DP Mathematics SL Questionbank

• Syllabus

2.4

Sub sections and their related questions

The quadratic function \(x \mapsto a{x^2} + bx + c\) : its graph, \(y\)-intercept \((0, c)\). Axis of symmetry.

• 12M.1.sl.TZ2.8a(i) and (ii): The function can be written in the form \(f(x) = a{(x - h)^2} + k\) . (i)     Write down the...
• 12M.1.sl.TZ2.8b: Find \(f(x)\)  , giving your answer in the form \(A{x^2} + Bx + C\) .
• 12M.1.sl.TZ2.8c: Calculate the area enclosed by the graph of f , the x-axis, and the lines \(x = 2\) and \(x = 4\) .
• 08N.2.sl.TZ0.1a: Express \(f(x)\) in the form \(f(x) = 2{(x - h)^2} + k\) .
• 08N.2.sl.TZ0.1b: Write down the equation of the axis of symmetry of the graph of f .
• 08N.2.sl.TZ0.1c: Express \(f(x)\) in the form \(f(x) = 2(x - p)(x - q)\) .
• 08M.1.sl.TZ1.9b(i), (ii), (iii) and (iv): For the graph of f (i)     write down the coordinates of the vertex; (ii)    write down the...
• 08M.1.sl.TZ1.9c: Hence sketch the graph of f .
• 08M.1.sl.TZ2.2a: Find both x-intercepts.
• 08M.1.sl.TZ2.2b: Find the x-coordinate of the vertex.
• 12M.2.sl.TZ1.2a(i) and (ii): (i)     Write down the coordinates of the vertex. (ii)    Hence or otherwise, express the...
• 12M.2.sl.TZ1.2b: Solve the equation \(f(x) = 0\) .
• 10N.1.sl.TZ0.9a: Find \((f \circ g)(x)\) .
• 10N.1.sl.TZ0.9b: The vector \(\left( {\begin{array}{*{20}{c}}3\\{ - 1}\end{array}} \right)\) translates the graph...
• 10N.1.sl.TZ0.9c: The vector \(\left( {\begin{array}{*{20}{c}}3\\{ - 1}\end{array}} \right)\) translates the graph...
• 10N.1.sl.TZ0.9d: The vector \(\left( {\begin{array}{*{20}{c}}3\\{ - 1}\end{array}} \right)\) translates the graph...
• 10M.1.sl.TZ1.1a: Find the x-intercepts of the graph.
• 10M.1.sl.TZ1.1b(i) and (ii): (i)     Write down the equation of the axis of symmetry. (ii)    Find the y-coordinate of the...
• 10M.1.sl.TZ2.1a: Write down the value of q and of r.
• 10M.1.sl.TZ2.1b: Write down the equation of the axis of symmetry.
• 10M.1.sl.TZ2.1c: Find the value of p.
• 09N.2.sl.TZ0.9c: Consider the graph of g . Write down (i)     the two x-intercepts; (ii)    the equation of the...
• 09M.2.sl.TZ1.10e: Write down the range of values for the gradient of \(f\) .
• SPNone.1.sl.TZ0.8b(i), (ii) and (iii): For the graph of f (i)     write down the coordinates of the vertex; (ii)    write down the...
• SPNone.1.sl.TZ0.8c: Hence sketch the graph of f .
• 11N.1.sl.TZ0.1a: Write down the equation of the axis of symmetry.
• 11N.1.sl.TZ0.1b: The function f can be written in the form \(f(x) = a{(x - h)^2} + k\) . Write down the value of...
• 11N.1.sl.TZ0.1c: The function f can be written in the form \(f(x) = a{(x - h)^2} + k\) . Find a .
• 11M.2.sl.TZ1.2a: Write down the coordinates of the vertex of the graph of g .
• 11M.2.sl.TZ1.2b: Express g in the form \(g(x) = 3{(x - p)^2} + q\) .
• 11M.2.sl.TZ1.2c: The graph of h is the reflection of the graph of g in the x-axis. Write down the coordinates of...
• 11M.1.sl.TZ2.9a: Write down \(f(x)\) in the form \(f(x) = - 10(x - p)(x - q)\) .
• 11M.1.sl.TZ2.9b: Find another expression for \(f(x)\) in the form \(f(x) = - 10{(x - h)^2} + k\) .
• 11M.1.sl.TZ2.9c: Show that \(f(x)\) can also be written in the form \(f(x) = 240 + 20x - 10{x^2}\) .
• 11M.1.sl.TZ2.9d(i) and (ii): A particle moves along a straight line so that its velocity, \(v{\text{ m}}{{\text{s}}^{ - 1}}\)...
• 13M.1.sl.TZ2.9b: Find \(g(4)\) .
• 13M.1.sl.TZ2.9c: (i)     Write down the value of \(h\) . (ii)     Find the value of \(a\) .
• 14M.1.sl.TZ1.1a: Write down the value of \(h\) and of \(k\).  
• 14M.1.sl.TZ1.1b: Find the value of \(a\).
• 14M.1.sl.TZ2.8b: The graph of \(f\)has its vertex on the \(x\)-axis. Find the coordinates of the vertex of the...
• 14M.1.sl.TZ2.8d(i): The graph of \(f\) has its vertex on the \(x\)-axis. The function can be written in the form...
• 14M.1.sl.TZ2.8d(ii): The graph of \(f\) has its vertex on the \(x\)-axis. The function can be written in the form...
• 14M.1.sl.TZ2.8d(iii): The graph of \(f\) has its vertex on the \(x\)-axis. The function can be written in the form...
• 14M.2.sl.TZ2.2a: Find the \(x\)-coordinate of \({\text{A}}\) and of \({\text{B}}\).
• 13N.2.sl.TZ0.2a: Find the \(x\)-intercepts of the graph of \(f\).
• 13M.1.sl.TZ1.2a: Write down the \(x\)-intercepts of the graph of \(f\) .
• 13M.1.sl.TZ1.2b: Find the coordinates of the vertex of the graph of \(f\) .
• 14N.1.sl.TZ0.1a: Write down the \(y\)-intercept of the graph of \(f\).
• 16M.1.sl.TZ1.5b: Find the value of \(q\) and of \(r\).
• 18M.1.sl.TZ1.4a.i: The equation of the axis of symmetry is x = p. Find p.
• 18M.1.sl.TZ1.4a.ii: Hence, show that a = 2.
• 18M.1.sl.TZ1.4b: The equation of L is y = 5 . Find the value of c.
• 18M.1.sl.TZ2.6: Let \(f\left( x \right) = p{x^2} + qx - 4p\), where p ≠ 0. Find Find the number of roots for the...

The form \(x \mapsto a\left( {x - p} \right)\left( {x - q} \right)\) , \(x\)-intercepts \((p, 0)\) and \((q,0)\) .

• 08M.1.sl.TZ1.9b(i), (ii), (iii) and (iv): For the graph of f (i)     write down the coordinates of the vertex; (ii)    write down the...
• 10N.1.sl.TZ0.9a: Find \((f \circ g)(x)\) .
• 10M.1.sl.TZ1.1a: Find the x-intercepts of the graph.
• 10M.1.sl.TZ1.1b(i) and (ii): (i)     Write down the equation of the axis of symmetry. (ii)    Find the y-coordinate of the...
• 10M.1.sl.TZ2.1a: Write down the value of q and of r.
• 10M.1.sl.TZ2.1b: Write down the equation of the axis of symmetry.
• 10M.1.sl.TZ2.1c: Find the value of p.
• 09N.2.sl.TZ0.9c: Consider the graph of g . Write down (i)     the two x-intercepts; (ii)    the equation of the...
• SPNone.1.sl.TZ0.8a: Show that \(f(x) = 3{x^2} + 6x - 9\) .
• SPNone.1.sl.TZ0.8b(i), (ii) and (iii): For the graph of f (i)     write down the coordinates of the vertex; (ii)    write down the...
• 14M.2.sl.TZ2.2a: Find the \(x\)-coordinate of \({\text{A}}\) and of \({\text{B}}\).
• 13N.2.sl.TZ0.2a: Find the \(x\)-intercepts of the graph of \(f\).
• 13M.1.sl.TZ1.2a: Write down the \(x\)-intercepts of the graph of \(f\) .
• 13M.1.sl.TZ1.2b: Find the coordinates of the vertex of the graph of \(f\) .
• 16M.1.sl.TZ1.5b: Find the value of \(q\) and of \(r\).
• 18M.1.sl.TZ1.4a.i: The equation of the axis of symmetry is x = p. Find p.
• 18M.1.sl.TZ1.4a.ii: Hence, show that a = 2.
• 18M.1.sl.TZ1.4b: The equation of L is y = 5 . Find the value of c.
• 18M.1.sl.TZ2.6: Let \(f\left( x \right) = p{x^2} + qx - 4p\), where p ≠ 0. Find Find the number of roots for the...

The form \(x \mapsto a{\left( {x - h} \right)^2} + k\) , vertex \((h, k)\) .

• 08N.2.sl.TZ0.1a: Express \(f(x)\) in the form \(f(x) = 2{(x - h)^2} + k\) .
• 08N.2.sl.TZ0.1c: Express \(f(x)\) in the form \(f(x) = 2(x - p)(x - q)\) .
• 10M.1.sl.TZ1.1a: Find the x-intercepts of the graph.
• 10M.1.sl.TZ1.1b(i) and (ii): (i)     Write down the equation of the axis of symmetry. (ii)    Find the y-coordinate of the...
• SPNone.1.sl.TZ0.8a: Show that \(f(x) = 3{x^2} + 6x - 9\) .
• SPNone.1.sl.TZ0.8b(i), (ii) and (iii): For the graph of f (i)     write down the coordinates of the vertex; (ii)    write down the...
• 11N.1.sl.TZ0.1a: Write down the equation of the axis of symmetry.
• 11N.1.sl.TZ0.1b: The function f can be written in the form \(f(x) = a{(x - h)^2} + k\) . Write down the value of...
• 11N.1.sl.TZ0.1c: The function f can be written in the form \(f(x) = a{(x - h)^2} + k\) . Find a .
• 11M.2.sl.TZ1.2a: Write down the coordinates of the vertex of the graph of g .
• 11M.2.sl.TZ1.2b: Express g in the form \(g(x) = 3{(x - p)^2} + q\) .
• 11M.2.sl.TZ1.2c: The graph of h is the reflection of the graph of g in the x-axis. Write down the coordinates of...
• 13M.1.sl.TZ2.9c: (i)     Write down the value of \(h\) . (ii)     Find the value of \(a\) .
• 14M.1.sl.TZ1.1a: Write down the value of \(h\) and of \(k\).  
• 14M.1.sl.TZ1.1b: Find the value of \(a\).
• 14M.1.sl.TZ2.8b: The graph of \(f\)has its vertex on the \(x\)-axis. Find the coordinates of the vertex of the...
• 14M.1.sl.TZ2.8d(i): The graph of \(f\) has its vertex on the \(x\)-axis. The function can be written in the form...
• 14M.1.sl.TZ2.8d(ii): The graph of \(f\) has its vertex on the \(x\)-axis. The function can be written in the form...
• 14M.1.sl.TZ2.8d(iii): The graph of \(f\) has its vertex on the \(x\)-axis. The function can be written in the form...
• 16M.1.sl.TZ1.5b: Find the value of \(q\) and of \(r\).
• 18M.1.sl.TZ1.4a.i: The equation of the axis of symmetry is x = p. Find p.
• 18M.1.sl.TZ1.4a.ii: Hence, show that a = 2.
• 18M.1.sl.TZ1.4b: The equation of L is y = 5 . Find the value of c.
• 18M.1.sl.TZ2.6: Let \(f\left( x \right) = p{x^2} + qx - 4p\), where p ≠ 0. Find Find the number of roots for the...