DP Mathematics SL Questionbank

• Syllabus

6.4

Sub sections and their related questions

Indefinite integration as anti-differentiation.

• 08M.1.sl.TZ1.5a: Find  \(\int {\frac{1}{{2x + 3}}} {\rm{d}}x\) .
• 15M.2.sl.TZ1.10d: Verify that \(\ln 3 + \int_2^a {g'(x){\text{d}}x = g(a)} \), where \(0 \le a \le 10\).
• 17M.2.sl.TZ1.7a.i: Write down the first value of \(t\) at which P changes direction.
• 17M.2.sl.TZ1.7a.ii: Find the total distance travelled by P, for \(0 \leqslant t \leqslant 8\).
• 17M.2.sl.TZ1.7b: A second particle Q also moves along a straight line. Its velocity,...
• 18M.1.sl.TZ1.8a: Find f (x).
• 18M.1.sl.TZ1.8b: The graph of f has a point of inflexion at x = p. Find p.
• 18M.1.sl.TZ1.8c: Find the values of x for which the graph of f is concave-down.
• 18M.1.sl.TZ2.2a: Find \(\int {\left( {6{x^2} - 3x} \right){\text{d}}x} \).
• 18M.1.sl.TZ2.2b: Find the area of the region enclosed by the graph of \(f\), the x-axis and the lines x = 1 and x...

Indefinite integral of \({x^n}\left( {n \in \mathbb{Q}} \right)\) , \(\sin x\) , \(\cos x\) , \(\frac{1}{x}\) and \({{\text{e}}^x}\) .

• 13M.1.sl.TZ1.6: Let \(f(x) = \int {\frac{{12}}{{2x - 5}}} {\rm{d}}x\) , \(x > \frac{5}{2}\) . The graph of...
• 13N.2.sl.TZ0.3b: Find \(\int {f(x){\text{d}}x} \).
• 18M.1.sl.TZ1.8a: Find f (x).
• 18M.1.sl.TZ1.8b: The graph of f has a point of inflexion at x = p. Find p.
• 18M.1.sl.TZ1.8c: Find the values of x for which the graph of f is concave-down.
• 18M.1.sl.TZ2.2a: Find \(\int {\left( {6{x^2} - 3x} \right){\text{d}}x} \).
• 18M.1.sl.TZ2.2b: Find the area of the region enclosed by the graph of \(f\), the x-axis and the lines x = 1 and x...

The composites of any of these with the linear function \(ax + b\) .

• 12M.1.sl.TZ1.6: Given that \(\int_0^5 {\frac{2}{{2x + 5}}} {\rm{d}}x = \ln k\) , find the value of k .
• 13M.1.sl.TZ1.6: Let \(f(x) = \int {\frac{{12}}{{2x - 5}}} {\rm{d}}x\) , \(x > \frac{5}{2}\) . The graph of...
• 18M.1.sl.TZ2.2a: Find \(\int {\left( {6{x^2} - 3x} \right){\text{d}}x} \).
• 18M.1.sl.TZ2.2b: Find the area of the region enclosed by the graph of \(f\), the x-axis and the lines x = 1 and x...

Integration by inspection, or substitution of the form \(\mathop \int \nolimits f\left( {g\left( x \right)} \right)g'\left( x \right){\text{d}}x\) .

• 08M.1.sl.TZ2.9c: Let \(g(x) = \sqrt 3 \sin x{(\cos x)^{\frac{1}{2}}}\) for \(0 \le x \le \frac{\pi }{2}\) . Find...
• SPNone.1.sl.TZ0.5a: Find \(\int {\frac{{{{\rm{e}}^x}}}{{1 + {{\rm{e}}^x}}}} {\rm{d}}x\) .
• SPNone.1.sl.TZ0.5b: Find \(\int {\sin 3x\cos 3x{\rm{d}}x} \) .
• 14M.1.sl.TZ2.10b: Find \(\int {\frac{{2x}}{{{x^2} + 5}}{\text{d}}x} \).
• 14N.1.sl.TZ0.6: The following diagram shows the graph of \(f(x) = \frac{x}{{{x^2} + 1}}\), for \(0 \le x \le 4\),...
• 16M.1.sl.TZ1.9a: Find the \(x\)-coordinate of P.
• 16M.1.sl.TZ1.9b: Find \(f(x)\), expressing your answer as a single logarithm.
• 16M.1.sl.TZ1.9c: The graph of \(f\) is transformed by a vertical stretch with scale factor \(\frac{1}{{\ln 3}}\)....
• 17M.1.sl.TZ1.5a: Find \(\int {x{{\text{e}}^{{x^2} - 1}}{\text{d}}x} \).
• 17M.1.sl.TZ1.5b: Find \(f(x)\), given that \(f’(x) = x{{\text{e}}^{{x^2} - 1}}\) and \(f( - 1) = 3\).
• 17M.1.sl.TZ2.5: Let \(f’(x) = \frac{{3{x^2}}}{{{{({x^3} + 1)}^5}}}\). Given that \(f(0) = 1\), find \(f(x)\).
• 18M.1.sl.TZ1.5a: Find \(\int {{{\left( {f\left( x \right)} \right)}^2}{\text{d}}x} \).
• 18M.1.sl.TZ1.5b: Part of the graph of f is shown in the following diagram. The shaded region R is enclosed by...