A random heating question, that randomly picks a material, and then heats it through either one or two phase changes, provides an example graph of the heating with scaled temperature ranges (though not with scaled latent and specific heats), and a table with the suitable constants.

A random heating question, that randomly picks a material, and then heats it, then plunges it into water. The student must calculate the energy change in the water, and use this to calculate the original temperature of the material. 

Basic indefinite integrals, Basic definite integrals, integration by substitution

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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.