Transformations
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Transformations — Free MYP4 Mathematics (Extended) Practice Questions

1QuestionStretch/compressionConcept Practice
4 marks~6 minCriterion A
A photographer uses editing software to adjust image brightness. The software models the original brightness of a pixel as f(x)=x2f(x) = x^2, where xx is the input light value. The adjusted brightness is g(x)=a⋅f(x)g(x) = a \cdot f(x).

The point (2,4)(2, 4) lies on ff and the point (2,8)(2, 8) lies on gg.
a
Deduce the value of aa. [1]
b
Explain what the vertical stretch by factor aa means for how the software changes pixel brightness. [1]
c
A pixel has input value x=5x = 5. The software requires adjusted brightness to exceed 60 to display correctly. Justify whether this pixel displays correctly after the transformation. [2]
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Solutions

2QuestionStretch/compressionAssessment Practice
6 marks~9 minCriterion C
A graphic designer is resizing a logo for a billboard and a business card. The logo's outline is defined by vertices A(2, 1)A(2,\ 1), B(6, 1)B(6,\ 1), C(7, 4)C(7,\ 4), and D(1, 4)D(1,\ 4). The designer applies a vertical stretch by factor 2.52.5, followed by a horizontal compression by factor 0.40.4.
a
Determine the coordinates of the transformed vertices A′A', B′B', C′C', and D′D' after both transformations are applied in the given order. [2]
b
Calculate the area of the original logo and the area of the transformed logo. Show that the two areas are equal, and explain why this result occurs. [2]
c
Advise the designer whether this transformation is suitable for both media, justifying your answer with reference to the effect of non-uniform scaling on the logo's proportions and the significance of the equal-area result. [2]
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Solutions

3QuestionReflectionsConcept Practice
2 marks~3 minCriterion B
A graphic designer uses coordinate geometry to create a reflected logo. The original logo contains the point P(3,−5)P(3, -5). The designer reflects the entire logo across the xx-axis, as shown by the pattern below.

(2, 3)→(2, −3)(2,\ 3) \rightarrow (2,\ -3)

(−1, 5)→(−1, −5)(-1,\ 5) \rightarrow (-1,\ -5)

(4, −2)→(4, 2)(4,\ -2) \rightarrow (4,\ 2)

Deduce the general rule for reflecting any point (x,y)(x, y) across the xx-axis. [1]

State the image of P(3,−5)P(3, -5) after reflection across the xx-axis. [1]

Solutions

4QuestionHorizontal shiftsAssessment Practice
6 marks~9 minCriterion D
Seismologists model the P-wave arrival time tt (seconds) at a recording station using

t=dv+ht = \frac{d}{v} + h

where dd is the distance (km) from the epicentre, vv is the wave speed (km/s), and hh is the station's clock offset (seconds).

Station A is 120 km from an epicentre. The wave speed is v=6v = 6 km/s and the clock offset is h=0.5h = 0.5 s.

Station B is 200 km from the same epicentre, with v=6v = 6 km/s. Its recorded arrival time is 34.234.2 s and its clock offset hBh_B is unknown.
a
Calculate the predicted arrival time tAt_A at Station A. [2]
b
Determine the clock offset hBh_B at Station B. [2]
c
Clock offsets carry a ±0.5\pm 0.5 s uncertainty and wave speed is assumed constant across all rock layers. Advise a seismologist whether this model is sufficiently reliable to locate the epicentre for emergency response purposes. [2]
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Solutions

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