DP Mathematical Studies Questionbank

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• 18M.2.sl.TZ2.5c: Giovanni adds a point D to his diagram, such that BD = 45 m, and another triangle is...
• 18M.2.sl.TZ2.5b: Find the percentage error on Giovanni’s diagram.
• 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.TZ2.5a.ii: Use Giovanni's diagram to calculate the length of AX.
• 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.TZ1.1f: Calculate the total length of metal required for one support.
• 18M.2.sl.TZ1.1e: Show that Farmer Brown is incorrect.
• 18M.2.sl.TZ1.1d: Calculate the length of AE.
• 18M.2.sl.TZ1.1c: Calculate the length of MN.
• 18M.2.sl.TZ1.1b: Calculate the total volume of the barn.
• 18M.2.sl.TZ1.1a: Calculate the area of triangle EAD.
• 17N.1.sl.TZ0.10c: Find the vertical height of B above the ground.
• 17N.1.sl.TZ0.10b: Write down the angle of elevation of B from E.
• 17N.1.sl.TZ0.10a: Find the length of EB.
• 17M.1.sl.TZ2.3b: Find the total length of wire needed to construct this wireframe. Give your answer in centimetres...
• 17M.1.sl.TZ2.3a: Find the length of one of the straight pieces in the wireframe.
• 17M.2.sl.TZ1.2e: Calculate the length of CF.
• 17M.2.sl.TZ1.2d: Find the length of the perimeter of ABCDE.
• 17M.2.sl.TZ1.2c: Show that angle \({\rm{B\hat AE}} = 67.4^\circ \), correct to one decimal place.
• 17M.2.sl.TZ1.2b: Find the length of CD.
• 17M.2.sl.TZ1.2a.ii: Show that the equation in part (a)(i) simplifies to \(3{x^2} + 19x - 414 = 0\).
• 17M.2.sl.TZ1.2a.i: Write down an equation for the area of ABCDE using the above information.
• 16M.2.sl.TZ2.4f: Calculate the maximum number of cups that can be completely filled with the...
• 16M.2.sl.TZ2.4e: Chavi is celebrating her birthday with her friends on the playground. Her mother brings a...
• 16M.2.sl.TZ2.4d: Chavi estimates that the height of the tree is \(6\,{\text{m}}\). Calculate the percentage error...
• 16M.2.sl.TZ2.4c: There is a tree at \({\text{C}}\), perpendicular to the ground. The angle of elevation to the top...
• 16M.2.sl.TZ2.4b: Calculate angle \({\text{ADC}}\).
• 16M.2.sl.TZ2.4a: A playground, when viewed from above, is shaped like a quadrilateral, \({\text{ABCD}}\),...
• 16M.1.sl.TZ2.3c: Calculate the obtuse angle made by the ladder with the ground.
• 16M.1.sl.TZ2.3b: Calculate the distance between the top of the ladder and the base of the wall.
• 16M.1.sl.TZ2.3a: A ladder is standing on horizontal ground and leaning against a vertical wall. The length of the...
• 16M.2.sl.TZ1.4f: Ahmad and his friends like to sit in the pyramid’s shadow, \({\text{ABW}}\), to cool down.At...
• 16M.2.sl.TZ1.4e: Ahmad is a tour guide at the Great Pyramid of Giza. He claims that the amount of stone used to...
• 16M.2.sl.TZ1.4d: Write down your answer to part (c) in the form \(a \times {10^k}\)  where...
• 16M.2.sl.TZ1.4c: Find the volume of the pyramid.
• 16M.2.sl.TZ1.4b: Calculate the height of the pyramid, \({\text{VO}}\) .
• 16M.2.sl.TZ1.4a: The Great Pyramid of Giza in Egypt is a right pyramid with a square base. The pyramid is made of...
• 16M.1.sl.TZ1.7d: Write your answer to part (c) in the form \(ax + by + d = 0\)  where \(a\), \(b\) and...
• 16M.1.sl.TZ1.2b: William also has a sailing boat with a sail in the shape of a right-angled triangle,...
• 16M.1.sl.TZ1.2a: Temi’s sailing boat has a sail in the shape of a right-angled triangle,...
• 16N.1.sl.TZ0.11b: Calculate the angle of depression from A to B.
• 16N.1.sl.TZ0.11a: Calculate CD, the height of the observation deck above the ground.
• 13N.1.sl.TZ0.5b: \({\text{D}}\) is the point on \({\text{AB}}\) such that \(\tan ({\rm{D\hat CB}}) = 0.6\). Find...
• 10M.1.sl.TZ2.1b: José estimates the angle between the horizontal and the top of the cliff as 28.3° and uses it to...
• 10M.2.sl.TZ1.4b: Show that the height of the pyramid is 18.0 metres correct to 3 significant figures.
• 10N.2.sl.TZ0.3d: Show that the distance from D to T is 2.06 km correct to three significant figures.
• 10M.2.sl.TZ2.4c.i: Find the angle FCH.
• 12M.2.sl.TZ1.3e: The cylinder was melted and recast into a solid cone, shown in the following diagram. The base...
• 12M.2.sl.TZ1.3f: The cylinder was melted and recast into a solid cone, shown in the following diagram. The base...
• 12M.2.sl.TZ2.4d: Show that the angle between the line VM and the base of the pyramid is 52° correct to 2...
• 09M.1.sl.TZ1.4c: The acute angle between the line AB and the x-axis is θ. Show θ on the diagram.
• 09M.1.sl.TZ1.4d: The acute angle between the line AB and the x-axis is θ. Calculate the size of θ.
• 11M.1.sl.TZ2.10a: Calculate the size of \({\text{A}}\hat {\text{B}}{\text{C}}\).
• 13M.2.sl.TZ2.3f: A pole is placed from V to M, the midpoint of PS. Find in metres, (i) the height of the tent,...
• 13M.2.sl.TZ2.3a: Show that the length of side ST is 1.95 m, correct to 3 significant figures.
• SPM.1.sl.TZ0.2b: Calculate, SF, the distance between the ship and the fishing boat. Give your answer correct to...
• SPM.1.sl.TZ0.2a: Calculate, SB, the distance between the ship and the bottom of the cliff.
• SPM.1.sl.TZ0.6b: Calculate the angle between VC and the base ABCD.
• SPM.2.sl.TZ0.2e: Calculate the angle CQ makes with BC.
• 07M.2.sl.TZ0.2ii.b: Calculate the vertical height TG of the top of the tower.
• 08M.2.sl.TZ1.4ii.b: Show that the height of the pyramid is \(13.7{\text{ cm}}\), to 3 significant figures.
• 08M.2.sl.TZ1.4ii.c: Calculate (i)     the length of \({\text{EG}}\); (ii)    the size of angle \({\text{DEC}}\).
• 08M.1.sl.TZ2.3a: (i) Sketch a diagram to illustrate this information. Label the points \({\text{A, B, C}}\). Show...
• 11M.2.sl.TZ2.4d: N is the point on AB such that CN is perpendicular to AB. M is the midpoint of CN. Calculate...
• 08M.2.sl.TZ2.3ii.b: \({\text{M}}\) is the midpoint of the base of one of the triangles and \({\text{O}}\) is the apex...
• 10M.2.sl.TZ2.4c.ii: Calculate the distance MN from one side of the garden bed to the other, passing through C.
• 14M.1.sl.TZ1.8a: Calculate OV, the height of the cone.
• 14M.2.sl.TZ1.4d: A vertical mobile phone mast, \({\text{TB}}\), is built next to the field with its base...
• 14M.1.sl.TZ2.10a: Calculate the horizontal distance, \({\text{GH}}\), of the plane from Günter. Give your answer to...
• 14M.1.sl.TZ2.10b: The plane took off from a point \({\text{T}}\), which is \(250\) metres from where Günter is...
• 15M.1.sl.TZ2.12b: Find the size of the angle that the sloping edge \({\text{VA}}\) makes with the base of the pyramid.
• 15M.1.sl.TZ2.2b: Find the distance, BC, from the base of the building to the car.
• 15M.1.sl.TZ2.2a: Show, in the appropriate place on the diagram, the values of (i)     the height of the...
• 15M.2.sl.TZ1.4g: The race is filmed from a helicopter, \({\text{H}}\), which is flying vertically above point...
• 15M.2.sl.TZ1.4e: To comply with safety regulations, the area inside the triangular course must be kept clear of...
• 15M.2.sl.TZ1.4f: The race is filmed from a helicopter, \({\text{H}}\), which is flying vertically above point...