DP Mathematical Studies Questionbank

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Directly related questions

• 18M.1.sl.TZ2.14c: Find the x-coordinate of the point at which the normal to the graph of f has...
• 18M.1.sl.TZ2.14b: Find the gradient of the graph of f at \(x =  - \frac{1}{2}\).
• 18M.1.sl.TZ2.14a: Find f'(x)
• 18M.1.sl.TZ1.5c: Find the equation of the line DC. Write your answer in the form ax + by + d = 0 where a , b and d...
• 18M.1.sl.TZ1.5b: Find the gradient of the line DC.
• 18M.1.sl.TZ1.5a: Write down the coordinates of C, the midpoint of line segment AB.
• 17N.1.sl.TZ0.2c.ii: Write down, in the form \(y = mx + c\), the equation of \({L_2}\).
• 17N.1.sl.TZ0.2c.i: Write down the gradient of \({L_2}\).
• 17N.1.sl.TZ0.2b: Find the gradient of \({L_1}\).
• 17N.1.sl.TZ0.2a: Find the coordinates of M.
• 17M.1.sl.TZ2.13c: Draw the line \(N\) on the diagram above.
• 17M.1.sl.TZ2.13b: Find the equation of \(N\). Give your answer in the form \(ax + by + d = 0\) where \(a\), \(b\),...
• 17M.1.sl.TZ2.13a: Write down the value of \(f(1)\).
• 17M.2.sl.TZ1.6e: Find the \(y\)-coordinate of the local minimum.
• 17M.2.sl.TZ1.6d.ii: Hence justify that \(g\) is decreasing at \(x =  - 1\).
• 17M.2.sl.TZ1.6d.i: Find \(g’( - 1)\).
• 17M.2.sl.TZ1.6c: Use your answer to part (a) and the value of \(k\), to find the \(x\)-coordinates of the...
• 17M.2.sl.TZ1.6b.ii: Find the equation of the tangent to the graph of \(y = g(x)\) at \(x = 2\). Give your answer in...
• 17M.2.sl.TZ1.6b.i: Show that \(k = 6\).
• 17M.2.sl.TZ1.6a: Find \(g'(x)\).
• 17M.1.sl.TZ1.11c: Determine the equation of \({L_2}\). Give your answer in the form \(ax + by + d = 0\), where...
• 17M.1.sl.TZ1.11b: Find the \(y\)-coordinate of P.
• 17M.1.sl.TZ1.11a: Write down the gradient of \({L_1}\).
• 16M.1.sl.TZ2.12e: Find the equation of \({L_3}\) . Give your answer in the form \(ax + by + d = 0\) , where \(a\) ,...
• 16M.1.sl.TZ2.12d: The line \({L_3}\) is perpendicular to \({L_1}\) and passes through the point \(( -...
• 16M.1.sl.TZ2.12c: The line \({L_2}\) is parallel to \({L_1}\) and passes through the point \((0,\,\,3)\) . Write...
• 16M.1.sl.TZ2.12b: Write down the gradient of \({L_1}\) .
• 16M.1.sl.TZ2.12a: The equation of the straight line \({L_1}\) is \(y = 2x - 3.\) Write down the \(y\)-intercept of...
• 10M.1.sl.TZ2.15b: The point P(−2, 3) lies on the graph of f (x). Write down the equation of the tangent to the...
• 10M.2.sl.TZ1.3f: The line, L, is the tangent to the graph of f (x) at P. Find the equation of L in the form y =...
• 10N.2.sl.TZ0.5f: Lines L1 and L2 are parallel, and they are tangents to the graph of f (x) at points A and B...
• 12N.2.sl.TZ0.5d: The line T is the tangent to the graph of y = g(x) at the point where x = 1. The gradient of T is...
• 12M.2.sl.TZ1.5g: Find the equation of the tangent to the graph of f (x) at the point where x is –1.
• 12M.1.sl.TZ2.13b: The equation of the line L is \(6x + 2y = -1\). Find the x-coordinate of the point on the curve...
• 11M.1.sl.TZ2.11d: Draw the tangent to the parabola at the point with the value of \(x\) found in part (c).
• 13M.2.sl.TZ1.4i: Find the equation of L. Give your answer in the form \(y = mx + c\).
• SPM.1.sl.TZ0.14b: Find the equation of the tangent to the graph of \(y = f(x)\) at \((1{\text{, }}3)\) .
• 07N.2.sl.TZ0.5e: Find (i) the gradient of the tangent to P at the point with coordinates (2, − 6). (ii) the...
• 08N.2.sl.TZ0.5e: It is known that \(\frac{{{\text{d}}y}}{{{\text{d}}x}} > 0\) for \(x < - 2\) and...
• 08M.1.sl.TZ1.3c: Find the equation of the tangent to the curve of \(y = f(x)\) at the point \((2{\text{, }}3)\).
• 08M.1.sl.TZ2.12c: Find the equation of the tangent to the curve of \(f\) at the point \((1{\text{, }}1.5)\).
• 08M.1.sl.TZ2.15a: Write down the equation of the tangent to the graph of \(f(x)\) at \({\text{P}}\).
• 09M.2.sl.TZ1.5e, iii: The graph of f has a local minimum at point P. Let T be the tangent to the graph of f at...
• 09M.2.sl.TZ2.5d, ii: Let T be the tangent to the graph of f at P. Find the equation of T.
• 14M.1.sl.TZ2.13d: Draw the tangent to the curve at \(x = 1\) on the graph.
• 14M.1.sl.TZ2.13e: Write down the equation of the tangent at \(x = 1\).
• 15M.2.sl.TZ2.5d: Let \(T\) be the tangent to the graph of \(f\) at \(x =  - 2\). Write down the equation of \(T\).
• 15M.2.sl.TZ2.5f: Let \(T\) be the tangent to the graph of \(f\) at \(x =  - 2\). Draw \(T\) on your sketch.