Edexcel IAL P3 Trigonometric Functions Questions
sec, cosec and cot; arcsin, arccos, arctan and their domains/ranges; sec²θ = 1 + tan²θ and cosec²θ = 1 + cot²θ.
- P3 · Pure Mathematics 3
- Calculator allowed
- 30 practice questions
What the questions test
The 30 P3 trigonometric functions practice questions cover:
Worked example 1
Solve $3 \cot^2 \theta + 5 \text{cosec} \theta + 1 = 0$ for $0^\circ \le \theta \le 360^\circ$.
Mark scheme
- M1 for substituting $\cot^2 \theta = \text{cosec}^2 \theta - 1$ to form $3(\text{cosec}^2 \theta - 1) + 5\text{cosec} \theta + 1 = 0$.
- M1 for simplifying to the quadratic $3\text{cosec}^2 \theta + 5\text{cosec} \theta - 2 = 0$.
- M1 for factorising to $(3\text{cosec} \theta - 1)(\text{cosec} \theta + 2) = 0$.
- M1 for showing $\text{cosec} \theta = \frac{1}{3} \implies \sin \theta = 3$ yields no real solutions.
- M1 for solving $\text{cosec} \theta = -2 \implies \sin \theta = -0.5$.
- A1 for finding the two correct angles: $210^\circ$ and $330^\circ$.
Worked example 2
Solve $\text{cosec}^2 x + \cot^2 x = 3$ for $0^\circ \le x \le 360^\circ$.
Mark scheme
- M1 for using the identity $\text{cosec}^2 x = 1 + \cot^2 x$ to obtain $1 + 2\cot^2 x = 3$.
- M1 for rearranging to $\cot^2 x = 1$.
- M1 for taking the square root to find $\tan x = \pm 1$.
- A1 for finding the principal values $45^\circ$ and $135^\circ$.
- A1 for stating all four correct solutions: $45^\circ, 135^\circ, 225^\circ, 315^\circ$.
FAQ
What trigonometric functions is in Edexcel IAL P3?
sec, cosec and cot; arcsin, arccos, arctan and their domains/ranges; sec²θ = 1 + tan²θ and cosec²θ = 1 + cot²θ.
Is P3 a calculator paper?
Yes, a calculator is allowed in P3, but method marks are only given for working you write down.
How are P3 trigonometric functions 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.