DP Mathematical Studies Questionbank

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• 16N.2.sl.TZ0.6d: Show that \(A = \pi {r^2} + \frac{{1\,000\,000}}{r}\).
• 18M.1.sl.TZ2.15b: The total external surface area of the pencil case rounded to 3 significant figures is 570...
• 18M.1.sl.TZ2.15a: Find an expression for the slant height of the cone in terms of r.
• 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.
• 18M.2.sl.TZ1.6f: The designer claims that the new trash can has a capacity that is at least 40% greater than the...
• 18M.2.sl.TZ1.6e: Using your graphic display calculator, find the value of r which maximizes the value of V.
• 18M.2.sl.TZ1.6c: Find the height of the cylinder, h , of the new trash can, in terms of r.
• 18M.2.sl.TZ1.6b: Find the total volume of the trash can.
• 18M.2.sl.TZ1.6a: Write down the height of the cylinder.
• 18M.1.sl.TZ1.14c: Calculate the curved surface area of the remaining solid.
• 18M.1.sl.TZ1.14b: Calculate the curved surface area of the cone which has been removed.
• 18M.1.sl.TZ1.14a: Calculate the radius of the base of the cone which has been removed.
• 17M.1.sl.TZ2.12b: Find the value of \(h\).
• 17M.1.sl.TZ2.12a: Find the volume of water in the container.
• 17M.2.sl.TZ1.4f: In the context of this model, state what the value of 19 represents.
• 17M.2.sl.TZ1.4e: Calculate, to the nearest second, the time since the pizza was taken out of the oven until it can...
• 17M.2.sl.TZ1.4d: Find the temperature that the pizza will be 5 minutes after it is taken out of the oven.
• 17M.2.sl.TZ1.4c: Find the value of \(a\).
• 17M.2.sl.TZ1.4b: Find the radius of the sphere in cm, correct to one decimal place.
• 17M.2.sl.TZ1.4a: Calculate the volume of this pan.
• 17M.1.sl.TZ1.9c: Find the curved surface area of the cone.
• 17M.1.sl.TZ1.9b: Find the slant height, \(l\), of the cone.
• 17M.1.sl.TZ1.9a: Find the radius, \(r\), of the circular base of the cone.
• 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.TZ2.11c: Dan is going to paint the curved surface and the base of the snack container. Calculate the area...
• 16M.1.sl.TZ2.11b: Calculate the area of the base of the container.
• 16M.1.sl.TZ2.11a: A snack container has a cylindrical shape. The diameter of the base is \(7.84\,{\text{cm}}\). The...
• 16M.1.sl.TZ2.1b: The surface area of the Earth that is covered by water is approximately...
• 16M.1.sl.TZ2.1a: Assume that the Earth is a sphere with a radius, \(r\) , of \(6.38 \times {10^3}\,{\text{km}}\)...
• 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.TZ1.4b: The price of tuna per \({\text{c}}{{\text{m}}^3}\) is the same for each brand. A can of FreshWave...
• 16M.1.sl.TZ1.4a: FreshWave brand tuna is sold in cans that are in the shape of a cuboid with length...
• 16N.2.sl.TZ0.6h: Find the least number of cans of water-resistant material that will coat the area in part (g).
• 16N.2.sl.TZ0.6g: Find the value of this minimum area.
• 16N.2.sl.TZ0.6f: Using your answer to part (e), find the value of \(r\) which minimizes \(A\).
• 16N.2.sl.TZ0.6e: Find \(\frac{{{\text{d}}A}}{{{\text{d}}r}}\).
• 16N.2.sl.TZ0.6c: Write down, in terms of \(r\) and \(h\), an equation for the volume of this water container.
• 16N.2.sl.TZ0.6b: Express this volume in \({\text{c}}{{\text{m}}^3}\).
• 16N.2.sl.TZ0.6a: Write down a formula for \(A\), the surface area to be coated.
• 16N.1.sl.TZ0.7b: Calculate the radius of the balloon following this increase.
• 16N.1.sl.TZ0.7a: Calculate the volume of the balloon.
• 10M.1.sl.TZ1.5a: Calculate the volume of the sphere. Give your answer correct to two decimal places.
• 10M.2.sl.TZ1.4e: Calculate the volume of the tower.
• 10N.1.sl.TZ0.3a: Find the volume of the box.
• 10N.1.sl.TZ0.12c: The height of the prism is 20 cm. Find the volume of the prism.
• 11N.1.sl.TZ0.9a: Calculate the volume of the observatory.
• 11N.1.sl.TZ0.9b: The hemispherical roof is to be painted. Calculate the area that is to be painted.
• 12N.1.sl.TZ0.4b: This circle is the base of a solid cylinder of height 25 cm. Write down the volume of the solid...
• 12N.1.sl.TZ0.4c: This circle is the base of a solid cylinder of height 25 cm. Find the total surface area of the...
• 12N.2.sl.TZ0.3d: He next marks a fourth point, D, on the ground at a distance of 6 m from B , such that angle BDC...
• 12N.2.sl.TZ0.3e: He next marks a fourth point, D, on the ground at a distance of 6 m from B , such that angle BDC...
• 10M.2.sl.TZ2.4d: Find the volume of soil used.
• 12M.2.sl.TZ1.3c: Find the total surface area of the cylinder.
• 12M.2.sl.TZ1.3g: The cylinder was melted and recast into a solid cone, shown in the following diagram. The base...
• 10M.2.sl.TZ2.5b.i: Find an expression for the curved surface area of the can, in terms of x. Simplify your answer.
• 12M.2.sl.TZ1.3b: Show that the volume of the metal used in the cylinder is 402 cm3, given correct to three...
• 12M.2.sl.TZ1.3d: The cylinder was melted and recast into a solid cone, shown in the following diagram. The base...
• 12M.2.sl.TZ2.4c: Calculate the volume of the pyramid.
• 12M.2.sl.TZ2.5b: Show that the volume V m3 of the container is given by V = 24x2 − 6x3
• 12M.2.sl.TZ2.5g: The shipping container is to be painted. One litre of paint covers an area of 15 m2 . Paint comes...
• 09M.1.sl.TZ1.13b: Calculate the volume of the empty space in the tube when four tennis balls have been placed in it.
• 09M.1.sl.TZ1.13a: Find the volume of one tennis ball.
• 09M.2.sl.TZ1.4b: Find the total surface area of the chocolate bar.
• 09M.2.sl.TZ2.3f: A layer of earth 3 cm thick is removed from ABD. Find the volume removed in cubic metres.
• 11M.1.sl.TZ2.8a: Calculate the total volume of all \(75\) metal cannon balls excavated.
• 13M.1.sl.TZ2.1a: Calculate the exact value of the volume of the cuboid, in cm3.
• 13M.2.sl.TZ2.3d: Calculate the total surface area of the tent, including the base.
• 13M.2.sl.TZ2.3e: Calculate the volume of the tent.
• SPM.1.sl.TZ0.12b: Calculate the area that is painted red.
• SPM.2.sl.TZ0.2c: Calculate the volume of the office block.
• 07M.2.sl.TZ0.2i.a: Calculate the volume of the cylinder in cm3. Give your answer correct to two decimal places.
• 07M.2.sl.TZ0.2i.c: (i) Jenny fills the cylinder with the number of balls found in part (b) and puts the lid on....
• SPM.2.sl.TZ0.6a: Calculate(i)     the area of the base of the wastepaper bin;(ii)    the height, \(h\) , of...
• SPM.2.sl.TZ0.6d: Show that the total external surface area, \(A\) , of the bin is...
• SPM.2.sl.TZ0.6b: State whether Nadia’s design is practical. Give a reason.
• SPM.2.sl.TZ0.6c: Write down an equation in \(h\) and \(r\) , using the given volume of the bin.
• SPM.2.sl.TZ0.6g: Determine whether Merryn’s design is an improvement upon Nadia’s. Give a reason.
• 07N.2.sl.TZ0.2a: Calculate the volume of the pyramid.
• 07N.2.sl.TZ0.2e: Calculate the total surface area of the pyramid.
• 08M.2.sl.TZ1.4ii.e: Find the volume of the pyramid.
• 08M.2.sl.TZ1.4ii.d: Find the total surface area of the pyramid.
• 08M.2.sl.TZ1.5ii.a: Show that \(4{x^2} + 6xy = 300\).
• 08M.2.sl.TZ1.5ii.c: Hence show that the volume \(V\) of the box is given by \(V = 100x - \frac{4}{3}{x^3}\).
• 08M.2.sl.TZ2.3ii.c: Calculate the volume of the pyramid.
• 08M.2.sl.TZ2.3ii.d: Daniel wants to make a rectangular prism with the same volume as that of Sylvia’s pyramid. The...
• 10M.2.sl.TZ2.5b.ii: Hence write down an expression for A, the total surface area of the can, in terms of x.
• 14M.1.sl.TZ2.4a: Find the volume of 1 chocolate.
• 14M.1.sl.TZ2.4c: The diagram shows the chocolate box from above. The 20 chocolates fit perfectly in the box with...
• 14M.1.sl.TZ2.4d: The diagram shows the chocolate box from above. The 20 chocolates fit perfectly in the box with...
• 14M.2.sl.TZ2.5a: Express the volume of the parcel in terms of \(l\) and \(w\).
• 14M.2.sl.TZ2.6g: The water tank is shown below. It is partially filled with water.   The water tank has a...
• 13N.2.sl.TZ0.2e: Show that the total surface area of one block is \({\text{2190 c}}{{\text{m}}^2}\), correct to...
• 13N.2.sl.TZ0.2c: Assuming that no wood is wasted, show that the volume of wood required to make all \(2600\)...
• 13N.2.sl.TZ0.2f: The blocks are to be painted. One litre of paint will cover \(22{\text{...
• 14M.1.sl.TZ1.8b: Calculate the volume of wood used to make the toy.
• 14M.2.sl.TZ1.6b: The volume of the lobster trap is \(0.75{\text{ }}{{\text{m}}^{\text{3}}}\). Write down an...
• 17N.2.sl.TZ0.6f: Find the value of \(x\).
• 17N.2.sl.TZ0.6e: Find the total cost of the ingredients of one special dessert.
• 17N.2.sl.TZ0.6d: Show that there is \(20{\text{ c}}{{\text{m}}^3}\) of orange paste in each special dessert.
• 17N.2.sl.TZ0.6c: Find the cost of \(100{\text{ c}}{{\text{m}}^3}\) of chocolate mousse.
• 17N.2.sl.TZ0.6b: Calculate the radius, \(r\), of a hemisphere shaped glass.
• 17N.2.sl.TZ0.6a: Show that the volume of a cone shaped glass is \(160{\text{ c}}{{\text{m}}^3}\), correct to 3...
• 15M.1.sl.TZ1.9b: Calculate the volume of the pyramid.
• 15M.1.sl.TZ1.15a: Find the value of \(a\).
• 15M.1.sl.TZ1.5a: Calculate the volume of the Earth in \({\text{k}}{{\text{m}}^3}\). Give your answer in the form...
• 15M.2.sl.TZ2.2c: Temi makes some crafts with perfume bottles, like the one above, once they are empty. Temi wants...
• 15M.2.sl.TZ2.2d: Temi covers the perfume bottles with a paint that costs 3 South African rand (ZAR) per...
• 15M.2.sl.TZ2.2a: (i)     Show that the vertical height of the cone is \(2.65\) cm correct to three significant...
• 15M.2.sl.TZ2.2b: The bottle contains \({\text{125 c}}{{\text{m}}^{\text{3}}}\) of perfume. The bottle is not full...
• 14N.2.sl.TZ0.3d: A company designs cone-shaped tents to resemble the traditional tepees. These cone-shaped tents...
• 14N.2.sl.TZ0.3f: A company designs cone-shaped tents to resemble the traditional tepees. These cone-shaped tents...
• 14N.2.sl.TZ0.3a: Show that the slant height, \(l\), is \(5\) m, correct to the nearest metre.