Edexcel IAL P2 Further Trigonometry Questions
tan θ = sin θ / cos θ and sin²θ + cos²θ = 1; solving trigonometric equations in a given interval (degrees or radians), including quadratics in sin/cos/tan.
- P2 · Pure Mathematics 2
- Calculator allowed
- 46 practice questions
What the questions test
The 46 P2 further trigonometry practice questions cover:
Worked example 1
Solve $2\sin^2 x + 3\cos x - 3 = 0$ for $0^\circ \le x \le 360^\circ$.
Mark scheme
- M1 for substituting $\sin^2 x$ with $1 - \cos^2 x$ to get $2(1 - \cos^2 x) + 3\cos x - 3 = 0$.
- M1 for expanding and rearranging to form the quadratic $2\cos^2 x - 3\cos x + 1 = 0$.
- M1 for factorising the quadratic as $(2\cos x - 1)(\cos x - 1) = 0$.
- A1 for finding the solutions from $\cos x = 0.5$ giving $x = 60^\circ$ and $300^\circ$.
- A1 for finding the solutions from $\cos x = 1$ giving $x = 0^\circ$ and $360^\circ$.
Worked example 2
Solve the equation $2\cos^2 x - \sin x - 1 = 0$ for $0^\circ \le x \le 360^\circ$.
Mark scheme
- M1 for using the identity $\cos^2 x = 1 - \sin^2 x$ to rewrite the equation: $2(1 - \sin^2 x) - \sin x - 1 = 0$.
- M1 for simplifying to a quadratic in $\sin x$: $2\sin^2 x + \sin x - 1 = 0$.
- M1 for factorising the quadratic to $(2\sin x - 1)(\sin x + 1) = 0$.
- A1 for finding the solutions from $\sin x = 0.5$, which are $x = 30^\circ, 150^\circ$.
- A1 for finding the solution from $\sin x = -1$, which is $x = 270^\circ$.
FAQ
What further trigonometry is in Edexcel IAL P2?
tan θ = sin θ / cos θ and sin²θ + cos²θ = 1; solving trigonometric equations in a given interval (degrees or radians), including quadratics in sin/cos/tan.
Is P2 a calculator paper?
Yes, a calculator is allowed in P2, but method marks are only given for working you write down.
How are P2 further trigonometry questions marked?
With M marks for a correct method, A marks for accurate answers that depend on the M mark before them, and B marks for independent results, as in the worked examples on this page.