Edexcel IAL P1 Trigonometry Questions
Sine and cosine rules; area of a triangle = ½ab sin C; radian measure, arc length and sector area; graphs of sin, cos and tan and their symmetries; exact values.
- P1 · Pure Mathematics 1
- Non-calculator
- 67 practice questions
What the questions test
The 67 P1 trigonometry practice questions cover:
Worked example 1
Triangle $ABC$ has sides $AB = 4$ cm and $BC = 5$ cm, with angle $ABC = 60^\circ$. Triangle $ACD$ shares side $AC$ and has a right angle at $C$. If $CD = 7$ cm, find the exact length of $AD$.
Mark scheme
- M1 for using the cosine rule in triangle ABC to find $AC^2$: $AC^2 = 4^2 + 5^2 - 2(4)(5)\cos 60^\circ$.
- M1 for evaluating to get $AC^2 = 16 + 25 - 40(0.5) = 21$.
- M1 for recognising that triangle $ACD$ is right-angled at $C$, so Pythagoras' theorem applies: $AD^2 = AC^2 + CD^2$.
- M1 for substituting the known values: $AD^2 = 21 + 7^2 = 21 + 49 = 70$.
- A1 for finding $AD = \sqrt{70}$ cm.
Worked example 2
Two identical circles of radius $8$ cm intersect such that the circumference of each passes through the centre of the other. Find the exact area of the overlapping region.
Mark scheme
- M1 for recognising that lines drawn from the intersection points to the centres form two equilateral triangles, hence the central angle in each circle covering the overlap is $\frac{2\pi}{3}$.
- M1 for establishing the overlapping region consists of two identical segments, so Area $= 2 \times \frac{1}{2}(8^2)(\frac{2\pi}{3} - \sin\frac{2\pi}{3})$.
- M1 for substituting $\sin\frac{2\pi}{3} = \frac{\sqrt{3}}{2}$.
- M1 for expanding the expression $64(\frac{2\pi}{3} - \frac{\sqrt{3}}{2})$.
- A1 for the exact simplified area $\frac{128\pi}{3} - 32\sqrt{3} \text{ cm}^2$.
FAQ
What trigonometry is in Edexcel IAL P1?
Sine and cosine rules; area of a triangle = ½ab sin C; radian measure, arc length and sector area; graphs of sin, cos and tan and their symmetries; exact values.
Is P1 a calculator paper?
No. P1 is non-calculator, so every trigonometry question has to be done by hand, with exact values where the question asks for them.
How are P1 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.