DP Mathematics HL Questionbank

• Syllabus

3.1

Sub sections and their related questions

The circle: radian measure of angles.

• 12M.2.hl.TZ2.9: Two discs, one of radius 8 cm and one of radius 5 cm, are placed such that they touch each other....
• 08M.1.hl.TZ1.3: A circular disc is cut into twelve sectors whose areas are in an arithmetic sequence. The angle...
• 11M.1.hl.TZ2.7c: Using your results from part (a) and part (b), show that...
• 11M.2.hl.TZ2.1: The points P and Q lie on a circle, with centre O and radius 8 cm, such that...
• 13M.2.hl.TZ1.5: A rectangle is drawn around a sector of a circle as shown. If the angle of the sector is 1 radian...
• 10M.2.hl.TZ2.13: The interior of a circle of radius 2 cm is divided into an infinite number of sectors. The areas...
• 13M.2.hl.TZ2.1a: Find \({\rm{A\hat OB}}\), expressing your answer in radians correct to four significant figures.
• 13M.2.hl.TZ2.1b: Determine the area of the shaded region.
• 11N.1.hl.TZ0.1: From a vertex of an equilateral triangle of side \(2x\), a circular arc is drawn to divide the...
• 11N.1.hl.TZ0.8a: Show that \(t = \frac{2}{3}(2\cos \theta + \theta )\).
• 11M.2.hl.TZ1.6: The radius of the circle with centre C is 7 cm and the radius of the circle with centre D is 5...
• 14M.2.hl.TZ2.4: The following diagram shows two intersecting circles of radii 4 cm and 3 cm. The centre C of the...
• 13N.2.hl.TZ0.8a: Show that the shaded area can be expressed as \(50\theta  - 50\sin \theta \).
• 15M.1.hl.TZ1.1a: Find, in radians, the value of the angle \(\theta \), as indicated on the diagram.
• 15M.1.hl.TZ1.1b: Find the total length of the perimeter of the logo.
• 15N.1.hl.TZ0.1: The following diagram shows a sector of a circle where \({\rm{A\hat OB}} = x\) radians and the...
• 16M.2.hl.TZ1.4: The diagram below shows a fenced triangular enclosure in the middle of a large grassy field. The...
• 16N.2.hl.TZ0.9a: Find an expression for the shaded area in terms of \(\alpha \), \(\theta \) and \(r\).
• 16N.2.hl.TZ0.9b: Show that \(\alpha  = 4\arcsin \frac{1}{4}\).
• 16N.2.hl.TZ0.9c: Hence find the value of \(r\) given that the shaded area is equal to 4.
• 17N.2.hl.TZ0.3: This diagram shows a metallic pendant made out of four equal sectors of a larger circle of radius...
• 18M.2.hl.TZ2.4a.i: Find AM.
• 18M.2.hl.TZ2.4a.ii: Find \({\text{A}}\mathop {\text{M}}\limits^ \wedge  {\text{P}}\) in radians.
• 18M.2.hl.TZ2.4b: Find the area of the shaded region.

Length of an arc; area of a sector.

• 12M.2.hl.TZ2.9: Two discs, one of radius 8 cm and one of radius 5 cm, are placed such that they touch each other....
• 08M.1.hl.TZ1.3: A circular disc is cut into twelve sectors whose areas are in an arithmetic sequence. The angle...
• 11M.2.hl.TZ2.1: The points P and Q lie on a circle, with centre O and radius 8 cm, such that...
• 09M.1.hl.TZ1.6: The diagram below shows two straight lines intersecting at O and two circles, each with centre O....
• 10M.2.hl.TZ2.13: The interior of a circle of radius 2 cm is divided into an infinite number of sectors. The areas...
• 11M.2.hl.TZ1.6: The radius of the circle with centre C is 7 cm and the radius of the circle with centre D is 5...
• 09N.2.hl.TZ0.3: (a)     Show that the area of the shaded region is \(8\sin x - 2x\) . (b)     Find the maximum...
• 09M.2.hl.TZ2.12: (a)     Explain why \(x < 40\) . (b)     Show that cosθ = x −10 50. (c)     (i)     Find an...
• 15M.1.hl.TZ1.1a: Find, in radians, the value of the angle \(\theta \), as indicated on the diagram.
• 15M.1.hl.TZ1.1b: Find the total length of the perimeter of the logo.
• 15M.2.hl.TZ2.8a: Given that the rope is 5 m long, calculate the percentage of Bill’s field that Gruff is able to...
• 15M.2.hl.TZ2.8b: Bill replaces Gruff’s rope with another, this time of length \(a,{\text{ }}4 < a < 10\), so...
• 15N.1.hl.TZ0.1: The following diagram shows a sector of a circle where \({\rm{A\hat OB}} = x\) radians and the...
• 16M.2.hl.TZ1.4: The diagram below shows a fenced triangular enclosure in the middle of a large grassy field. The...
• 16N.2.hl.TZ0.9a: Find an expression for the shaded area in terms of \(\alpha \), \(\theta \) and \(r\).
• 16N.2.hl.TZ0.9b: Show that \(\alpha  = 4\arcsin \frac{1}{4}\).
• 16N.2.hl.TZ0.9c: Hence find the value of \(r\) given that the shaded area is equal to 4.
• 17N.2.hl.TZ0.3: This diagram shows a metallic pendant made out of four equal sectors of a larger circle of radius...
• 18M.2.hl.TZ2.4a.i: Find AM.
• 18M.2.hl.TZ2.4a.ii: Find \({\text{A}}\mathop {\text{M}}\limits^ \wedge  {\text{P}}\) in radians.
• 18M.2.hl.TZ2.4b: Find the area of the shaded region.