Moderate -0.8 This is a straightforward function transformation question requiring students to identify and correctly order three basic transformations (horizontal translation, vertical stretch, vertical translation). While the 5 marks suggest detail is needed in the description, the transformations themselves are standard AS-level content with no problem-solving or novel insight required—just systematic application of transformation rules.
The curve \(y = x^2\) is transformed to the curve \(y = 4(x-3)^2 - 8\).
Describe fully a sequence of transformations that have been combined, making clear the order in which the transformations have been applied. [5]
Stretch factor 4 in y-direction/parallel to the y axis/vertically.
B1
Allow in/on/along the y axis or ‘the x axis is
invariant.’
Translation
3
or 3 parallel to the x axis or in the x direction, allow horizontally.
0
0
or 8 parallel to the y axis or in the y direction, allow vertically.
Answer
Marks
Guidance
8
B2
Condone ‘Shift’.
3
These translations can be combined as , this
8
counts as 2 elements.
Give priority to a correct vector over any incorrect
wording.
B2 for all 3
B1 for 2 out of 3
Answer
Marks
Guidance
Two translations, one in each direction, and a stretch only.
M1
Condone inaccurate terminology, such as up, down,
left and right, if the intention is clear.
Correct order of operations. The stretch which must be in the in the y direction
Answer
Marks
Guidance
must come before the translation in the y direction.
A1
Condone inaccurate terminology if the intention is
clear but numerical values must be correct.
Answer
Marks
Guidance
Question
Answer
Marks
2
Alternative Method for Question 2
Translation
3
or 3 parallel to the x axis or in the x direction, allow horizontally.
0
0
or 2 parallel to the y axis or in the y direction, allow vertically.
Answer
Marks
Guidance
2
(B2)
Condone ‘Shift’.
3
These translations can be combined as , this
2
counts as 2 elements.
Give priority to a correct vector over any incorrect
wording.
B2 for all 3.
B1 for 2 out of 3.
Answer
Marks
Guidance
Stretch factor 4 in y-direction/parallel to the y axis/vertically.
(B1)
Allow use of SF in place of factor.
Allow in/on/along the y axis or “the x axis is
invariant.”
Answer
Marks
Guidance
Two translations, one in each direction, and a stretch only.
(M1)
Condone inaccurate terminology, such as transform,
move, up, down, left and right, if the intention is
clear.
Correct order of operations. The stretch which must be in the in the y direction
Answer
Marks
Guidance
must come after the translation in the y direction.
(A1)
Condone inaccurate terminology if the intention is
clear but numerical values must be correct.
5
Answer
Marks
Guidance
Question
Answer
Marks
Question 2:
2 | Stretch factor 4 in y-direction/parallel to the y axis/vertically. | B1 | Allow use of SF in place of factor.
Allow in/on/along the y axis or ‘the x axis is
invariant.’
Translation
3
or 3 parallel to the x axis or in the x direction, allow horizontally.
0
0
or 8 parallel to the y axis or in the y direction, allow vertically.
8 | B2 | Condone ‘Shift’.
3
These translations can be combined as , this
8
counts as 2 elements.
Give priority to a correct vector over any incorrect
wording.
B2 for all 3
B1 for 2 out of 3
Two translations, one in each direction, and a stretch only. | M1 | Condone inaccurate terminology, such as up, down,
left and right, if the intention is clear.
Correct order of operations. The stretch which must be in the in the y direction
must come before the translation in the y direction. | A1 | Condone inaccurate terminology if the intention is
clear but numerical values must be correct.
Question | Answer | Marks | Guidance
2 | Alternative Method for Question 2
Translation
3
or 3 parallel to the x axis or in the x direction, allow horizontally.
0
0
or 2 parallel to the y axis or in the y direction, allow vertically.
2 | (B2) | Condone ‘Shift’.
3
These translations can be combined as , this
2
counts as 2 elements.
Give priority to a correct vector over any incorrect
wording.
B2 for all 3.
B1 for 2 out of 3.
Stretch factor 4 in y-direction/parallel to the y axis/vertically. | (B1) | Allow use of SF in place of factor.
Allow in/on/along the y axis or “the x axis is
invariant.”
Two translations, one in each direction, and a stretch only. | (M1) | Condone inaccurate terminology, such as transform,
move, up, down, left and right, if the intention is
clear.
Correct order of operations. The stretch which must be in the in the y direction
must come after the translation in the y direction. | (A1) | Condone inaccurate terminology if the intention is
clear but numerical values must be correct.
5
Question | Answer | Marks | Guidance
The curve $y = x^2$ is transformed to the curve $y = 4(x-3)^2 - 8$.
Describe fully a sequence of transformations that have been combined, making clear the order in which the transformations have been applied. [5]
\hfill \mbox{\textit{CAIE P1 2024 Q2 [5]}}