Find $\displaystyle \int \frac{a}{(bx+c)^n}\;dx$

Find $\displaystyle \int ae ^ {bx}+ c\sin(dx) + px ^ {q}\;dx$.

Integration by Substitution

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Definite Integrals

Integration by susbtitution, no hint given

Definite Intgerals

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Definite Integrals

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Antiderivatives

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Trigonometric Integral

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Integration using partial fractions

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Partial Fractions

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Integration by parts

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The student's answer is a fraction of two polynomials. First check that the student's answer is a fraction, then check that the numerator is of the form $x+a$.

To find the script, look in the Scripts tab of part a.

Show one of several blocks of text depending on the value of a question variable.

As well as a simple check for the value of a variable, the condition to display a block of text can be a complex expression in any of the question variables - in this example, depending on the discriminant of the generated quadratic.

Critical points, absolute minimum, local maximum and minimum points, increasing and decreasing, concavity

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Real life problems with differentiation

Introduction to using the product rule

Find modulus and argument of the complex number $z_1$ and find the $n$th roots of $z_1$ where $n=5,\;6$ or $7$.

Two players collide. Given the masses, final speeds and impulse imparted on each, find their initial speeds.

aij  notation and definition of the order of a matrix.

Elementary Exercises in multiplying matrices. 

Compute the weighted average salary in a department, given four salary levels and the percentages of staff earning them.

(Added to calculator test.)

Find the determinant and inverse of three $2 \times 2$ invertible matrices.

Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

Multiplying two 2 x 2 matrices.

Multiplication of $2 \times 2$ matrices.

In the Gaussian integer ring $\mathbb{Z}[i]$ , find the remainder $r=r_1+r_2i$, where $a \gt 0,\;b \gt 0$ , on dividing $a+bi$ by $c+di$ .

Questions on linear programming techniques, with interactive graphics.

Multiplying two 2 x 2 matrices.

Given an oracle function that will output its value given an input: first estimate the derivative, and second calculate its shape.