DP Mathematics SL Questionbank

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• 18M.1.sl.TZ2.10c: Let L2 be the tangent to the graph of g at P. L1 intersects L2 at the point Q. Find the...
• 18M.1.sl.TZ2.10b: Show that the graph of g has a gradient of 6 at P.
• 18M.1.sl.TZ2.10a.ii: Find \(f\left( 2 \right)\).
• 18M.1.sl.TZ2.10a.i: Write down \(f'\left( 2 \right)\).
• 18M.1.sl.TZ1.7: Consider f(x), g(x) and h(x), for x∈\(\mathbb{R}\) where h(x) = \(\left( {f \circ g}...
• 17M.1.sl.TZ2.10d: Given that the area of triangle ABC is \(p\) times the area of \(R\), find the value of \(p\).
• 17M.1.sl.TZ2.10c: Find the area of triangle ABC, giving your answer in terms of \(k\).
• 17M.1.sl.TZ2.10b: Show that the \(x\)-coordinate of B is \( - \frac{k}{2}\).
• 17M.1.sl.TZ2.10a.ii: Find the gradient of \(L\).
• 17M.1.sl.TZ2.10a.i: Write down \(f'(x)\).
• 17M.1.sl.TZ1.9c: The line \(y = kx - 5\) is a tangent to the curve of \(f\). Find the values of \(k\).
• 17M.1.sl.TZ1.6a.ii: Find the equation of the normal to the curve of \(f\) at P.
• 17M.1.sl.TZ1.6a.i: Write down the gradient of the curve of \(f\) at P.
• 16M.1.sl.TZ2.10c: Let \({A_T}\) be the area of the triangle OPQ. Given that \({A_T} = k{A_R}\), find the value of...
• 16M.1.sl.TZ2.10b: Show that \({A_R} = \frac{2}{3}{a^3}\).
• 16M.1.sl.TZ2.10a: (i)     Given that \(f'(x) = \frac{{2{a^2} - 4{x^2}}}{{\sqrt {{a^2} - {x^2}} }}\), for...
• 16M.1.sl.TZ1.10d: Let \(h(x) = f(x) \times g(x)\). Find the equation of the tangent to the graph of \(h\) at the...
• 16M.1.sl.TZ1.10c: Find \(g(1)\).
• 16M.1.sl.TZ1.10b: Write down \(g'(1)\).
• 16M.1.sl.TZ1.10a: Find \(f'(1)\).
• 16N.2.sl.TZ0.2b: (i)     sketch the graph of \(f\), clearly indicating the point A; (ii)    sketch the tangent to...
• 17N.1.sl.TZ0.8c: Find the \(x\)-coordinate of Q.
• 17N.1.sl.TZ0.8d: Find the area of the region enclosed by the graph of \(f\) and the line \(L\).
• 17N.1.sl.TZ0.8b: Find the equation of \(L\) in the form \(y = ax + b\).
• 17N.1.sl.TZ0.8a: Show that \(f’(1) = 1\).
• 08N.2.sl.TZ0.9b: Let the line L be the normal to the curve of f at \(x = 0\) . Find the equation of L .
• 08M.1.sl.TZ1.8d: The line L is the tangent to the curve of f at \((3{\text{, }}12)\). Find the equation of L in...
• 08M.2.sl.TZ2.9d: Let L be the normal to the curve of f at \({\text{P}}(0{\text{, }}1)\) . Show that L has equation...
• 12M.1.sl.TZ1.3a: Write down \(f'(x)\) .
• 12M.1.sl.TZ1.3b(i) and (ii): The tangent to the graph of f at the point \({\text{P}}(0{\text{, }}b)\) has gradient m...
• 12M.1.sl.TZ1.3c: Hence, write down the equation of this tangent.
• 10M.1.sl.TZ2.5: Let \(f(x) = k{x^4}\) . The point \({\text{P}}(1{\text{, }}k)\) lies on the curve of f . At P,...
• 09N.1.sl.TZ0.10a: Show that the equation of L is \(y = - 4x + 18\) .
• 09N.2.sl.TZ0.5: Consider the curve with equation \(f(x) = p{x^2} + qx\) , where p and q are constants. The point...
• 09M.1.sl.TZ1.3: Let \(f(x) = {{\rm{e}}^x}\cos x\) . Find the gradient of the normal to the curve of f at...
• 09M.2.sl.TZ2.6b: The normal to the curve at P cuts the x-axis at R. Find the coordinates of R.
• 11N.1.sl.TZ0.10b: Find the area of the region enclosed by the curve of g , the x-axis, and the lines \(x = 2\) and...
• 11N.1.sl.TZ0.10a: Find the equation of L .
• 11N.1.sl.TZ0.10c: The graph of g is reflected in the x-axis to give the graph of h . The area of the region...
• 11M.1.sl.TZ2.8c(i) and (ii): The shaded region R is enclosed by the graph of f , the line T , and the x-axis. (i)     Write...
• 11M.1.sl.TZ2.8a: Show that the equation of T is \(y = 4x - 2\) .
• 11M.1.sl.TZ2.8b: Find the x-intercept of T .
• 13M.1.sl.TZ2.9d: Find the value of \(x\) for which the tangent to the graph of \(f\) is parallel to the tangent to...
• 13M.1.sl.TZ2.10d: find the equation of the normal to the graph of \(h\) at P.
• 14M.2.sl.TZ1.7: Let \(f(x) = \frac{{g(x)}}{{h(x)}}\), where \(g(2) = 18,{\text{ }}h(2) = 6,{\text{ }}g'(2) = 5\),...
• 13N.1.sl.TZ0.6: Let \(f(x) = {{\text{e}}^{2x}}\). The line \(L\) is the tangent to the curve of \(f\) at...
• 15M.1.sl.TZ1.9d: Find the equation of the tangent to the curve of \(f\) at \(( - 2,{\text{ }}1)\), giving your...
• 15N.1.sl.TZ0.10d: The following diagram shows the shaded regions \(A\), \(B\) and \(C\). The regions are...