Area of circle

Solve 4 first order differential equations of two types:$\displaystyle \frac{dy}{dx}=\frac{ax}{y},\;\;\frac{dy}{dx}=\frac{by}{x},\;y(2)=1$ for all 4.

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Definite Intgerals

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Indefinite Integrals

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Antiderivatives

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Given th original formula the student enters the transformed formula

READY TO USE

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.

Quiz to assess matrix addition, subtraction, multiplication and multiplication by scalar, determinants and inverses, solving a system of simultaneous equations.

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

Use the quotient rule to differentiate various functions.

Use the product rule to differentiate various functions.

Use the chain rule to differentiate various functions.

Find $\frac{\mathrm{d}y}{\mathrm{d}x}$ by differentiating an implicit equation.

Find an integral by choosing a suitable substitution.

Integrate the product of two functions by the method of integration by parts.

Integrate various functions by rewriting them as partial fractions.

Questions which rely on knowledge of standard integrals.

Find the integral of an improper fraction.

Practice questions on these topics.

Approximate the integral of a function by Riemann sums.

Practice bank of multivariable calculus questions

A collection of true/false questions aiming to reveal misconceptions about concepts encountered in a first year pure maths course.

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Asks to determine whether or not 6 statements are propositions or not i.e. we can determine a truth value or not.

Approximating integral of a quadratic by Riemann sums . Includes an interactive graph in Advice showing the approximations given by the upper and lower sums and how they vary as we increase the number of intervals.

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Given  $P(A)$, $P(A\cup B)$, $P(B^c)$ find $P(A \cap B)$, $P(A^c \cap B^c)$, $P(A^c \cup B^c)$ etc..

Differentiate $\displaystyle \cos(e^{ax}+bx^2+c)$

Differentiate

\[ \sqrt{a x^m+b})\]