DP Mathematical Studies Questionbank

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Directly related questions

• 16N.2.sl.TZ0.6d: Show that \(A = \pi {r^2} + \frac{{1\,000\,000}}{r}\).
• 18M.1.sl.TZ2.13c: Find the number of shirts produced when the cost of production is lowest.
• 18M.1.sl.TZ2.13b: Find the value of s.
• 18M.1.sl.TZ2.13a: Find the cost of producing 70 shirts.
• 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.TZ1.6d: Show that the volume, V cm3 , of the new trash can is given by \(V = 110\pi {r^3}\).
• 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.
• 17N.1.sl.TZ0.15d: Find the price, \(p\), that will give Maria the highest weekly profit.
• 17N.1.sl.TZ0.15c: Write down an expression for \(W\) in terms of \(p\).
• 17N.1.sl.TZ0.15b: Find how much Maria earns in one week, from selling cheese, if the price of a kilogram of cheese...
• 17N.1.sl.TZ0.15a: Write down how many kilograms of cheese Maria sells in one week if the price of a kilogram of...
• 16M.2.sl.TZ2.5g: Sketch the graph of \(V = 4{x^3} - 51{x^2} + 160x\) , for the possible values of \(x\) found...
• 16M.2.sl.TZ2.5f: Calculate the maximum volume of the tray.
• 16M.2.sl.TZ2.5e: Using your answer from part (d), find the value of \(x\) that maximizes the volume of the tray.
• 16M.2.sl.TZ2.5d: Find \(\frac{{dV}}{{dx}}.\)
• 16M.2.sl.TZ2.5c: Show that the volume, \(V\,{\text{c}}{{\text{m}}^3}\), of this tray is given...
• 16M.2.sl.TZ2.5b: (i)     State whether \(x\) can have a value of \(5\). Give a reason for your answer. (ii)  ...
• 16M.2.sl.TZ2.5a: Hugo is given a rectangular piece of thin cardboard, \(16\,{\text{cm}}\) by \(10\,{\text{cm}}\)....
• 16M.1.sl.TZ1.15b: Calculate the value of \(r\) that minimizes the surface area of a can.
• 16M.1.sl.TZ1.15a: A company sells fruit juices in cylindrical cans, each of which has a volume of...
• 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.
• 10M.2.sl.TZ2.5c: Differentiate A in terms of x.
• 10M.2.sl.TZ2.5d: Find the value of x that makes A a minimum.
• 10M.2.sl.TZ2.5e: Calculate the minimum total surface area of the dog food can.
• 12M.2.sl.TZ2.5c: Find \( \frac{{\text{d}V}}{{\text{d}x}}\).
• 12M.2.sl.TZ2.5d: Find the value of x for which V is a maximum.
• 12M.2.sl.TZ2.5e: Find the maximum volume of the container.
• 12M.2.sl.TZ2.5f: Find the length and height of the container for which the volume is a maximum.
• SPM.1.sl.TZ0.15c: Use your answer to part (b) to find the selling price of each machine in order to maximize...
• SPM.2.sl.TZ0.6f: (i)     Find the value of \(r\) that minimizes the total external surface area of the wastepaper...
• SPM.2.sl.TZ0.6g: Determine whether Merryn’s design is an improvement upon Nadia’s. Give a reason.
• 08M.2.sl.TZ1.5ii.e: (i)     Hence find the value of \(x\) and of \(y\) required to make the volume of the box a...
• 08M.2.sl.TZ2.4ii.c: Calculate the minimum cost per person.
• 14M.2.sl.TZ2.5f: The parcel is tied up using a length of string that fits exactly around the parcel, as shown in...
• 14M.2.sl.TZ2.5g: The parcel is tied up using a length of string that fits exactly around the parcel, as shown in...
• 14M.2.sl.TZ2.5h: The parcel is tied up using a length of string that fits exactly around the parcel, as shown in...
• 14M.2.sl.TZ1.6f: The lobster trap is designed so that the length of steel used in its frame is a...
• 14M.2.sl.TZ1.6e: The lobster trap is designed so that the length of steel used in its frame is a minimum. Show...
• 14M.2.sl.TZ1.6g: The lobster trap is designed so that the length of steel used in its frame is a...
• 15M.1.sl.TZ1.15b: Find the value of \(x\) that makes the volume a maximum.
• 14N.2.sl.TZ0.3f: A company designs cone-shaped tents to resemble the traditional tepees. These cone-shaped tents...