Vector Representation and Notation

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Vector Representation and Notation — Free MYP5 Mathematics (Extended) Practice Questions

1QuestionColumn Vector NotationAssessment Practice

5 marks~8 minCriterion C

The diagram shows a coordinate grid with triangle

ABC

, where

A = (1, 4)

B = (3, 1)

, and

C = (5, 3)

Triangle

ABC

is translated by the vector

\begin{pmatrix} -4 \\ 2 \end{pmatrix}

. Write down the coordinates of

A'

B'

, and

C'

. [1]

Triangle

ABC

is then enlarged from the origin

O = (0, 0)

with scale factor

-2

. Find the coordinates of

A''

B''

, and

C''

. [2]

A student claims that the enlargement in part (b) is equivalent to a rotation of

180°

about the origin followed by an enlargement of scale factor

2

from the origin. Justify whether the student's claim is correct by comparing the image coordinates from both transformation sequences. [2]

Solutions

2QuestionColumn Vector NotationAssessment Practice

6 marks~9 minCriterion B

The diagram shows a pattern of figures made from small equilateral triangles. Figure 1 has 1 shaded triangle, Figure 2 has 4 shaded triangles, and Figure 3 has 9 shaded triangles.

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

Find a rule for the number of shaded triangles

T

in Figure

n

. [2]

A student claims that Figure

k

is the first figure with more than 200 shaded triangles. Justify whether the student's claim that

k = 15

is correct. [3]

Solutions

3QuestionColumn Vector NotationAssessment Practice

6 marks~9 minCriterion A

Point

P

has coordinates

(3, -2)

and point

Q

has coordinates

(-1, 4)

Write down the midpoint

M

of segment

PQ

. [1]

Find the equation of the perpendicular bisector of

PQ

, giving your answer in the form

y = mx + c

. [3]

A circle passes through both

P

and

Q

. Its centre lies on the perpendicular bisector of

PQ

and also on the line

y = x - 1

. Justify whether the point

(4, 3)

is the centre of this circle. [2]

Solutions

4QuestionColumn Vector NotationAssessment Practice

8 marks~12 minCriterion D

A school tuck shop models its weekly profit

P

(in dollars) from selling

x

snack packs using the quadratic function

P(x) = -2x^2 + 60x - 200.

The shop owner records the actual weekly profit at three different sales levels.

Sales level (snack packs)	10	20	25
Actual profit (dollars)	190	570	410

Calculate the predicted profit for each sales level using

P(x)

, and complete the table below by finding the percentage error for each sales level. Give each percentage error correct to 1 decimal place.

\text{Percentage error} = \frac{|\text{predicted} - \text{actual}|}{\text{actual}} \times 100\%

Sales level (snack packs)	10	20	25
Predicted profit (dollars)	?	?	?
Percentage error (%)	?	?	? [3]

Show that

P(x)

can be written in the form

P(x) = a(x - h)^2 + k

, and state the value of

x

that maximises

P(x)

and the maximum predicted weekly profit. [3]

The owner claims the model is reliable for sales levels between 10 and 25 snack packs. Using your results from part (a), advise the owner whether this claim should be trusted, and suggest one limitation of using a quadratic model to predict the shop's profit. [2]

Solutions

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