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...