Year 11 Maths Advanced Module 2 Checkpoint 3

Checkpoint Quiz 3

This checkpoint covers Solving Trigonometric Equations Graphically, Modelling with Trigonometric Functions, and Review (Lessons 8–10).

🎯

📋

Quick Review

Solving graphically: Find intersections of $y = \sin x$ (or $\cos x$ or $\tan x$) with a horizontal line $y = k$. Use ASTC and reference angles to list all solutions in the given domain.
Multiple solutions: $\sin\theta = k$ has two solutions per period (one in Q1/Q2 or Q3/Q4 depending on sign). Use $\theta = \pi - \alpha$ (Q2), $\theta = \pi + \alpha$ (Q3), $\theta = 2\pi - \alpha$ (Q4) from the reference angle $\alpha$.
Modelling: $y = A\sin(Bx + C) + D$, identify amplitude $|A|$, period $\dfrac{2\pi}{|B|}$, phase shift $-\dfrac{C}{B}$, and equilibrium $D$ from a graph or context description.
Key connections: The Pythagorean identities, reciprocal functions, and graph transformations all link together. Converting between $\sin$ and $\cos$ forms uses phase shifts of $\pm\dfrac{\pi}{2}$.

5 random questions from the Checkpoint 3 bank, feedback shown immediately

Great work finishing Checkpoint 3 and completing Trigonometric Identities and Equations.

If you struggled with any questions, go back to Lessons 8–10 to review the concepts before sitting the module quiz.

Tick when you're ready to attempt the Module 2 quiz.