Vector Proofs and Applications
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Vector Proofs and Applications — Free MYP5 Mathematics (Extended) Practice Questions

1QuestionProving Collinearity Using VectorsConcept Practice
5 marks~8 minCriterion A
The diagram shows three points AA, BB, and CC plotted on a coordinate grid.

The coordinates of the points are A(1,2)A(1, 2), B(3,5)B(3, 5), and C(7,11)C(7, 11).
a
Write down the gradient of the line segment ABAB. [1]
b
Find the equation of the straight line passing through AA and CC, giving your answer in the form y=mx+cy = mx + c. [2]
c
A fourth point DD has coordinates (d,20)(d, 20) and lies on the line through AA and CC. Find the value of dd, then justify whether DD lies between CC and the origin or beyond CC on the same line. [2]
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Solutions

2QuestionApplications in Navigation and DesignAssessment Practice
5 marks~8 minCriterion D
The diagram shows a right-angled triangle OABOAB where OO is the origin. A ship leaves OO, sails 12 km due east to point AA, then 5 km due north to point BB.
a
Write down the distance OBOB, the straight-line distance from OO to BB. [1]
b
Find the bearing of BB from OO, giving your answer to the nearest degree. [2]
c
A second ship travels directly from OO to BB. It arrives at the same time as the first ship, which sailed via AA at a constant speed of 10 km/h. The port authority requires all vessels to travel at no less than 7.5 km/h in this zone. Justify whether the second ship complies with this regulation. [2]
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Solutions

3QuestionApplications in Navigation and DesignAssessment Practice
5 marks~8 minCriterion C
A surveyor walks 7 km due east from point AA to point BB, then 24 km due north from BB to point CC.
a
State the straight-line distance from AA to CC. [1]
b
Find the bearing of CC from AA, giving your answer to the nearest degree. [2]
c
A second surveyor claims that point DD, located on the direct path from AA to CC at a distance of 13 km from AA, is exactly 5 km east of AA. Justify whether this claim should be accepted or rejected. [2]
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Solutions

4QuestionApplications in Navigation and DesignAssessment Practice
6 marks~9 minCriterion B
The diagram shows the first four figures of a pattern made from dots arranged in rows.

Figure 1 has 2 dots, Figure 2 has 6 dots, Figure 3 has 12 dots, and Figure 4 has 20 dots.
a
Write down the number of dots in Figure 5. [1]
b
Find a rule for the number of dots DD in Figure nn, giving your answer in the form D=n(n+1)D = n(n + 1). Show that your rule is consistent with Figure 3. [3]
c
A student claims that no figure in this pattern can contain exactly 50 dots. Justify whether the student is correct. [2]
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Solutions

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