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Math Problems
Grade 7
Write variable expressions for arithmetic sequences
Solve the formula
A
=
1
2
h
(
a
+
b
)
A=\frac{1}{2} h(a+b)
A
=
2
1
h
(
a
+
b
)
for
a
a
a
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For a function
g
g
g
, the graph of
y
=
g
(
x
)
y=g(x)
y
=
g
(
x
)
is shown. When
g
(
x
)
g(x)
g
(
x
)
is divided by
(
x
+
10
)
(x+10)
(
x
+
10
)
, the remainder is
−
20
-20
−
20
. Which of the following is closest to the remainder when
g
(
x
)
g(x)
g
(
x
)
is divided by
(
x
−
10
)
(x-10)
(
x
−
10
)
?
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Paradigm
\newline
Specialising in O Level Mathematics
\newline
5
5
5
In the diagram,
A
B
C
A B C
A
BC
is a triangle where
M
M
M
is the midpoint of
A
C
A C
A
C
.
\newline
The point
P
P
P
lies on the line
B
M
B M
BM
such that
B
P
=
1
3
B
M
B P=\frac{1}{3} B M
BP
=
3
1
BM
.
\newline
The point
Q
Q
Q
lies on the line
B
C
B C
BC
such that
B
Q
:
Q
C
=
1
:
4
B Q: Q C=1: 4
BQ
:
QC
=
1
:
4
.
\newline
Given that
A
B
undefined
=
b
\overrightarrow{A B}=b
A
B
=
b
and
M
M
M
0
0
0
.
\newline
(a) Express, as simply as possible, in terms of
M
M
M
1
1
1
and or
M
M
M
2
2
2
,
\newline
(i)
M
M
M
3
3
3
,
\newline
(ii)
M
M
M
4
4
4
,
\newline
(iii)
M
M
M
5
5
5
,
\newline
(iv)
M
M
M
6
6
6
.
\newline
(b) Write down two facts about
M
M
M
7
7
7
and
Q
Q
Q
.
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Which of the following is a whole number?
\newline
Choices:
\newline
(A)
0
0
0
\newline
(B)
8
\sqrt{8}
8
\newline
(C)
4
3
\frac{4}{3}
3
4
\newline
(D)
4.555
…
4.555\ldots
4.555
…
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Which of the following is a whole number?
\newline
Choices:
\newline
(A)
0
0
0
\newline
(B)
8
8
8
\newline
(C)
4
3
\frac{4}{3}
3
4
\newline
(D)
4.555
…
4.555\ldots
4.555
…
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Complete the recursive formula of the geometric sequence
\newline
56
,
−
28
,
14
,
−
7
,
…
56,-28,14,-7,\dots
56
,
−
28
,
14
,
−
7
,
…
.
\newline
d
(
1
)
=
d(1)=
d
(
1
)
=
\newline
d
(
n
)
=
d
(
n
−
1
)
⋅
d(n)=d(n-1)\cdot
d
(
n
)
=
d
(
n
−
1
)
⋅
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Complete the recursive formula of the geometric sequence
\newline
7
,
−
14
,
28
,
−
56
,
…
7,-14,28,-56,\dots
7
,
−
14
,
28
,
−
56
,
…
\newline
a
(
1
)
=
□
a(1)=\square
a
(
1
)
=
□
\newline
a
(
n
)
=
a
(
n
−
1
)
⋅
□
a(n)=a(n-1) \cdot \square
a
(
n
)
=
a
(
n
−
1
)
⋅
□
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