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...