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.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.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.1.sl.TZ2.8b: Calculate the area of the park.
• 18M.1.sl.TZ2.8a: Calculate the length of side AC in km.
• 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.
• 17N.1.sl.TZ0.3b: Find the distance from the Earth to Polaris in millions of km. Give your answer in the form...
• 17N.1.sl.TZ0.3a: Calculate the time, in minutes, it takes for light from the Sun to reach the Earth.
• 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.2.sl.TZ1.1f: State whether it is valid to use the regression line to estimate the average weight of the brain...
• 17M.2.sl.TZ1.1e: Find the percentage error in your estimate in part (d).
• 17M.2.sl.TZ1.1d: Use your regression line to estimate the average weight of the brain of grey wolves.
• 17M.2.sl.TZ1.1c: Write down the equation of the regression line \(y\) on \(x\), in the form \(y = mx + c\).
• 17M.2.sl.TZ1.1b.ii: For the data from these seven species describe the correlation between the average body weight...
• 17M.2.sl.TZ1.1b.i: For the data from these seven species calculate \(r\), the Pearson’s product–moment correlation...
• 17M.2.sl.TZ1.1a: Find the range of the average body weights for these seven species of mammal.
• 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.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.TZ2.9c: Use the line of best fit to estimate the number of cold drinks that are sold on a day when the...
• 16M.1.sl.TZ2.9b: Draw the line of best fit on the scatter diagram.
• 16M.1.sl.TZ2.9a: Each day a supermarket records the midday temperature and how many cold drinks are sold on that...
• 16M.1.sl.TZ2.6b: Calculate the area of the Bermuda triangle.
• 16M.1.sl.TZ2.6a: When Bermuda \({\text{(B)}}\), Puerto Rico \({\text{(P)}}\), and Miami \({\text{(M)}}\) are...
• 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.1.sl.TZ2.1b: The surface area of the Earth that is covered by water is approximately...
• 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.2.sl.TZ1.3f: The nearest coastguard can see the flare when its height is more than \(40\) metres above sea...
• 16M.2.sl.TZ1.3e: i)     Show that the flare reached its maximum height \(40\) seconds after being fired. ii)  ...
• 16M.2.sl.TZ1.3d: Find \(h'\,(t)\,.\)
• 16M.2.sl.TZ1.3c: The flare fell into the sea \(k\) seconds after it was fired. Find the value of \(k\) .
• 16M.2.sl.TZ1.3b: Find the height of the flare \(15\) seconds after it was fired.
• 16M.2.sl.TZ1.3a: A distress flare is fired into the air from a ship at sea. The height, \(h\) , in metres, of the...
• 16M.2.sl.TZ1.1d: Ernesto’s school is located \(14\,{\text{km}}\) from the power plant. He uses the equation of...
• 16M.2.sl.TZ1.1c: Write down the equation of the regression line \(y\) on \(x\) .
• 16M.2.sl.TZ1.1b: Calculate i)      \({\bar x}\) , the mean distance from the power plant; ii)     \({\bar y}\) ,...
• 16M.2.sl.TZ1.1a: For an ecological study, Ernesto measured the average concentration \((y)\) of the fine...
• 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.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.1.sl.TZ2.1a: Express this distance in metres.
• 10N.2.sl.TZ0.3f: The average speed of the bus while it is moving on the road is 70 km h–1. The bus stops for 5...
• 12M.1.sl.TZ1.3a: Calculate the exact time, in hours, for the spacecraft to reach the star Ross.
• 10M.2.sl.TZ2.4e: Find the number of kilograms of soil required for this garden bed.
• 11N.2.sl.TZ0.5b: In a revolution, C reaches points A and B , which are at the same height above the ground as the...
• 09M.2.sl.TZ2.3f: A layer of earth 3 cm thick is removed from ABD. Find the volume removed in cubic metres.
• 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.b: The cylinder is used for storing tennis balls. Each ball has a radius of 3.25 cm. Calculate how...
• 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....
• 07N.2.sl.TZ0.2b: The glass weighs 9.3 grams per cm3. Calculate the weight of the pyramid.
• 08M.1.sl.TZ1.14b: Calculate how long Michael takes in seconds.
• 10M.2.sl.TZ1.4f: To calculate the cost of air conditioning, engineers must estimate the weight of air in the...
• 14M.2.sl.TZ2.2a: Using ‘distance = speed \( \times \) time’, show that the distance...
• 14M.2.sl.TZ2.2b: The distance from \({\text{B}}\) to \({\text{C}}\) is \(850\) metres. Running this part of the...
• 15M.2.sl.TZ1.4b: It is estimated that the fastest boat in the race can travel at an average speed of...
• 15M.2.sl.TZ2.2d: Temi covers the perfume bottles with a paint that costs 3 South African rand (ZAR) per...