Vector Arithmetic and Scalar Multiplication

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Vector Arithmetic and Scalar Multiplication — Free MYP4 Mathematics (Extended) Practice Questions

1QuestionVector Arithmetic Word ProblemsConcept Practice

5 marks~8 minCriterion A

A delivery drone travels between three checkpoints in a city grid. Starting from point

A

, it flies 5 km due east to point

B

, then 3 km due north to point

C

, then 4 km due west to point

D

.

The diagram shows the drone's path on a coordinate grid, with

A

at the origin.

Write down the coordinates of

D

relative to

A

. [1]

Find the straight-line distance

DA

, giving your answer in exact form. [2]

The drone's battery allows a maximum straight-line return distance of 4 km. Advise the drone operator whether the drone can safely return directly from

D

A

, justifying your advice using your result from part (b). [2]

Solutions

2QuestionScalar Multiplication of VectorsAssessment Practice

6 marks~9 minCriterion C

A delivery drone is launched from a depot at the origin

O

. Its position is tracked on a coordinate grid where each unit represents 1 km. At time

t = 0

minutes, the drone is at point

A(4, 2)

. The drone flies in a straight line so that at

t = 6

minutes it reaches point

B

, which is exactly 3 times as far from the depot as

A

is, in the same direction.

The diagram shows the depot at

O

, point

A(4, 2)

, and point

B

Write down the coordinates of

B

. [1]

Find the straight-line distance

OB

. Give your answer in km, correct to 3 significant figures. [2]

The drone travels from

O

B

at constant speed. A logistics planner claims: "Since $B$ is 3 times as far as $A$ from the depot, the drone must have taken 3 times as long to reach $A$ as it did to reach $B$ ."

Justify whether the planner's claim is correct, showing any necessary calculations. [3]

Solutions

3QuestionVector Arithmetic Word ProblemsAssessment Practice

7 marks~11 minCriterion B

The diagram shows a growing pattern of dot-and-line figures. In each figure, dots are arranged in rows and connected by horizontal line segments.

Figure 1	1 row	2 dots	1 segment.
Figure 2	2 rows	6 dots	4 segments.
Figure 3	3 rows	12 dots	9 segments.

Figure number $n$	1	2	3
Number of dots $D$	2	6	12
Number of segments $S$	1	4	9

Write down the number of segments in Figure 4. [1]

Find a formula for

S

in terms of

n

. Hence find the figure number that contains exactly 225 segments. [3]

A student claims that

D = n(n+1)

.

Verify this formula for

n = 3

, and justify why the factor

(n+1)

appears by referring to the structure of the figures. [3]

Solutions

4QuestionVector Arithmetic Word ProblemsAssessment Practice

7 marks~11 minCriterion D

A harbour master records the journey of a sailboat that travels 12 km due east, then 8 km due north, then 6 km due west. A rescue boat travels in a straight line from the sailboat's starting point to its finishing point.

The diagram shows the sailboat's path and the direct route of the rescue boat.

Calculate the straight-line distance the rescue boat travels. Give your answer in kilometres. [2]

The sailboat consumes fuel at a rate of 0.5 litres per km. The rescue boat consumes fuel at a rate of 0.4 litres per km. Find the difference in total fuel used between the two boats for this journey. Give your answer in litres. [3]

The harbour master claims: "The rescue boat will always use less fuel than the sailboat on any journey of this type, regardless of the consumption rates."

Advise the harbour master whether this claim is reliable, by finding the condition on the rescue boat's fuel consumption rate

r

(litres per km) for which the rescue boat uses less fuel than the sailboat on this specific journey. [2]

Solutions

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