Evaluate $\int_1^{\,m}(ax ^ 2 + b x + c)^2\;dx$, $\int_0^{p}\frac{1}{x+d}\;dx,\;\int_0^\pi x \sin(qx) \;dx$, $\int_0^{r}x ^ {2}e^{t x}\;dx$

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5 questions on indefinite integration. Includes integration by parts and integration by substitution.

$A$ a $3 \times 3$ matrix. Using row operations on the augmented matrix $\left(A | I_3\right)$ reduce to $\left(I_3 | A^{-1}\right)$.

$A$ a $3 \times 3$ matrix. Using row operations on the augmented matrix $\left(A | I_3\right)$ reduce to $\left(I_3 | A^{-1}\right)$.

Questions on integration using various methods such as parts, substitution, trig identities and partial fractions.

This is a set of questions designed to help you practice adding, subtracting, multiplying and dividing fractions.

All of these can be done without a calculator.

5 questions on definite integrals - integrate polynomials, trig functions and exponentials; find the area under a graph; find volumes of revolution.

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

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Basic indefinite integrals, Basic definite integrals, integration by substitution

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Integration by Parts

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5 indefinite integrals containing exponential functions

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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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Integration by susbtitution, no hint given

Integration using partial fractions

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Integration by parts

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Using three -part ratio and amounts of each colour available, calculate how much of a particular shade of paint can be made.

Given the ratio of ingredients and the total amount of ingredients work out how much of one of the ingredients is needed.

A block of given mass is sliding down the plane, with given acceleration. Find the normal reaction force, the coefficient of friction, and the distance travelled before reaching a given speed.

This quiz is designed to help you practise your integration techniques.

Improvements needed:

• Add some definite integrals to Q2
• Use different variables

4 questions testing the precedence of operations applied to integers. In other words testing BIDMAS: Brackets, Indices, Division/Multiplication and Addition/Subtraction.

4 questions testing the precedence of operations applied to integers. In other words testing BIDMAS: Brackets, Indices, Division/Multiplication and Addition/Subtraction.

Based on section 3 of the maths-aid/mathcentre workbook on numerical reasoning.

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A test of basic concepts to do with SI units and concentrations of solutions.

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