Transformations
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Transformations — Free MYP4 Mathematics (Standard) Practice Questions

1QuestionCombined transformationsConcept Practice
2 marks~3 minCriterion A
A graphic designer maps logo elements onto a coordinate grid. Triangle ABCABC has vertices A(2,1)A(2, 1), B(5,1)B(5, 1), and C(3,4)C(3, 4). To reposition the logo, the triangle is first translated by the vector (3−2)\begin{pmatrix} 3 \\ -2 \end{pmatrix}, then reflected across the yy-axis.
a
Calculate the coordinates of vertex AA after both transformations. [1]
b
The designer requires vertex AA to land in the second quadrant after both transformations. Justify whether this requirement is met, using the coordinates found in part (a). [1]
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Solutions

2QuestionHorizontal shiftsAssessment Practice
4 marks~6 minCriterion D
A coastal engineer models tide height at a port using h(t)=3cos⁡(0.5(t−2))+4h(t) = 3\cos(0.5(t - 2)) + 4, where hh is in metres and tt is hours after midnight. The horizontal shift of 2 hours represents a lag from a reference tide. A vessel requires a minimum depth of 6.5 m to enter the port safely.
a
Deduce the first two times after midnight at which high tide occurs. [2]
b
Advise the port authority which of the two high tide times is more operationally suitable for the vessel to enter, justifying your recommendation with both the mathematical result and a real-world reason. [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

4QuestionStretch/compressionAssessment Practice
4 marks~6 minCriterion C
A sports analyst models the vertical height (in metres) of a ball's bounce using the function f(x)=x2f(x) = x^2, where xx is time in seconds. A new surface increases all heights by a factor of 3 and reduces the launch height by 2 metres, giving a transformed function g(x)g(x).
a
Deduce the equation of g(x)g(x). [1]
b
Calculate g(4)g(4). [1]
c
The analyst claims: "At x=4x = 4 seconds, the ball reaches a height above 50 metres, so the surface is unsuitable for regulation play." Advise the analyst whether this conclusion is supported by the model. [2]

Solutions

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