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Access custom-built, exam-style problems for 2d & 3d geometry. Each problem has a full solution and mark-scheme, as well as AI grading and support.
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The voltage of two alternating electrical currents are given by V0=3sin(ωt) and V1=8sin(ωt+120°).
The voltages add to give a total of Vsin(ωt+θ).
Find V and θ.
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The circle below shows two sectors of equal area, QPR and TPR.
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The sector PQR has perimeter 4.5 and the combined sector QPT has perimeter 5.5.
Find the interior angle of sector QPR.
Hence or otherwise, find the area of the combined sector PQT.
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The following diagram shows triangle PQR with PR =3, PQ =x and QR =2x, where x∈R.
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It is given that sinQ^=53, where Q^ is acute.
Find the area of the triangle.
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The circular sector AOB centered at O has radius R=9 and central angle AO^B=2π. At the midpoint of the sector's first radius is the point M, and point C lies on the second radius of the sector.
A semicircle centered at M with diameter 9 is drawn inside the circular sector. A second semicircle of radius r centered at C is drawn such that the two semicircles are tangent. The line segment MC passes through X, the point of tangency between the semicircles.
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Show that [CB]=3.
Find the area of R1.
Hence find R2.
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Solve the equation cos4x=sin2x for x∈[0,π]
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Consider the function g(x)=asinbx+c for 0≤x≤24. The graph of g is shown in the diagram below.
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The x-intercepts are q and r, and the point P lies at the minimum.
Find the coordinates of P.
Find the value of q and the value of r.
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