DP Mathematics SL Questionbank

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• 17N.2.sl.TZ0.5b: The following diagram shows part of the graph of $f$. The region enclosed by the graph of...
• 17N.2.sl.TZ0.5a: Find the value of $p$.
• 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.1.sl.TZ2.10c: Find the area of triangle ABC, giving your answer in terms 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 $- \frac{k}{2}$.
• 16M.1.sl.TZ2.10c: Let ${A_T}$ be the area of the triangle OPQ. Given that ${A_T} = k{A_R}$, find the value of...
• 16M.1.sl.TZ2.10b: Show that ${A_R} = \frac{2}{3}{a^3}$.
• 16M.1.sl.TZ2.10a: (i)     Given that $f'(x) = \frac{{2{a^2} - 4{x^2}}}{{\sqrt {{a^2} - {x^2}} }}$, for...
• 16N.2.sl.TZ0.9d: (i)     Find the total distance travelled by P between $t = 1$ and $t = p$. (ii)     Hence...
• 16N.2.sl.TZ0.9c: (i)     Find the value of $q$. (ii)     Hence, find the speed of P when $t = q$.
• 16N.2.sl.TZ0.9b: Find the value of $p$.
• 16N.2.sl.TZ0.9a: Find the initial velocity of $P$.
• 12N.1.sl.TZ0.10a: Find $f'(x)$ .
• 12N.1.sl.TZ0.10b: Let $g(x) = \ln \left( {\frac{{6x}}{{x + 1}}} \right)$ , for $x > 0$ . Show that...
• 12M.1.sl.TZ2.8a(i) and (ii): The function can be written in the form $f(x) = a{(x - h)^2} + k$ . (i)     Write down the...
• 12M.1.sl.TZ2.8b: Find $f(x)$  , giving your answer in the form $A{x^2} + Bx + C$ .
• 18M.2.sl.TZ2.9e: Find the total distance travelled by P.
• 18M.2.sl.TZ2.9d: Find the acceleration of P when it changes direction.
• 18M.2.sl.TZ2.9c: Write down the number of times that the acceleration of P is 0 m s−2 .
• 18M.2.sl.TZ2.9b: Find the maximum speed of P.
• 18M.2.sl.TZ2.9a: Find the initial velocity of P.
• 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...
• 18M.1.sl.TZ2.2a: Find $\int {\left( {6{x^2} - 3x} \right){\text{d}}x}$.
• 12M.1.sl.TZ2.8c: Calculate the area enclosed by the graph of f , the x-axis, and the lines $x = 2$ and $x = 4$ .
• 12N.1.sl.TZ0.10c: Let $h(x) = \frac{1}{{x(x + 1)}}$ . The area enclosed by the graph of h , the x-axis and the...
• 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.TZ0.10c: Find an expression for the area of R .
• 09M.1.sl.TZ1.10c: It is given that $\int {f(x){\rm{d}}x = \frac{a}{2}} \ln ({x^2} + 1) + C$ . (i)     Find the...
• 09M.2.sl.TZ2.8a: Find the area of R.
• 09M.2.sl.TZ2.8c: The diagram below shows a part of the graph of a quadratic function $g(x) = x(a - x)$ . The...
• 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.TZ2.6c: Find $\int_p^q {f(x){\rm{d}}x}$ . Explain why this is not the area of the shaded region.
• 10M.2.sl.TZ2.6b(i) and (ii): Find the value of (i)     p ; (ii)    q .
• SPNone.2.sl.TZ0.9c(i) and (ii): Let R be the region in the first quadrant enclosed by the graph of h , the x-axis and the line...
• 11N.1.sl.TZ0.10b: Find the area of the region enclosed by the curve of g , the x-axis, and the lines $x = 2$ and...
• 11N.1.sl.TZ0.10a: Find the equation of L .
• 11N.1.sl.TZ0.10c: The graph of g is reflected in the x-axis to give the graph of h . The area of the region...
• 11M.1.sl.TZ2.8c(i) and (ii): The shaded region R is enclosed by the graph of f , the line T , and the x-axis. (i)     Write...
• 11M.1.sl.TZ2.8a: Show that the equation of T is $y = 4x - 2$ .
• 11M.1.sl.TZ2.8b: Find the x-intercept of T .
• 14M.1.sl.TZ2.10c: The following diagram shows part of the graph of $f$. The shaded region is enclosed by the...
• 13M.1.sl.TZ2.7a: Find $\int_0^2 {f(x){\rm{d}}x}$ .
• 13M.1.sl.TZ2.7b: The shaded region is enclosed by the graph of $f$ , the $x$-axis, the $y$-axis and the line...
• 15M.1.sl.TZ1.7: Let $f(x) = \cos x$, for $0$ $\le$ $x$ $\le$ $2\pi$. The following diagram shows...
• 15M.2.sl.TZ1.10e: The following diagram shows the graph of $g'$, the derivative of $g$. The shaded region...
• 14N.1.sl.TZ0.6: The following diagram shows the graph of $f(x) = \frac{x}{{{x^2} + 1}}$, for $0 \le x \le 4$,...
• 15N.1.sl.TZ0.10c: The following diagram shows the shaded regions $A$, $B$ and $C$. The regions are...