DP Mathematical Studies Questionbank

• Syllabus

6.6

Sub sections and their related questions

Drawing accurate graphs.

• 09M.2.sl.TZ2.2ii, b: Using the values in the table above, draw the graph of N for 0 ≤ t ≤ 20. Use 1 cm to represent 2...
• 13M.2.sl.TZ1.3c: Use the seven results in the table to draw a graph that shows how the temperature of the coffee...
• SPM.2.sl.TZ0.4d: The table below gives the intensity of light (correct to the nearest integer) at different...
• 07M.2.sl.TZ0.3ii.d: Draw a graph showing the path of the football from the point where it is kicked to the point...
• 08N.2.sl.TZ0.4b: The following table shows values for \(m\) and \(T(m)\). (i)     Write down the value of...
• 08N.2.sl.TZ0.4c: Consider the function \(S(m) = 20m - 40\) for \(2 \leqslant m \leqslant 6\) . The function...
• 08M.2.sl.TZ2.4i.c: As \(x\) increases from \( - 1\), the graph of \(y = f(x)\) reaches a maximum value and then...
• 14M.2.sl.TZ2.5d: The parcel is tied up using a length of string that fits exactly around the parcel, as shown in...
• 14N.1.sl.TZ0.14c: (i)     Find the value of \(b\) and the value of \(c\). (ii)     Draw the graph of the function...
• 16M.1.sl.TZ2.8a: Consider the curve \(y = 1 + \frac{1}{{2x}},\,\,x \ne 0.\) For this curve, write down i)  ...
• 17M.1.sl.TZ1.12a: Write down the domain of the function.
• 17M.1.sl.TZ1.12b.i: Draw the line \(y =  - 6\) on the axes.
• 17M.1.sl.TZ1.12b.ii: Write down the number of solutions to \(f(x) =  - 6\).
• 17M.1.sl.TZ1.12c: Find the range of values of \(k\) for which \(f(x) = k\) has no solution.
• 17N.2.sl.TZ0.5a: Find the exact value of each of the zeros of \(f\).
• 17N.2.sl.TZ0.5b.i: Expand the expression for \(f(x)\).
• 17N.2.sl.TZ0.5b.ii: Find \(f’(x)\).
• 17N.2.sl.TZ0.5c: Use your answer to part (b)(ii) to find the values of \(x\) for which \(f\) is increasing.
• 17N.2.sl.TZ0.5d: Draw the graph of \(f\) for \( - 3 \leqslant x \leqslant 3\) and...
• 17N.2.sl.TZ0.5e: Write down the coordinates of the point of intersection.
• 18M.2.sl.TZ1.4a: Find the value of k.
• 18M.2.sl.TZ1.4b: Using your value of k , find f ′(x).
• 18M.2.sl.TZ1.4c: Use your answer to part (b) to show that the minimum value of f(x) is −22 .
• 18M.2.sl.TZ1.4d: Write down the two values of x which satisfy f (x) = 0.
• 18M.2.sl.TZ1.4e: Sketch the graph of y = f (x) for 0 < x ≤ 6 and −30 ≤ y ≤ 60.Clearly indicate the minimum...
• 18M.2.sl.TZ2.6a: Sketch the curve for −1 < x < 3 and −2 < y < 12.
• 18M.2.sl.TZ2.6b: A teacher asks her students to make some observations about the curve. Three students...
• 18M.2.sl.TZ2.6c: Find the value of y when x = 1 .
• 18M.2.sl.TZ2.6d: Find \(\frac{{{\text{dy}}}}{{{\text{dx}}}}\).
• 18M.2.sl.TZ2.6e: Show that the stationary points of the curve are at x = 1 and x = 2.
• 18M.2.sl.TZ2.6f: Given that y = 2x3 − 9x2 + 12x + 2 = k has three solutions, find the possible values of k.

Creating a sketch from information given.

• 10N.2.sl.TZ0.5e: Sketch the graph of f (x) for \( - 5 \leqslant x \leqslant 7\) and...
• 12N.2.sl.TZ0.5f: (i) Sketch the graph of y = g(x) for −2 ≤ x ≤ 5 and −15 ≤ y ≤ 25, indicating clearly your answer...
• 12M.1.sl.TZ1.4b: Sketch the graph of y = f (x) on the axes below for 0 ≤ x ≤ 4 . Mark clearly on the sketch the...
• 12M.2.sl.TZ1.5a: Sketch the graph of y = f (x) for −3 ≤ x ≤ 6 and −10 ≤ y ≤ 10 showing clearly the axes intercepts...
• 12M.2.sl.TZ1.5h: Sketch the tangent to the graph of f (x) at x = −1 on your diagram for (a).
• 11N.2.sl.TZ0.5c: The sketch below shows the graph of the function, \(h(t)\) , for the height above ground of C,...
• 09M.2.sl.TZ1.5f: Sketch the graph of the function f, for −3 ≤ x ≤ 6 and −7 ≤ y ≤ 15. Indicate clearly the point P...
• 11M.2.sl.TZ1.3b: Sketch the graph of the function \(y = f(x)\) for \( - 5 \leqslant x \leqslant 5\) and...
• 11M.2.sl.TZ2.5e: Sketch the graph of \(f(x)\) for \( - 10 \leqslant x \leqslant 10\) and...
• 08M.2.sl.TZ1.1a: Sketch the graph of the function \(f(x)\), for \( - 10 \leqslant x \leqslant 10\) . Indicating...
• 13N.1.sl.TZ0.10a: Sketch the graphs of \(y = f(x)\) and \(y = g(x)\) on the axes below. Indicate clearly the points...
• 13N.2.sl.TZ0.4d: The graph of the function \(f(x)\) has a local minimum at the point where \(x =  - 2\). Sketch...
• 15M.2.sl.TZ1.5f: The graph of \(y = f(x)\) has a local minimum point at \(x = 4\). Sketch the graph of...
• 15M.2.sl.TZ2.5e: Let \(T\) be the tangent to the graph of \(f\) at \(x =  - 2\). Sketch the graph of \(f\) for...
• 15M.2.sl.TZ2.5f: Let \(T\) be the tangent to the graph of \(f\) at \(x =  - 2\). Draw \(T\) on your sketch.
• 18M.2.sl.TZ1.4a: Find the value of k.
• 18M.2.sl.TZ1.4b: Using your value of k , find f ′(x).
• 18M.2.sl.TZ1.4c: Use your answer to part (b) to show that the minimum value of f(x) is −22 .
• 18M.2.sl.TZ1.4d: Write down the two values of x which satisfy f (x) = 0.
• 18M.2.sl.TZ1.4e: Sketch the graph of y = f (x) for 0 < x ≤ 6 and −30 ≤ y ≤ 60.Clearly indicate the minimum...
• 18M.2.sl.TZ2.6a: Sketch the curve for −1 < x < 3 and −2 < y < 12.
• 18M.2.sl.TZ2.6b: A teacher asks her students to make some observations about the curve. Three students...
• 18M.2.sl.TZ2.6c: Find the value of y when x = 1 .
• 18M.2.sl.TZ2.6d: Find \(\frac{{{\text{dy}}}}{{{\text{dx}}}}\).
• 18M.2.sl.TZ2.6e: Show that the stationary points of the curve are at x = 1 and x = 2.
• 18M.2.sl.TZ2.6f: Given that y = 2x3 − 9x2 + 12x + 2 = k has three solutions, find the possible values of k.

Transferring a graph from GDC to paper.

• 10M.1.sl.TZ1.15a.i: On the axes below sketch the graph of f (x) and show the behaviour of the curve as x increases.  
• 11N.1.sl.TZ0.13b: Sketch the graph of \(y = f(x)\) for the domain \( - 1 \leqslant x \leqslant 3\).
• 12N.2.sl.TZ0.5f: (i) Sketch the graph of y = g(x) for −2 ≤ x ≤ 5 and −15 ≤ y ≤ 25, indicating clearly your answer...
• 12M.2.sl.TZ1.5a: Sketch the graph of y = f (x) for −3 ≤ x ≤ 6 and −10 ≤ y ≤ 10 showing clearly the axes intercepts...
• 11M.2.sl.TZ1.3b: Sketch the graph of the function \(y = f(x)\) for \( - 5 \leqslant x \leqslant 5\) and...
• 11M.2.sl.TZ2.5e: Sketch the graph of \(f(x)\) for \( - 10 \leqslant x \leqslant 10\) and...
• SPM.1.sl.TZ0.7a: On the grid below sketch the graph of the function \(f(x) = 2{(1.6)^x}\) for the domain...
• 08N.2.sl.TZ0.4b: The following table shows values for \(m\) and \(T(m)\). (i)     Write down the value of...
• 08N.2.sl.TZ0.4c: Consider the function \(S(m) = 20m - 40\) for \(2 \leqslant m \leqslant 6\) . The function...
• 08M.2.sl.TZ2.4i.c: As \(x\) increases from \( - 1\), the graph of \(y = f(x)\) reaches a maximum value and then...
• 13N.1.sl.TZ0.10a: Sketch the graphs of \(y = f(x)\) and \(y = g(x)\) on the axes below. Indicate clearly the points...
• 13N.2.sl.TZ0.4d: The graph of the function \(f(x)\) has a local minimum at the point where \(x =  - 2\). Sketch...
• 15M.2.sl.TZ1.5f: The graph of \(y = f(x)\) has a local minimum point at \(x = 4\). Sketch the graph of...
• 15M.2.sl.TZ2.5e: Let \(T\) be the tangent to the graph of \(f\) at \(x =  - 2\). Sketch the graph of \(f\) for...
• 18M.2.sl.TZ1.4a: Find the value of k.
• 18M.2.sl.TZ1.4b: Using your value of k , find f ′(x).
• 18M.2.sl.TZ1.4c: Use your answer to part (b) to show that the minimum value of f(x) is −22 .
• 18M.2.sl.TZ1.4d: Write down the two values of x which satisfy f (x) = 0.
• 18M.2.sl.TZ1.4e: Sketch the graph of y = f (x) for 0 < x ≤ 6 and −30 ≤ y ≤ 60.Clearly indicate the minimum...

Reading, interpreting and making predictions using graphs.

• 10M.2.sl.TZ1.3d: Let P be the point where the graph of f (x) intersects the y axis. Write down the coordinates of P.
• 12M.2.sl.TZ1.5i: P and Q are points on the curve such that the tangents to the curve at these points are...
• 09M.2.sl.TZ2.2ii, c: Use your graph to estimate the number of days for the population of fleas to reach 55.
• SPM.1.sl.TZ0.5b: where the function attains its least value;
• SPM.1.sl.TZ0.5c: where the function attains its greatest value;
• 07M.2.sl.TZ0.3ii.e: The goal posts are 35 m from the point where the ball is kicked. At what height does the ball...
• 08N.2.sl.TZ0.4d: Consider the function \(S(m) = 20m - 40\) for \(2 \leqslant m \leqslant 6\) . The function...
• 08N.2.sl.TZ0.4e: Consider the function \(S(m) = 20m - 40\) for \(2 \leqslant m \leqslant 6\) . The function...
• 10M.1.sl.TZ1.15a.ii: Write down the coordinates of any intercepts with the axes.
• 14N.1.sl.TZ0.11c: Write down the interval for the values of \(x\) for which \(f(x) > g(x)\).
• 15M.2.sl.TZ1.5g: The graph of \(y = f(x)\) has a local minimum point at \(x = 4\). Write down the coordinates of...
• 18M.2.sl.TZ1.4a: Find the value of k.
• 18M.2.sl.TZ1.4b: Using your value of k , find f ′(x).
• 18M.2.sl.TZ1.4c: Use your answer to part (b) to show that the minimum value of f(x) is −22 .
• 18M.2.sl.TZ1.4d: Write down the two values of x which satisfy f (x) = 0.
• 18M.2.sl.TZ1.4e: Sketch the graph of y = f (x) for 0 < x ≤ 6 and −30 ≤ y ≤ 60.Clearly indicate the minimum...

Included all the functions above and additions and subtractions.

• 18M.2.sl.TZ1.4a: Find the value of k.
• 18M.2.sl.TZ1.4b: Using your value of k , find f ′(x).
• 18M.2.sl.TZ1.4c: Use your answer to part (b) to show that the minimum value of f(x) is −22 .
• 18M.2.sl.TZ1.4d: Write down the two values of x which satisfy f (x) = 0.
• 18M.2.sl.TZ1.4e: Sketch the graph of y = f (x) for 0 < x ≤ 6 and −30 ≤ y ≤ 60.Clearly indicate the minimum...