Lovkush Agarwal

Two quadratic graphs are sketched with some area beneath them shaded. Question is to determine the area of shaded regions using integration. The first graph's area is all above the $x$-axis. The second graph has some area above and some below the $x$-axis.

several statements are given regarding trig identities. student is to select which are true and which are false

A function $f(x) = cln(ax^2+bx) -x$ is sketched and tangent is also drawn. The equation of the tangent line is asked for and $x$-coordinate for horizontal tangent is asked for. Calculator.

Q1 is true/false question covering some core facts, notation and basic examples.  Q2 has two functions for which second derivative needs to be determined.

A graph is drawn. A student is to identify the derivative of this graph from four other graphs. There are four such questions.

Questions about how the course is organised.

(a) Equation given, and five coordinates. Student should select those coordinates which lie on the line. (b) Gradient and a point on line is given. Student is to calculate coordinates of other points on the line.

A graph is drawn. A student is to identify the derivative of this graph from four other graphs. There are four such questions.

There are copious comments in the definition of the function eqnline about the voodoo needed to have a JSXGraph diagram interact with the input box for a part.

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A graph of $f$ is drawn. Graph of a transformed version of $f$ is to be sketched, by dragging various points around.

A graph of $f$ is drawn. Graph of a transformed version of $f$ is to be sketched, by dragging various points around.

A graph of $f$ is drawn. Graph of a transformed version of $f$ is to be sketched, by dragging various points around.

A graph of $f$ is drawn. Graph of a transformed version of $f$ is to be sketched, by dragging various points around.

A graph of $f$ is drawn. Graph of a transformed version of $f$ is to be sketched, by dragging various points around.

A graph of $f$ is drawn. Graph of a transformed version of $f$ is to be sketched, by dragging various points around.

A graph of $f$ is drawn. Graph of a transformed version of $f$ is to be sketched, by dragging various points around.

A graph of $f$ is drawn. Graph of a transformed version of $f$ is to be sketched, by dragging various points around.

Horizontal and vertical shifts and scales of a random cubic spline

Three lines given with different information provided. Equation of the line is asked for.

Standard simple integrals asked for (1/x, sin(x), cos(x), x^2, x, e^x)

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Standard derivatives asked for (e.g. $x^n$, $1/x^n$, $\sqrt(x)$, $\ln(x)$, $\sin(x)$, etc.) .  

Questions which try to emphasise that f(x) does not mean f times x.

Expression of the (a+bx)^n is given and a couple of coefficients are asked for.

A function of the form (ax+b)/(x+c) is plotted. Student is asked to calculate the shaded area. Area is both above and below the x-axis.

A quadratic is and a graph of it is given. A tangent is also sketched. The equation of the tangent line is asked for.

$f(x)= ae^{-bt}+c$ is given and plotted. A few points are plotted on the curve. $x$-coordinates are provided for two of them and $y$-coordinate provided for third. Student is required to determine other coordinates.