Mathematics: Transformations and Trigonometric Functions

Vocabulary practice flashcards covering function transformations, mark scheme requirements, examiner guidance, and trigonometric curves with stationary points.

Single transformation mapping $y = x^2 + 3$ onto $y = 2x^2 + 6$

A stretch parallel to the $y$-axis (or in the $y$-direction) with a scale factor of $2$.

Disallowed terms for stretch (Question 4a)

Terms such as "squash" or "enlargement", which are explicitly rejected in the mark scheme.

Penalty for describing two transformations (Question 4a)

Results in $M0$ marks if two transformations (such as a stretch and a translation) are described when a single transformation is requested.

Mark scheme breakdown for Question 4(a)

Awarded as $M1$ for identifying the transformation as a "stretch" and $A1$ for specifying both "parallel to $y$-axis" (or equivalent) and "scale factor $2$" (or equivalent).

Examiner-noted candidate errors (Question 4a)

Unfamiliarity with terminology leading to describing transformations with equations or long-winded sentences, using words like "enlargement" or "translation", and describing two transformations instead of one.

Fig. 4 curve

The curve $y = f(x)$, where f(x) = a + \frac{1}{1}\times \text{}\[0pt]\n\cos(bx) defined on the interval $0 \le x \le 2\pi$, where $a$ and $b$ are positive constants.

Stationary points of $f(x) = a + \cos(bx)$ (Fig. 4)

The turning points located at the coordinates $(0, 3)$ and $(2\pi, 1)$.

Domain of $f(x)$ in Question 6

The set of $x$-values defined by the inequality $0 \le x \le 2\pi$.

Components required for Question 6(b)

Finding the expression for the inverse function $f^{-1}(x)$ alongside stating its domain and its range.