Lovkush Agarwal

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

Some quadratics are to be solved by factorising

A quadratic equation (equivalent to $(x+a)^2-b$) is given and sketched. Three equations are given that can be solved using the graph. There is a chance there will only be one solution.

A few quadratic equations are given, to be solved by completing the square. The number of solutions is randomised.

A quadratic function is given. The graph of the function is drawn with three coordinates on the graph, without any x or y ticks.  The $x$ coordinate is given for a couple and $y$ coordinate given for the third, and coordinates are asked for.

A graph of an (invertible) cubic is given. The question is to determine values of $f$ from graph.

Practice with adding, subtracting and dividing basic algebraic fractions

student is to re-arrange the equations $pV=nRT$ and $mgh = \frac{1}{2}mv^2$

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Four sinusoidal graphs are given. Student should select the one which is sine and cosine.

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

15 questions based on module so far. 

Question is to calculate the area bounded by a cubic and the $x$-axis. Requires finding the roots by solving a cubic equation. Calculator question

Function $f(x) = xe^{ax}$ is sketched and area shaded. Question is to determine the area under graph, exactly and (calculator) to 3 s.f. Area is above x-axis.

Graphs are given with areas underneath them shaded. The student is asked to select the correct integral which calculates its area.

Q1. True/false questions about basic facts.

Q2 and Q3. Velocity-time graphs are given with areas underneath them shaded. The area of the shaded regions are given. From this, definite integrals of v ar eto be determined.

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Q1. True/false questions about basic facts.

Q2 and Q3. Velocity-time graphs are given with areas underneath them shaded. The area of the shaded regions are given. From this, changes in position, distances are to be calculated.

Graphs are given with areas underneath them shaded. The area of the shaded regions are given and from this the value of various integrals are to be deduced.

Questions about how the course is organised.

Some quadratics are to be solved by factorising

Several graphs are drawn. Student should select those that are cubics

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Finding unknown sides/angles in right-angled triangles.  6 different combinations of unknowns are included in this single question. Makes my previous questions redundant

$x$ is given and (sin(x),cos(x)) is plotted on a unit circle.  Then the student is asked to determine sin(y) and cos(y), where y is closely related to x (e.g. y=-x, y=180+x, etc.)

Student is asked to sketch $f(x)=\log_2(x)$, by plotting several points and selecting the correct graph.

A quadratic function $ax^2+bs+c$ is given. Six parabolas are sketched. Question is to select the correct parabola.  Need to consider the y-intercept, the coefficient of x^2, and the x-coordinate of the minimum/maximum point.

Student is asked to sketch $f(x)=2^x$, by plotting several points and selecting the correct graph.

Five graphs are sketch. Task is to select those that look like parabolas/quadratics.

Several quadratics are given and students are asked to complete the square.