Year 11 Maths Advanced Module 2 Checkpoint 2

Checkpoint Quiz 2

This checkpoint covers Domains and Ranges, Graphs of Sine and Cosine, Graphs of Tangent and Cotangent, and Phase Shifts (Lessons 4–7).

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Quick Review

Domains and ranges: $\sin$ and $\cos$ have domain all reals and range $[-1,\,1]$. $\tan$ has domain all reals except $\frac{\pi}{2} + n\pi$ ($n \in \mathbb{Z}$) and range all reals.
Standard sin/cos graphs: $y = \sin x$ and $y = \cos x$ have period $2\pi$ and amplitude 1. $y = \cos x$ is a horizontal shift of $y = \sin x$ by $\frac{\pi}{2}$ to the left.
Tangent and cotangent: $y = \tan x$ has period $\pi$ with vertical asymptotes at $x = \frac{\pi}{2} + n\pi$. $y = \cot x$ has period $\pi$ with vertical asymptotes at $x = n\pi$.
Transformations: For $y = A\sin(Bx + C) + D$: amplitude $= |A|$, period $= \dfrac{2\pi}{|B|}$, phase shift $= -\dfrac{C}{B}$ (positive $= $ right), vertical shift $= D$.

5 random questions from the Checkpoint 2 bank, feedback shown immediately

Great work finishing Checkpoint 2.

If you struggled with any questions, go back to Lessons 4–7 to review the concepts before moving on.

Tick when you're ready to continue to Lesson 8.