DP Mathematics SL Questionbank

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• 18M.1.sl.TZ2.10c: Let L2 be the tangent to the graph of g at P. L1 intersects L2 at the point Q. Find the...
• 18M.1.sl.TZ2.10b: Show that the graph of g has a gradient of 6 at P.
• 18M.1.sl.TZ2.10a.ii: Find $f\left( 2 \right)$.
• 18M.1.sl.TZ2.10a.i: Write down $f'\left( 2 \right)$.
• 18M.1.sl.TZ1.7: Consider f(x), g(x) and h(x), for x∈$\mathbb{R}$ where h(x) = \(\left( {f \circ g}...
• 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.TZ2.10b: Show that the $x$-coordinate of B is $- \frac{k}{2}$.
• 17M.1.sl.TZ2.10a.ii: Find the gradient of $L$.
• 17M.1.sl.TZ2.10a.i: Write down $f'(x)$.
• 17M.1.sl.TZ1.9c: The line $y = kx - 5$ is a tangent to the curve of $f$. Find the values of $k$.
• 17M.1.sl.TZ1.6a.ii: Find the equation of the normal to the curve of $f$ at P.
• 17M.1.sl.TZ1.6a.i: Write down the gradient of the curve of $f$ at P.
• 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...
• 16M.1.sl.TZ1.10d: Let $h(x) = f(x) \times g(x)$. Find the equation of the tangent to the graph of $h$ at the...
• 16M.1.sl.TZ1.10c: Find $g(1)$.
• 16M.1.sl.TZ1.10b: Write down $g'(1)$.
• 16M.1.sl.TZ1.10a: Find $f'(1)$.
• 16N.2.sl.TZ0.2b: (i)     sketch the graph of $f$, clearly indicating the point A; (ii)    sketch the tangent to...
• 17N.1.sl.TZ0.8c: Find the $x$-coordinate of Q.
• 17N.1.sl.TZ0.8d: Find the area of the region enclosed by the graph of $f$ and the line $L$.
• 17N.1.sl.TZ0.8b: Find the equation of $L$ in the form $y = ax + b$.
• 17N.1.sl.TZ0.8a: Show that $f’(1) = 1$.
• 08N.2.sl.TZ0.9b: Let the line L be the normal to the curve of f at $x = 0$ . Find the equation of L .
• 08M.1.sl.TZ1.8d: The line L is the tangent to the curve of f at $(3{\text{, }}12)$. Find the equation of L in...
• 08M.2.sl.TZ2.9d: Let L be the normal to the curve of f at ${\text{P}}(0{\text{, }}1)$ . Show that L has equation...
• 12M.1.sl.TZ1.3a: Write down $f'(x)$ .
• 12M.1.sl.TZ1.3b(i) and (ii): The tangent to the graph of f at the point ${\text{P}}(0{\text{, }}b)$ has gradient m...
• 12M.1.sl.TZ1.3c: Hence, write down the equation of this tangent.
• 10M.1.sl.TZ2.5: Let $f(x) = k{x^4}$ . The point ${\text{P}}(1{\text{, }}k)$ lies on the curve of f . At P,...
• 09N.1.sl.TZ0.10a: Show that the equation of L is $y = - 4x + 18$ .
• 09N.2.sl.TZ0.5: Consider the curve with equation $f(x) = p{x^2} + qx$ , where p and q are constants. The point...
• 09M.1.sl.TZ1.3: Let $f(x) = {{\rm{e}}^x}\cos x$ . Find the gradient of the normal to the curve of f at...
• 09M.2.sl.TZ2.6b: The normal to the curve at P cuts the x-axis at R. Find the coordinates of R.
• 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 .
• 13M.1.sl.TZ2.9d: Find the value of $x$ for which the tangent to the graph of $f$ is parallel to the tangent to...
• 13M.1.sl.TZ2.10d: find the equation of the normal to the graph of $h$ at P.
• 14M.2.sl.TZ1.7: Let $f(x) = \frac{{g(x)}}{{h(x)}}$, where $g(2) = 18,{\text{ }}h(2) = 6,{\text{ }}g'(2) = 5$,...
• 13N.1.sl.TZ0.6: Let $f(x) = {{\text{e}}^{2x}}$. The line $L$ is the tangent to the curve of $f$ at...
• 15M.1.sl.TZ1.9d: Find the equation of the tangent to the curve of $f$ at $( - 2,{\text{ }}1)$, giving your...
• 15N.1.sl.TZ0.10d: The following diagram shows the shaded regions $A$, $B$ and $C$. The regions are...