DP Mathematical Studies Questionbank

The derivative of functions of the form f(x)=axn+bxn−1+…, where all exponents are integers.
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- 18M.2.sl.TZ2.6f: Given that y = 2x3 − 9x2 + 12x + 2 = k has three solutions, find the possible values of k.
- 18M.2.sl.TZ2.6e: Show that the stationary points of the curve are at x = 1 and x = 2.
- 18M.2.sl.TZ2.6d: Find dydx.
- 18M.2.sl.TZ2.6c: Find the value of y when x = 1 .
- 18M.2.sl.TZ2.6b: A teacher asks her students to make some observations about the curve. Three students...
- 18M.2.sl.TZ2.6a: Sketch the curve for −1 < x < 3 and −2 < y < 12.
- 18M.1.sl.TZ2.14c: Find the x-coordinate of the point at which the normal to the graph of f has...
- 18M.1.sl.TZ2.14b: Find the gradient of the graph of f at x=−12.
- 18M.1.sl.TZ2.14a: Find f'(x)
- 18M.2.sl.TZ1.6f: The designer claims that the new trash can has a capacity that is at least 40% greater than the...
- 18M.2.sl.TZ1.6e: Using your graphic display calculator, find the value of r which maximizes the value of V.
- 18M.2.sl.TZ1.6d: Show that the volume, V cm3 , of the new trash can is given by V=110πr3.
- 18M.2.sl.TZ1.6c: Find the height of the cylinder, h , of the new trash can, in terms of r.
- 18M.2.sl.TZ1.6b: Find the total volume of the trash can.
- 18M.2.sl.TZ1.6a: Write down the height of the cylinder.
- 17N.1.sl.TZ0.14b: Find the point on the graph of f at which the gradient of the tangent is equal to 6.
- 17N.1.sl.TZ0.14a: Write down the derivative of f.
- 17N.2.sl.TZ0.5e: Write down the coordinates of the point of intersection.
- 17N.2.sl.TZ0.5d: Draw the graph of f for −3⩽x⩽3 and...
- 17N.2.sl.TZ0.5c: Use your answer to part (b)(ii) to find the values of x for which f is increasing.
- 17N.2.sl.TZ0.5b.ii: Find f′(x).
- 17N.2.sl.TZ0.5b.i: Expand the expression for f(x).
- 17N.2.sl.TZ0.5a: Find the exact value of each of the zeros of f.
- 17M.2.sl.TZ2.6d.ii: Write down the intervals where the gradient of the graph of y=f(x) is positive.
- 10M.2.sl.TZ1.3b: Write down f ′(x).
- 10N.2.sl.TZ0.5b: Find f′(x).
- 11N.1.sl.TZ0.14a: Find f′(x) .
- 12N.1.sl.TZ0.15a: Find f'(x).
- 12N.2.sl.TZ0.5b: Write down g′(x) .
- 12M.2.sl.TZ1.5d: Find f '(x).
- 10M.2.sl.TZ2.5c: Differentiate A in terms of x.
- 12M.1.sl.TZ2.13a: Find dydx.
- 12M.2.sl.TZ2.5c: Find dVdx.
- 09N.1.sl.TZ0.6a: Find f′(x).
- 11N.2.sl.TZ0.4b: Find f′(x) .
- 09N.2.sl.TZ0.5B, b, i: The gradient of the curve y=px2+qx−4 at the point (2, –10) is 1. Find...
- 09M.2.sl.TZ1.5a: Differentiate f(x) with respect to x.
- 11M.2.sl.TZ1.3c: Find f′(x) .
- 09M.2.sl.TZ2.5a: Write down an expression for f′(x).
- 09M.1.sl.TZ2.11a: Find f′(x).
- 11M.1.sl.TZ2.11a: Differentiate f(x) with respect to x .
- 11M.1.sl.TZ2.11b: Differentiate g(x) with respect to x .
- 13M.1.sl.TZ1.15a: Find f′(x).
- 13M.2.sl.TZ1.4b: Find f′(x).
- 11M.2.sl.TZ2.5b: Find f′(x) .
- 13M.1.sl.TZ2.11a: Find f′(x).
- 13M.2.sl.TZ2.5b: Find the derivative of y=−x210+272x.
- SPM.1.sl.TZ0.9a: Write down dydx.
- SPM.1.sl.TZ0.14a: Write down f′(x) .
- SPM.1.sl.TZ0.15b: Find the number of machines that should be made and sold each month to maximize P(x) .
- 07M.2.sl.TZ0.3i.b: Find f′(x).
- 07M.2.sl.TZ0.3ii.b: Find dydx.
- SPM.2.sl.TZ0.6e: Write down dAdr.
- 07N.1.sl.TZ0.15a: Find f′(x) .
- 08N.2.sl.TZ0.5c: Find dydx .
- 08M.1.sl.TZ1.3a: Find f′(x).
- 08M.2.sl.TZ1.5ii.d: Find dVdx.
- 08M.1.sl.TZ2.12a: Find f′(x).
- 08M.1.sl.TZ2.12b: Find f″(x).
- 08M.2.sl.TZ2.4ii.a: Find C′(x).
- 14M.1.sl.TZ2.15a: Write down the derivative of the function.
- 14M.2.sl.TZ2.5e: The parcel is tied up using a length of string that fits exactly around the parcel, as shown in...
- 13N.1.sl.TZ0.9b: Differentiate f(x)=x(2x3−1).
- 13N.2.sl.TZ0.4b: Find f′(x).
- 14M.1.sl.TZ1.10a: Write down f′(x).
- 14M.1.sl.TZ1.15a: Write down dydx.
- 14M.2.sl.TZ1.6d: The volume of the lobster trap is 0.75 m3. Find...
- 15M.1.sl.TZ1.15b: Find the value of x that makes the volume a maximum.
- 15M.2.sl.TZ1.5a: Write down f′(x).
- 15M.2.sl.TZ2.5b: Find f′(x).
- 14N.1.sl.TZ0.15a: Find dydx.
- 14N.2.sl.TZ0.3e: A company designs cone-shaped tents to resemble the traditional tepees. These cone-shaped tents...