DP Mathematics SL Questionbank

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Directly related questions

• 18M.2.sl.TZ1.10b.ii: For the graph of $f$, write down the period.
• 18M.2.sl.TZ1.10e: Find the first time when the ball’s speed is changing at a rate of 2 cm s−2.
• 18M.2.sl.TZ1.10d: Find the maximum speed of the ball.
• 18M.2.sl.TZ1.10c: Hence, write $f\left( x \right)$ in the form $p\,\,{\text{cos}}\,\left( {x + r} \right)$.
• 18M.2.sl.TZ1.10b.i: For the graph of $f$, write down the amplitude.
• 18M.2.sl.TZ1.10a: Find the coordinates of A.
• 18M.1.sl.TZ1.8c: Find the values of x for which the graph of f is concave-down.
• 18M.1.sl.TZ1.8b: The graph of f has a point of inflexion at x = p. Find p.
• 18M.1.sl.TZ1.8a: Find f (x).
• 17M.2.sl.TZ2.8d: Let $R$ be the region enclosed by the graph of $f$ , the $x$-axis, the line $x = b$ and...
• 17M.2.sl.TZ2.8c.ii: Find the the rate of change of $f$ at B.
• 17M.2.sl.TZ2.8c.i: Find the coordinates of B.
• 17M.2.sl.TZ2.8b.ii: Write down the rate of change of $f$ at A.
• 17M.2.sl.TZ2.8b.i: Write down the coordinates of A.
• 17M.2.sl.TZ2.8a: Find the value of $p$.
• 17M.2.sl.TZ1.10c: Let $d$ be the vertical distance from a point on the graph of $h$ to the line $y = x$....
• 17M.2.sl.TZ1.10b.ii: Hence, find the area of the region enclosed by the graphs of $h$ and ${h^{ - 1}}$.
• 17M.2.sl.TZ1.10b.i: Find $\int_{0.111}^{3.31} {\left( {h(x) - x} \right){\text{d}}x}$.
• 17M.2.sl.TZ1.10a.iii: Write down the value of $k$.
• 17M.2.sl.TZ1.10a.i: Write down the value of $q$;
• 17M.2.sl.TZ1.10a.ii: Write down the value of $h$;
• 16M.1.sl.TZ1.9c: The graph of $f$ is transformed by a vertical stretch with scale factor $\frac{1}{{\ln 3}}$....
• 16M.1.sl.TZ1.9b: Find $f(x)$, expressing your answer as a single logarithm.
• 16M.1.sl.TZ1.9a: Find the $x$-coordinate of P.
• 16N.2.sl.TZ0.10c: (i)     Find $w$. (ii)     Hence or otherwise, find the maximum positive rate of change of $g$.
• 16N.2.sl.TZ0.10b: (i)     Write down the value of $k$. (ii)     Find $g(x)$.
• 16N.2.sl.TZ0.10a: (i)     Find the value of $c$. (ii)     Show that $b = \frac{\pi }{6}$. (iii)     Find the...
• 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 .
• 08N.1.sl.TZ0.6a(i) and (ii): (i)     Write down the value of $f'(x)$ at C. (ii)    Hence, show that C corresponds to a...
• 08N.1.sl.TZ0.6b: Which of the points A, B, D corresponds to a maximum on the graph of f ?
• 08M.1.sl.TZ1.8b: Find the x-coordinate of M.
• 08M.2.sl.TZ1.5b: Complete the table, for the graph of $y = f(x)$ .
• 08M.1.sl.TZ2.10d: Find the value of $\theta$ when S is a local minimum, justifying that it is a minimum.
• 08M.2.sl.TZ2.9c: Write down the value of r and of s.
• 10M.1.sl.TZ1.8a: Find the coordinates of A.
• 10M.1.sl.TZ1.8b(i), (ii) and (iii): Write down the coordinates of (i)     the image of B after reflection in the y-axis; (ii)   ...
• 10M.1.sl.TZ2.8a: Use the second derivative to justify that B is a maximum.
• 10M.1.sl.TZ2.8b: Given that $f'(x) = \frac{3}{2}{x^2} - x + p$ , show that $p = - 4$ .
• 10M.1.sl.TZ2.8c: Find $f(x)$ .
• 09N.1.sl.TZ0.5b: There is a minimum value of $f(x)$ when $x = - 2$ . Find the value of $p$ .
• 11M.1.sl.TZ1.5a: Use the quotient rule to show that $g'(x) = \frac{{1 - 2\ln x}}{{{x^3}}}$ .
• 11M.1.sl.TZ1.5b: The graph of g has a maximum point at A. Find the x-coordinate of A.
• 13N.1.sl.TZ0.10b: There is a minimum on the graph of $f$. Find the $x$-coordinate of this minimum.
• 13N.1.sl.TZ0.10c: Write down the value of $p$.
• 14N.1.sl.TZ0.9a: Find the $x$-coordinate of $A$.
• 15N.1.sl.TZ0.10a: Explain why the graph of $f$ has a local minimum when $x = 5$.