Integration by susbtitution, no hint given

Integration by susbtitution, no hint given

Simple Indefinite Integrals

Simple Indefinite Integrals

Practice with adding, subtracting and dividing basic algebraic fractions

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.

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Introduction to using the product rule

A basic introduction to differentiation

This question concerns the evaluation of the eigenvalues and corresponding eigenvectors of a 2x2 matrix.

Linear program described in words. Student must write out constraints as equations in standard form, then identify the optimal solution in a finished simplex tableau.

This question contains a "choose several answers" part which has an "all-or-nothing" mark scheme: the student is only awarded marks if they tick all of the correct choices, and no incorrect choices.

$f(x)= ae^{-bt}+c$ 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.

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

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Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+a^2y=0,\;y(0)=c$ and $y(1)=d$.  (Equal roots example).

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A question to test basic differentiation of functions, including powers of x, trig, log and exponential functions.

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.

Solve the equation  5x - 8 = 32

This question provides practice at differentiating polynomials.

Introductory exercise about power sets.

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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

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