
+
2
and
y
=
−
3
x
−
2
\newline
x
=
y
=
\begin{array}{l} x= \\ y= \end{array}
x
=
y
=
\newline
\qquad
\newline
1112102
/
M
/
1
/
10
1112102 / \mathrm{M} / 1 / 10
1112102/
M
/1/10
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2
3
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