DP Mathematics HL Questionbank

• Syllabus

3.7

Sub sections and their related questions

The cosine rule.

• 12N.1.hl.TZ0.7a: For the case k = 4 , find the two possible values of QR.
• 12N.1.hl.TZ0.7b: Determine the values of k for which the conditions above define a unique triangle.
• 08M.2.hl.TZ1.12Part A: In triangle ABC, BC = a , AC = b , AB = c and [BD] is perpendicular to [AC].   (a)     Show...
• 11M.2.hl.TZ2.8: The vertices of an equilateral triangle, with perimeter P and area A , lie on a circle with...
• 09M.1.hl.TZ2.9: A triangle has sides of length \(({n^2} + n + 1)\), \((2n + 1)\) and \(({n^2} - 1)\) where...
• SPNone.1.hl.TZ0.6a: Determine BC, giving your answer in the form \(k\sqrt 3 \), \(k \in {\mathbb{Z}^ + }\) .
• SPNone.1.hl.TZ0.6b: The point D lies on (BC), and (AD) is perpendicular to (BC). Determine AD.
• SPNone.1.hl.TZ0.7a: Show that this system does not have a unique solution for any value of \(\lambda \) .
• SPNone.1.hl.TZ0.8: The vectors a , b , c satisfy the equation a + b + c = 0 . Show that a \( \times \) b = b...
• 13M.2.hl.TZ1.7a: Find, in terms of x, an expression for the cost of laying the cable.
• 10M.2.hl.TZ1.3: In the right circular cone below, O is the centre of the base which has radius 6 cm. The points B...
• 10M.2.hl.TZ2.5: Consider the triangle ABC where \({\rm{B\hat AC}} = 70^\circ \), AB = 8 cm and AC = 7 cm. The...
• 10N.2.hl.TZ0.1: Triangle ABC has AB = 5 cm, BC = 6 cm and area 10 \({\text{c}}{{\text{m}}^2}\). (a)     Find...
• 11M.2.hl.TZ1.3: Given \(\Delta \)ABC, with lengths shown in the diagram below, find the length of the line...
• 14M.1.hl.TZ1.7: The triangle ABC is equilateral of side 3 cm. The point D lies on [BC] such that BD = 1 cm. Find...
• 15M.2.hl.TZ1.4: A triangle \(ABC\) has \(\hat A = 50^\circ \), \({\text{AB}} = 7{\text{ cm}}\) and...
• 15M.2.hl.TZ2.1b: Find \(AC\).
• 15N.2.hl.TZ0.7: Triangle \(ABC\) has area \({\text{21 c}}{{\text{m}}^{\text{2}}}\). The sides \(AB\) and \(AC\)...
• 16M.1.hl.TZ1.5a: Expand and simplify \({\left( {1 - \sqrt 3 } \right)^2}\).
• 16M.1.hl.TZ1.5c: Find BC in the form \(a + \sqrt b \) where \(a,{\text{ }}b \in \mathbb{Z}\).
• 16M.2.hl.TZ2.1: ABCD is a quadrilateral where...
• 16N.2.hl.TZ0.7a: Use the cosine rule to find the two possible values for AC.
• 16N.2.hl.TZ0.7b: Find the difference between the areas of the two possible triangles ABC.
• 17N.2.hl.TZ0.5: Barry is at the top of a cliff, standing 80 m above sea level, and observes two yachts in the...
• 18M.1.hl.TZ1.11b: Show that the area of the quadrilateral Q is \(\frac{{21\sqrt 3 }}{2}\).

The sine rule including the ambiguous case.

• 12N.1.hl.TZ0.7b: Determine the values of k for which the conditions above define a unique triangle.
• 08M.1.hl.TZ1.4: In triangle ABC, AB = 9 cm , AC = 12 cm , and \(\hat B\) is twice the size of \({\hat C}\)...
• 08M.2.hl.TZ2.5: Consider triangle ABC with \({\rm{B}}\hat {\rm{A}}{\rm{C}} = 37.8^\circ \) , AB = 8.75 and BC = 6...
• 08N.2.hl.TZ0.1: In a triangle ABC, \(\hat A = 35^\circ \), BC = 4 cm and AC = 6.5 cm. Find the possible values of...
• SPNone.2.hl.TZ0.7a: the value of \(\theta \).
• SPNone.2.hl.TZ0.7b: the time at which the interception occurs, correct to the nearest minute.
• 10M.2.hl.TZ2.5: Consider the triangle ABC where \({\rm{B\hat AC}} = 70^\circ \), AB = 8 cm and AC = 7 cm. The...
• 15M.1.hl.TZ2.6a: Show that length \({\text{AB}} = \frac{3}{{\sqrt 3 \cos \theta  + \sin \theta }}\).
• 15M.2.hl.TZ1.4: A triangle \(ABC\) has \(\hat A = 50^\circ \), \({\text{AB}} = 7{\text{ cm}}\) and...
• 16M.1.hl.TZ1.5a: Expand and simplify \({\left( {1 - \sqrt 3 } \right)^2}\).
• 16M.1.hl.TZ1.5c: Find BC in the form \(a + \sqrt b \) where \(a,{\text{ }}b \in \mathbb{Z}\).
• 16M.2.hl.TZ2.1: ABCD is a quadrilateral where...
• 16N.2.hl.TZ0.7a: Use the cosine rule to find the two possible values for AC.
• 16N.2.hl.TZ0.7b: Find the difference between the areas of the two possible triangles ABC.
• 17N.2.hl.TZ0.5: Barry is at the top of a cliff, standing 80 m above sea level, and observes two yachts in the...
• 18M.1.hl.TZ1.11b: Show that the area of the quadrilateral Q is \(\frac{{21\sqrt 3 }}{2}\).

Area of a triangle as \(\frac{1}{2}ab\sin C\) .

• 12N.1.hl.TZ0.7b: Determine the values of k for which the conditions above define a unique triangle.
• 12N.2.hl.TZ0.13e: Let Y be a point on \({L_1}\) and Z be a point on \({L_2}\) such that XY is perpendicular to YZ...
• 11M.1.hl.TZ2.7a: Find the area of triangle AOP in terms of r and \(\theta \) .
• 11M.1.hl.TZ2.7b: Find the area of triangle POT in terms of r and \(\theta \) .
• 10M.2.hl.TZ1.13: Points A, B and C are on the circumference of a circle, centre O and radius \(r\) . A trapezium...
• 10N.2.hl.TZ0.1: Triangle ABC has AB = 5 cm, BC = 6 cm and area 10 \({\text{c}}{{\text{m}}^2}\). (a)     Find...
• 14N.2.hl.TZ0.9a: If \(n > 2\) and even, show that \(C = \frac{n}{{2\pi }}\sin \frac{{2\pi }}{n}\).
• 14N.2.hl.TZ0.10a: Show that the area, \(A\;{\text{c}}{{\text{m}}^2}\), of the triangle is given by...
• 15M.2.hl.TZ1.4: A triangle \(ABC\) has \(\hat A = 50^\circ \), \({\text{AB}} = 7{\text{ cm}}\) and...
• 15M.2.hl.TZ2.1a: Find the area of the triangle.
• 15N.2.hl.TZ0.7: Triangle \(ABC\) has area \({\text{21 c}}{{\text{m}}^{\text{2}}}\). The sides \(AB\) and \(AC\)...
• 16M.1.hl.TZ1.5a: Expand and simplify \({\left( {1 - \sqrt 3 } \right)^2}\).
• 16M.1.hl.TZ1.5c: Find BC in the form \(a + \sqrt b \) where \(a,{\text{ }}b \in \mathbb{Z}\).
• 16M.2.hl.TZ2.1: ABCD is a quadrilateral where...
• 16N.2.hl.TZ0.7a: Use the cosine rule to find the two possible values for AC.
• 16N.2.hl.TZ0.7b: Find the difference between the areas of the two possible triangles ABC.
• 17N.2.hl.TZ0.5: Barry is at the top of a cliff, standing 80 m above sea level, and observes two yachts in the...
• 18M.1.hl.TZ1.11b: Show that the area of the quadrilateral Q is \(\frac{{21\sqrt 3 }}{2}\).

Applications.

• 12N.1.hl.TZ0.7b: Determine the values of k for which the conditions above define a unique triangle.
• 16M.2.hl.TZ2.1: ABCD is a quadrilateral where...
• 18M.1.hl.TZ1.11b: Show that the area of the quadrilateral Q is \(\frac{{21\sqrt 3 }}{2}\).