DP Mathematical Studies Questionbank

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• 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...
• 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.TZ0.3a: 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...
• 14M.1.sl.TZ2.11c: Use your graphic display calculator to determine the time it takes for the amount of the drug in...
• 13N.1.sl.TZ0.10b: Use your graphic display calculator to solve \(f(x) = g(x)\).
• 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.2.sl.TZ1.3e: \(k\) is the smallest value of \(n\) for which \({v_n}\) is greater than \({u_n}\). Calculate...
• 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...