DP Mathematical Studies Questionbank

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• 16N.2.sl.TZ0.6d: Show that \(A = \pi {r^2} + \frac{{1\,000\,000}}{r}\).
• 16M.2.sl.TZ1.6d: The function \(f\) is the derivative of a function \(g\) . It is known that \(g(1) = 3.\) i)    ...
• 16M.2.sl.TZ1.6c: Sketch the graph of \(y = f(x)\) for \( - 2 \leqslant x \leqslant 6\) and...
• 16M.2.sl.TZ1.6b: Use your graphic display calculator to solve \(f(x) = 0.\)
• 16M.2.sl.TZ1.6a: A function, \(f\) , is given by \[f(x) = 4 \times {2^{ - x}} + 1.5x - 5.\] Calculate \(f(0)\)  
• 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.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...
• 16M.1.sl.TZ1.14c: An ecologist estimates that the island has enough food to support a maximum population of 1000...
• 16M.1.sl.TZ1.14b: Calculate the number of rabbits on the island after 10 weeks.
• 16M.1.sl.TZ1.14a: A population of \(200\) rabbits was introduced to an island. One week later the number of rabbits...
• 16M.1.sl.TZ1.13d: Find the value of \(x\) .
• 16M.1.sl.TZ1.13c: Phidias designs the windows so that the ratio between the longer side, \(y\) , and the...
• 16M.1.sl.TZ1.13b: Phidias is designing rectangular windows with adjacent sides of length \(x\) metres...
• 16M.1.sl.TZ1.13a: The golden ratio, \(r\) , was considered by the Ancient Greeks to be the perfect ratio...
• 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.2.sl.TZ0.3g: Find the area of ABCD.
• 16N.2.sl.TZ0.3f: Write down the length of MD correct to five significant figures.
• 16N.2.sl.TZ0.3e: Find the coordinates of D.
• 16N.2.sl.TZ0.3d: Show that the equation of \({L_2}\) is \(2y + x - 19 = 0\).
• 16N.2.sl.TZ0.3c: Find the length of AC.
• 16N.2.sl.TZ0.3b: Find the coordinates of M.
• 16N.2.sl.TZ0.3a: Show that A lies on \({L_1}\).
• 16N.1.sl.TZ0.15c: Find the value of \(n\).
• 16N.1.sl.TZ0.15b: Find the value of \(k\).
• 16N.1.sl.TZ0.15a: Write down, and simplify, an expression for the car’s value when Gabriella purchased it.
• 10M.1.sl.TZ1.15c: Write down the number of solutions to the equation f (x) = 5 .
• 10M.2.sl.TZ1.5B.f: Tn is the sum of the first n terms of the geometric sequence. Use your graphic display...
• 12N.2.sl.TZ0.5e: Using your graphic display calculator find the coordinates of the point where the graph of y =...
• 10M.2.sl.TZ2.3d: Find the number of complete years it will take for Ying’s investment to exceed Ruby’s investment.
• 12M.2.sl.TZ1.5c: Write down the coordinates of the y-intercept of the graph of f (x).
• 12M.2.sl.TZ1.5i: P and Q are points on the curve such that the tangents to the curve at these points are...
• 09N.1.sl.TZ0.11b: find the value of \(x\) given that \(f (x) =162\).
• 11N.2.sl.TZ0.4a: Write down (i)     the equation of the vertical asymptote to the graph of \(y = f (x)\)...
• 11N.2.sl.TZ0.4g: The line, \(L\) , passes through the point A and is perpendicular to the tangent at A. \(L\)...
• 09N.2.sl.TZ0.5A, d: Using your graphic display calculator, solve the equation 3 + 2x − x2 = 2x.
• 09M.2.sl.TZ2.5e: T intersects the graph again at R. Use your graphic display calculator to find the coordinates of R.
• 13M.1.sl.TZ2.13c: Calculate the time, in hours, for the number of bacteria to reach 5500.
• 13M.2.sl.TZ2.4f: Each lap Paco runs again takes him 10 seconds longer than his previous lap. After a certain...
• 13M.2.sl.TZ2.5f: Use your graphic display calculator to find the coordinates of the point where Scott first...
• SPM.1.sl.TZ0.7b: Write down the coordinates of the \(y\)-intercept of the graph of \(y = f(x)\) .
• SPM.1.sl.TZ0.7d: Use your graphic display calculator to solve \(f(x) = g(x)\) .
• SPM.1.sl.TZ0.14c: Write down the coordinates of the second point where this tangent intersects the graph of...
• SPM.2.sl.TZ0.4c: To be able to see clearly, a diver needs the intensity of light to be at least \(65\% \). Using...
• 08N.2.sl.TZ0.1e: Each January, one of these two schools, the one that has more students, is given extra money to...
• 08N.2.sl.TZ0.4b: The following table shows values for \(m\) and \(T(m)\). (i)     Write down the value of...
• 08N.2.sl.TZ0.4e: Consider the function \(S(m) = 20m - 40\) for \(2 \leqslant m \leqslant 6\) . The function...
• 08M.1.sl.TZ1.15c: Find how long it will take for there to be two million bacteria.
• 08M.2.sl.TZ1.1d: Using your graphical display calculator write down the coordinates of one of the points of...
• 08M.2.sl.TZ1.4i.d: (i)     Sketch the graphs of the two equations from parts (a) and (b). (ii)    Write down the...
• 08M.2.sl.TZ2.4i.f: (i) Draw and label the line \( y = 1\) on your graph. (ii) The equation \(f(x) = 1\) has two...
• 09M.2.sl.TZ1.5g, ii: T intersects the graph of f at a second point. Write down the x-coordinate of this point of...
• 13N.1.sl.TZ0.10b: Use your graphic display calculator to solve \(f(x) = g(x)\).
• 14M.2.sl.TZ1.3e: \(k\) is the smallest value of \(n\) for which \({v_n}\) is greater than \({u_n}\). Calculate...
• 14M.1.sl.TZ1.11c: To download a game to the mobile phone, an electrical charge of 2.4 units is needed. Find the...
• 14M.1.sl.TZ2.11c: Use your graphic display calculator to determine the time it takes for the amount of the drug in...
• 17M.2.sl.TZ2.6g: The equation \(f(x) = m\), where \(m \in \mathbb{R}\), has four solutions. Find the possible...
• 17M.2.sl.TZ2.6f: Write down the number of possible solutions to the equation \(f(x) = 5\).
• 17M.2.sl.TZ2.6e: Write down the range of \(f(x)\).
• 17M.2.sl.TZ2.6d.ii: Write down the intervals where the gradient of the graph of \(y = f(x)\) is positive.
• 17M.2.sl.TZ2.6d.i: Write down the \(x\)-coordinates of these two points;
• 17M.2.sl.TZ2.6c.ii: Find \(f(2)\).
• 17M.2.sl.TZ2.6c.i: Show that \(a = 8\).
• 17M.2.sl.TZ2.6b: Find \(f'(x)\).
• 17M.2.sl.TZ2.6a: Write down the \(y\)-intercept of the graph.
• 17M.2.sl.TZ2.5f: Find the lowest possible value for \(r\).
• 17M.2.sl.TZ2.5e.ii: Find how long it would take for the interest earned to be 2000 BGN.
• 17M.2.sl.TZ2.5e.i: Find the amount of money that Violeta would have after 6 years. Give your answer correct to two...
• 17M.2.sl.TZ2.5d: Show that Violeta earns 5000 BGN from selling the flowers grown on the plot.
• 17M.2.sl.TZ2.5c: Find the value of \(x\) that maximizes the area of the plot.
• 17M.2.sl.TZ2.5b: Write down the area of the plot in terms of \(x\).
• 17M.2.sl.TZ2.5a: Show that the width of the plot, in metres, is given by \(100 - x\).
• 17M.1.sl.TZ2.14c: Calculate how much extra money Jashanti needs.
• 17M.1.sl.TZ2.14b: Use your graphic display calculator to find how long it will take for Jashanti to have saved...
• 17M.1.sl.TZ2.14a: Write down the amount of money Jashanti saves per month.
• 17M.1.sl.TZ1.15c: Write down the second \(x\)-intercept of the function.
• 17M.1.sl.TZ1.15b: Find the value of \(a\) and of \(b\).
• 17M.1.sl.TZ1.15a: Write down the value of \(c\).
• 16M.1.sl.TZ2.15b: There are two points at which the gradient of the graph of \(f\) is \(11\). Find...
• 16M.1.sl.TZ2.15a: Consider the function \(f(x) = {x^3} - 3{x^2} + 2x + 2\) . Part of the graph of \(f\) is shown...
• 16M.1.sl.TZ2.13d: The population will stabilize when it reaches a size of \(k\) . Write down the value of \(k\) .
• 16M.1.sl.TZ2.13b: Find the size of the population after \(4\) days.
• 16M.1.sl.TZ2.13a: A population of mosquitoes decreases exponentially. The size of the population, \(P\) , after...
• 15M.2.sl.TZ1.5g: The graph of \(y = f(x)\) has a local minimum point at \(x = 4\). Write down the coordinates of...
• 15M.2.sl.TZ1.6e: After being placed in the room for one minute, the temperature of the water is 84°C. Find the...
• 14N.1.sl.TZ0.9c: Use your graphic display calculator to find the value of \(x\) and the value of \(y\).
• 14N.1.sl.TZ0.11b: Solve \(f(x) = g(x)\).
• 15M.2.sl.TZ2.5g: The tangent, \(T\), intersects the graph of \(f\) at a second point, P. Use your graphic display...