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39 questions at your level
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Level 1
Level 2
Level 3
Level 4
Level 5
Column vectors
16 questions
Lesson
Not started
Mark as done
A
A
A
is the point
(
2
,
7
)
(2, 7)
(
2
,
7
)
and
B
B
B
is the point
(
9
,
3
)
(9, 3)
(
9
,
3
)
.
(a)
Write
A
B
→
\overrightarrow{AB}
A
B
as a column vector.
(b)
Write down
B
A
→
\overrightarrow{BA}
B
A
as a column vector.
(c)
Work out
∣
A
B
→
∣
|\overrightarrow{AB}|
∣
A
B
∣
, giving your answer correct to
1
1
1
decimal place.
●●●
●●
Level 3
5 marks
Start
→
Mark as done
A drone flies from
P
P
P
to
Q
Q
Q
, and then from
Q
Q
Q
to
R
R
R
.
P
Q
R
Figure 1
(not accurately drawn)
P
Q
→
=
(
4
3
)
\overrightarrow{PQ} = \binom{4}{3}
P
Q
=
(
3
4
)
and
Q
R
→
=
(
−
6
1
)
\overrightarrow{QR} = \binom{-6}{1}
QR
=
(
1
−
6
)
.
(a)
Write
P
R
→
\overrightarrow{PR}
P
R
as a column vector.
(b)
P
P
P
is the point
(
1
,
2
)
(1, 2)
(
1
,
2
)
. Write down the coordinates of
R
R
R
.
(c)
Write down
R
P
→
\overrightarrow{RP}
R
P
as a column vector.
●●●
●●
Level 3
5 marks
Start
→
Vectors on a shape
13 questions
Lesson
Not started
Mark as done
O
A
B
OAB
O
A
B
is a triangle.
O
A
→
=
a
\overrightarrow{OA} = \mathbf{a}
O
A
=
a
and
O
B
→
=
b
\overrightarrow{OB} = \mathbf{b}
O
B
=
b
.
M
M
M
is the midpoint of
A
B
AB
A
B
.
(a)
Write
A
B
→
\overrightarrow{AB}
A
B
in terms of
a
\mathbf{a}
a
and
b
\mathbf{b}
b
. (1 mark)
(b)
Write
O
M
→
\overrightarrow{OM}
O
M
in terms of
a
\mathbf{a}
a
and
b
\mathbf{b}
b
. Give your answer in its simplest form. (2 marks)
●●●
●●
Level 3
3 marks
Start
→
Mark as done
O
A
B
OAB
O
A
B
is a triangle.
O
A
→
=
a
\overrightarrow{OA} = \mathbf{a}
O
A
=
a
and
O
B
→
=
b
\overrightarrow{OB} = \mathbf{b}
O
B
=
b
.
M
M
M
is the midpoint of
A
B
AB
A
B
.
a
b
O
A
B
M
The diagram is a sketch and is not accurately drawn.
(a)
Find
A
B
→
\overrightarrow{AB}
A
B
in terms of
a
\mathbf{a}
a
and
b
\mathbf{b}
b
.
(b)
Find
O
M
→
\overrightarrow{OM}
O
M
in terms of
a
\mathbf{a}
a
and
b
\mathbf{b}
b
, giving your answer in its simplest form.
●●●
●●
Level 3
4 marks
Start
→
Mark as done
A
B
C
D
ABCD
A
B
C
D
is a trapezium.
A
B
→
=
a
\overrightarrow{AB} = \mathbf{a}
A
B
=
a
and
B
C
→
=
b
\overrightarrow{BC} = \mathbf{b}
B
C
=
b
.
A
D
AD
A
D
is parallel to
B
C
BC
B
C
, and
A
D
=
3
×
B
C
AD = 3 \times BC
A
D
=
3
×
B
C
.
a
b
A
B
C
D
The diagram is a sketch and is not accurately drawn.
(a)
Write down
A
D
→
\overrightarrow{AD}
A
D
in terms of
b
\mathbf{b}
b
.
(b)
Find
D
C
→
\overrightarrow{DC}
D
C
in terms of
a
\mathbf{a}
a
and
b
\mathbf{b}
b
, giving your answer in its simplest form.
●●●
●●
Level 3
4 marks
Start
→
Mark as done
A
B
C
D
ABCD
A
B
C
D
is a quadrilateral.
A
B
→
=
a
\overrightarrow{AB} = \mathbf{a}
A
B
=
a
,
B
C
→
=
b
\overrightarrow{BC} = \mathbf{b}
B
C
=
b
and
C
D
→
=
2
b
−
a
\overrightarrow{CD} = 2\mathbf{b} - \mathbf{a}
C
D
=
2
b
−
a
.
a
b
2b − a
A
B
C
D
The diagram is a sketch and is not accurately drawn.
(a)
Find
A
D
→
\overrightarrow{AD}
A
D
in terms of
a
\mathbf{a}
a
and
b
\mathbf{b}
b
, giving your answer in its simplest form.
(b)
Find
D
B
→
\overrightarrow{DB}
D
B
in terms of
a
\mathbf{a}
a
and
b
\mathbf{b}
b
, giving your answer in its simplest form.
●●●
●●
Level 3
4 marks
Start
→
Vector proofs
12 questions
Lesson
Not started
Mark as done
P
P
P
,
Q
Q
Q
,
R
R
R
and
S
S
S
are four points.
P
Q
→
=
2
a
+
6
b
\overrightarrow{PQ} = 2\mathbf{a} + 6\mathbf{b}
P
Q
=
2
a
+
6
b
and
R
S
→
=
3
a
+
9
b
\overrightarrow{RS} = 3\mathbf{a} + 9\mathbf{b}
R
S
=
3
a
+
9
b
.
(a)
Show that
P
Q
PQ
P
Q
is parallel to
R
S
RS
R
S
.
(b)
Freya says: "This working also proves that
P
P
P
,
Q
Q
Q
,
R
R
R
and
S
S
S
all lie on the same straight line."
Freya is wrong. Explain why.
●●●
●●
Level 3
3 marks
Start
→
Mark as done
A
A
A
,
B
B
B
and
C
C
C
are three points.
A
B
→
=
4
a
−
2
b
\overrightarrow{AB} = 4\mathbf{a} - 2\mathbf{b}
A
B
=
4
a
−
2
b
and
B
C
→
=
10
a
−
5
b
\overrightarrow{BC} = 10\mathbf{a} - 5\mathbf{b}
B
C
=
10
a
−
5
b
.
Prove that
A
A
A
,
B
B
B
and
C
C
C
are collinear.
●●●
●●
Level 3
3 marks
Start
→