DP Mathematics SL Questionbank

• Syllabus

3.6

Sub sections and their related questions

Solution of triangles.

• 12M.2.sl.TZ2.1a: Find \({\rm{R\hat PQ}}\) .
• 08N.2.sl.TZ0.6a: Find the distance the second ship will travel.
• 08N.2.sl.TZ0.6b: Find the bearing of the course taken by the second ship.
• 08M.2.sl.TZ1.2a: Find \({\rm{P}}\widehat {\rm{R}}{\rm{Q}}\) .
• 09N.2.sl.TZ0.8a: Find AD.
• 09N.2.sl.TZ0.8b: Find OD.
• 09M.2.sl.TZ1.2a: Find AB.
• 09M.2.sl.TZ2.4a: Find the size of angle ACB.
• 09M.2.sl.TZ2.4b: Find the size of angle CAD.
• SPNone.2.sl.TZ0.6: Find the height of the building.
• 13M.2.sl.TZ1.8a: Find AC.
• 13M.2.sl.TZ1.8b: (i)     Find \(A\hat CD\) . (ii)     Hence, find \(A\hat CB\) .
• 13M.2.sl.TZ2.3b: Find BC.
• 14M.2.sl.TZ1.1a: Find AC.
• 14M.2.sl.TZ1.1b: Find \({\rm{B\hat CA}}\).
• 14M.2.sl.TZ2.5b: Given that \(\hat A\) is obtuse, find \({\text{BC}}\).
• 13N.2.sl.TZ0.8a: Find \({\rm{B\hat AC}}\).
• 13N.2.sl.TZ0.8b: Find \({\text{AC}}\).
• 13N.2.sl.TZ0.8c: Hence or otherwise, find the length of arc \({\text{ABC}}\).
• 14N.2.sl.TZ0.3b: Find \(AB\).
• 15N.2.sl.TZ0.8a: Find \(AC\).
• 15N.2.sl.TZ0.8d: Given that \(\theta \) is obtuse, find \(CD\).

The cosine rule.

• 12N.2.sl.TZ0.8a: Find the length of the chord [AB].
• 12N.2.sl.TZ0.8b: Find the area of triangle AOB.
• 12N.2.sl.TZ0.8c: Angle BOC is 2.4 radians. Find the length of arc ADC.
• 12N.2.sl.TZ0.8d: Angle BOC is 2.4 radians. Find the area of the shaded region.
• 12N.2.sl.TZ0.8e: Angle BOC is 2.4 radians. The shaded region is to be painted red. Red paint is sold in cans...
• 12M.2.sl.TZ2.10a: Use the cosine rule to show that \({\rm{PQ}} = 2r\sin \theta \) .
• 12M.2.sl.TZ2.10b: Let l be the length of the arc PRQ . Given that \(1.3{\rm{PQ}} - l = 0\) , find the value of...
• 12M.2.sl.TZ2.10c(i) and (ii): Consider the function \(f(\theta ) = 2.6\sin \theta  - 2\theta \) , for...
• 12M.2.sl.TZ2.10d: Use the graph of f to find the values of \(\theta \) for which \(l < 1.3{\rm{PQ}}\) .
• 08N.2.sl.TZ0.6a: Find the distance the second ship will travel.
• 12M.2.sl.TZ1.9a(i) and (ii): (i)     Show that \({p^2}(41 - 40\cos 0.7) = 36\) . (ii)    Find p .
• 12M.2.sl.TZ1.9b: Write down the length of BD.
• 12M.2.sl.TZ1.9c: Find \({\rm{A}}\widehat {\rm{D}}{\rm{B}}\) .
• 12M.2.sl.TZ1.9d(i) and (ii): (i)     Show that \({\rm{C}}\widehat {\rm{B}}{\rm{D}} = 1.29\) radians, correct to 2 decimal...
• 09N.2.sl.TZ0.8b: Find OD.
• 09M.2.sl.TZ1.2a: Find AB.
• 09M.2.sl.TZ2.4a: Find the size of angle ACB.
• 10N.2.sl.TZ0.6a: Find \({\rm{A}}\widehat {\rm{C}}{\rm{B}}\) .
• 10N.2.sl.TZ0.6b: Find AB.
• 10M.2.sl.TZ1.8a: Use the cosine rule to show that \({\rm{AC}} = \sqrt {41 - 40\cos x} \) .
• 10M.2.sl.TZ1.8b: Use the sine rule in triangle ABC to find another expression for AC.
• 10M.2.sl.TZ1.8c: (i)     Hence, find x, giving your answer to two decimal places. (ii)    Find AC .
• 10M.2.sl.TZ1.8d(i) and (ii): (i)     Find y. (ii)    Hence, or otherwise, find the area of triangle ACD.
• 10M.2.sl.TZ2.8a: Find the size of angle AOC .
• 10M.2.sl.TZ2.8b: Hence find the area of the shaded region.
• 10M.2.sl.TZ2.8c: The area of sector OCDE is \(45{\text{ c}}{{\text{m}}^2}\). Find the size of angle COE .
• 10M.2.sl.TZ2.8d: Find EF .
• 11M.2.sl.TZ1.1a: Find AC .
• 11M.2.sl.TZ1.1b: Find \({\rm{B}}\widehat {\rm{A}}{\rm{C}}\) .
• 11M.2.sl.TZ2.5a: Complete the diagram, showing clearly all the information above.
• 11M.2.sl.TZ2.5b: Find x .
• 13M.2.sl.TZ1.8a: Find AC.
• 13M.2.sl.TZ2.3b: Find BC.
• 14M.2.sl.TZ1.1a: Find AC.
• 14M.2.sl.TZ1.1b: Find \({\rm{B\hat CA}}\).
• 14M.2.sl.TZ2.5b: Given that \(\hat A\) is obtuse, find \({\text{BC}}\).
• 13N.2.sl.TZ0.8b: Find \({\text{AC}}\).
• 13N.2.sl.TZ0.8c: Hence or otherwise, find the length of arc \({\text{ABC}}\).
• 14N.2.sl.TZ0.3b: Find \(AB\).
• 15M.2.sl.TZ2.10a: Show that the area of the square \(ABCD\) is \(2{r^2}(1 - \cos \theta )\).
• 15N.2.sl.TZ0.8d: Given that \(\theta \) is obtuse, find \(CD\).
• 16M.2.sl.TZ1.3b: Find the distance from Town A to Town C.
• 16M.2.sl.TZ1.3c: Use the sine rule to find \({\rm{A\hat CB}}\).
• 16M.2.sl.TZ1.3a: Find \({\rm{A\hat BC}}\).
• 16M.2.sl.TZ2.2a: Find BD.
• 16M.2.sl.TZ2.2b: Find \({\rm{D\hat BC}}\).
• 16N.2.sl.TZ0.3c: Find AB.
• 17M.1.sl.TZ2.9a: Find the coordinates of A.
• 17M.1.sl.TZ2.9b.i: Find \(\overrightarrow {{\text{AB}}} \);
• 17M.1.sl.TZ2.9c: Find \(\cos {\rm{B\hat AC}}\).
• 17M.1.sl.TZ2.9d: Hence or otherwise, find the distance between \({P_1}\) and \({P_2}\) two seconds after they...
• 17M.1.sl.TZ2.9b.ii: Find \(\left| {\overrightarrow {{\text{AB}}} } \right|\).
• 17M.2.sl.TZ1.5: The following diagram shows the chord [AB] in a circle of radius 8 cm, where...
• 17M.2.sl.TZ2.9a: Find the bearing of A from E.
• 17M.2.sl.TZ2.9b: Finds CE.
• 17M.2.sl.TZ2.9c: Find DE.
• 17M.2.sl.TZ2.9d: When the ship reaches D, it changes direction and travels directly to the island at 50 km per...
• 17N.1.sl.TZ0.4a: Show that \({\text{AC}} = 7{\text{ cm}}\).
• 17N.1.sl.TZ0.4b: The shape in the following diagram is formed by adding a semicircle with diameter [AC] to the...
• 18M.2.sl.TZ1.6: Triangle ABC has a = 8.1 cm, b = 12.3 cm and area 15 cm2. Find the largest possible perimeter of...
• 18M.2.sl.TZ2.2a: Find DB.
• 18M.2.sl.TZ2.2b: Find DC.

The sine rule, including the ambiguous case.

• 12M.2.sl.TZ2.1b: Find PR .
• 08M.2.sl.TZ1.2a: Find \({\rm{P}}\widehat {\rm{R}}{\rm{Q}}\) .
• 12M.2.sl.TZ1.9a(i) and (ii): (i)     Show that \({p^2}(41 - 40\cos 0.7) = 36\) . (ii)    Find p .
• 12M.2.sl.TZ1.9b: Write down the length of BD.
• 12M.2.sl.TZ1.9c: Find \({\rm{A}}\widehat {\rm{D}}{\rm{B}}\) .
• 12M.2.sl.TZ1.9d(i) and (ii): (i)     Show that \({\rm{C}}\widehat {\rm{B}}{\rm{D}} = 1.29\) radians, correct to 2 decimal...
• 09N.2.sl.TZ0.8a: Find AD.
• 09N.2.sl.TZ0.8b: Find OD.
• 09M.2.sl.TZ2.4b: Find the size of angle CAD.
• 10M.2.sl.TZ1.8a: Use the cosine rule to show that \({\rm{AC}} = \sqrt {41 - 40\cos x} \) .
• 10M.2.sl.TZ1.8b: Use the sine rule in triangle ABC to find another expression for AC.
• 10M.2.sl.TZ1.8c: (i)     Hence, find x, giving your answer to two decimal places. (ii)    Find AC .
• 10M.2.sl.TZ1.8d(i) and (ii): (i)     Find y. (ii)    Hence, or otherwise, find the area of triangle ACD.
• 11N.2.sl.TZ0.4a: Find the two possible values of \({\rm{A}}\widehat {\rm{C}}{\rm{B}}\) .
• 11N.2.sl.TZ0.4b: Hence, find \({\rm{A}}\widehat {\rm{B}}{\rm{C}}\) , given that it is acute.
• 11M.2.sl.TZ1.1a: Find AC .
• 11M.2.sl.TZ1.1b: Find \({\rm{B}}\widehat {\rm{A}}{\rm{C}}\) .
• 13M.2.sl.TZ1.8b: (i)     Find \(A\hat CD\) . (ii)     Hence, find \(A\hat CB\) .
• 14M.2.sl.TZ1.1b: Find \({\rm{B\hat CA}}\).
• 13N.2.sl.TZ0.8a: Find \({\rm{B\hat AC}}\).
• 15M.2.sl.TZ2.1a: Find \(AC\).
• 15N.2.sl.TZ0.8a: Find \(AC\).
• 16M.2.sl.TZ1.3b: Find the distance from Town A to Town C.
• 16M.2.sl.TZ1.3c: Use the sine rule to find \({\rm{A\hat CB}}\).
• 16M.2.sl.TZ1.3a: Find \({\rm{A\hat BC}}\).
• 16M.2.sl.TZ2.2a: Find BD.
• 16M.2.sl.TZ2.2b: Find \({\rm{D\hat BC}}\).
• 17M.1.sl.TZ1.3: The following diagram shows triangle PQR. Find PR.
• 17M.2.sl.TZ2.9a: Find the bearing of A from E.
• 17M.2.sl.TZ2.9b: Finds CE.
• 17M.2.sl.TZ2.9c: Find DE.
• 17M.2.sl.TZ2.9d: When the ship reaches D, it changes direction and travels directly to the island at 50 km per...
• 17N.2.sl.TZ0.1a: Find BC.
• 17N.2.sl.TZ0.1b: Find the area of triangle ABC.
• 18M.2.sl.TZ2.2a: Find DB.
• 18M.2.sl.TZ2.2b: Find DC.

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

• 12N.2.sl.TZ0.8a: Find the length of the chord [AB].
• 12N.2.sl.TZ0.8b: Find the area of triangle AOB.
• 12N.2.sl.TZ0.8c: Angle BOC is 2.4 radians. Find the length of arc ADC.
• 12N.2.sl.TZ0.8d: Angle BOC is 2.4 radians. Find the area of the shaded region.
• 12N.2.sl.TZ0.8e: Angle BOC is 2.4 radians. The shaded region is to be painted red. Red paint is sold in cans...
• 12M.2.sl.TZ2.1c: Find the area of \(\Delta {\rm{PQR}}\) .
• 08N.2.sl.TZ0.8d: Hence, or otherwise, find the area of the parallelogram.
• 08M.2.sl.TZ1.2b: Find the area of triangle PQR.
• 08M.1.sl.TZ2.10a: Find the area of the triangle OPB, in terms of \(\theta \) .
• 08M.1.sl.TZ2.10b: Explain why the area of triangle OPA is the same as the area triangle OPB.
• 12M.2.sl.TZ1.9a(i) and (ii): (i)     Show that \({p^2}(41 - 40\cos 0.7) = 36\) . (ii)    Find p .
• 12M.2.sl.TZ1.9b: Write down the length of BD.
• 12M.2.sl.TZ1.9c: Find \({\rm{A}}\widehat {\rm{D}}{\rm{B}}\) .
• 12M.2.sl.TZ1.9d(i) and (ii): (i)     Show that \({\rm{C}}\widehat {\rm{B}}{\rm{D}} = 1.29\) radians, correct to 2 decimal...
• 09N.2.sl.TZ0.8d: Find the area of region ABCD.
• 09M.1.sl.TZ1.9c: (i)     Find \({\rm{sinR}}\widehat {\rm{P}}{\rm{Q}}\) . (ii)    Hence, find the area of triangle...
• 10N.2.sl.TZ0.6a: Find \({\rm{A}}\widehat {\rm{C}}{\rm{B}}\) .
• 10N.2.sl.TZ0.6b: Find AB.
• 10M.2.sl.TZ1.8a: Use the cosine rule to show that \({\rm{AC}} = \sqrt {41 - 40\cos x} \) .
• 10M.2.sl.TZ1.8b: Use the sine rule in triangle ABC to find another expression for AC.
• 10M.2.sl.TZ1.8c: (i)     Hence, find x, giving your answer to two decimal places. (ii)    Find AC .
• 10M.2.sl.TZ1.8d(i) and (ii): (i)     Find y. (ii)    Hence, or otherwise, find the area of triangle ACD.
• SPNone.2.sl.TZ0.7a: Find an expression for the area of the shaded region.
• 13M.2.sl.TZ2.3a: Find \(x\) .
• 14M.2.sl.TZ2.5a: Find the two possible values for \(\hat A\).
• 13M.2.sl.TZ1.8c: Find the area of triangle ADC.
• 13M.2.sl.TZ1.8d: Hence or otherwise, find the total area of the shaded regions.
• 14N.1.sl.TZ0.7: The following diagram shows triangle \(ABC\). Let...
• 15M.2.sl.TZ2.1b: Find the area of triangle \(ABC\).
• 15N.2.sl.TZ0.8b: Find the area of triangle \(ABC\).
• 15N.2.sl.TZ0.8c: The area of triangle \(ACD\) is half the area of triangle \(ABC\). Find the possible values of...
• 16M.1.sl.TZ2.5a: Find \({\rm{A\hat BC}}\).
• 16M.1.sl.TZ2.5b: Find the exact area of the sector BDC.
• 16N.1.sl.TZ0.8c: Write down an expression in terms of \(\theta \) for (i)     angle ADB; (ii)     area of...
• 17M.2.sl.TZ1.5: The following diagram shows the chord [AB] in a circle of radius 8 cm, where...
• 17N.2.sl.TZ0.1a: Find BC.
• 17N.2.sl.TZ0.1b: Find the area of triangle ABC.
• 18M.2.sl.TZ1.6: Triangle ABC has a = 8.1 cm, b = 12.3 cm and area 15 cm2. Find the largest possible perimeter of...
• 18M.2.sl.TZ2.8a.i: Find \(\mathop {{\text{PQ}}}\limits^ \to  \).
• 18M.2.sl.TZ2.8a.ii: Find \(\left| {\mathop {{\text{PQ}}}\limits^ \to  } \right|\).
• 18M.2.sl.TZ2.8b: Find the angle between PQ and PR.
• 18M.2.sl.TZ2.8c: Find the area of triangle PQR.
• 18M.2.sl.TZ2.8d: Hence or otherwise find the shortest distance from R to the line through P and Q.

Applications.

• SPNone.2.sl.TZ0.6: Find the height of the building.
• 17M.2.sl.TZ2.9a: Find the bearing of A from E.
• 17M.2.sl.TZ2.9b: Finds CE.
• 17M.2.sl.TZ2.9c: Find DE.
• 17M.2.sl.TZ2.9d: When the ship reaches D, it changes direction and travels directly to the island at 50 km per...