Simplify algebra expressions

Integration by Parts

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Given a graph of some function f, the student is asked for values of $f$ and its inverse. Function is cubic and invertible.

Indefinite Integrals

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Definite Integrals

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Antiderivatives

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Finding the stationary points of a cubic with two turning points

Multiple solutions of sin(x)=random  0<=x<=360

Practice dividing polynomials using the long division method.

3 questions on factorising quadratics. The second question also asks for the roots of the quadratic. The third question involves factorising quartic polynomials but which are quadratics in $x^2$.

5 indefinite integrals containing exponential functions

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Find $\displaystyle \int x(a x ^ 2 + b)^{m}\;dx$

Find $\displaystyle \int \frac{2ax + b}{ax ^ 2 + bx + c}\;dx$

Find $\displaystyle \int \sin(x)(a+ b\cos(x))^{m}\;dx$

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