DP Mathematics SL Questionbank

• Syllabus

2.2

Sub sections and their related questions

The graph of a function; its equation \(y = f\left( x \right)\) .

• 12N.2.sl.TZ0.7a: On the grid below, sketch the graph of \(s\) .
• 12N.2.sl.TZ0.9a: Sketch the graph of f , for \( - 1 \le x \le 5\) .
• 12N.2.sl.TZ0.9b: This function can also be written as \(f(x) = {(x - p)^2} - 3\) . Write down the value of p .
• 12N.2.sl.TZ0.9c: The graph of g is obtained by reflecting the graph of f in the x-axis, followed by a translation...
• 12N.2.sl.TZ0.9d: The graph of g is obtained by reflecting the graph of f in the x-axis, followed by a translation...
• 12N.2.sl.TZ0.9e: The graph of \(g\) is obtained by reflecting the graph of \(f\) in the x-axis, followed by a...
• 12M.2.sl.TZ2.2a: Find \(f'(x)\) .
• 12M.2.sl.TZ2.2b: On the grid below, sketch the graph of \(f'(x)\) .
• 12M.2.sl.TZ2.10a: Use the cosine rule to show that \({\rm{PQ}} = 2r\sin \theta \) .
• 12M.2.sl.TZ2.10b: Let l be the length of the arc PRQ . Given that \(1.3{\rm{PQ}} - l = 0\) , find the value of...
• 12M.2.sl.TZ2.10c(i) and (ii): Consider the function \(f(\theta ) = 2.6\sin \theta  - 2\theta \) , for...
• 12M.2.sl.TZ2.10d: Use the graph of f to find the values of \(\theta \) for which \(l < 1.3{\rm{PQ}}\) .
• 12M.1.sl.TZ1.9a: Find p .
• 12M.1.sl.TZ1.9b: The graph of f is reflected in the line \(y = x\) to give the graph of g . (i)     Write down...
• 12M.1.sl.TZ1.9c: The graph of \(f\) is reflected in the line \(y = x\) to give the graph of \(g\) . Find \(g(x)\) .
• 12M.2.sl.TZ1.4a: Find k .
• 12M.2.sl.TZ1.4b: The shaded region is rotated \(360^\circ \) about the x-axis. Let V be the volume of the solid...
• 12M.2.sl.TZ1.4c: The shaded region is rotated \(360^\circ \) about the x-axis. Let V be the volume of the solid...
• 12M.2.sl.TZ1.10a(i) and (ii): Find the distance between the ships (i)     at 13:00; (ii)    at 14:00.
• 12M.2.sl.TZ1.10b: Let \(s(t)\) be the distance between the ships t hours after noon, for \(0 \le t \le 4\) . Show...
• 12M.2.sl.TZ1.10c: Sketch the graph of \(s(t)\) .
• 12M.2.sl.TZ1.10d: Due to poor weather, the captain of ship A can only see another ship if they are less than 8 km...
• 13M.1.sl.TZ2.4a.i: Write down the value of \(f(2)\).
• 13M.1.sl.TZ2.4a.ii: Write down the value of \({f^{ - 1}}( - 1)\) .
• 15M.2.sl.TZ1.5b: Robin and Pat are planning a wedding banquet. The cost per guest, \(G\) dollars, is modelled by...
• 16M.1.sl.TZ1.3a: (i)     Write down the amplitude of \(f\). (ii)     Find the period of \(f\).
• 16M.1.sl.TZ1.3b: On the following grid sketch the graph of \(f\).
• 17M.2.sl.TZ2.6a: Show that \((f \circ g)(x) = {x^4} - 4{x^2} + 3\).
• 17M.2.sl.TZ2.6b: On the following grid, sketch the graph of \((f \circ g)(x)\), for...
• 17M.2.sl.TZ2.6c: The equation \((f \circ g)(x) = k\) has exactly two solutions, for...
• 17N.1.sl.TZ0.3a: Write down the range of \(f\).
• 17N.1.sl.TZ0.3b.i: Write down \(f(2)\);
• 17N.1.sl.TZ0.3b.ii: Write down \({f^{ - 1}}(2)\).
• 17N.1.sl.TZ0.3c: On the grid, sketch the graph of \({f^{ - 1}}\).
• 17N.2.sl.TZ0.2a: Find the \(x\)-intercept of the graph of \(f\).
• 17N.2.sl.TZ0.2b: The graph of \(f\) has a maximum at the point A. Write down the coordinates of A.
• 17N.2.sl.TZ0.2c: On the following grid, sketch the graph of \(f\).
• 18M.1.sl.TZ1.3a.i: Write down the value of f (0).
• 18M.1.sl.TZ1.3a.ii: Write down the value of f −1 (1).
• 18M.1.sl.TZ1.3b: Write down the range of f −1.
• 18M.1.sl.TZ1.3c: On the grid above, sketch the graph of f −1.
• 18M.2.sl.TZ1.4a: Write down the coordinates of the vertex of the graph of g.
• 18M.2.sl.TZ1.4b: On the grid above, sketch the graph of g for −2 ≤ x ≤ 4.
• 18M.2.sl.TZ1.4c: Find the area of the region enclosed by the graphs of f and g.
• 18M.1.sl.TZ2.5a: On the same axes, sketch the graph of \(f\left( { - x} \right)\).
• 18M.1.sl.TZ2.5b: Another function, \(g\), can be written in the form...
• 18M.1.sl.TZ2.10a.i: Write down \(f'\left( 2 \right)\).
• 18M.1.sl.TZ2.10a.ii: Find \(f\left( 2 \right)\).
• 18M.1.sl.TZ2.10b: Show that the graph of g has a gradient of 6 at P.
• 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...

Function graphing skills.

• 12N.2.sl.TZ0.7b: Find the maximum velocity of the particle.
• 08N.2.sl.TZ0.4a: Sketch the graph of f on the following set of axes.
• 08M.2.sl.TZ1.4a: On the grid below, sketch the graph of \(y = f(x)\) .
• 09N.2.sl.TZ0.7: The fencing used for side AB costs \(\$ 11\) per metre. The fencing for the other three sides...
• 09N.2.sl.TZ0.9a: On the same diagram, sketch the graphs of f and g .
• 09M.2.sl.TZ2.10a: Sketch the graph of f .
• 09M.2.sl.TZ2.10b: Write down (i)     the amplitude; (ii)    the period; (iii)   the x-intercept that lies...
• SPNone.2.sl.TZ0.2b: On the grid below, sketch the graph of f .
• SPNone.2.sl.TZ0.9b(i), (ii) and (iii): (i)     Sketch the graph of h for \( - 4 \le x \le 4\) and \( - 5 \le y \le 8\) , including any...
• SPNone.2.sl.TZ0.10c(i) and (ii): (i)     On graph paper, using a scale of 1 cm to 1 second, and 1 cm to 10 m, plot the data given...
• 11N.2.sl.TZ0.10a: Sketch the graph of f .
• 11N.2.sl.TZ0.10b(i) and (ii): (i)     Write down the x-coordinate of the maximum point on the graph of f . (ii)    Write down...
• 11N.2.sl.TZ0.10c: Show that \(f'(x) = \frac{{20 - 6x}}{{{{\rm{e}}^{0.3x}}}}\) .
• 11N.2.sl.TZ0.10d: Find the interval where the rate of change of f is increasing.
• 11M.1.sl.TZ1.10a: Write down the velocity of the particle when \(t = 0\) .
• 11M.1.sl.TZ1.10b(i) and (ii): When \(t = k\) , the acceleration is zero. (i)     Show that \(k = \frac{\pi }{4}\) . (ii)   ...
• 11M.1.sl.TZ1.10c: When \(t < \frac{\pi }{4}\) , \(\frac{{{\rm{d}}v}}{{{\rm{d}}t}} > 0\) and when...
• 11M.1.sl.TZ1.10d(i) and (ii): Let d be the distance travelled by the particle for \(0 \le t \le 1\) . (i)     Write down an...
• 13M.1.sl.TZ1.10d: There is a point of inflexion on the graph of \(f\) at \(x = \sqrt[4]{3}\)...
• 13M.2.sl.TZ1.5a: On the grid below, sketch the graph of \(v\) .
• 13M.2.sl.TZ2.10a: (i)     Sketch the graphs of \(f\) and \(g\) on the same axes. (ii)     Find the area of \(R\) .
• 14M.2.sl.TZ1.9a: Sketch the graph of \(f\).
• 13N.2.sl.TZ0.5a: On the grid below, sketch the graph of \(v\), for \(0 \leqslant t \leqslant 4\).
• 15M.2.sl.TZ1.5a: On the following grid, sketch the graph of \(G\).
• 15M.2.sl.TZ2.5a: On the following grid, sketch the graph of \(f\).
• 16M.1.sl.TZ1.3a: (i)     Write down the amplitude of \(f\). (ii)     Find the period of \(f\).
• 16M.1.sl.TZ1.3b: On the following grid sketch the graph of \(f\).
• 16N.2.sl.TZ0.2a: Find the coordinates of A.
• 17M.2.sl.TZ2.6a: Show that \((f \circ g)(x) = {x^4} - 4{x^2} + 3\).
• 17M.2.sl.TZ2.6b: On the following grid, sketch the graph of \((f \circ g)(x)\), for...
• 17M.2.sl.TZ2.6c: The equation \((f \circ g)(x) = k\) has exactly two solutions, for...
• 17N.1.sl.TZ0.3a: Write down the range of \(f\).
• 17N.1.sl.TZ0.3b.i: Write down \(f(2)\);
• 17N.1.sl.TZ0.3b.ii: Write down \({f^{ - 1}}(2)\).
• 17N.1.sl.TZ0.3c: On the grid, sketch the graph of \({f^{ - 1}}\).
• 17N.2.sl.TZ0.2a: Find the \(x\)-intercept of the graph of \(f\).
• 17N.2.sl.TZ0.2b: The graph of \(f\) has a maximum at the point A. Write down the coordinates of A.
• 17N.2.sl.TZ0.2c: On the following grid, sketch the graph of \(f\).
• 18M.1.sl.TZ1.3a.i: Write down the value of f (0).
• 18M.1.sl.TZ1.3a.ii: Write down the value of f −1 (1).
• 18M.1.sl.TZ1.3b: Write down the range of f −1.
• 18M.1.sl.TZ1.3c: On the grid above, sketch the graph of f −1.
• 18M.2.sl.TZ1.4a: Write down the coordinates of the vertex of the graph of g.
• 18M.2.sl.TZ1.4b: On the grid above, sketch the graph of g for −2 ≤ x ≤ 4.
• 18M.2.sl.TZ1.4c: Find the area of the region enclosed by the graphs of f and g.
• 18M.1.sl.TZ2.5a: On the same axes, sketch the graph of \(f\left( { - x} \right)\).
• 18M.1.sl.TZ2.5b: Another function, \(g\), can be written in the form...
• 18M.1.sl.TZ2.10a.i: Write down \(f'\left( 2 \right)\).
• 18M.1.sl.TZ2.10a.ii: Find \(f\left( 2 \right)\).
• 18M.1.sl.TZ2.10b: Show that the graph of g has a gradient of 6 at P.
• 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...

Investigation of key features of graphs, such as maximum and minimum values, intercepts, horizontal and vertical asymptotes, symmetry, and consideration of domain and range.

• 12N.2.sl.TZ0.3a: Write down the x-coordinate of P.
• 12N.2.sl.TZ0.3b: Write down the gradient of the curve at P.
• 12N.2.sl.TZ0.3c: Find the equation of the normal to the curve at P, giving your equation in the form \(y = ax + b\) .
• 12N.2.sl.TZ0.5a(i) and (ii): Write down the value of (i)     \(a\) ; (ii)    \(c\) .
• 12N.2.sl.TZ0.5b: Find the value of b .
• 12N.2.sl.TZ0.5c: Find the x-coordinate of R.
• 12M.1.sl.TZ2.10a: Use the quotient rule to show that \(f'(x) = \frac{{2{x^2} - 2}}{{{{( - 2{x^2} + 5x - 2)}^2}}}\) .
• 12M.1.sl.TZ2.10b: Hence find the coordinates of B.
• 12M.1.sl.TZ2.10c: Given that the line \(y = k\) does not meet the graph of f , find the possible values of k .
• 12M.2.sl.TZ2.9a: Show that \(8a + 4b + c = 9\) .
• 12M.2.sl.TZ2.9b: The graph of f has a local minimum at \((1{\text{, }}4)\) . Find two other equations in a , b...
• 12M.2.sl.TZ2.9c: Find the value of a , of b and of c .
• 08N.2.sl.TZ0.4b: The graph of f intersects the x-axis when \(x = a\) , \(a \ne 0\) . Write down the value of a.
• 08M.2.sl.TZ2.9b: Write down the equation of the horizontal asymptote.
• 10M.1.sl.TZ2.10a(i) and (ii): Solve for \(0 \le x < 2\pi \) (i)     \(6 + 6\sin x = 6\) ; (ii)    \(6 + 6\sin x = 0\) .
• 10M.1.sl.TZ2.10b: Write down the exact value of the x-intercept of f , for \(0 \le x < 2\pi \) .
• 10M.1.sl.TZ2.10c: The area of the shaded region is k . Find the value of k , giving your answer in terms of \(\pi \) .
• 10M.1.sl.TZ2.10d: Let \(g(x) = 6 + 6\sin \left( {x - \frac{\pi }{2}} \right)\) . The graph of f is transformed to...
• 10M.1.sl.TZ2.10e: Let \(g(x) = 6 + 6\sin \left( {x - \frac{\pi }{2}} \right)\) . The graph of f is transformed to...
• 09N.1.sl.TZ0.9a: (i)     Find the coordinates of A. (ii)    Show that \(f'(x) = 0\) at A.
• 09N.1.sl.TZ0.9d: Write down the range of \(f\) .
• 09N.1.sl.TZ0.10b: Point A is the x-intercept of L . Find the x-coordinate of A.
• 09N.2.sl.TZ0.7: The fencing used for side AB costs \(\$ 11\) per metre. The fencing for the other three sides...
• 09M.2.sl.TZ2.10b: Write down (i)     the amplitude; (ii)    the period; (iii)   the x-intercept that lies...
• 10N.2.sl.TZ0.7a: There are two points of inflexion on the graph of f . Write down the x-coordinates of these points.
• 10N.2.sl.TZ0.7b: Let \(g(x) = f''(x)\) . Explain why the graph of g has no points of inflexion.
• 10N.2.sl.TZ0.8a: Find the value of a and of b .
• 10N.2.sl.TZ0.8b: The graph of f has a maximum value when \(x = c\) . Find the value of c .
• 10N.2.sl.TZ0.8c: The region under the graph of f from \(x = 0\) to \(x = c\) is rotated \({360^ \circ }\) about...
• 10N.2.sl.TZ0.8d: Let R be the region enclosed by the curve, the x-axis and the line \(x = c\) , between \(x = a\)...
• 10M.2.sl.TZ2.6a: Write down the x-coordinate of A.
• 10M.2.sl.TZ2.6b(i) and (ii): Find the value of (i)     p ; (ii)    q .
• 10M.2.sl.TZ2.6c: Find \(\int_p^q {f(x){\rm{d}}x} \) . Explain why this is not the area of the shaded region.
• 10M.2.sl.TZ2.10a(i) and (ii): Let P and Q be points on the curve of f where the tangent to the graph of f is parallel to the...
• 10M.2.sl.TZ2.10b: Let \(g(x) = {x^3}\ln (4 - {x^2})\) , for \( - 2 < x < 2\) . Show that...
• 10M.2.sl.TZ2.10c: Let \(g(x) = {x^3}\ln (4 - {x^2})\) , for \( - 2 < x < 2\) . Sketch the graph of \(g'\) .
• 10M.2.sl.TZ2.10d: Let \(g(x) = {x^3}\ln (4 - {x^2})\) , for \( - 2 < x < 2\) . Consider \(g'(x) = w\) ....
• SPNone.2.sl.TZ0.2a: Find the x-intercepts of the graph of f .
• SPNone.2.sl.TZ0.9b(i), (ii) and (iii): (i)     Sketch the graph of h for \( - 4 \le x \le 4\) and \( - 5 \le y \le 8\) , including any...
• 11N.2.sl.TZ0.10a: Sketch the graph of f .
• 11N.2.sl.TZ0.10b(i) and (ii): (i)     Write down the x-coordinate of the maximum point on the graph of f . (ii)    Write down...
• 11N.2.sl.TZ0.10c: Show that \(f'(x) = \frac{{20 - 6x}}{{{{\rm{e}}^{0.3x}}}}\) .
• 11N.2.sl.TZ0.10d: Find the interval where the rate of change of f is increasing.
• 11M.1.sl.TZ1.7a: Find the value of k .
• 11M.1.sl.TZ1.7b: The line \(y = p\) intersects the graph of f . Find all possible values of p .
• 13M.2.sl.TZ1.5b.i: Find the total distance travelled by the particle in the first five seconds.
• 14M.2.sl.TZ1.9b: Find the values of \(x\) where the function is decreasing.
• 14M.2.sl.TZ2.2a: Find the \(x\)-coordinate of \({\text{A}}\) and of \({\text{B}}\).
• 13N.1.sl.TZ0.8c(i): Find the \(y\)-intercept of the graph of \(h\).
• 15M.2.sl.TZ1.4a: For the graph of \(f\) (i)     find the \(x\)-intercept; (ii)     write down the equation of...
• 15M.2.sl.TZ1.7a: Find the coordinates of the local minimum point.
• 15M.2.sl.TZ1.7b: The graph of \(f\) is translated to the graph of \(g\) by the vector...
• 15M.2.sl.TZ1.10a: The graph of \(f\) has a local maximum point when \(x = p\). State the value of \(p\), and...
• 15M.2.sl.TZ2.7: Let \(f(x) = k{x^2} + kx\) and \(g(x) = x - 0.8\). The graphs of \(f\) and \(g\) intersect at two...
• 15N.2.sl.TZ0.3a: Find the equation of the vertical asymptote to the graph of \(f\).
• 15N.2.sl.TZ0.3b: Find the \(x\)-intercept of the graph of \(f\).
• 16M.1.sl.TZ1.5a: Show that the two zeros are 3 and \( - 6\).
• 16M.2.sl.TZ1.9a: Find the displacement of P from O after 5 seconds.
• 16M.2.sl.TZ1.9b: Find when P is first at rest.
• 16M.2.sl.TZ1.9c: Write down the number of times P changes direction.
• 16M.2.sl.TZ1.9d: Find the acceleration of P after 3 seconds.
• 16M.2.sl.TZ1.9e: Find the maximum speed of P.
• 16M.1.sl.TZ2.1a: Write down the value of \(h\) and of \(k\).
• 16M.1.sl.TZ2.1b: Write down the value of \(a\) and of \(b\).
• 16M.1.sl.TZ2.1c: Find the \(y\)-intercept.
• 16M.2.sl.TZ2.9a: Write down the equation of the horizontal asymptote of the graph of \(f\).
• 16M.2.sl.TZ2.9b: Find \(f'(x)\).
• 16M.2.sl.TZ2.9c: Write down the value of \(b\).
• 16M.2.sl.TZ2.9d: Given that \(g'(1) =  - e\), find the value of \(a\).
• 16M.2.sl.TZ2.9e: There is a value of \(x\), for \(1 < x < 4\), for which the graphs of \(f\) and \(g\) have...
• 16N.2.sl.TZ0.2b: (i)     sketch the graph of \(f\), clearly indicating the point A; (ii)    sketch the tangent to...
• 17M.1.sl.TZ1.9a: Find the value of \(p\).
• 17M.1.sl.TZ1.9b: Find the value of \(a\).
• 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.TZ2.10a.i: Write down \(f'(x)\).
• 17M.1.sl.TZ2.10a.ii: Find the gradient of \(L\).
• 17M.1.sl.TZ2.10b: Show that the \(x\)-coordinate of B is \( - \frac{k}{2}\).
• 17M.1.sl.TZ2.10c: Find the area of triangle ABC, giving your answer in terms of \(k\).
• 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.2.sl.TZ2.8a: Find the value of \(p\).
• 17M.2.sl.TZ2.8b.i: Write down the coordinates of A.
• 17M.2.sl.TZ2.8b.ii: Write down the rate of change of \(f\) at A.
• 17M.2.sl.TZ2.8c.i: Find the coordinates of B.
• 17M.2.sl.TZ2.8d: Let \(R\) be the region enclosed by the graph of \(f\) , the \(x\)-axis, the line \(x = b\) and...
• 17N.2.sl.TZ0.2a: Find the \(x\)-intercept of the graph of \(f\).
• 17N.2.sl.TZ0.2b: The graph of \(f\) has a maximum at the point A. Write down the coordinates of A.
• 17N.2.sl.TZ0.2c: On the following grid, sketch the graph of \(f\).
• 18M.2.sl.TZ1.4a: Write down the coordinates of the vertex of the graph of g.
• 18M.2.sl.TZ1.4b: On the grid above, sketch the graph of g for −2 ≤ x ≤ 4.
• 18M.2.sl.TZ1.4c: Find the area of the region enclosed by the graphs of f and g.
• 18M.2.sl.TZ2.3a: Find the x-intercept of the graph of \(f\).
• 18M.2.sl.TZ2.3b: The region enclosed by the graph of \(f\), the y-axis and the x-axis is rotated 360° about the...
• 18M.2.sl.TZ2.7a: The line x = 3 is a vertical asymptote to the graph of f. Find the value of c.
• 18M.2.sl.TZ2.7b: Write down the equation of the horizontal asymptote to the graph of f.
• 18M.2.sl.TZ2.7c: The line y = k, where \(k \in \mathbb{R}\) intersects the graph...

Use of technology to graph a variety of functions, including ones not specifically mentioned.

• 08N.2.sl.TZ0.4a: Sketch the graph of f on the following set of axes.
• 08M.2.sl.TZ1.4a: On the grid below, sketch the graph of \(y = f(x)\) .
• 09N.2.sl.TZ0.9a: On the same diagram, sketch the graphs of f and g .
• 09M.2.sl.TZ2.10a: Sketch the graph of f .
• 10N.2.sl.TZ0.2a: On the grid below, sketch the graph of v , clearly indicating the maximum point.
• 10N.2.sl.TZ0.2b(i) and (ii): (i)     Write down an expression for d . (ii)    Hence, write down the value of d .
• 10N.2.sl.TZ0.8a: Find the value of a and of b .
• 10N.2.sl.TZ0.8b: The graph of f has a maximum value when \(x = c\) . Find the value of c .
• 10N.2.sl.TZ0.8c: The region under the graph of f from \(x = 0\) to \(x = c\) is rotated \({360^ \circ }\) about...
• 10N.2.sl.TZ0.8d: Let R be the region enclosed by the curve, the x-axis and the line \(x = c\) , between \(x = a\)...
• 10M.2.sl.TZ1.3a: Find \(f'(x)\) .
• 10M.2.sl.TZ1.3b: On the grid below, sketch the graph of \(y = f'(x)\) .
• 10M.2.sl.TZ2.5a: On the diagram above, sketch the graph of g.
• 10M.2.sl.TZ2.5b: Solve \(f(x) = g(x)\) .
• 10M.2.sl.TZ2.5c: Write down the set of values of x such that \(f(x) > g(x)\) .
• 10M.2.sl.TZ2.10a(i) and (ii): Let P and Q be points on the curve of f where the tangent to the graph of f is parallel to the...
• 10M.2.sl.TZ2.10b: Let \(g(x) = {x^3}\ln (4 - {x^2})\) , for \( - 2 < x < 2\) . Show that...
• 10M.2.sl.TZ2.10c: Let \(g(x) = {x^3}\ln (4 - {x^2})\) , for \( - 2 < x < 2\) . Sketch the graph of \(g'\) .
• 10M.2.sl.TZ2.10d: Let \(g(x) = {x^3}\ln (4 - {x^2})\) , for \( - 2 < x < 2\) . Consider \(g'(x) = w\) ....
• SPNone.2.sl.TZ0.9a: Find \({h^{ - 1}}(x)\) .
• 11M.2.sl.TZ2.2a: Sketch the graph of g on the following set of axes.
• 11M.2.sl.TZ2.2b: Hence find the value of x for which \(g(x) = - 1\) .
• 11M.2.sl.TZ2.3a: Write down the number of terms in this expansion.
• 11M.2.sl.TZ2.3b: Find the term containing \({x^2}\) .
• 13M.2.sl.TZ1.5a: On the grid below, sketch the graph of \(v\) .
• 13M.2.sl.TZ2.10a: (i)     Sketch the graphs of \(f\) and \(g\) on the same axes. (ii)     Find the area of \(R\) .
• 14M.2.sl.TZ1.9a: Sketch the graph of \(f\).
• 13N.2.sl.TZ0.5a: On the grid below, sketch the graph of \(v\), for \(0 \leqslant t \leqslant 4\).

The graph of \(y = {f^{ - 1}}\left( x \right)\) as the reflection in the line \(y = x\) of the graph of \(y = f\left( x \right)\).

• 08N.1.sl.TZ0.4a: On the same diagram, sketch the graph of \({f^{ - 1}}\) .
• 11M.2.sl.TZ1.10a: Show that \(f(x) = {\log _3}2x\) .
• 11M.2.sl.TZ1.10b: Find the value of \(f(0.5)\) and of \(f(4.5)\) .
• 11M.2.sl.TZ1.10c(i), (ii) and (iii): The function f can also be written in the form \(f(x) = \frac{{\ln ax}}{{\ln b}}\) . (i)    ...
• 11M.2.sl.TZ1.10d: Write down the value of \({f^{ - 1}}(0)\) .
• 11M.2.sl.TZ1.10e: The point A lies on the graph of f . At A, \(x = 4.5\) . On your diagram, sketch the graph of...
• 13M.1.sl.TZ2.4b: Sketch the graph of \({f^{ - 1}}\) on the grid below.
• 14M.1.sl.TZ2.3c: On the grid above, sketch the graph of \({f^{ - 1}}\).
• 13N.1.sl.TZ0.8d(i): For the graph of \({h^{ - 1}}\), write down the \(x\)-intercept;
• 13N.1.sl.TZ0.8d(ii): For the graph of \({h^{ - 1}}\), write down the equation of the vertical asymptote.