DP Mathematical Studies Questionbank

• Syllabus

5.3

Sub sections and their related questions

Use of the sine rule: $\frac{a}{{\sin A}} = \frac{b}{{\sin B}} = \frac{c}{{\sin C}}$.

• 10N.2.sl.TZ0.3b: Find the size of the angle CAB.
• 12N.2.sl.TZ0.3b: He next marks a fourth point, D, on the ground at a distance of 6 m from B , such that angle BDC...
• 12M.1.sl.TZ1.10b: Calculate the size of angle ACB.
• 12M.1.sl.TZ1.13a: Find the length of AC.
• 12M.2.sl.TZ2.4f: Ahmed is at point P , a distance x metres from M on horizontal ground, as shown in the following...
• 11N.2.sl.TZ0.3c: Calculate the size of angle BCD.
• 11N.2.sl.TZ0.3d: Show that the triangle ABC is not right angled.
• 09N.2.sl.TZ0.1B, c: Inside the forest a second path forms the three sides of another triangle named ABC. Angle BAC is...
• 09M.1.sl.TZ1.10a: Calculate the size of angle ACB.
• 11M.2.sl.TZ1.5c: Show that the size of angle ABD is ${18.8^ \circ }$ , correct to three significant figures.
• 09M.2.sl.TZ2.3a: Find the size of BĈA.
• 13M.2.sl.TZ1.5b: Calculate the length of AQ.
• 11M.2.sl.TZ2.4b: Calculate the length of AC.
• 13M.1.sl.TZ2.5a: Find the length of AC in centimetres.
• 07M.2.sl.TZ0.2ii.a: (i) Find the value of angle ${\text{B}}\hat {\rm T}{\text{L}}$. (ii) Use triangle BTL to...
• 07N.1.sl.TZ0.9b: Find the size of angle BAC.
• 08N.2.sl.TZ0.2b: (i)     Write down the size of angle BCA. (ii)    Calculate the length of AB.
• 08M.1.sl.TZ1.7b: Calculate the length of ${\text{AB}}$.
• 14M.2.sl.TZ2.2e: The distance from ${\text{B}}$ to ${\text{C}}$ is $850$ metres. Running this part of the...
• 14M.2.sl.TZ1.4a: Find the size of angle $ABC$.
• 14N.2.sl.TZ0.4b: The surveyor measures the size of angle ${\text{CDE}}$ to be twice that of angle...
• 15M.2.sl.TZ1.4c: It is estimated that the fastest boat in the race can travel at an average speed of...
• 17N.1.sl.TZ0.10a: Find the length of EB.
• 17N.1.sl.TZ0.10b: Write down the angle of elevation of B from E.
• 17N.1.sl.TZ0.10c: Find the vertical height of B above the ground.
• 17N.2.sl.TZ0.3a: Show that ${\text{BD}} = 93{\text{ m}}$ correct to the nearest metre.
• 17N.2.sl.TZ0.3b: Calculate angle ${\rm{B\hat CD}}$.
• 17N.2.sl.TZ0.3c: Find the area of ABCD.
• 17N.2.sl.TZ0.3d.i: Calculate Abdallah’s estimate for the area.
• 17N.2.sl.TZ0.3d.ii: Find the percentage error in Abdallah’s estimate.
• 18M.2.sl.TZ1.1a: Calculate the area of triangle EAD.
• 18M.2.sl.TZ1.1b: Calculate the total volume of the barn.
• 18M.2.sl.TZ1.1c: Calculate the length of MN.
• 18M.2.sl.TZ1.1d: Calculate the length of AE.
• 18M.2.sl.TZ1.1e: Show that Farmer Brown is incorrect.
• 18M.2.sl.TZ1.1f: Calculate the total length of metal required for one support.
• 18M.1.sl.TZ2.8a: Calculate the length of side AC in km.
• 18M.1.sl.TZ2.8b: Calculate the area of the park.
• 18M.2.sl.TZ2.5a.i: Use Giovanni’s diagram to show that angle ABC, the angle at which the Tower is leaning relative...
• 18M.2.sl.TZ2.5a.ii: Use Giovanni's diagram to calculate the length of AX.
• 18M.2.sl.TZ2.5a.iii: Use Giovanni's diagram to find the length of BX, the horizontal displacement of the Tower.
• 18M.2.sl.TZ2.5b: Find the percentage error on Giovanni’s diagram.
• 18M.2.sl.TZ2.5c: Giovanni adds a point D to his diagram, such that BD = 45 m, and another triangle is...

Use of the cosine rule: ${a^2} = {b^2} + {c^2} - 2bc\cos A$ ; $\cos A = \frac{{{b^2} + {c^2} - {a^2}}}{{2bc}}$.

• 10M.1.sl.TZ1.7b: Calculate the length of BC in cm.
• 10M.2.sl.TZ1.2e: It is known that AC = 5 and BC = 8.06. Calculate the size of angle ACB.
• 10N.2.sl.TZ0.3a: Find the length of the road AB.
• 12N.2.sl.TZ0.3a: Find the length of BC.
• 12M.1.sl.TZ1.10a: Calculate the length of AC.
• 10M.2.sl.TZ2.4b.i: Find the length of BC.
• 12M.2.sl.TZ2.4g: Ahmed is at point P , a distance x metres from M on horizontal ground, as shown in the following...
• 11N.2.sl.TZ0.3a: Calculate the size of angle ADB.
• 09N.2.sl.TZ0.1B, a: Calculate the length of the third side of the triangle. Give your answer correct to the nearest...
• 09M.2.sl.TZ1.4d: A different chocolate bar made with the same mixture also has the shape of a triangular prism....
• 11M.2.sl.TZ1.5a: Calculate the length of the fence.
• 09M.2.sl.TZ2.3b: Calculate the length of AD.
• 11M.1.sl.TZ2.10b: Calculate the length of AC.
• 13M.2.sl.TZ1.5e: Find the size of the angle AQC.
• 11M.2.sl.TZ2.4e: A goat is attached to one end of a rope of length 7 m. The other end of the rope is attached to...
• 13M.1.sl.TZ2.5b: Find the size of angle ADC.
• SPM.2.sl.TZ0.2a: Calculate the size of angle ACB.
• 07M.2.sl.TZ0.2ii.c: Leonardo now walks to point M, a distance 200 m from B on the opposite side of the tower....
• 07N.1.sl.TZ0.9a: Find the distance between A and C.
• 07N.2.sl.TZ0.2d: Calculate the angle at the vertex, ${\text{B}}{\operatorname {\hat V}}{\text{C}}$.
• 08N.2.sl.TZ0.2a: Find the length of AC.
• 08M.2.sl.TZ2.3i.b: Find the length of ${\text{AC}}$.
• 14M.2.sl.TZ2.2c: The distance from ${\text{B}}$ to ${\text{C}}$ is $850$ metres. Running this part of the...
• 13N.2.sl.TZ0.2a: Calculate the length of ${\text{AC}}$.
• 14M.2.sl.TZ1.4c: ${\text{M}}$ is the midpoint of ${\text{AC}}$. Find the length of ${\text{BM}}$.
• 14N.2.sl.TZ0.4a: (i)     Find the size of angle ${\rm{ACB}}$. (ii)     Show that the size of angle...
• 15M.1.sl.TZ2.8c: Find the length of ${\rm{CB}}$.
• 15M.2.sl.TZ1.4a: Calculate the total length of the course.
• 16N.2.sl.TZ0.5b: the size of angle DAB;
• 17N.1.sl.TZ0.10a: Find the length of EB.
• 17N.1.sl.TZ0.10b: Write down the angle of elevation of B from E.
• 17N.1.sl.TZ0.10c: Find the vertical height of B above the ground.
• 17N.2.sl.TZ0.3a: Show that ${\text{BD}} = 93{\text{ m}}$ correct to the nearest metre.
• 17N.2.sl.TZ0.3b: Calculate angle ${\rm{B\hat CD}}$.
• 17N.2.sl.TZ0.3c: Find the area of ABCD.
• 17N.2.sl.TZ0.3d.i: Calculate Abdallah’s estimate for the area.
• 17N.2.sl.TZ0.3d.ii: Find the percentage error in Abdallah’s estimate.
• 18M.2.sl.TZ1.1a: Calculate the area of triangle EAD.
• 18M.2.sl.TZ1.1b: Calculate the total volume of the barn.
• 18M.2.sl.TZ1.1c: Calculate the length of MN.
• 18M.2.sl.TZ1.1d: Calculate the length of AE.
• 18M.2.sl.TZ1.1e: Show that Farmer Brown is incorrect.
• 18M.2.sl.TZ1.1f: Calculate the total length of metal required for one support.
• 18M.1.sl.TZ2.8a: Calculate the length of side AC in km.
• 18M.1.sl.TZ2.8b: Calculate the area of the park.
• 18M.2.sl.TZ2.5a.i: Use Giovanni’s diagram to show that angle ABC, the angle at which the Tower is leaning relative...
• 18M.2.sl.TZ2.5a.ii: Use Giovanni's diagram to calculate the length of AX.
• 18M.2.sl.TZ2.5a.iii: Use Giovanni's diagram to find the length of BX, the horizontal displacement of the Tower.
• 18M.2.sl.TZ2.5b: Find the percentage error on Giovanni’s diagram.
• 18M.2.sl.TZ2.5c: Giovanni adds a point D to his diagram, such that BD = 45 m, and another triangle is...

Use of the area of a triangle $= \frac{1}{2}ab\sin C$.

• 10M.2.sl.TZ1.2f: It is known that AC = 5 and BC = 8.06. Calculate the area of triangle ACB.
• 10N.1.sl.TZ0.12b: Find the area of the triangle AOB.
• 12N.2.sl.TZ0.3c: He next marks a fourth point, D, on the ground at a distance of 6 m from B , such that angle BDC...
• 12M.1.sl.TZ1.13b: Find the area of triangle ABC.
• 12M.1.sl.TZ2.7c: The area of triangle ABC is 360 cm2. Calculate the length of side AC. Express your answer in...
• 11N.2.sl.TZ0.3b: Find the area of triangle ADB.
• 09N.2.sl.TZ0.1B, b: Calculate the area enclosed by the path that goes around the forest.
• 11M.2.sl.TZ1.5d: Calculate the area of triangle ABD .
• 09M.2.sl.TZ2.3e: Calculate the area of the triangle ABD.
• 13M.2.sl.TZ1.5f: Calculate the total area of the glass needed to construct (i) the two rectangular faces of the...
• 11M.2.sl.TZ2.4c: Calculate the area of the field ABC.
• 13M.2.sl.TZ2.3b: Calculate the area of the triangle PTS.
• SPM.2.sl.TZ0.2b: Calculate the area of the building’s footprint, ABC.
• 08N.2.sl.TZ0.2c: Show that the area of the sandbox is $31.1{\text{ }}{{\text{m}}^2}$ correct to 3 s.f.
• 08M.1.sl.TZ1.7c: Find the area of triangle ${\text{ABC}}$.
• 08M.2.sl.TZ2.3i.a: Angle ${\text{ABC}}$ is acute. Show that the angle ${\text{ABC}}$ is ${30^ \circ }$.
• 09M.2.sl.TZ1.4a, ii: Hence or otherwise find the area of the triangular end of the chocolate bar.
• 10M.2.sl.TZ2.4b.iii: Calculate the area of the lawn.
• 14M.2.sl.TZ2.2f: The distance from ${\text{B}}$ to ${\text{C}}$ is $850$ metres. Running this part of the...
• 13N.2.sl.TZ0.2b: Calculate the area of triangle ${\text{ABC}}$.
• 14M.2.sl.TZ1.4b: Find the area of the triangular field.
• 14N.2.sl.TZ0.4c: Calculate the area of triangle ${\text{DEC}}$.
• 15M.1.sl.TZ2.12c: Hence, or otherwise, find the area of the triangle ${\text{CAV}}$.
• 15M.2.sl.TZ1.4d: To comply with safety regulations, the area inside the triangular course must be kept clear of...
• 17N.1.sl.TZ0.10a: Find the length of EB.
• 17N.1.sl.TZ0.10b: Write down the angle of elevation of B from E.
• 17N.1.sl.TZ0.10c: Find the vertical height of B above the ground.
• 17N.2.sl.TZ0.3a: Show that ${\text{BD}} = 93{\text{ m}}$ correct to the nearest metre.
• 17N.2.sl.TZ0.3b: Calculate angle ${\rm{B\hat CD}}$.
• 17N.2.sl.TZ0.3c: Find the area of ABCD.
• 17N.2.sl.TZ0.3d.i: Calculate Abdallah’s estimate for the area.
• 17N.2.sl.TZ0.3d.ii: Find the percentage error in Abdallah’s estimate.
• 18M.2.sl.TZ1.1a: Calculate the area of triangle EAD.
• 18M.2.sl.TZ1.1b: Calculate the total volume of the barn.
• 18M.2.sl.TZ1.1c: Calculate the length of MN.
• 18M.2.sl.TZ1.1d: Calculate the length of AE.
• 18M.2.sl.TZ1.1e: Show that Farmer Brown is incorrect.
• 18M.2.sl.TZ1.1f: Calculate the total length of metal required for one support.
• 18M.1.sl.TZ2.8a: Calculate the length of side AC in km.
• 18M.1.sl.TZ2.8b: Calculate the area of the park.
• 18M.2.sl.TZ2.5a.i: Use Giovanni’s diagram to show that angle ABC, the angle at which the Tower is leaning relative...
• 18M.2.sl.TZ2.5a.ii: Use Giovanni's diagram to calculate the length of AX.
• 18M.2.sl.TZ2.5a.iii: Use Giovanni's diagram to find the length of BX, the horizontal displacement of the Tower.
• 18M.2.sl.TZ2.5b: Find the percentage error on Giovanni’s diagram.
• 18M.2.sl.TZ2.5c: Giovanni adds a point D to his diagram, such that BD = 45 m, and another triangle is...

Construction of labelled diagrams from verbal statements.

• 10M.2.sl.TZ1.4a.ii: Sketch the triangle VCA showing clearly the length of VC and the size of angle VCA.
• 18M.2.sl.TZ1.1a: Calculate the area of triangle EAD.
• 18M.2.sl.TZ1.1b: Calculate the total volume of the barn.
• 18M.2.sl.TZ1.1c: Calculate the length of MN.
• 18M.2.sl.TZ1.1d: Calculate the length of AE.
• 18M.2.sl.TZ1.1e: Show that Farmer Brown is incorrect.
• 18M.2.sl.TZ1.1f: Calculate the total length of metal required for one support.
• 18M.1.sl.TZ2.8a: Calculate the length of side AC in km.
• 18M.1.sl.TZ2.8b: Calculate the area of the park.
• 18M.2.sl.TZ2.5a.i: Use Giovanni’s diagram to show that angle ABC, the angle at which the Tower is leaning relative...
• 18M.2.sl.TZ2.5a.ii: Use Giovanni's diagram to calculate the length of AX.
• 18M.2.sl.TZ2.5a.iii: Use Giovanni's diagram to find the length of BX, the horizontal displacement of the Tower.
• 18M.2.sl.TZ2.5b: Find the percentage error on Giovanni’s diagram.
• 18M.2.sl.TZ2.5c: Giovanni adds a point D to his diagram, such that BD = 45 m, and another triangle is...