Year 12 Maths Advanced MAV-12-01 Checkpoint 1

Checkpoint Quiz 1

This checkpoint covers Transformations of Trigonometric Functions, amplitude, period, phase shift, vertical shift, and sketching transformed graphs (Lesson 1).

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Quick Review

  • General form: $y = a \cdot f(bx + c) + d$. $a$ controls amplitude and reflection, $b$ controls the period, $c$ combines with $b$ to give the phase shift, $d$ is the vertical shift.
  • Amplitude and period: Amplitude $= |a|$ (always positive, even when $a < 0$). Maximum $= d + |a|$, minimum $= d - |a|$. Period $= \dfrac{2\pi}{|b|}$ for sin/cos; period $= \dfrac{\pi}{|b|}$ for tan.
  • Phase shift and midline: Factor out $b$ first, $y = a \cdot f\!\left(b\!\left(x + \dfrac{c}{b}\right)\!\right) + d$, so phase shift $= -\dfrac{c}{b}$ (positive $\to$ right, negative $\to$ left). Midline is the line $y = d$.
  • Sketching and solving: Use the five-key-point method (phase shift, $+T/4$, $+T/2$, $+3T/4$, $+T$) to sketch one cycle. To solve $a\sin(bx+c)+d = k$, isolate the trig ratio, substitute $u = bx + c$, adjust the domain, solve for $u$, then back-substitute for $x$.
MC

Multiple Choice

5 random questions from the Checkpoint 1 bank, feedback shown immediately

Checkpoint 1 Complete

Great work finishing Checkpoint 1.

If you struggled with any questions, go back to Lesson 1 to review amplitude, period, phase shift and sketching before moving on.

Mark checkpoint as complete

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