vectors questions - mme
TRANSCRIPT
Vectors
(Level 6 - 9)
2
1 πΎπΏπ is a scalene triangle. (Level 6)
Point P is half way along ππΏ.
ππΎ = ππ, πΎπΏ = π.
1(a) Write the vector ππΏ in terms of π and π.
[1 mark]
Answer
1(b) Find ππ in terms of π and π.
[1 mark]
Answer
1(c) A new point π is to the right of πΏ.
ππ is 4 times the length of ππ.
Write ππ as a column vector.
[1 mark]
Answer
Turn over βΊ
3
Not drawn
accurately
π πΏ
πΎ
2π
π
π
3
2 πΈπΉπΊ is a scalene triangle. (Level 6)
πΈπΊ = π β 5π, πΈπΉ = 3π + 4π.
πΊπ», not shown, is 3 times the length of and parallel to πΊπΉ.
Find πΊπ» in terms of π and π.
[3 marks]
Answer
Turn over βΊ
3
E
G
F
π β 5π
3π + 4π
Not drawn
accurately
4
3 π΄π΅πΆπ· is a rhombus. Opposite sides are parallel. (Level 7)
π΅πΈ is an extension of π΄π΅, such that π΄π΅ βΆ π΅πΈ = 4: 3
The point F is halfway along πΆπ·
Find πΉπΈ in terms of π and π.
[3 marks]
Answer
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Turn over βΊ
3
π΅ πΈ
πΆ
a
b
π΄
π· πΉ
Not drawn
accurately
5
4 KLMN is an irregular quadrilateral. (Level 7)
ππΏ = ππ, ππ = 2π + ππ, ππΎ = 3π + π.
Point P is positioned such that πΏπ: ππΎ = 1: 2
4(a) Find the vector πΏπΎ in terms of π and π.
[2 marks]
Answer
4(b) Show that ππ = ππΎ.
[4 marks]
Answer
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Turn over βΊ
6
πL
K
3π + π
2π + 2πP
π
2π
Not drawn
accurately
6
5 The diagram below shows a regular hexagon ABCDEF. (Level 7)
X is the point at the center of the hexagon.
ππ΅ = π
πΈπ· = π
Write down the following vectors in terms of a and b.
5(a) π΅πΆ
[1 mark]
5(b) π΅πΈ
[1 mark]
5(c) π΄πΈ
[1 mark]
5(d) πΉπ΅
[1 mark]
Turn over for next question
Turn over βΊ
4
π΅
π΄
πΆ
π·
πΈ
πΉ
π
π
π
Not drawn
accurately
7
6 π΄π΅πΆ is an isosceles triangle. (Level 7)
Point π is halfway along the triangle base, π΄πΆ.
Point π· is positioned such that π΄πΆ and π΄π· are collinear.
Point πΈ is positioned such that π΄π΅ and π΄πΈ are collinear.
π΄π΅:π΅πΈ = 3:2
ππ΄ = π, π΄π΅ = 3π, π΄π· = 2π΄πΆ.
Find π·πΈ in terms of π and π.
[4 marks]
Answer
Turn over for next question.
Turn over βΊ
4
π΄ πΆ
π΅
b
3a
Not drawn
accurately
M π·
E
8
7 On the diagram below: (Level 7)
AE is a straight line
π΄π΅ = π
π΄πΆ = π
π΄πΆ = πΆπΈ
π·πΈ =1
4πΆπΈ
Find expressions for the vectors below in terms of a and b.
7(a) π΅πΆ
[1 mark]
Answer
7(b) π·π΅
[4 marks]
Answer
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Turn over βΊ
5
π΄
π΅
πΆ π· πΈπ
π
Not drawn
accurately
9
8 π΄π΅πΆ is a scalene triangle. (Level 8)
π΄πΆ = 3π, π΄π΅ = 2π.
Point D is positioned such that π΅π·:π·πΆ = 1: 3
Point E is positioned such that π΄πΈ:πΈπ· = 1: 1
Find π΄πΈ in terms of π and π.
[5 marks]
Answer
Turn over for next question
Turn over βΊ
5
A C
B
3b
2a
D
E
Not drawn
accurately
10
9 On the diagram below: (Level 8)
π΄π΅ = π΅πΆ = π
π΄π· = ππ
π΄πΈ is a straight line
πΆπ΅πΈπΉ is a parallelogram
π΄π·: π΅πΈ: πΆπΉ = 3: 2: 2
Find expressions for the vectors below in terms of a and b.
9(a) π·πΆ
[1 mark]
Answer
9(b) πΉπ·
[2 marks]
Answer
Question continues on next page
Turn over βΊ
3
π΄
π΅
π·3π
π
πΆ
πΈ
πΉ
πNot drawn
accurately
11
9(c) DE is extended upwards until it hits the line πΆπΉ.
The point of intersection is π.
What is the ratio πΆπ: ππΉ?
[3 marks]
Answer
Turn over βΊ
3
12
10 On the diagram below: (Level 9)
π΄π· = π
π·π΅ = ππ β π
π΄πΆ and π΄π΅ are straight lines
π΄π·:π·π: ππΆ = 1: 1: 1
π΄π: ππ΅ = 2: 1
Show that ππ is parallel to BC.
[3 marks]
Answer
End of Questions
END
3
π©
π¨ πͺππ«
πΏ
π
ππ β π
Not drawn
accurately